CFA Level I notes....Free for ever body

The Code of Ethics and The Standards of Professional Conduct
Standards of Practice Handbook, 7th edition (AIMR 1996)
Pages 5-10
Chris Bellefeuille, CFA
Mulvihill Wealth Management
Suite 2600, 121 King Street West
Toronto, Ontario
M5H 3T9
(416) 681-3994
(416) 681-3901 (fax)
email: cbelfay@mulvihill.com
Code of Ethics
Integrity Credit to Profession Independent Judgement Competence
Standards of Professional Conduct
I Fundamental Duties
I(a) Must maintain Knowledge and Compliance with laws , rules, regulations
I(b) Not Knowingly Participate or Assist in violation
International - held to higher standard of law or THE ASSOCIATION
II Relationships and Responsibilities to the Profession
II (A) Use of Designation
II (B) Misconduct
II (C) Plagiarism
III Relationships w ith and Responsibilities to Employer IIIA-inform of obligation to comply and give them a
copy of the Code and Standards
IIIB- Duty to Employer
IIIC: Conflicts -ownership &employer’s prohibited activities
IIID- Dollars - additional Compensation
IIIE – Duties of Supervisors
IV Relationships w ith and Responsibilities to Clients
A: Investment Process
Reasonable Basis: Diligence, Adequate basis, avoid Misrepresentations & Maintain
files
Research Reports: Relevant factors, Opinion vs. Fact, Basic characteristics of
investment
Objectivity & Independence
B: Interactions w ith Clients and Prospects
Fiduciary Duties ( Loyal Prudes Diversify Effectively)
Recommendations/Actions (Know what suits the client)
Fair Dealing (fair - not necessarily equal)
Priority of Transactions (Client, Firm, Self- Benef.int)
Confidentiality (maintain unless illegal)
Misrepresentation ( services, qualifications, credentials)
Conflicts (disclose anything which biases member )
Referral Fees (must disclose fees for recommendations)
V. Relationships with and Responsibilities to the Investing Public
(a) Prohibition against use of material non-public information
(b) Performance Presentation
Standards of Professional Conduct
Fun Fundamental Duties
Professionals R&R to Profession
Employ to Employer
Clients to Clients & prospects
Publicly to investing public
I Fundamental Duties KC over PA
I(a) Must maintain Knowledge and Compliance with laws , rules, regulations
I(b) Not Knowingly Participate or Assist in violation
International - held to higher standard of law or THE ASSOCIATION
II Relationships and Responsibilities to the Profession UMP
II(a) Use of Designation:
A1- Dignified & judicious manner
A2- Use “Chartered Financial Analyst” or “CFA”
A3 - Candidates can state that they are candidates but no partial completion recognised.
II (b) Misconduct
Goes beyond obligations to comply with laws.
includes felony convictions and any behaviour which reflects adversely on self and
profession
dishonesty, fraud, breach of trust, intoxication at work etc.
II C Prohibition against Plagiarism
· using other’s work without noting the source
· using vague references i.e investment experts
· using forecasts without incl. Caveats
· using charts or graphs without source
· using proprietary software without permission
Exception: material from recognised reporting service; eg. S&P 500
III Relationships with and Responsibilities to Employer ABCDE
Remember: always disclose in writing
A: Always Copy Information
IIIA- Inform of obligation to comply with Code
give them a copy of the Code and Standards
B: BOSS must OK competition ( client too)
IIIB- Boss must OK - Duty to Employer
Can’t Compete w ithout w ritten permission
If leaving you can’t take clients, lists, softw are, presentation materials,
confidential materials other employees w hile still employed
C: Conflicts ownership &employer’s prohibited activities
1- must disclose if conflicts exist to make unbiased and objective recommendations
eg ownership or beneficial interest.
2- must comply with employer’s rules regarding conflicts - trading
D: extra Dollars- additional compensation
IIID- Dollars - additional Compensation
Disclose in writing any direct or indirect compensation from third parties
E: Ensure Supervisors supervise:
Reasonable supervision must be exercised to prevent and detect violations. A
compliance program should be implemented or the supervisory position should be
declined in writing
IV Relationships with and Responsibilities to CLIENTS
A: Investment Process (D.A.M.M. R.O.B. be OBJECTIVE)
Reasonable Basis: DAMM
Diligence, Adequate basis, avoid Misrepresentations & Maintain files
Research Reports: ROB
Relevant factors, Opinion vs. Fact, Basic characteristics of investment
Objectivity & Independence
IV Relationships with and Responsibilities to CLIENTS
B: Interactions with Clients and Prospects (FISH RECOMMEND FAIR DEALING PRIOR to
CONFIDENTIALLY MISREPRESENTING CONFLICTING REFERRAL FEES)
Fiduciary Duties ( Loyal Prudes Diversify Effectively)
Recommendations/Actions (Know what suits the client)
Fair Dealing (fair - not necessarily equal)
Priority of Transactions (Client,Firm,Self- Benef.int)
Confidentiality (maintain unless illegal)
Misrepresentation ( services,qualifications,credentials)
Conflicts (disclose anything which biases member )
Referral Fees (must disclose fees for recommendations)
V Relationships with and Responsibilities to the INVESTING PUBLIC
Insider Trading
Prohibition against use of material non-public information Shall not trade, or cause
trading in, security to which privy to information member knows was given in breach of
duty. OR If no duty is breached but info was misappropriated. Member should encourage
public dissemination
Chiarella & Dirks cases Key points:Must be a breach of trust or fiduciary responsibility for
insider trading
V(b)Performance Presentation Hint: Think of Joe Friday on Dragnet:“Just the FACts
Miss”
When communicated directly or indirectly performance information should be fair
accurate & complete
Misrepresentation: shall not make any statements, orally or in writing, which misrepresent
actual or expected performance
1. Analysts must not Misrepresent
2. Effort to ensure Fair Accurate Complete
3. Inform employer of PPS and encourage compliance
4. If performance complies then Analyst is in compliance
5. Disclaimer may be used if in compliance


CFA® Level I 2003
The revision guide for the CFA® Level I exam
What do you need to know to pass the exam?
This revision guide gives you the big picture. Use it as a checklist while you are studying notes or
doing question practice to ensure that you are covering all the important concepts. In the week
before the exam, it will serve you as a quick refresher.
This revision guide is not intended to replace textbooks, study notes, or a practice question bank.
Each concept is explained very briefly and often only in shorthand. Nevertheless, most
explanations are complete and if you do not understand a point, you probably need to review it in
your textbook/study notes.
Which topics will be tested in the exam?
With 240 questions in the exam, AIMR® has scope to pick practically any of the 700+ LOS/topics
in the Level 1 curriculum, except the preliminary readings. Still, AIMR® does have some favorites
topics, which usually crop up in every exam in some form or another. These topics are listed on
the first two pages following the index.
How to use this guide
The rest of this guide contains brief descriptions of the key topics, grouped by Reading
Assignment. The material may seem vast, but a few hours of intensive study will turn it into a
good investment.
As you work through notes, check off the topics that you understand with a pen. Then, if
you understand all the topics in a given Reading assignment, cross it out in the index. This
approach will create a personalized list of topics that you want to read in the final few days before
the exam.
Good luck for the exam
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
Table of contents
Old AIMR favorites . 1
Quantitative Analysis ....................................................................................................................... 1
Economic Analysis .......................................................................................................................... 1
Financial Statement Analysis .......................................................................................................... 1
Corporate Fi 2
Equity Investments .......................................................................................................................... 2
Debt Investme 2
Derivative Investments .................................................................................................................... 2
Alternate I 2
Portfolio Management ..................................................................................................................... 2
SS2: Quantitative Methods I ................................................................................................................. 3
SS2_RA1-A: Time Value of Money ................................................................................................. 3
SS2_RA1-B: Statistics..................................................................................................................... 3
SS2_RA1-C: Probability .................................................................................................................. 3
SS2_RA1-D: Probability Distributions ............................................................................................. 4
SS3: Quantitative Methods II................................................................................................................ 4
SS3-RA1-A: Sampling and Estimation ............................................................................................ 4
SS3_RA1-B: Hypothesis testing and correlation............................................................................. 5
SS3_RA1-C: Correlation and Regression ....................................................................................... 6
SS4: Economics: Macroeconomic Analysis ........................................................................................ 7
SS4_PrelimA&B: Economic indicators ............................................................................................ 7
SS4_PrelimC: Aggregate demand and supply................................................................................ 7
SS4-PrelimD: Keynesian macroeconomics..................................................................................... 8
SS4_RA1-A: Fiscal policy................................................................................................................ 8
SS4_RA1-B: Money and the banking system ................................................................................. 9
SS4_RA1-C: Monetary policy.......................................................................................................... 9
SS4_RA1-D: Stabilizing output and employment............................................................................ 9
SS4_RA1-E: Phillips Curve ........................................................................................................... 10
SS5: Economics: Microeconomic Analysis........................................................................................10
SS5-PrelimA: Supply and demand in the market.......................................................................... 10
SS5-PrelimB: Supply and demand applications............................................................................ 10
SS5_RA1-A Demand and consumer choice ................................................................................. 11
SS5_RA1-B Costs and supply of goods........................................................................................ 11
SS5_RA1-C Price takers and the competitive process................................................................. 11
SS5_RA1-D Price-Searcher markets with low entry barriers........................................................ 12
SS5_RA1-E Price-searcher markets with high entry barriers ....................................................... 12
SS5_RA1-F Supply and demand of resources ............................................................................. 13
SS6: Economics: Global Economic Analysis.....................................................................................13
SS6_RA1-A Gaining from international trade................................................................................ 13
SS6_RA1-B Dynamics of exchange rates..................................................................................... 14
SS6_RA2 Foreign exchange market............................................................................................. 15
SS7: Financial Statement Analysis: Basic Concepts........................................................................16
SS7_RA1 Accrual concept ............................................................................................................ 16
SS7_RA2 Percentage-of-completion versus completed contract ................................................. 17
SS7_RA3 Analysis of cash flows................................................................................................... 17
SS8: Financial Statement Analysis: Financial Ratios and EPS.......................................................17
SS8_RA1 Analysis of financial statements ................................................................................... 17
SS8_RA2 Earnings per share and dilution.................................................................................... 18
SS8_RA3 Indicators of earnings quality........................................................................................ 18
SS9: Financial Statement Analysis: Assets .......................................................................................19
SS9_RA1-A Analysis of inventories .............................................................................................. 19
SS9_RA1-B Capitalization of long-lived assets............................................................................. 20
SS9_RA1-C Depreciation and impairment.................................................................................... 20
SS10: Financial Statement Analysis: Liabilities ...............................................................................21
SS10_RA1-A Analysis of income taxes ........................................................................................ 21
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
SS10_RA1-B Analysis of financing ............................................................................................... 22
SS10_RA1-C Leases and off-balance-sheet debt ........................................................................ 23
SS11: Corporate Investing and Financing Decisions.....................................................................25
SS11_RA1-B Cost of Capital......................................................................................................... 25
SS11_RA1-C Basics of Capital Budgeting.................................................................................... 25
SS11_RA1-D Cash Flow Estimation ............................................................................................. 25
SS11_RA1-E Risk Analysis & Optimal Capital Budget ................................................................. 26
SS11_RA1-F Capital Structure and Leverage .............................................................................. 26
SS11_RA1-G Dividend Policy ....................................................................................................... 27
SS11_RA2 DCF Applications ........................................................................................................ 27
SS12: Markets and Instruments .........................................................................................................27
SS12_Prelim Selecting Investments in a Global Market............................................................... 27
SS12_RA1-A Organization and Functioning of Securities Markets .............................................. 28
SS12_RA1-B Security-Market Indicator Series............................................................................. 29
SS12_RA1-C Efficient Capital Markets ......................................................................................... 30
SS13: Equity Investments....................................................................................................................30
SS13_RA1-A Introduction to Security Valuation ........................................................................... 30
SS13_RA1-B Stock market analysis ............................................................................................. 31
SS13_RA1-C Industry analysis ..................................................................................................... 31
SS13_RA1-D Company analysis and stock selection................................................................... 31
SS13_RA1-E Overview of technical analysis................................................................................ 32
SS13_RA2 DCF Applications ........................................................................................................ 32
SS14: Debt Investments: Basic Concepts .........................................................................................33
SS14_RA1-A Features of Fixed Income Securities ...................................................................... 33
SS14_RA1-B Bond investment risks............................................................................................. 33
SS14_RA1-C Bond sectors and instruments ................................................................................ 34
SS14_RA1-D Yield spreads .......................................................................................................... 35
SS14_RA2 Alternative Bond Issues.............................................................................................. 36
SS15: Debt Investments: Analysis and Valuation...........................................................................36
SS15_RA1-A Principles of bond valuation .................................................................................... 36
SS15_RA1-B Measures of yield .................................................................................................... 37
SS15_RA1-C Measurement of interest rate risk ........................................................................... 37
SS15_RA2 Term structure of interest rates .................................................................................. 38
SS15_RA3 DCF Applications ........................................................................................................ 38
SS16: Derivative Investments .............................................................................................................39
SS16_RA1-A Introduction to derivatives ....................................................................................... 39
SS16_RA1-B Futures markets ...................................................................................................... 39
SS16_RA1-C Introduction to the options market .......................................................................... 40
SS16_RA1-D Option payoffs and strategies ................................................................................. 40
SS16_RA1-E Introduction to the swaps market............................................................................ 40
SS17: Alternate Investments ..............................................................................................................41
SS17_RA1 Real estate investments ............................................................................................. 41
SS17_RA2 Professional Asset Management................................................................................ 41
SS17_RA3 Venture Capital ........................................................................................................... 41
SS18: Capital Market Theory: Basic Concepts .................................................................................43
SS18_RA1-A Investment Setting .................................................................................................. 43
SS18_RA1-B Asset Allocation Decision........................................................................................ 43
SS18_RA1-C Selecting Investments in a Global Market .............................................................. 43
SS18_RA1-D Introduction to Portfolio Management..................................................................... 44
SS18_RA1-E Introduction to Asset Pricing Models....................................................................... 44
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 1
Old AIMR favorites
Quantitative Analysis
Basic TVM - calculating PV, or FV, or PMT given everything else.
Calculate value of annuity due.
Mean, mode, median, skewness and kurtosis {mostly qualitative}.
Calculate geometric mean.
Calculate PV or FV for continuously compounded return {exp(RT), exp(-RT)}.
Calculate NPV/IRR of uneven cash flows {can be quite lengthy}.
Type I and Type II errors and power of a test {definitional questions}.
Coefficient of variation {remember to take square root if variance is given}.
Application of Roy’s criterion using safety-first ratios {highest SFR is best}.
Expected return given probabilities of three potential outcomes for return.
Given P(market) and P(stock|market), calculate return {total probability rule}.
Using Chebyshev’s theorem or normal distribution to predict % of population within a given
range.
Economic Analysis
Expenditure multiplier {straight-forward calculation}.
Interpretation of Keynesian, Crowding out, New classical and Supply-side models.
Explain the effect of a given monetary policy.
Problems with timing fiscal policy {topical given Bush’s proposed tax cuts}.
Effects of fiscal and monetary policy that are anticipated/unanticipated.
Applying reserve ratio and deposit expansion multiplier.
M*V = P*Y {straight-forward calculation}.
Application of adaptive and rational expectations.
Calculating elasticity of demand and applying it to find the change in prices.
How do governments regulate a natural monopoly.
Gaining from trade - comparative advantage {trade is generally good}.
Determinants of exchange rates.
Financial Statement Analysis
Basic enquiries about stuff you would see in an annual report.
Calculate of CFO, CFI, CFF from given data.
Basic and diluted EPS.
The effects of change in taxes on LIFO reserve/COGS/Net income.
Liquidation of LIFO reserve.
Calculation of depreciation.
Reversal of deferred tax liability.
Recording a debt issue in IS, BS, or CF statement.
Checking for capital lease and calculating lease expense.
Questions qualitatively asking for the effect of the following on a pair of ratios: {Choices:
higher-higher, lower-lower, higher-lower, lower-higher}.
o FIFO versus LIFO.
o SL versus accelerated depreciation.
o Capital leases versus operating leases.
o Capitalization versus expensing.
o High coupon versus low/zero coupon debt.
o Percentage-of-completion versus completed contract.
o Off-balance sheet financing.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 2
Corporate Finance
Calculating after-tax cost of debt, cost of equity using CAPM, and WACC.
Determine the breakeven point at which a firm has to raise fresh equity.
NPV/IRR analysis of projects (best left for the end).
Calculate operating/total leverage or use them to say what if sales fall by x…
Dividend policy application.
Equity Investments
Unweighted index with geometric weighting.
Efficient market hypotheses - definitions and evidence for and against.
Calculation of stock value using constant growth DDM {watch out for whether
earnings/dividend given is historical or prospective}.
Calculate sustainable growth rate {often as a part of the DDM calculation}.
Calculate expected rate of return from constant growth DDM.
Calculate P/E ratio using constant growth DDM. Also qualitative stuff like what happens to
P/E if ROE rises, or k falls.
Application of contrarian and smart money rules.
Debt Investments
Simple questions on meaning of call, refund and sinking fund provisions.
Equivalent taxable yield for a given muni yield.
Calculate bond price or bond yield {simple TVM stuff}.
Application of yield > coupon » price < par and vice versa.
Assumptions inherent in the definition of yield.
Calculate effective duration or use it to calculate approx price change.
Calculate convexity or use it to calculate approx price change.
Calculate forward rates from spot rates.
Basic definitions of term structure theories.
Derivative Investments
Futures margin definition and calculation, role of clearing house.
Definitions of in-the-money, margins, American/European.
Payoffs (gain/loss) for purchase/sale of a call/put option {lots of mind twisters - you can waste
too much time and work yourself into a frenzy so move on}
Payoffs of covered call (stock-call option) and protective put (stock+put option).
Calculate net cash flow in a swap from perspective of fixed payer / fixed receiver.
Alternate Investments
Basic understanding of comparative sales and capitalization approach.
Real estate valuation with discounted cash flows (best left for the end).
Basic facts about REIT.
Portfolio Management
Steps in the asset allocation process.
Objectives and constraints in the investor policy statement.
Calculate correlation given covariance and vice versa.
Interpret a given value correlation {pick the lowest, most negative correlation for best
diversification}.
Markowitz and CML work with total risk, while SML works with systematic risk.
Qualitative conclusions using SML, CAPM, Beta.
Contrast the assumptions of APT with those of CAPM.
CFA® Level I
The revision guide for the CFA® Level I exam
page 3
SS2: Quantitative Methods I
SS2_RA1-A: Time Value of Money
FV = PV x (1 + r)^N. PV = FV / (1 + r)^N. Simple concept but appears frequently in Quant and
other topic areas.
Know the N, I, PMT, FV and PV keys on the financial calculator and how to calculate one of
these given the other four. Take care with the BGN and END modes and clearing the results
of previous calculations
Single sum: Investments with no intermediate payments. Enter PMT = 0.
Annuity: Series of equal cash flows that occur at the end of regular intervals. FV = 0. PMT =
cash flow amount.
Annuity due: Series of equal cash flows that occur at the start of regular intervals (beginning
today). FV = 0. PMT = cash flow amount. Turn on the BGN mode.
Perpetuity: Never-ending annuity. PV = PMT / I (on BAII I is entered as a percentage like 6,
whereas this I is 0.06).
Multiple compounding periods: For p periods/year multiply N by p and divide I and PMT by
p before inputting them in.
Effective rate = (1 + Stated rate / p)^p - 1.
Stated rate = [(1 + Effective rate)^(1/p) - 1] x p.
Continuously compounded rate = ln(FV/PV)/N.
Continuously compounded return FV = PV x exp(I x N). Know the ln and e (exponential)
keys on the calculator.
SS2_RA1-B: Statistics
Holding period return = (End price - Start price + Dividends) / Start price.
Nominal scale only counts data points, does not rank them. Ordinal scale ranks data.
Interval scale ranks plus ensures that differences between scale values are equal. Ratio
scale introduces a zero reference point. Nominal weakest, ratio strongest.
Arithmetic mean = (X1 + X2 + … + Xn) / n.
Geometric mean = (X1 * X2 *… * Xn) ^ (1/n).
Weighted mean = (w1*X1 + w2*X2 + … + wn*Xn) / (w1 + w2 + … + wn).
Median = 50th percentile point. Mode = most frequently occurring value.
Range = Highest value - lowest value.
Variance = [(X1-Xa)^2 + (X2-Xa)^2 + … + (Xn-Xa)^2] / n.
Standard deviation (SD) = Variance^0.5. Remember to take the square root.
Chebyshev's inequality: At least (1-1/(k^2))% of observations lie within k standard
deviations of the mean. Using k=2, 75% of observations lie within ±2 std dev of mean.
Coefficient of variation = Standard deviation / Mean (enables comparison between different
distributions/securities prices).
Sharpe measure = (Portfolio return - RFR) / Portfolio standard deviation (higher values
better than lower values).
Positively skewed distribution has a long tail on the right and mean > median > mode.
Negatively skewed distribution has a long tail on the left and mean < median < mode.
Relative skewness = Skewness / Standard deviation^3.
Kurtosis: Peakedness of distribution. Normal distribution has kurtosis of 3. Excess Kurtosis =
Kurtosis - 3
SS2_RA1-C: Probability
Properties of probability: 0 <= P(Ei) <= 1. Sum[P(Ei)] = 1.
Empirical probability - estimated from data. Subjective probability - personal judgment. A
priori probability - calculated using logical analysis.
Conditional probability of A if B = Joint probability of A and B / Unconditional probability of B.
P(A|B) = P(AB) / P(B).
Multiplication rule: P(A and B) = P(AB) = P(A|B) x P(B) = P(B|A) x P(A).
Addition rule: P(A or B) = P(A) + P(B) - P(AB).
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 4
Independent events: P(A|B) = P(A). So P(AB) = P(A) x P(B).
Total probability rule: P(A) = P(A|B1) x P(B1) + P(A|B2) x P(B2)…
Expected value of asset = Sum[Pi x Xi].
Variance of asset = Sum[Pi x (Xi - Xa)^2].
Standard deviation = Variance^0.5.
Covariance of two assets = Sum[Pi x (Xi - Xa) x (Yi - Ya)].
Correlation of two assets = Covariance_XY / (SD_X x SD_Y) (enables comparison
between different pairs of assets).
Expected return of a two asset portfolio = w1 x E(R1) + w2 x E(R2).
Variance of a two asset portfolio = w1^2 x Var_1 + w2^2 x Var_2 + 2 x w1 x w2 x
Covariance_12) = w1^2 x Var_1 + w2^2 x Var_2 + 2 x w1 x w2 x SD_1 x SD_2 x
Correlation_12.
Bayes' formula: Posterior P(A) = Prior P(A) x [P(B|A) / P(B)].
Factorial: n! = 1 x 2 x … x n.
Combination = n! / [(n-r)! x r!] (selections of r from n).
Permutation = n! / (n-r)! (ordered selections of r from n).
SS2_RA1-D: Probability Distributions
Properties of probability function: 0 <= f(x) <= 1. Integral[f(x)] = 1
Binomial variable: Expected value = p over single trial, n x p over n trials. Variance = p x (1-
p) over single trial, n x p x (1-p) over n trials.
Normal distribution
Range: -infinity to +infinity (probability outside ± 3 SD is extremely low).
Completely defined by mean and standard deviation.
Skewness = 0 » symmetric » mean = median = mode.
Kurtosis = 3. Excess kurtosis = 0.
Linear combination of normal variables is also normal.
68 percent of the area within ± 1.00 standard deviations of mean.
90 percent of the area within ± 1.65 standard deviations of mean.
95 percent of the area within ± 1.96 standard deviations of mean.
99 percent of the area within ± 2.58 standard deviations of mean.
Standard normal distribution: Z = (X - M) / S, where X is a normally distributed variable
with a mean of M and standard deviation of S. Know how to read standard z table.
Shortfall risk: Risk that the value of portfolio will fall below a minimum threshold.
Safety-first ratio = [E(R) - Threshold] / SD.
Roy's safety-first criterion: Choose portfolio with the highest SFR.
SS3: Quantitative Methods II
SS3-RA1-A: Sampling and Estimation
Simple sampling: Pick random elements. Stratified sampling: Divide the population and pick
random elements from each division.
Time-series data: Single variable over time. Cross-sectional data: Several variables at a
single point in time. Panel data: Several variables over time.
Central limit theorem: for any population with any distribution, the means of samples drawn
from the population are normally distributed. Mean of sample means = Mean of the
population. Variance of sample means = Variance of population / Sample size.
Standard error of the sample mean = Standard deviation / Sample size^0.5.
Desirable properties of an estimate: Lack of bias {expected value of estimator = true value of
pop parameter}, efficiency {low variance}, and consistency {accuracy must increase with
sample size}.
Confidence interval = Point estimate ± Reliability factor x Standard error. For small samples
coming from a population with unknown variance, reliability factor should be looked up from
Student's t table {Look up df=n-1, p=significance/2 = (1-confidence)/2}. For populations with
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 5
known variance or for large samples, you can use critical z from normal distribution.
Memorize the following commonly used values.
Confidence Reliability factor:
90% 1.645
95% 1.960
99% 2.575
Student's t-distribution: Symmetrical distribution, looks like normal distribution but less
peaked. Important to be able to look up Student's t tables given degrees of freedom and
probability in the right tail.
Data-snooping bias: Conclusions of one analyst are guided by conclusions of others.
Data-mining bias: Analyst keeps searching for patterns and trading rules until he can find
one that matches the data.
Sample selection bias: Certain securities or time periods are excluded from the analysis.
Survivorship bias: Only funds/stocks that have survived to date are included. Big problem
with stock indices.
Look-ahead bias: Based on information that did not actually exist at the time of analysis.
Time-period bias: Conclusions may apply only to a specific time period and are not
repeatable over longer time periods.
SS3_RA1-B: Hypothesis testing and correlation
Hypothesis testing: (1) State the hypothesis. (2) Identify test statistic and its probability
distribution. (3) Specify significance level. (4) State decision rule. (5) Calculate test statistic.
(6) Make statistical decision. (7) Make economic decision.
Null Hypothesis (Ho): Hypothesis being tested {the hypothesis that you want to disprove}.
Alternative Hypothesis (Ha): Accepted if the null hypothesis is rejected.
Two-tailed tests {Ho: Mean = X}. One-tailed tests {Ho: Mean <= X, or Ho: Mean >= X}.
Test statistic = (Sample statistic - Hypothesized value) / Standard error.
Significance level: Controls how much evidence required to reject Ho. Common values are
0.1, 0.05, and 0.01.
Type I error: True Ho is rejected. Type II error: False Ho is not rejected.
Power of a test = 1 - probability of Type II error = Probability of correctly rejecting Ho.
Decision rule: If test statistic > critical value reject Ho accept Ha. If test statistic < critical
value, do not reject Ho {do NOT accept Ho either}.
Statistical decision does not automatically lead to economic decision, other factors may need
to be considered.
p-value: Lowest significance level at which Ho can be rejected. Lower the p-value, stronger
the evidence to reject Ho.
t-test: It can be used when the population variance is unknown for large samples and small
samples with normally distributed pop. Test stat = (Sample mean - Hypothesized mean) /
Standard error. Standard error = Sample standard deviation / n^0.5. Critical value comes
from Student’s t table {Look up df=n-1, p=significance for 1-sided test or p=significance/2 for
2-sided test}. Reject null if test stat is higher than critical, else do not reject null. Never accept
null.
z-test: Same test stat as t-test. Critical value comes from normal distribution. It can be used
when population is normally distributed with known variance; also for large samples with
unknown variance.
Significance 1-sided 2-sided
0.10 1.280 1.645
0.05 1.645 1.960
0.01 2.330 2.575
Test of differences between means: t-test using a pooled variance. {Look up df=n1+n2-2,
p=significance}.
Test of mean differences/paired comparison: Simple t-test based on the variable being
the difference between pairs of sample values. {Look up df=n-1, p=significance}.
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Chi-squared test: Test stat = [(n-1) x Sample variance] / Hypothesized variance. Critical
value comes from chi-squared table. Asymmetrical distribution. {Look up df=n-1,
p=significance for 1-sided test or p=significance/2 for 2-sided test}.
F-test: Test stat = Sample 1 variance / Sample 2 variance. Choose the sample with higher
variance in the numerator. Critical value comes from F table. {Look up df1=n1 - 1, df2 = n2 -
1, p=significance}.
Non-parametric tests: {median, runs} become useful if population is strongly non-normal
and data is only available on ordinal scale.
SS3_RA1-C: Correlation and Regression
Variance of asset = Sum[(Xi - Xa)^2] / (n-1).
Standard deviation = Variance^0.5.
Covariance = Sum[(Xi - Xa) x (Yi - Ya)] / (n-1).
Correlation = Cov(XY) / [SD(X) x SD(Y)]. Always between -1 and 1.
Test of correlation: Ho: correlation coefficient = 0. Test statistic = Correlation x (n-2)^0.5 / (1
- Correlation^2)^0.5. df = n-2. p = (Significance level)/2.
Problems with correlations: Outliers {extreme values that should be excluded} and
spurious correlation {correlation between X and Y does not always mean Y is dependent on
X}.
Linear regression: Y = a + b X + error. a is intercept, b is slope.
Expected value of slope E(b) = Cov(XY) / Var(X). Expected value of intercept E(a) = Mean(Y)
- E(b) x Mean(X).
Assumptions in linear regression: Relationship exists {else we get spurious correlation},
E(error) = 0 {else estimated coefficients are not correct}, Var(error) is constant {else we get
heteroskedasticity}, error is not correlated across observations {else we get autocorrelation}
and is normally distributed {else significance of coefficients cannot be tested}
Standard error of the estimate (SEE) = Sum[(Yi - a - b Xi)^2] / (n-2). Standard deviation of
error terms {differences between actual values and regression line}.
Coefficient of determination (R-squared) = Correlation^2 = 1 - (Unexplained variation /
Total variation).
Confidence interval for regression coefficient = Point estimate ± Reliability factor x
Standard error. {Look up df=n-2, p=significance/2 on Student's t table for reliability factor}
Testing regression coefficient: Test stat = (Calculated coefficient - Hypothesized value) /
Standard error; Critical value comes from Student’s t table {Look up df=n-1, p=significance for
1-sided test or p=significance/2 for 2-sided test}. Reject null if test stat is higher than critical,
else do not reject null. Never accept null.
ANOVA tables: R-squared = SSR / SST. SEE = MSE^0.5. F-statistic = MSR / MSE.
If F-statistic is higher than the critical value {from F-table} independent variable does not
adequately explain dependent variable.
Limitations of regression analysis: Relationships can change over time and depend on
actions of market participants who are reacting to past relationship.
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SS4: Economics: Macroeconomic Analysis
SS4_PrelimA&B: Economic indicators
GDP: produced within a country, includes income earned by foreigners resident in the
country and excludes income earned by its citizens living abroad. GNP produced by citizens
of the country.
Real GDP = Nominal GDP x (Base year GDP deflator / (Current GDP deflator). GDP deflator
a broader index of price of goods and services than CPI.
Expenditure approach: GDP = Personal consumption + gross private investment +
government consumption and gross investment + net exports
Resource cost-income approach: GDP = employee compensation + proprietor’s income +
rents + corporate profits + interest income + indirect business taxes + depreciation + net
income of foreigners = National Income + indirect business taxes + depreciation + net income
of foreigners
Limitations of GDP: Does not account for household work, underground economy, leisure,
improvements in the quality of goods and services, and damage to the environment.
Problems with measuring unemployment: Part-time workers {counting them as employed
understates unemployment}. Discouraged workers {not counted in unemployed, understates
unemployment}. Unserious benefit registrants {opportunists who are not really looking to
work, overstates unemployment}. Underground workers {not counted in employed, overstates
unemployment}.
Types of unemployment: Frictional {workers cannot be immediately matched with existing
jobs}. Structural {economic restructuring throws people out of jobs}. Cyclical {workers loose
jobs due to a recession}.
Natural rate of unemployment: Consistent with frictional and structural factors in an economy.
Inflation: Rate at which price of the representative basket of goods and services is rising
over time.
Deflation: Negative inflation. Rate at which price of the representative basket is falling.
Stagflation = High inflation + Low real GDP growth.
Consumer Price Index (CPI): Tracks the price of a representative basket of goods and
services.
Inflation = (Current level of CPI - Previous level of CPI) / Previous level of CPI.
Unanticipated inflation: Not widely expected. Harms people who have fixed income {jobs,
pension, savers} and beneficial for individuals who have fixed expenses {borrowers}. Distorts
contracts, increases uncertainty, and depresses investment and growth.
Anticipated inflation: Widely expected and factored into all sorts of contracts. A low level (2-
3%) is considered fine for a growing economy.
SS4_PrelimC: Aggregate demand and supply
Aggregate demand (AD) curve: Quantity demanded on y-axis. Price on x-axis.
Aggregate supply (AS) curve: Quantity supplied on the y-axis. Price on the x-axis. Shortrun
AS (SRAS) is a different curve from long-run AS (LRAS).
Factors that shift AD curve to the right: (1) Increase in real wealth. (2) Decrease in real rate
of interest {saving becomes less attractive}. (3) Positive business expectations/sentiment. (4)
Expectation of future inflation. (5) Increase in income of other countries. (6) Fall in the value
of the domestic currency. The reverse of these factors would push AD curve to the left.
Factors that shift LRAS curve to the right: (1) Improvements in productivity. (2) Permanent
increase in supply of resources. (3) Increase in efficiency of resource utilization.
Factors that shift SRAS curve to the right: All three factors that shift LRAS plus: (4)
Temporary increase in the supply of resources. (5) Favorable supply shocks.
Impact of unanticipated increase in AD: Increases output in short run, but in the long run only
increases prices with the output unchanged.
Self-correcting mechanisms that dampen the economic cycle: (1) Consumer demand
{tends to lag changes in income}. (2) Real interest rates {rise during boom and fall in
depression}. (3) Resource prices {rise during boom and fall in depression}.
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SS4-PrelimD: Keynesian macroeconomics
Keynesian economics: Fluctuations in aggregate demand are the source of economic
disturbance. Resource prices and wages are inflexible in the downward direction. This
causes friction and does not allow the economy to grow at its full potential. The government
can help the economy by boosting demand.
Keynesian or aggregate expenditure (AE) model: Real GDP = C + I + G + NX.
Keynesian macroequilibrium: If actual output equals the planned output given by the AE
model, the economy will be in equilibrium. If actual expenditure is lower, inventories will build
up. If actual expenditure is higher, inventories will be depleted.
Marginal propensity to consume (MPC) = Proportion of each additional dollar of income
spent on personal consumption = Marginal increase in consumption / Marginal increase in
income.
Expenditure multiplier = 1/ (1 - MPC).
SS4_RA1-A: Fiscal policy
Fiscal policy: Government spending, taxation and borrowing.
Timing lags in fiscal policy: Recognition lag {between the need for a fiscal policy shift and
when policy makers recognize it}. Administrative lag {between recognition of the need and
when the policy shift is implemented}. Impact lag {between implementation of the policy shift
and its impact on the economy}.
Keynesian model: Recommends that fiscal policy should be used to smooth the business
cycle. Expansionary fiscal policy to help the economy out of recessions and boost
employment. Restrictive fiscal policies to rein in aggregate demand when the economy is
growing too fast.
Crowding out model: Counters Keynesian view by suggesting that Expansionary fiscal
policy » budget deficits and higher interest rates » lower private investment » inefficient public
sector crowds out efficient private sector without any gain in GDP.
New classical model: Expansionary fiscal policy » budget deficits and debt » private
individuals realize that taxes will eventually increase and so increase saving » fall in private
consumption » negates the rise in government spending.
Supply side model: Governments should fuel economic growth by promoting supply rather
than demand. Lower marginal tax rates » increase in efficient private sector investment »
higher incomes » increased tax receipts despite lower tax rates.
Automatic stabilizers: (1) Progressive income taxes. (2) Corporate taxes. (3)
Unemployment benefits.
Supply-side fiscal policy: High marginal tax rates retard growth by discouraging work and
reducing improvements in efficiency. They slow the rate of capital formation and encourage
tax avoidance. Cutting marginal taxes helps to encourage people to work more, save more
and improve production efficiency.
Budget deficits and real interest rates: According to the crowding out model - deficits »
higher demand for loanable funds » higher real interest rates. However, any rise in real
interest rates increases the supply of capital from home and abroad. Empirical evidence
suggests that the link between the two is very weak.
Budget deficits and trade deficits: Deficit » foreign capital flows into the country » domestic
currency appreciates » imports flood in and exports become unviable » higher trade deficit.
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SS4_RA1-B: Money and the banking system
Basic functions of money: medium of exchange, unit of value, store of value.
M1 = notes and coins in circulation + demand deposits + other checkable deposits such as
NOW accounts + traveler’s checks.
M2 = M1 + money market deposits + money market mutual funds held by individuals +
overnight Eurodollar deposits and repurchase agreements + time deposits of less than
$100,000.
Fractional reserve banking system: The Fed requires all deposit-taking banks to hold a
fraction of those deposits as reserves. Since these reserves do not earn interest, banks try
not to hold any excess reserves.
Deposit expansion multiplier: Increase in money supply due to one additional dollar of
deposits. Potential multiplier = 1 / Required reserve ratio. Actual multiplier is lower due to
currency leakages {some people may hold currency and not deposit it in a bank} and excess
bank reserves {some banks are not able to loan out excess funds}.
Fed’s monetary tools: Open market operations {buying Treasuries in the repo market »
injects money » lowers Fed Funds rate}. Discount rate {lowering this rate makes it more
attractive for banks to borrow money from Fed}. Reserve requirement {lower required reserve
ratio » more funds available for lending. Rarely used}.
Expansionary monetary policy: Buy Treasuries, Lower discount rate or Lower required
reserve ratio.
Restrictive monetary policy: Sell Treasuries, Raise discount rate or Raise required reserve
ratio.
Problems in measuring money supply in the US: Widespread use of US dollars outside of
the US. Emergence of low-fee mutual funds as substitutes for time deposits. Emergence of
debit cards and electronic money as substitutes for physical currency.
SS4_RA1-C: Monetary policy
Demand for money: Higher interest rate » higher cost of opportunity of holding cash » lower
demand for money. Graph of money demanded versus interest rates is downward sloping.
Supply of money: Controlled by the Fed. Graph of money supply versus interest rate is a
vertical line.
Expansionary monetary policy: In a recession Fed increases money supply by buying
securities » lower interest rates » higher investment, consumer spending and exports »
higher output and fall in unemployment.
Restrictive monetary policy: If the economy is overheating, the Fed decreases money
supply by selling securities » higher interest rates » lower investment, consumer spending
and exports » lower output and rise in unemployment.
Quantity theory of money: Increase in money supply will simply result in an increase in
prices. M * V = P * Y.
Impact of expansionary monetary policy:
Unanticipated short-run Anticipated short-run and long-run
Inflation Small increase Increase
Real GDP Increase Not affected
Unemployment Falls Not affected
Money market rate Falls Rises
Real interest rate Falls Not affected
SS4_RA1-D: Stabilizing output and employment
Index of leading economic indicators: Composite of ten leading economic indicators.
Supposedly good for making forward-looking policy decisions but has a mixed record in
making predictions.
Adaptive expectations: People forecast the future based on actual observations from the
most recent periods. Leads to systematic errors that can destabilize the economy and extend
the period before the economy returns to its natural equilibrium.
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Rational expectations: People forecast the future based on all the information available to
them. Decision makers may make errors, but these are random and there is no systematic
bias.
The success of monetary and fiscal policies relies on people having adaptive expectations
and not anticipating policy shifts.
Fiscal policy in particular suffers from recognition lag, administrative lag and impact lag.
Non-activist view: Governments cannot control GDP growth and should rely on automatic
stabilizers. Based on the belief in rational expectations.
Non-activist strategies: (1) Monetary policy directed to ensure price stability {low inflation}.
(2) The central bank should grow money supply at the long-term growth rate of the economy.
(3) Governments should eschew discretionary fiscal policy and should aim for a balanced
budget over the business cycle. (4) Government should focus on structural factors rather than
fiscal stimulus to promote GDP growth and reduce unemployment.
SS4_RA1-E: Phillips Curve
Original Phillips Curve: Unemployment and inflation are inversely related. Supports the
case for interventionist monetary policies directed at lowering the unemployment rate.
Adaptive expectation hypothesis supports the original Phillips Curve, while rational
expectation hypothesis rejects it.
Modern view of the Phillips Curve:
If inflation is steady, unemployment quickly equilibrates to the economy’s natural rate of
unemployment.
Expansionary monetary policy is anticipated. So it merely causes inflation without changing
unemployment.
Even if individuals initially fail to anticipate a rise in inflation, they eventually wake up to it. In
the long run, expansionary monetary policy always causes higher inflation without any
permanent fall in unemployment.
SS5: Economics: Microeconomic Analysis
SS5-PrelimA: Supply and demand in the market
Law of supply: Higher price » more quantity supplied.
Law of demand: Higher price » less quantity demanded.
Movement along demand/supply curve: Changes in quantity demanded / supplied with
change in price.
Market equilibrium: Quantity demanded = Quantity supplied. Intersection of demand and
supply curves.
Shift to the right implies increase in demand / supply. Shift to the left implies decrease in
demand / supply.
Factors that shift demand curve: Consumer income. Number of consumers.
Demographics. Consumer preferences. Price of substitutes. Price of complementary goods.
Consumer price expectations
Factors that shift supply curve: Changes in resource prices. Technology improvements.
Disruptions.
Short-run supply curve is relatively inelastic since producers cannot turn up production in
response to increased demand and the resulting shortage will increase price.
Long-run supply curve is relatively elastic since producers can increase their production.
Invisible hand: Market prices direct individuals, who are pursuing their own interests, to
promote the economic well-being of the whole society.
SS5-PrelimB: Supply and demand applications
Price ceilings: Maximum price for a resource set by governments. A low ceiling leads to
resource shortage.
Price floors: Minimum prices for a resource set by governments. A high floor leads to
resource surplus.
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Black markets: Suffer from inefficiency, defective products, exorbitant profits for those who
escape being caught, and use of violence to settle disputes. Highlights value of IP rights,
enforcement of contracts, and access to unbiased courts.
Taxes: Drive a wedge between price paid by buyers and that received by sellers and create
deadweight loss {reduction in quantity of goods traded}. Deadweight loss is greatest if both
supply and demand curves are relatively elastic. It is less if either the demand or supply is
inelastic.
Statutory incidence of tax: How the legal burden of paying taxes is split between buyers
and sellers.
Actual incidence of tax: May differ from statutory incidence. If the demand curve is
relatively inelastic, the tax burden will mostly fall on buyers. If the supply curve is relatively
inelastic, the tax burden will mostly fall on sellers.
SS5_RA1-A Demand and consumer choice
Law of diminishing marginal utility: Utility of each addition unit of a good consumed is
lower than the previous one.
Price elasticity of demand = % change in quantity demanded / % change in price.
The price elasticity of demand faced by an individual firm is higher than that faced by the
entire industry.
The price elasticity of demand tends to increase in the long run.
Income elasticity of demand = % change in quantity demanded / % change in income.
Necessities have low income elasticity, while luxury goods have high income elasticity.
Consumer indifference curves: Convex curves that do not intersect. Based on assumptions
that: (1) More is preferable to less. (2) Goods are substitutable. (3) Marginal utility of a good
falls as more of it is consumed.
Budget constraint: Straight line that defines combinations of the goods that an individual
can afford. Point of tangency between budget constraint and highest obtainable indifference
curve is optimal level of consumer satisfaction.
Increase in income shifts the budget constraint line to right, while the substitution effect
rotates the budget constraint line.
SS5_RA1-B Costs and supply of goods
Economic profit considers both explicit and implicit costs, while accounting profit ignores
implicit costs.
In the short run producers cannot change their production methods but in the long run they
can.
Types of costs: Sunk costs {already incurred due to past decisions}. Marginal cost {for
producing the next unit of output}. Fixed costs {do not vary with output}. Variable costs {vary
with output}. Opportunity costs {return available from alternative investments}.
Average total cost = (Total fixed cost + Total variable cost) / (Total output).
Average variable cost = (Total variable cost) / (Total output).
Law of diminishing marginal returns: As more resources are devoted to a production
process output rises, but at a decreasing rate.
Economies of scale: ATC falls with an increase in output due to fixed costs.
Diseconomies of scale: At high levels of production, ATC starts to rise with increase in
output.
Factors that shift cost curves: Change in resource prices, taxes, and regulations.
Improvements in technology.
SS5_RA1-C Price takers and the competitive process
Price takers: Small output compared to the whole market. Can sell entire output at market
price but nothing at a higher price. Face a perfectly elastic (horizontal) demand curve.
Price searchers: Have some price setting power. Can choose to charge higher prices but
will sell less. Face a downward sloping demand curve.
Purely competitive market requirement: Large number of firms producing identical
products with small market shares and no barriers to entry or exit.
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Purely competitive market: Price is determined by the market’s supply and demand. All
firms are price takers and make no economic profit {can earn a positive accounting profit to
cover their cost of capital}.
In short run, price takers can make profit = P – ATC.
In long run due to competitive pressures, P = LRATC and no price taker makes an economic
profit.
For an individual price taker, when the ATC curve falls below P {market demand curve is a
horizontal line at market price, P}, it can make a profit. Profit maximizing level of output is
where MC = P = MR.
For an individual price taker, when the entire ATC curve lies above the market price, it will
make an economic loss. The firm faces three choices: (1) If the AVC curve falls below P and
the situation is temporary, the firm is covering its variable costs and should continue
operating in the short run. (2) If the AVC curve lies entirely above P but the situation is
temporary, the firm is not covering variable costs and should shut down temporarily. (3) If the
firm believes that the ATC will never fall below P, then it should go out of business.
Short-run supply curve: Sum of MC curves for all firms above minimum AVC. Market price
cannot fall below minimum AVC.
Long-run supply curve: Horizontal for constant cost industries. Downward sloping for
decreasing cost industries. Upward sloping for increasing cost industries.
LRAS more elastic (flatter) than SRAS, since in the long run firms have more time to adjust
and produce at a lower cost.
SS5_RA1-D Price-Searcher markets with low entry barriers
Monopolistic competition (a.k.a. Competitive price-searcher markets) requirements:
Large number of firms producing differentiated products and no barriers to entry or exit.
Monopolistic competition: All firms are price searcher and face a downward sloping
demand curve {which is highly elastic due to availability of close substitutes}.
In the short run, price searcher maximizes profits by setting output where MR = MC
In the long run, competition drives demand curve down to the point where MR = ATC, and
economic profit falls to zero.
Contestable markets: Small number of producers that are forced to behave as in a highly
competitive market due to low costs of entry and exit {threat of new competitors}.
Entrepreneurs: Neglected by economic models but contribute significantly to the economy by
discovering new markets and methods of production.
Price discrimination: Charging different prices to different consumers for the same product.
Increases total output and improves allocative efficiency.
Price discrimination requirements: (1) A downward sloping demand curve. (2) Two or
more groups of customers with different price elasticity. (3) Ability to prevent arbitrage
between customer groups.
Importance of competition: Forces firms to operate at an optimal level of production to
increase efficiency and consumer satisfaction.
SS5_RA1-E Price-searcher markets with high entry barriers
Entry barriers: Patents, control over a resource, economies of scale, and government
license/legal barrier.
Monopoly: Entire supply of product (with no good substitutes) produced by a single firm that
has no potential competitors due to high barriers to entry.
Oligopoly: Small number of interdependent competitors in a market with significant
economies of scale and high barriers to entry.
Prices and output under a monopoly: Monopolist faces a downward sloping demand curve
and will make a profit only if some part of the ATC curve lies below demand curve. The profit
maximizing quantity for the monopolist is where MR = MC, and profit per unit = (Price from
demand curve - Price from ATC curve) at this level of output.
Prices and output under an oligopoly: Maximizing profits is not so simple. Must consider
reaction of rival oligopolists. In the absence of collusion, output rises to where demand =
LRATC and no oligopolist makes an economic profit. With perfect collusion, output is held
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down to where MR = LRATC and profit per unit = (Price from demand curve - Price from
LRATC curve) at this level of output.
Oligopolists have a strong incentive to collude {to keep the price high}, but also a strong
incentive to cheat {to increase output and market share}.
Obstacles to collusion: (1) Large number of competitors. (2) Difficulty in detecting and
eliminating cheating. (3) Low barriers to entry. (4) Unstable demand. (5) Vigorous antitrust
action by the government.
Government policies for reducing collusion: (1) Antitrust actions {Break up monopolies
and disapprove mergers}. (2) Reduce quotas, tariffs, and other barriers to competition. (3)
Regulate the price and output. (4) Set up government-owned firms to produce and supply the
goods. (1) and (2) are approved by economists, while (3) and especially (4) are not.
Natural monopoly: If an industry has declining average costs over the entire schedule, it is
most optimal for a single firm to produce the entire output.
Regulation of a protected monopoly: Governments may prefer to keep natural monopoly
intact and regulate its output and prices forcing it to operate at P = ATC {average cost pricing
- monopolist makes a zero economic profit} or P = MC {marginal cost pricing - monopolist
incurs a loss and is propped up with a subsidy}.
Problems with regulation of a protected monopoly: Lack of information {of ATC, MC and
demand schedules}. Cost shifting {If the price is fixed, the firm has no incentive to improve
efficiency. If the rate of return is fixed, the firm may even have an incentive to be wasteful}.
Special interest effect {monopolist has a vested interest to influence regulators}.
SS5_RA1-F Supply and demand of resources
Demand for a resource is a derivative of demand for the goods that can be produced with it.
Demand curve for a resource is downward sloping due to: (1) Substitution of the resource
with other resources in the production of the good. (2) Substitution of the good with other
goods.
Factors that shift demand curve. Change in: demand for the goods, productivity of the
resource, and price of related resources.
Marginal revenue product (MRP): Increase in revenue from employing one more unit of a
resource.
Marginal product (MP): Increase in output from employing one more unit of a resource.
Marginal revenue (MR): Increase in revenue from one unit increase in output.
MRP = MP x MR.
MRP and profit maximization: MRP = Resource price.
MRP and cost-minimization: Adjust level of utilization of resources such that (MP of
resource A / Price of resource A) = (MP of resource B / Price of resource B).
In a competitive environment, firms will continue to identify opportunities that generate more
value from a given resource. Drives their prices ever higher.
SS6: Economics: Global Economic Analysis
SS6_RA1-A Gaining from international trade
Absolute advantage: A country’s ability to produce a good using fewer resources than other
countries.
Comparative advantage: A country’s ability to produce a good at a lower opportunity cost
than other countries, i.e. sacrificing the fewest units of other goods to produce one more unit
of the given good.
Law of comparative advantage: Countries should specialize in producing the goods in
which they have a comparative advantage.
Tariffs: Taxes levied on imported products. Revenue for government. Cost for consumer.
Indirect subsidy for domestic producers.
Quota: Limit on the amount of a good that can be imported. Reward foreign producers with
higher prices, penalize the domestic consumers, and do not create any revenue for
government. More harmful than tariffs.
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Voluntary export restraints (VER): Quotas with soft limits.
Exchange-rate controls: Restrict on dollars provided for imports.
Trade is a beneficial: Countries should produce and export goods in which they have a
comparative advantage and import those in which they do not.
Why do nations restrict trade? (1) National defense/security {retain key production
technology and skills}. (2) Protect infant industries {only in their early development while they
build economies of scale}. (3) Anti-dumping {discourage foreign suppliers from selling
products below cost}. (4) Save jobs {most misguided reason}.
Trade restrictions may save a few jobs in the short run, but in the long run they destroy jobs.
(1) Increase prices of goods. (2) Reduce jobs that depend on processing imports. (3) Reduce
jobs that depend on exports {by preventing trading partners from increasing their purchasing
power}.
Importing goods from low wage countries increases exports from high wage countries,
allowing both to increase their productivity and wealth.
Winners and losers from trade tariffs.
Domestic producers: Clear winners in the short run. In the long run, they may become
inefficient and uncompetitive.
Domestic consumers: Clear losers.
Domestic government: Tariffs are an inefficient way to raise revenue and create a
deadweight loss.
Foreign producers: Clear losers from tariffs. Could win or lose from quotas.
SS6_RA1-B Dynamics of exchange rates
Factors that cause changes in exchange rates in a floating rate system:
(1) Income growth differential {higher income growth » high imports » cash outflow » currency
depreciation}.
(2) Inflation rate differential {higher inflation » currency depreciation}.
(3) Real interest rate differential {higher real interest rates » inflow of investments » currency
appreciation}.
Fixed exchange rate system is maintained with the help of trade barriers, currency controls,
periodic readjustments (usually devaluation), and restrictive monetary policy - raise interest
rates to dampen inflation and raise the value of the domestic currency.
Balance of payments: Debits and credits in a nation’s accounts must balance.
Current account balance + Capital account balance + Reserve account balance = 0.
Current account: Cash flows due to trade in goods {balance of trade} and trade in services
{invisibles}.
Capital account: Cash flows due to transactions involving physical assets and investments.
Reserve account: Holdings of gold, foreign currency (mostly dollar) and SDRs.
In countries with flexible exchange rates, the current account is automatically balanced by
capital account with little variation in reserve account.
In countries with fixed exchange rates, reserve account balances build up in times of
combined capital + current account surplus and are depleted in times of combined deficit.
Impact of expansionary monetary policy:
Current account Surplus Lower exchange rate spurs exports
Capital account Deficit Lower interest rates drive capital abroad
Currency Depreciation Due to capital outflow
Impact of expansionary fiscal policy:
Current account Deficit Higher demand sucks in imports
Capital account Surplus Foreign investment flows in
Currency Appreciation Due to capital inflow
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SS6_RA2 Foreign exchange market
Quotes in bank market.
American terms: Number of USD per foreign currency unit ($/FC).
European terms: Number of foreign currency units per USD (FC/$).
Quotes in non-bank market.
Direct quotes: Number of units of domestic currency per unit of foreign currency (DC/FC).
Indirect quotes: Number of units of FC per unit of DC (FC/DC).
Bid rate = Left hand side of quote = Rate at which dealer will buy currency in denominator.
Ask rate = Right hand side of quote = Rate at which dealer will sell currency in denominator.
Factors affecting bid-ask spread: Liquidity {low liquidity widens spread}. Volatility {high
volatility widens spread}. Settlement {forward spreads are wider}. Counter-party {inter-bank
spreads are narrower}. Transaction size. Dealer’s position.
Cross rate calculation: Two currencies in European terms: DC/FC = (DC/$) / (FC/$).
Cross rate calculation: Two currencies in American terms: DC/FC = ($/FC) / ($/DC).
Cross rate calculation - one European, one American: DC/FC = (DC/$) x ($/FC).
Currency arbitrage: (FC/$) not equal to ($/FC). To exploit this arbitrage, buy dollars via the
cheaper rate and sell them via the expense rate.
Triangular arbitrage: Cross rate for (FC1/FC2) not equal to actual rate for (FC1/FC2). Given
rates for FC1 and FC2 against $, first calculate the cross rate. Then buy FC1 via the cheaper
rate and sell it via the expense rate.
Absolute forward premium/discount = Forward rate - Spot rate.
Annualized premium or discount: [(Forward rate - Spot rate) / Spot rate] x (360 / forward
period).
Interest Rate Parity Theory (IRPT): Forward(DC/FC) / Spot(DC/FC) = (1+r_DC)/(1+r_FC). If
foreign interest rates are high, the foreign currency forward will trade at a discount and vice
versa.
Covered interest arbitrage: If IRPT fails, there is an opportunity to make arbitrage profits =
(1+r_DC) - (1+r_FC) x Forward(DC/FC) / Spot(DC/FC)
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SS7: Financial Statement Analysis: Basic Concepts
SS7_RA1 Accrual concept
Requirements for revenue recognition: Completion of the earnings process. Accurate
measurement of revenue. Accurate measurement of COGS. Transfer of risk of ownership to
buyer. Arm-length transaction with no possibility of cancellation. Reasonable assurance of
payment.
Sales basis: Recognize revenue at the time of sale. Most common method.
Percentage-of-completion method: Recognize revenues and expenses in proportion to
work completed. Used by contractors and service firms for long-term projects.
Completed contract method: Recognize revenues and expenses upon the full completion
of contract. Preferred over percentage of completion when revenue and cost estimates are
unreliable.
Installment sales method: Recognize gross profit in proportion to cash collected.
Cost recovery method: Recognize revenue as cash is received but book no gross profit
until COGS are recovered. Conservative form of installment sales method.
Unusual or infrequent items: Reported above the line. Examples: impairment, write-offs,
provisions for environmental action and litigation, gain/loss from sale of investment in a
subsidiary, and restructuring costs.
Unusual and infrequent item = Extraordinary item. Reported below the line. Examples:
expropriations by governments, gain/loss from early retirement of debt, and uninsured losses
due to natural disasters.
Discontinued operations: After-tax net income and gain/loss due to discontinued operations
reported below the line.
Sales
- Cost of goods sold
- Selling, general and administrative
-------------------------------------------------------------------
= Operating profit or EBITDA
-------------------------------------------------------------------
- Depreciation and amortization
-------------------------------------------------------------------
= EBIT
-------------------------------------------------------------------
- Interest expense
-------------------------------------------------------------------
= EBT
-------------------------------------------------------------------
- Taxes
- Unusual items
- Infrequent items
-------------------------------------------------------------------
= Income from continuing operations
- Extraordinary items
- Discontinued operations
-------------------------------------------------------------------
= Net income
Changes in accounting principles: Changes in inventory methods, depreciation schedules,
recognition of post-retirement benefits, etc. due to changes in GAAP or management’s
decision. Disclosure required - nature of the change, justification, and effect on net income.
Changes in inventory method and revenue recognition method are retroactive. Cumulative
result of the changes net of tax is reported below the line.
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Prior period adjustments: Errors from previous accounting periods. NOT reported on the
income statement. Adjustment made to retained earnings at the start of the period. Full
disclosure required.
SS7_RA2 Percentage-of-completion versus completed contract
Impact of the use of percentage-of-completion versus completed contract in the years before
the completion of the contract:
Impact Comment
Cash flows No impact Cash flow schedule specified in contract
Assets Higher
Liabilities Lower
Equity Higher Due to higher income
Revenues Higher Revenue in completed contract = 0
COGS Higher COGS in completed contract = 0
Net Income Higher Higher revenues outweigh higher COGS
Volatility of income Lower Income smoothened out
Profitability (ROE, ROA) Higher Higher NI outweighs higher equity
Leverage (Debt/Equity) Lower Due to higher equity
SS7_RA3 Analysis of cash flows
Cash flows from operations (CFO) = Sales - COGS - Other cash expenses - Cash interest paid
- Cash taxes paid - Change in inventory - Change in AR + Change in AP {Direct method}.
Cash flows from operations (CFO) = Net income + Depreciation - Gains from sale of assets +
Losses from sale of assets + Other non-cash expenses - Change in inventory - Change in AR +
Change in AP {Indirect method}.
Cash flow from investing (CFI) = - Capital expenditures due to purchase of long-term assets +
proceeds from the sales of long-term assets - New investments made.
Cash flow from financing (CFF) = Sale of stock - Repurchase of stock - Dividends paid + Debt
issued - Debt retired.
SS8: Financial Statement Analysis: Financial Ratios and EPS
SS8_RA1 Analysis of financial statements
Internal liquidity ratios:
Current ratio = Current assets / Current liabilities.
Quick ratio = (Cash + Marketable securities + Receivables) / Current liabilities.
Cash ratio = (Cash + Marketable securities) / Current liabilities.
Receivables turnover = Sales / Average receivables.
Inventory turnover = COGS / Average inventories.
Payables turnover = COGS / Average payables.
Receivables period = 365 / Receivables turnover.
Inventory processing period = 365 / Inventory turnover.
Payables period = 365 / Payables turnover.
Cash cycle = Receivables period + Inventory period - Payables period.
Operating efficiency:
Total asset turnover = Sales / Average total net assets.
Fixed asset turnover = Sales / Average net fixed assets.
Equity turnover = Sales / Average equity.
Gross margin = Gross profit / Sales = (Sales - COGS) / Sales.
Operating margin = Operating profit / Sales = EBIT / Sales.
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Net margin = Net income / Sales.
Return on total capital = (NI + Interest expense) / Average total capital.
Return on total equity = NI / Average total equity.
Return on owners’ equity = (NI - Preferred dividends) / (Average total equity - Preferred
stock).
Financial risk:
Debt to equity = LT debt / Total equity.
LT debt to total capital = LT debt / LT capital.
Total debt ratio = Total interest bearing debt / (Total capital - Non interest bearing liabilities).
Interest coverage = EBIT / Interest expense.
Fixed charge coverage = EBIT / [Interest expense + Lease payments + Preferred dividends /
(1-t)].
DuPont and sustainable growth.
Basic DuPont: ROE = Net margin x Asset turnover x Equity multiplier = (Net income/Sales) x
(Sales/Assets) x (Assets/Equity).
Extended DuPont: ROE = [(EBIT/Sales) x (Sales/Assets) - (Interest expense/Assets)] x
(Assets/ Equity) x (1 - Tax rate).
Retention rate = 1 - Dividend payout.
Sustainable growth rate = ROE x RR = Return on equity x Retention rate.
SS8_RA2 Earnings per share and dilution
Simple capital structure has no potentially dilutive securities, while complex capital structure
does.
Basic EPS = (Net income - Preferred dividends) / Weighted average outstanding stock = (NI
- PD) / (WS).
Weighted average outstanding stock = Sum[Period t in months x Number of stocks
outstanding in period t] / 12.
Adjustment for splits and stock dividends: Assuming that X new stocks are awarded for
every existing one, the EPS of the given period, as well as the EPS of previous periods,
should be divided by (1 + X).
Adjustment for convertible preferred stock: EPS after conversion = NI / (WS + New stock
issued upon conversion of preferred stock). If EPS after conversion is lower than basic EPS,
the convertible preferred stock is dilutive » use EPS after conversion. Else convertible
preferred stock is anti-dilutive » use basic EPS.
Adjustment for convertible bonds: EPS after conversion = (NI - PD + Interest expense x
(1-Tax rate)) / (WS + New stock issued upon conversion of bonds). If EPS after conversion is
lower than basic EPS, the convertible bonds are dilutive » use EPS after conversion. If not,
convertible bonds are anti-dilutive » use basic EPS.
Adjustment for stock options: EPS after conversion = (NI - PD) / (WS + New stock issued
due to options).
New stock issued due to options = Total shares issued upon the exercise of options x
[(Average price - Exercise price) / Average price] {Treasury method}.
Fully diluted EPS = EPS after adjusting for all potentially dilutive securities.
EPS presentation and disclosure: Present the diluted EPS as well as basic. EPS for previous
periods must be restated to account for stock splits and stock dividends.
SS8_RA3 Indicators of earnings quality
Income statement
Conservative revenue recognition.
Use of the completed contract method when accounting for project revenues.
No non-recurring gains.
No non-cash earnings.
Expensing of all interest, overhead and software costs.
Expensing of start-up costs associated with new ventures.
Balance sheet
Use of LIFO for inventory during times of rising prices.
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High bad debt reserves relative to the past credit losses.
Use of accelerated depreciation, short asset lives and low salvage values.
No off-balance sheet financing.
Quick write-off of goodwill and other intangibles.
Clear and adequate disclosures.
Adequate provision for contingencies.
Adequate provision for employee benefit plans.
SS9: Financial Statement Analysis: Assets
SS9_RA1-A Analysis of inventories
Beginning inventory + Purchases = COGS + Ending inventory.
FIFO: Inventory acquired first is sold first. Ending inventory is valued close to its current
market value but the COGS are based on old prices.
LIFO: Inventory acquired last is sold first. COGS reflect the current cost of goods, but ending
inventory is based on old prices.
Average Cost method: All units in the inventory have the same value. Effect of any price
changes spread proportionately between COGS and ending inventory.
Impact of LIFO (versus FIFO) when prices are rising, inventory is rising or stable*
Comment
CFO Higher (more +ve) Due to lower taxes
CFI No impact
Net cash position Higher (more +ve) Due to lower taxes
Inventory/Working capital Lower
Assets Lower Due to lower inventory
Liabilities No impact
Equity Lower Due to lower income
COGS Higher
Taxes Lower Due to lower EBT
Net income Lower Higher COGS outweigh lower tax
Profitability (ROE, ROA) Lower Lower NI outweighs lower equity
Leverage (Debt/Equity) Higher Due to lower equity
Liquidity (Current ratio) Lower Due to lower inventory
Inventory turnover Higher Higher COGS and lower inventory
* the situation is reversed when prices are falling.
Conservative practice in ratio analysis: Use LIFO for profitability ratio and FIFO for liquidity
ratio.
LIFO reserve = FIFO inventory - LIFO inventory.
Adjusting for LIFO - balance sheet: Add the LIFO reserve to LIFO inventories. Add (LIFO
reserve) x (Tax rate) to deferred tax liability. Add (LIFO reserve) x (1 - Tax rate) to retained
earnings.
Adjusting for LIFO - income statement: Add the change in LIFO reserves to LIFO COGS.
Add (change in LIFO reserves) x Tax rate to Tax expense. Resulting net income will change
by (change in LIFO reserves) x (1 - Tax rate).
LIFO reserves build up when number of units in the inventory is rising and/or the price is
rising. LIFO reserve liquidation occurs when the number of units in the inventory is falling
and/or the price is falling.
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SS9_RA1-B Capitalization of long-lived assets
When a firm concludes that a resource being acquired is a long-lived asset, its cost can be
capitalized and then amortized over its life.
Capitalization of interest costs: In general, interest costs are expensed. Exception: for a
loan taken for construction of a long-lived asset, the interest costs during the construction
period can be capitalized.
Rules for capitalization of interest: (1) Only the interest incurred during construction period
can be capitalized. (2) If the firm has no debt, it cannot capitalize any interest costs. (3) If a
loan has been taken specifically for the construction, only the interest on that loan may be
capitalized. (4) If no specific loan can be linked to the construction, capitalization must be
based on weighted average cost of borrowing.
Cost of intangibles purchased from a third party may be capitalized, while the cost of
intangibles developed internally must be expensed.
Franchise/license costs may be capitalized and expensed over the period of contract.
Under US GAAP R&D costs should be expensed as incurred. However, under IASB GAAP,
some development costs may be capitalized.
Goodwill generated in the purchase method acquisition is capitalized. US GAAP does not
permit amortization of this goodwill, while IASB GAAP does.
Advertising costs are generally expensed, except the cost of the direct response
advertising program, which may be may be capitalized.
Software development costs must be expensed if the software has not yet reached the
point of economic feasibility. After this point, further costs may be capitalized.
Impact of Capitalization (versus expensing) Comment
CFO Higher (more +ve) Interest expense removed
CFI Lower (more -ve) Interest expense added
Net cash position No impact CFO and CFI balance out
Assets Higher Interest added to fixed assets
Liabilities No impact
Equity Higher Due to higher income
Net income Higher Lower expense now (higher later)
Volatility of income Lower Amortization smoothens expense
Profitability (ROE, ROA) Higher Higher NI outweighs high equity
Leverage (Debt/Equity) Lower Due to higher equity
Coverage (EBIT/Interest expense) Healthier Due to lower interest, higher CFO
Liquidity (Current ratio) No impact No change in CR or CL
SS9_RA1-C Depreciation and impairment
Depreciation: Process of allocating the cost of a long-lived tangible asset over its useful life.
Depletion: Allocation of the value of a natural resource {crude oil, ore, etc.} as it is exploited.
Amortization: Allocation of the cost of intangible assets over their life.
Straight-line (SL) depreciation = (Original cost - Salvage value) / Depreciable life.
Double declining balance (DDB) depreciation = 2 x [(Original cost - Accumulated
depreciation) / Depreciable life].
Sum of year’s digits (SOYD) depreciation = (Original cost - Salvage value) x (Remaining
useful life / SOYD). SOYD = Sum [1 + 2 + …+ Depreciable life].
Units-of-production (UOP) depreciation = (Original cost - Salvage value) x (Units produced
in a given period / Total units expected over depreciable life).
Depreciation for tax accounts: MACRS used in the US. Accelerated depreciation delays taxes
payable, which is positive considering TVM.
Effect of inflation: Economic logic requires that depreciation be based on the current cost of
assets. But in some environments, firms continue to use historical costs, which understates
expense and overstates earnings.
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Average depreciable life = Gross asset value / Depreciation expense.
Average age = Accumulated depreciation / Depreciation expense.
Impact of accelerated depreciation Comment
Cash flow No impact Taxes payable not dependent on
depreciation in financial accounts
Assets Lower Faster depreciation
Liabilities No impact
Equity Lower Due to lower income now
Net income Lower Lower now, higher later
Profitability (ROE, ROA) Lower Lower NI outweighs lower equity
Leverage (Debt/Equity) Higher Due to lower equity
Coverage (EBIT/Interest expense) Worse Due to lower EBIT
Liquidity (Current ratio) No impact No change in CR or CL
Asset turnover Higher Due to lower assets
Change in depreciation method for assets purchased in the future: no specific disclosure
required.
Change in estimates of useful lives and salvage values: constitutes a change in accounting
estimates and no disclosure is required.
Change in depreciation method for all assets existing as well as new: Constitutes a change in
accounting principles, requires disclosure and the recalculation of accumulated depreciation.
Impairment - recoverability test: If sum of undiscounted expected cash flows from asset <
net book value, write down net book value to fair market value {or PV of cash flows, if market
value is not known}.
Rules of impairment: (1) Based on evidence of irrecoverability. (2) Write-down cannot be
restored later. (3) Write-down is reported above the line. (4) Original cost is also written
down. (5) Write-down is not immediately tax deductible, and so creates deferred tax asset.
Impact of impairment Comment
Cash flow No impact No cash flow takes place
Assets Lower
Liabilities No impact
Equity Lower Due to lower income
Net income* Lower Write-down reported above the line
Profitability (ROE, ROA) Lower Lower NI outweighs lower equity
Leverage (Debt/Equity) Higher Due to lower equity
Liquidity (Current ratio) No impact No change in CR or CL
Asset turnover Higher Due to lower assets
* Future income is boosted as lower asset values lead to lower depreciation.
SS10: Financial Statement Analysis: Liabilities
SS10_RA1-A Analysis of income taxes
Taxable income: Income used for calculating income taxes in tax accounts.
Taxes payable (a.k.a. current tax expense): Actual taxes owed to IRS based on taxable
income.
Taxes paid: Cash paid to IRS, incl. payments or refunds from other periods.
Pretax income (EBT): Income before tax reported in financial accounts.
Income tax expense: Tax calculated based on EBT in financial statements.
Timing differences: Differences between income tax expense and taxes payable that lead
to the creation of deferred tax (DT) assets and liabilities.
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Income tax expenses > Taxes payable » Deferred tax liability.
Income tax expenses < Taxes payable » Deferred tax asset.
Valuation allowance: If the chance that a deferred tax asset will not be realized is over 50%, it
becomes doubtful and a reserve must be set up against it.
Permanent differences between income tax expense and taxes payable never reverse.
Examples: tax-exempt income {interest from munis, insurance claims} and non-deductible
expenses {employee perks and insurance premium}.
Temporary differences between income tax expense and taxes payable reverse themselves
over time. Examples: depreciation {use of accelerated depreciation in tax accounts versus SL
in financial accounts creates a DT liability}, revenue recognition {booking sales sooner in
financial accounts than tax accounts creates a DT liability}, warranties and customer
compensations {create DT assets}.
How should an analyst deal with DT liabilities or assets? If they are expected to reverse
in the future, they should be treated as normal liabilities or assets. If they are not expected to
reverse in the future, remove the DT liability from liabilities and add it to equity. Remove the
DT asset from assets and subtract it from equity.
Liability method under US GAAP: Calculate Tax expense = Taxes payable + Change in
deferred tax liability - Change in deferred tax asset.
Fall in tax rates » reduces deferred tax liabilities » reduces tax expense » increases net
income.
Rise in tax rates » increases deferred tax liabilities » increase tax expense » reduces net
income.
SS10_RA1-B Analysis of financing
Impact of LT debt on cash flows: Proceeds from debt issue added to CFF and redemption
of debt subtracted from CFF. Interest payments subtracted from CFO.
Impact of LT debt on balance sheet: PV of debt at the time of issue recorded as a liability.
Impact of LT debt on Income statement: Interest expense based on yield rather than the
coupon rate.
Bonds issued at premium (coupon > yield): Initial liabilities value > Par value. Interest
expense < Coupon payments. (Coupon payments - Interest expense) = Bond premium
amortized over the life of the bond.
Bonds issued at discount (coupon < yield): Initial liabilities value < Par value. Interest
expense > Coupon payments. (Interest expense - Coupon payments) = Bond discount
amortized over the life of the bond.
Zero coupon debt: Extreme case of a discounted bond issue. Coupon rate = 0, so the entire
interest expense goes towards amortization of the bond discount. The carrying value of the
bond grows towards par over the life of the bond.
Convertibles: The conversion option is ignored in accounts and the bond is booked in the
same way as non-convertibles. Creates a potential loophole, since the interest expense of
the convertible is lower {due to the conversion option the firm gives to bondholders, which is
not reflected in liabilities}.
How should an analyst treat convertibles: If current stock price << conversion price » treat
like an ordinary bond. If current stock price >> conversion price » treat like equity. If current
stock price is close to the conversion price » choose the more conservative treatment.
Alternatively, use option-adjusted yield as the true cost of debt.
Warrants: GAAP requires the issuer to calculate the fair value and report this separately in
stockholders’ equity. Accounting for bonds with warrants is closer to economic reality than
that of convertible bonds.
Redeemable preferred stock: Often recorded as a separate item between equity and debt.
Should be treated as debt and its dividends as interest payments.
Changes in bond value due to changes in interest rates are not reflected in the value of bond
liability. However, analysts should consider the market value of debt in the financial analysis.
Early retirement of debt: (Carrying value of debt liability - Price at which it is purchased
back) recorded as an extraordinary item, because: (1) This gain/loss is not due to the firm’s
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performance, and (2) The cause behind the gain/loss (change in interest rates) could have
occurred in a different period.
SS10_RA1-C Leases and off-balance-sheet debt
Lessee: Firm leasing the asset for its use. Makes the lease payments.
Lessor: Firm leasing out the asset. Receives the lease payments.
Capital lease: Benefits of ownership and risk rest with lessee. Equivalent to borrowing
money and buying the asset.
Operating lease: Lessor retains beneficial ownership of the asset.
A lease is classified as a capital lease if it meets any of the following four criteria. If not, it
is classified as an operating lease. (1) Title/legal ownership of the asset passes to the lessee
at the end of the lease period. (2) The lessee has a bargain purchase option. (3) The lease
term is equal to or greater than 75% of the remaining life of the asset. (4) PV of minimum
lease payments => 90% of fair value of the assets.
Financial reporting from lessee’s perspective: The operating lease has no impact on the
balance sheet and lease payments are treated as an operating expense (rental). The capital
lease creates an asset and liability equal to the PV of lease payments discounted using lower
of the lessor’s implicit rate and the lessee’s marginal borrowing rate. The asset is amortized
as normal. Lease payments are split into two parts: (1) Interest expense, which is included in
the income statement and CFO, and (2) Repayment of the lease principal, which reduces
lease liability on balance sheet and is included in CFF.
Impact of Capital (versus Operating) lease for lessee
Comment
CFO Higher (more +ve) Part of lease payment shifted to CFF
CFF Lower (more -ve) Part of lease payment shifted to CFF
Net cash position No impact CFO and CFF balance out
Assets Higher Due to lease asset
Liabilities Higher Due to lease liability
Equity No impact
Depreciation Higher Due to lease asset depreciation
Interest expense Higher Due to lease liability
Net income Lower Lower now, higher later
Profitability (ROA) Lower Lower NI higher assets
Leverage (Debt/Equity) Higher Higher liability, lower equity
Liquidity (Current ratio) No impact No change in CR or CL
Asset turnover Lower Due to higher assets
Accounting motivations against capitalization: Firms often favor operating leases to boost
their profitability, leverage and activity ratios.
Tax motivations: Most advantageous for the party with the higher marginal tax to retain
ownership of the asset and take the depreciation deductions. If the lessor has a higher tax
rate, an operating lease is better. If the lessee has a higher tax rate, a capital lease is better.
Financial reporting from the lessor’s perspective: The lessor can take the lease asset off
its balance if it meets one of the four criteria for capital lessee {see above}, and two further
criteria: (1) The Minimum Lease Payments (MLPs) are reasonably certain to be collected and
(2) No significant uncertainties exist regarding the reimbursement of costs incurred by the
lessor under the lease contract. If these criteria are not met, the lessor must retain the
underlying assets on its balance sheet. If they are met, the lease must be treated as salestype
or direct financing type lease.
Sales-type lease: The lessor is also the producer or dealer who has sold the lease. In this
case: (1) Lessor recognizes (Selling price - Cost of the asset) as gross profit at inception. (2)
The implicit interest rate is the rate at which PV of MLPs = Selling price of asset. (3) A part of
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the lease payment {= Implicit interest rate x Net value of lease remaining} is booked as
interest income and the rest is used to amortize the net value of the lease.
Direct-financing lease: The lessor is not the producer or dealer who sold the lease. (1) No
sale or gross profit is recognized at inception. (2) The lease is recorded with reduction in
inventory and increase in lease receivables. (3) The implicit interest rate is the rate at which
PV of MLPs = Cost of asset. (4) A part of lease payment (= Implicit interest rate x Net value
of lease remaining) is booked as interest income and the rest is used to reduce the lease
receivable.
Impact at inception of the lease: Direct-financing lease has no impact. Sales-type lease
results in an increase in revenue, net income, current assets due to the gross profit booked
upfront. It also increases CFO and decreases CFI.
Impact over the life of the lease: Direct-financing lease results in a relatively higher interest
income {this includes gross profit from sale}, and relatively higher CFO and lower CFI than a
sales-type lease. Net cash flows are same for both methods.
Impact of off-balance-sheet financing: Reduces assets and liabilities. Boosts leverage
(debt/equity), profitability (ROA), and Activity (Sales/Assets) ratios.
Take-or-pay/Throughput contracts: Buyer commits to purchase a minimum quantity of
input over a specified time period. Buyer effectively receives the use of a productive asset
without reporting it on its balance sheet. Disclosure rules require firms to report the minimum
future payments.
To reflect economic reality of TOP contracts an analyst should add the PV of the
minimum payments to both the assets and liabilities. This increases leverage and reduces
asset turnover.
Sale of receivables no-recourse basis: Truly removed from balance sheet.
Sale of receivables limited recourse basis: Firms recorded them by reducing AR and
increasing CFO. But economically they are just collateralized loans.
To reflect economic reality of sale of receivables limited recourse basis, an analyst
should: (1) Add back sold receivables to AR and create a current liability equal to the
proceeds of sale. (2) Subtract sold receivables from CFO and CFI. (3) Increase revenues and
interest expense by effective interest paid on the transaction. These adjustments reduce the
current ratio, increase the leverage and reduce the interest coverage.
Financing subsidiaries: Not consolidated in parent company’s accounts if ownership is less
than 50%. Firms often manipulate accounts by shifting their assets and liabilities out to
subsidiaries.
Joint ventures: May create obligations for parent firms if any direct or indirect guarantees
are given to secure financing.
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SS11: Corporate Investing and Financing Decisions
SS11_RA1-B Cost of Capital
Cost of debt = Pre-tax cost of debt x (1 – Marginal tax rate).
Cost of preferred stock = Preferred dividends / (Net issuing price - Flotation costs).
CAPM approach: Cost of retained earnings = RFR + (Market rate – RFR) x Beta.
Dividend yield plus growth approach: Required rate of return = D1/P + g.
Growth (g) = ROE(1 – dividend payout ratio)
Bond yield plus risk premium approach: Required rate of return = Bond yield + Equity risk
premium.
Cost of external equity = D1/[P x (1 – % flotation cost)] + g.
WACC = wd * kd * (1 – t) + wp * kp + ws * ks.
Target capital structure: Debt/equity desired by the firm.
Marginal cost of capital: Cost of next dollar of funding based on target capital structure.
Use external equity in marginal WACC only if the equity portion {calculate from debt/equity
ratio} of the required funding cannot be met from retained earnings.
To affect the cost of capital company can control capital structure, dividend policy and
investment policy. Cost of capital also depends on interest rates and tax rates that are out of
the company’s control.
SS11_RA1-C Basics of Capital Budgeting
Payback period = number of years (including fractions) that it takes nominal cash inflows
from project to equal original investment.
Discounted payback period = number of years (including fractions) that it takes discounted
cash inflows from project to equal original investment.
NPV = Sum[Cfi / (1+k)^i ]. Know how to calculate NPV on financial calculator.
NPV rule: Accept all projects with NPV > 0 as they add to shareholder value. In case of
mutually exclusive projects, the project with the highest NPV should be accepted.
IRR: value of k that makes NPV = 0. Know how to calculate IRR on financial calculator.
IRR rule: Accept all independent projects with IRR > cost of capital.
Multiple IRR: If cash flows change sign more than once during the project then there may be
more than one IRR.
For a single independent project NPV and IRR methods always give the same accept or
reject decisions.
For mutually exclusive projects, NPV and IRR can lead to different decisions. Accept the
NPV decision.
Post-audit: improves future forecasts and efficiency of the operations.
SS11_RA1-D Cash Flow Estimation
Net cash flow = Net income + Depreciation.
Change in NWC = Change in inventories + Change in AR – Change in AP.
Expansion project valuation: (1) Calculate initial outlay = upfront costs + change in NWC.
(2) Estimate cash flows = (revenue – expenses) x (1-t) + depreciation x t. (3) Estimate
terminal cash flow {= salvage value + return of NWC}. (4) Find NPV of all cash flows and
accept if positive.
Replacement project valuation: Cash flows due to asset being replaced must be
considered. Include sale of asset and loss of revenue from previous project.
Comparing projects with unequal lives - Replacement chain approach: (1) Repeat the
shorter project enough times to meet the term of the longer project. (2) Compare the NPVs of
the shorter project chain and longer project.
Comparing projects with unequal lives - Equivalent annual annuity (EAA) approach: (1)
Calculate each project’s NPV. (2) Using NPV as PV and FV = 0, calculate PMT over the life
of the project. This is the EAA. (3) Select the project with the higher EAA.
Modified accelerated cost recovery system (MACRS): An accelerated depreciation
method. 3-year assets depreciate over four years, 5-year assets over six years and so on.
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Ignore salvage value. You will be given the percentage depreciation for each year, just apply
this percentage to the gross asset values.
SS11_RA1-E Risk Analysis & Optimal Capital Budget
Stand-alone risk: Due to individual project. Measured as the variability of expected returns.
Easier to estimate than corporate or market risk. Relevant to division undertaking the project.
Corporate risk: Measures net effect of project on the firm’s total risk. Relevant to firm’s
management.
Market risk (beta risk): Measures net effect of project on firm’s beta (systematic risk).
Relevant to investor holding a diversified portfolio.
Sensitivity analysis: Change in project NPV for a unit change in an input variable.
Scenario analysis: Compare NPV of project for best-case and worst-case scenarios with
expected NPV.
Monte Carlo simulation: Compute project NPV for a large number of scenarios to generate
a distribution.
Discount rate for project (required rate of return) = RFR + Beta x (Market return – RFR).
Use project beta where given, or adjust firm beta for project’s relative risk.
Pure play method: Project beta = average of betas of firms that specialize in operation
similar to the project.
Accounting method: Project beta = slope of regression of accounting ROA against market
ROA.
A firm that does not adjust beta for project risk will be biased towards high-risk projects.
Theoretically, a firm should expand until MR from new investments = MC of capital. In
practice, firms cannot reach this point, so they need to ration available capital.
SS11_RA1-F Capital Structure and Leverage
Determinants of target (optimal) capital structure: Business risk {business risk firms should
keep low debt/equity}, Taxes {tax deductibility of interest drives firms towards higher debt},
Financial flexibility {ability to raise capital on reasonable terms in future}, and Managerial
style.
Breakeven quantity of sales = Total fixed cost / (Price per unit - Variable cost per unit) = F /
(P – V).
Degree of operating leverage (DOL) = % change in EBIT / % change in Sales = Q x (P – V)
/ [Q x (P – V) – F].
Degree of financial leverage (DFL) = % change in EPS / % change in EBIT = EBIT / (EBIT
– Interest costs).
Degree of total leverage (DTL) = % change in EPS / % change in Sales = DOL x DFL = Q x
(P – V) / [Q x (P – V) – F - I].
Cost of debt rises with leverage due to the increased probability of default. Cost of debt rises
when leverage becomes excessive due to potential bankruptcy costs.
As a debt-free firm takes on increasing amounts of debt, the expected value of EPS rises but
so does its variability. Shareholder value rises initially, peaks and then falls at high levels of
debt.
Modigliani and Miller (MM) showed that the capital structure does not affect firm value. But
MM is based on unrealistic assumptions - no taxes, no brokerage costs, no bankruptcy costs,
EBIT not affected by debt, investors can borrow at same rate as firms, and symmetric
information {investors have same information as managers}.
Trade-off theory of leverage: A firm’s optimal capital structure is one at which the value of
tax shield due to debt = increased cost of debt and bankruptcy costs. Improves on MM by
accounting for taxes and bankruptcy costs.
Signalling theory: Management is privy to more information and sends clues about future
prospects to investors by its choice of capital structure.
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SS11_RA1-G Dividend Policy
Dividend irrelevance theory / Modigliani and Miller (MM): Dividend policy has no effect on
cost of capital or firm value. If a firm pays no dividend, shareholders can simulate a dividend
by selling part of their holdings, and if the firm does pay dividend then investors can reinvest
them back into the firm.
Bird-in-the-hand theory: Investors prefer dividends and lack of dividends increases cost of
equity.
Tax preference theory: Tax laws (specifically the rates of income and capital gains taxes)
affect the level of dividends.
Signaling hypothesis: Managers have better information and can send signals via dividend
policy. A cut in dividends is seen as a bad sign {dividends can’t be maintained}, while an
increase in dividends is seen as a good sign {future earnings will be higher}.
Clientele effect: Different groups of investors have different preferences for dividend
policies. Firms use dividend policies to attract and retain a certain set of investors.
Residual dividend model: Firms determine optimal capital budget and the amount of equity
required for this budget in line with target capital structure. They use retained earnings to
fund equity portion, and distribute the remaining earnings as dividends. This contradicts the
theory that dividends must be kept stable.
Dividend payment dates: Declaration date {directors declare dividend}. Holder-of-record
date {firm closes stock transfer book}. Ex-dividend date {stock starts trading minus dividend
value}. Payment date {dividend checks are mailed}.
Stock splits: Expressed as the number of new stocks issued in lieu of old ones, e.g. a three
for two split means that three new shares are issued for every two existing ones. This
increases the number of shares outstanding by 50% and reduces EPS and DPS by 50%.
Stock dividends: Dividends paid in the form of stocks. Similar to stock splits, e.g. for a 50%
stock dividend, a stockholder owning 100 stocks would receive 50 additional stocks.
Due to the positive signal to the market, the stock price (adjusted for the number of stocks)
rises when the stock dividend or split is announced. The accessibility of high-priced stocks
increases, but so do trading commissions.
Stock repurchases: A firm buys back its stock in the secondary market. Decreases number
of outstanding stocks and increases EPS and DPS. If conducted at the right price, it
enhances shareholder value. A firm may repurchase stock if it has excess cash or if it wants
to reduce equity in its capital structure.
Advantages of stock repurchases: Viewed as a positive signal. Remove overhang {stocks
held by sceptical investors}. One-off nature makes them preferable to dividends that are
“sticky” (residual income model).
Disadvantages of stock repurchases: Investors may prefer regular, dependable dividends.
Investors may make wrong decisions. The firm may pay a price that is too high.
SS11_RA2 DCF Applications
NPV = Sum[CFi / (1+k)^i ]. Know how to calculate NPV using calculator.
IRR = the k that makes NPV = 0. Know how to calculate IRR using calculator.
NPV rule: Select projects with NPV > 0. If several mutually exclusive projects have NPV > 0,
choose the one with the highest NPV.
IRR rule: Select projects with IRR > Cost of the capital. If several mutually exclusive projects
have IRRs > Cost of capital, select the one with higher IRR.
If NPV and IRR rules conflict, use the NPV rule.
SS12: Markets and Instruments
SS12_Prelim Selecting Investments in a Global Market
US government securities (Treasuries): Virtually free of default risk. Pay a fixed coupon.
Exposed to market risk. Agency issuer – effectively backed by US Gov and virtually default
risk free. Trade at higher yields than Treasuries.
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Municipal bonds (Munis): Issued by state or local governments. Often tax-exempt but NOT
free of default risk. General obligation bonds {backed by the full taxing power of the issuing
authority and so safer}. Revenue bonds {backed only by the cash flow of the project with no
recourse to the issuing authority}.
Tax exempt rate = Equivalent rate for taxable bond x (1 - Tax rate)
Corporate bonds: Senior secured bonds {backed by all of the issuer’s assets and highest
priority in bankruptcy}. Mortgage bonds {backed by specific assets}. Debentures {backed only
by issuer’s promise to pay}. Subordinate bonds {lowest ranking bonds}.
Corporate bonds bells and whistles: Sinking fund bonds {issuer sets aside funds to redeem
some bonds before scheduled maturity}. Callable bonds {issuer can redeem before
scheduled maturity}. Putable bonds {bondholders can sell bonds back to issuer before
scheduled maturity}. Convertible bonds {bondholders can exchange into issuer’s stock}. Zero
coupon bonds {pay no coupons, issued at steep discount to par}. Income bonds {interest paid
only if issuer makes a profit, else accumulated and paid later}. Preferred stock {pay fixed
dividend}.
International bonds: Yankees {dollar bonds sold to US investors by non-US companies}.
Eurobonds {bonds sold to investors outside country of denomination, e.g. dollar bonds issued
in London}. Local currency-denominated issues.
Foreign equities: Difficult and expensive for US investors to invest directly in foreign
companies. Two better options are international mutual funds and ADRs.
American Depository Receipts (ADRs): Negotiable receipts backed by common stock of a
non-US firm held by a US bank. Level 1 ADRs are only traded via illiquid pink sheets. Level 2
ADRs are traded on US stock exchanges but cannot be used to raise any new funds. Level 3
ADRs are traded on US stock exchanges and can be used to raise new funds.
Derivative investments: Financial contracts or securities whose payoff depends on
underlying assets. Futures create an obligation to conduct a future transaction. Options give
a right, but not an obligation, to conduct a future transaction. Call options give the right to
buy. Put options give the right to sell.
Warrant: Essentially call options issued by the firm. They have longer lives than exchangetraded
options and are dilutive.
Investment companies: Allow investors to invest in a well-diversified portfolio. Examples
include money market funds, bond funds, stock funds and balanced funds.
Real estate: Low correlation with other financial markets, therefore good for diversification.
Investments made generally via REITs. Construction REITs lend to property developers.
Mortgage REITs give commercial loans. Equity REITs own and manage properties.
Low liquidity investments: Art, antiques and stamps are merely hobbies.
SS12_RA1-A Organization and Functioning of Securities Markets
Primary markets: Where issuers sell securities to investors. Governments generally issue
via auctions or private placements. Corporates hire investment banks to structure, price,
distribute and underwrite new issues. Rule 415 (shelf registration) allows firms to register
securities and issue intermittently. Rule 144A allows private placement to large sophisticated
investors without registration.
Well-functioning markets: Provide (1) timely and accurate information, (2) high liquidity
{marketability, price continuity, and depth}, (3) access and settlement at a low cost.
Call / fixing market: Trades are executed at scheduled time using market-clearing price.
Continuous market: Trading takes place at any time during opening hours.
Price-driven market: Brokers do not take positions, simply match customer buy and sell
orders.
Order-driven / dealer market: Market makers post bid ask quotes to buy and sell on their
own account.
Registered exchanges: Continuous markets. Impose tough listing criteria.
Over-the-counter (OTC) market: Negotiated market. Traders deal over telephones and
other networks.
Third market: OTC trading in exchange-listed securities.
Fourth market: Direct trading between investors without any intermediation.
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Types of orders: Market orders {filled immediately}. Limit orders {set a limit on price for
transaction – below market price for buy order, above market price for sell order}. Stop orders
{triggered if stop price is reached – below market price for sell order, above market price for
buy order}.
Short selling: Order to sell securities that seller does not actually own. The seller must
borrow securities via a broker and return them to the lender at the end of loan period. Short
seller believes that current price is too high and will fall soon.
Rules of short selling: (1) Shorting only allowed if previous price movement is up (uptick
rule). (2) Short seller must pay dividends due to the security lender. (3) Short seller must
deposit margin money to guarantee the repurchase of the security (to cover the possibility of
the price rising after the short sale).
Margin trading: Buying securities with borrowed money. Margin funds provided by brokers
at a rate above bank call money rate. 100% of the purchase cannot be with borrowed funds.
Percentage of own funds (equity) is called margin requirement. Fed sets minimum initial
margin but brokers can set a higher level.
Initial margin: Initial equity required for margin purchase.
Maintenance margin: Minimum equity required as a fraction of the total value of the stock in
the margin account.
Margin call: Request for funds made by the broker if the value of the margin account falls
below the maintenance margin level. Investor must deposit sufficient funds to return
percentage of equity to the initial margin level.
Variation margin: Money deposited to bring the margin account back to required level.
Leverage factor = 1 / % Initial margin.
Levered return = Holding period return x Leverage factor.
Margin call for long position is triggered when price falls to: (Purchase price) x (1 – % Initial
margin) / (1 – % Maintenance margin).
Margin call for short position is triggered when price rises to: (Purchase price) x (1 + % Initial
margin) / (1 + % Maintenance margin)
Institutionalization of markets has led to: decrease in commissions, rise of block trading,
increase of electronic trading, stock price volatility and increased competition between
exchanges.
SS12_RA1-B Security-Market Indicator Series
Market indexes: Used to track the market movements, construct market-tracking (index)
portfolios, evaluate the performance of actively-managed funds, and calculate market risk
premium and betas.
Unweighted index: Assigns an equal weight to all constituent securities. Equivalent to a
portfolio with $1 invested in each security. Arithmetic or geometric averages can be used.
Geometric has a downward bias so is always lower than arithmetic.
Price-weighted index: Assigns a weight proportional to the price of each security.
Equivalent to a portfolio with one unit of each security. Higher priced stocks have a greater
influence on the index. Price must be adjusted to reflect stock splits, causing a downward
bias, since successful firms split stocks and lose weight in index.
Value-weighted index: Assigns a weight proportional to the market cap of each security.
Uses geometric averaging. The index ends up controlled by a few large firms.
Price-weighted index value = Sum(Stock prices) / (Number of stocks after splits).
Value-weighted index value = [Sum(Stock price today x Number of stocks) / Sum(Stock
price in base year x Number of stocks)] x Index value in base year.
Dow Jones (DJIA): Price-weighted index of 30 stocks traded on NYSE. Criticized for being
too limited and representing only large blue chips and downward bias due to price weighting.
Studies show that DJIA tracks NSYE well on daily/monthly basis, but not in the long term.
Other Equity indexes: S&P 500 {value-weighted index of 500 US stocks}. Nikkei {priceweighted
index of the 225 Japanese stocks}. FTSE 100 {value-weighted index of 100 UK
stocks}. FT/S&P Actuaries {value-weighted indexes of 2,500 international stocks}. MSCI
Indexes {value-weighted indexes of over 1,400 stocks}.
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Bond market indexes: Relatively more difficult to construct than equity indexes because: (1)
the bond universe is too broad (2) the bond universe is constantly changing (3) price volatility
of bonds is affected by duration, which is constantly changing (4) with the exception of
Treasuries, bond prices are not available on a continuous basis.
SS12_RA1-C Efficient Capital Markets
Efficient market: Prices of securities reflect all available information.
Requirements for market efficiency: (1) large number of profit maximizing, independent
buyers and sellers, (2) random order of new information, (3) rapid adjustment of price
expectations in response to news, (4) risk reflected in security prices and returns.
Weak form EMH: Security prices reflect all historical information. Implies that technical
analysis cannot generate excess returns.
Tests of weak form EMH: Supported by statistical tests {autocorrelation and runs} that show
returns to be independent over time. Trading rule tests that show no excess return can be
generated after accounting for transaction costs.
Semi-strong form EMH: Security prices reflect all publicly-available information. Implies that
fundamental analysis cannot generate excess returns either.
Tests of semi-strong form EMH: Supported by event studies {abnormal returns around
stock splits, IPOs and accounting changes}. Rejected by time series tests {term structure of
interest rates and dividend yield can be used predict prices} and cross sectional tests
{neglected, low PE, and high P/B firms have higher returns}
Strong form EMH: Security prices reflect all public and private information. Implies that no
investor group can generate superior returns.
Tests of strong form EMH: Supported by evidence that after accounting for transaction
costs security analysts and portfolio managers cannot generate excess returns. Corporate
insiders and stock market specialists are exceptions who can generate excess returns.
Implications for technical analysis: dire.
Implications for fundamental analysis: also dire.
Implications for portfolio manager: Active managers will under perform the market especially
after management fees are taken into account. Investors should put their money in an index
fund.
Portfolio management in efficient markets: Portfolio managers can still add value by
implementing the portfolio management process. (1) Determine investor’s risk and return
objectives. (2) Specify policies and strategies required to meet objectives. (3) Allocate funds
according to investment policy. (4) Diversify investments to eliminate unsystematic risk. (5)
Monitor capital markets and client’s needs to rebalance if necessary. (6) Minimize taxes,
turnover of assets and liquidity costs.
SS13: Equity Investments
SS13_RA1-A Introduction to Security Valuation
Top-down approach to valuation: Macroeconomic analysis » industry analysis » stock
analysis.
Rationale for top-down approach: Performance of individual firms is largely explained by
economic and industry trends. Studies show that asset allocation is far more important than
selection of individual securities.
Valuation process: (1) Forecast expected cash flows. (2) Determine required rate of return.
(3) Discount the cash flows. (4) Make investment decision.
Generic dividend discount model: Value of stock = Sum[Di / (1 + k)^i].
One-period DDM: Value of stock = (Expected selling price + D1) / (1 + k).
Two-period DDM: Value of stock = D1/(1+k) + (Expected selling price + D2) / (1 + k)^2.
Infinite period (a.k.a. constant growth) DDM: Value of stock = D1 / (k - g) = [D0 x (1+g)] /
(k - g), where the growth rate (g) is lower than the cost of capital (k) and stays constant
forever.
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DDM with supernormal growth: Value of stock = D1 / (1 + k) + D2 / (1 + k)^2 + … + Dn / (1 +
k)^n + [Dn+1 / (k - g)] / (1 + k)^n.
Value of a preferred stock = Dividend / Required rate of return.
PE ratio: Leading P0/E1 = Dividend payout / (k - g). Trailing P0/E0 = [Dividend payout x (1 +
g)] / (k - g).
Required rate of return = (Real RFR + Expected inflation) + Risk premium.
= Nominal RFR + Risk premium.
= Nominal RFR + Beta x (Market return - Nominal RFR).
Dividend growth rate = Retention rate x Return on equity.
Return on equity = Net income / Equity = Profit margin x Asset turnover x Leverage.
SS13_RA1-B Stock market analysis
Market earnings multiplier: PE1 = Dividend payout / (k - g).
Required rate of return = Nominal RFR + Equity market premium.
Growth rate = RR x ROE = RR x Profit margin x Asset turnover x Leverage.
EPS = [(Sales x Operating margin) - Depreciation - Interest expense] x (1 - Tax rate).
Expected return from market series = (Ending value - Beginning value + Dividends)/
Beginning level.
SS13_RA1-C Industry analysis
Industry trends: Cyclical {due to expansion and contraction in GDP}. Structural
{reorganization in which some go up and others go down}.
Consumer staples: (Pharma, food, etc.) outperform in recession.
Consumer durables: (DVDs, cars) outperform as the economy is pulling out of recession.
Capital goods: (Heavy goods, chemicals, etc.) outperform further on in recovery.
Basic industries: (Mining, oil, etc.) outperform best at the top of the GDP cycle.
Structural changes: Demographics, psychographics (lifestyle), technology, regulation and
politics
Industry life cycle: Pioneering development {low or negative profitability and low demand} »
rapidly accelerating growth {most profitable phase with few competitors, excess demand and
growing economies of scale} » Mature growth {competitors growth and, although the industry
is still growing, profit margins start to fall} » Stabilization {growth rates and profit margins
match those of the general economy} » Deceleration and decline {demand shifts away and
profit margins fall further}.
Michael Porter’s five forces that shape an industry: (1) Rivalry among the existing
competitors {several competitors of comparable size}. (2) Threat of new entrants {barriers to
entry}. (3) Threat of substitute products {commodity versus branded products}. (4)
Bargaining power of buyers {number and size of the buyers}. (5) Bargaining power of
suppliers {number and size of the suppliers}.
Industry earnings multiplier: PE1 = Dividend payout / (k - g).
Required rate of return = Nominal RFR + Industry premium.
Dividend growth rate = Retention rate x Return on equity = Retention rate x Profit margin x
Asset turnover x Leverage.
EPS = [(Sales x Operating margin) - Depreciation - Interest expense] x (1 - Tax rate).
SS13_RA1-D Company analysis and stock selection
Performance of stock versus performance of company: a good company is not necessarily a
good investment, and an average company is not necessarily a bad investment. A stock’s
performance depends on its intrinsic value relative to its price in the market.
EPS = [(Sales x Operating margin) - Depreciation - Interest expense] x (1 - Tax rate).
Required rate of return = RFR + Beta x (Market return - RFR).
Growth rate = RR x ROE = RR x Profit margin x Asset turnover x Leverage.
Earnings multiplier: PE1 = Dividend payout / (k - g).
If estimated value of the stock (= E1 x PE1) is higher than the market price, buy the stock. If
not, do not buy.
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Other ratios: Price/book value {especially useful for finance and commodity firms and for
firms that have negative earnings}. Price/cash flow {cash flows less easily manipulated than
earnings, and tend to be less volatile}. Price/sales {of limited value}.
SS13_RA1-E Overview of technical analysis
Underlying assumptions: Security prices are determined solely by supply and demand,
which are driven by irrational factors. Prices patterns persist for appreciable lengths of time.
Technical analysts believe that the market is slow to adjust to new information, giving them
the opportunity to profit. Fundamental analysts believe that the price adjustment is faster but
still leaves time for those who have analyzed the underlying factors. EMH contends that
prices adjust instantaneously, so any form of analysis is futile.
Advantages of technical analysis: Quick and simple.
Challenges to technical analysis: Empirical studies back EMH and show that technical
analysis rules cannot be used to generate excess returns.
Contrary opinion rules: Contrarians believe that the majority is always wrong and would
buy stocks when: (1) Mutual fund cash positions are high. (2) Credit balances in brokerage
accounts are high. (3) Investment advisory opinions are bearish. (4) OTC versus NYSE
volume is low. (5) CBOE put/call ratio is high (>0.5). (6) Index futures positions are bearish.
Smart money rules: Smart money analysts follow the experts and would buy stocks when:
(1) Confidence index is higher (approaching 100). (2) T-bill Eurodollar spread (or high quality
/ low quality bond spread) is low. (3) Short sales by specialists as a percentage of the overall
short sales are low. (4) Debit balances in brokerage accounts are high.
SS13_RA2 DCF Applications
Dividend discount model (DDM): Stock value = Sum[Dividend t / (1 + k)^t].
One-period DDM: Value of stock = (Expected selling price + D1) / (1 + k).
Two-period DDM: Value = D1/(1+k) + (Expected selling price + D2) / (1 + k)^2.
Infinite period DDM: Value of stock = D1 / (k - g) = [D0 x (1+g)] / (k - g), (a.k.a. constant
growth model) where the growth rate (g) is lower than the cost of capital (k) and stays
constant forever.
DDM with supernormal growth: Value of stock = D1 / (1 + k) + D2 / (1 + k)^2 + … + Dn / (1 +
k)^n + [Dn+1 / (k - g)] / (1 + k)^n.
Value of a preferred stock = Preferred dividend / Required rate of return.
Dollar-weighted portfolio return: The IRR of all the cash flows into and out of the portfolio,
i.e. the discount rate that makes PV(inflows) = PV(outflows). Remember to count cash flows
due to the purchase and sale of stock as well as dividends received.
Time-weighted portfolio return: Geometric average of the returns generated by the
portfolio over a given set of periods, where the return in each period = Ending portfolio /
Beginning portfolio value – 1.
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SS14: Debt Investments: Basic Concepts
SS14_RA1-A Features of Fixed Income Securities
Terminology: Maturity date, term {in years}, par value {usually $100 or $1,000}, coupon {paid
in 2 semi-annual installments in the US}, yield {BEY basis}, price {quoted as % of par value}.
Indenture and covenants: Affirmative covenants {things that the issuer promises to do, like
paying interest and principal} and negative covenants {things that issuer is not allowed to do}.
Types of bonds: Bullet/straight bond. Zero coupon bond {coupon rate = 0}. Step up bond
{coupon rate increases over time}. Deferred coupon bond {coupon paid at maturity}. Floating
rate note/Floaters {variable coupon rate = reference rate}. Capped floater {variable coupon
with a maximum limit}. Collared floater {variable coupon with maximum and minimum limits}.
Dual index floater {coupon rate = difference between two reference rates}. Range note
{coupon rate = reference rate if within a certain range, else coupon rate = 0}, Ratchet bond
{rate adjusts only in one direction}. Stepped spread floater {coupon rate = reference rate +
variable spread}. Non-interest rate index floater {coupon linked to a commodity or equity
index}.
Accrued interest: Interest earned since the last coupon payment date. Paid by the buyer to
the seller along with the clean price of the bond.
Full price = Clean price + Accrued interest.
Scheduled retirement provisions: Bullet maturity {most common}. Serial bonds {bond
maturity varies with serial numbers}. Amortizing bond {principal repaid in installments}.
Sinking fund provision {issuer required to retire bond issue according to a schedule}.
Early retirement provisions: Call provision {issuer can retire the bond before maturity date}.
Refunding provision {issuer can call the bond using proceeds of a new debt issue}.
Prepayment option {found in mortgage-backed securities}. Accelerated sinking fund provision
{when issuer can retire more than what is required by sinking fund}. Index amortization
{principal amortized is governed by level of a reference rate}
Nonrefundable versus noncallable bond: A bond can be callable with or without being
refundable. But a refundable bond must be callable. A callable, refundable bond is the
easiest one to call. A no-call provision in early years gives the investor some protection.
Embedded options: Call option. Prepayment provision. Accelerated sinking fund. Put option
{allows bondholders the right to sell the bond back to issuer at a specified price before
maturity}. Conversion option {allows investors to exchange bond for the issuer’s stock}.
Repurchase agreements (a.k.a. repo): One party (seller or security lender) sells a security
to another (buyer or security borrower) with an agreement to buy it back at a specified price
on a later date. Security lender does a repo, security borrower does a reverse repo.
Margin buying: The practice of buying stock partly with cash and partly with a loan. Used by
individual and institutional borrowers in equity markets. The Fed sets the cash component, or
the margin, at 50%. Cost of loan = Call money rate + service charge.
Reverse repo: Used by institutional investors in bond markets. Allows for the financing of a
larger portion of the purchase price than margin buying.
SS14_RA1-B Bond investment risks
Bond price sensitivity: When interest rates go up, investors’ bond prices fall. When interest
rates go down, bond prices rise.
Coupon rate < Yield » Price < Par value {bond trades at a discount}.
Coupon rate = Yield » Price = Par value {bond trades at par}.
Coupon rate > Yield » Price > Par value {bond trades at a premium}.
Factors that affect bond price sensitivity: Maturity {higher maturity » higher sensitivity}.
Coupon rate {higher coupon rate » lower sensitivity}. Yield {higher yield » lower sensitivity
due to positive convexity}. Embedded options {can increase or decrease sensitivity}.
Interest rate risk of FRN is lower than that of a fixed-coupon bond. Still, it exists due to:
fixed coupon until the next reset period; change in credit quality; and the presence of a cap
on the floating rate.
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Duration of a bond = Percentage change in price for a 100 basis point change in yield = (V_
- V+) / (2 x Vo x dy).
Approximate bond price change = -1 x Duration x Price x dy.
Dollar duration = -1 x Duration x Price / 100.
Yield curve risk: Exposure to movements of the whole yield curve. Represented by key rate
duration.
Call and prepayment risk: Call provision makes the bond’s cash flows unpredictable,
increases reinvestment risk, and limits the potential for price appreciation. Prepayment risk is
similar.
Reinvestment risk: The proceeds from an investment may have to be reinvested at a lower
rate than the rate available from the investment itself. The reinvestment risk for callable
bonds and amortizing bonds is higher than bullet bonds. Zero coupon bonds have no
reinvestment risk.
Credit risk: The loss due to a debtor’s inability to meet its bond obligations. Credit spread
risk {widening of bond spread over the benchmark - happens before ratings downgrade}.
Downgrade risk {fall in the bond price due to a ratings downgrade}. Default risk {issuer
actually fails to make interest and principal payments}.
Liquidity risk: Investors will not be able to realize the true value of their investments due to a
widening of the bid-ask spread and a lack of buyers or sellers. Increases in extreme events or
if one or more dealers leave the market.
Bid-ask spread: Highest Bid - Lowest Ask.
Exchange rate risk: Exists with bonds denominated in foreign currencies.
Inflation risk: Unexpected rise in inflation raises yields and lowers the price of all bonds
except TIPS.
Yield volatility risk: Rise in yield volatility increases value of embedded options » lowers price
of callable bonds, increases price of putable bonds.
Event risk: Natural and corporate events can affect the issuer’s ability to pay.
Regulatory risk: Bond price changes due to changes in regulations.
Political risk: With governments and municipalities, investors must evaluate the willingness to
pay as well as the ability to pay.
SS14_RA1-C Bond sectors and instruments
US Treasury securities: T-bills {91, 182 or 364 days, issued at a discount to par and
redeem at par value}. T-notes {medium-term up to ten years, semi-annual coupon}. T-bonds
{long-term over ten years, semi-annual coupon}. TIPS {medium to long-term coupon,
principal adjusted for the prevailing level of inflation}.
TIPS: Adjusted principal = Principal x (1 + Annual inflation / 2).
TIPS: Coupon = Adjusted principal at end of period x Coupon rate / 2.
Treasury auction process: Dutch auctions held by Fed NY. Competitive {yield and quantity}
and non-competitive {quantity only} bids. Most recently issued Treasury becomes on-the-run
and trades at a higher price relative to off-the-run issues due to higher liquidity.
Treasury stripping: Treasuries can be decomposed into zero coupon securities under
STRIPS program with coupons (ci) and principal (bp or np) cash flows. Creates a negative
cash flow problem if interest accrues, but taxes must be paid.
Federal agencies: Federally related/owned agencies like Ginnie Mae, and governmentsponsored
enterprises like Fannie Mae, Freddie Mac, Sally Mae, issue debentures {no
collateral} and mortgage-backed or asset-backed securities {backed by mortgages, student
loans, etc.}.
Home mortgages: Consist of equal monthly payments {interest plus principal} and allow
borrowers to prepay all or a part of the loan.
Mortgage-backed securities: Backed by a pool of home mortgages. Pass-throughs simply
channel the cash flows from underlying mortgages to the holders of securities.
Collateralized mortgage obligations (CMOs) subdivide the mortgage pool into several
tranches with different cash flows and prepayment risk profiles {junior tranches bear more
prepayment risk than senior tranches}.
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The revision guide for the CFA® Level I exam
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Municipal securities (or munis): Issued by state and local governments in the US. NOT
free of credit risk {municipalities do go bust}. Income is tax-exempt but capital gains are
taxed. Tax-backed debt obligations secured by taxes, while revenue bonds secured only by
revenues from specific project.
Types of tax-backed debt obligations: General obligation debt {secured by an unlimited tax
pledge (stronger) or by a limited tax pledge}. Appropriation-backed obligations {secured
by a non-binding tax pledge}. Debt obligations supported by public credit enhancement
programs, i.e. legal backing of the state or a federal agency.
Insured bonds: Insured by an insurance firm in addition to being secured by tax revenues.
Prefunded bonds: Fully backed by US Treasury securities.
Corporate bonds: If a firm goes bankrupt, bondholders have priority over stockholders.
Secured debt holders have the highest chance of recovering their investment. Corporates are
rated by rating agencies for risk of default {four C’s of credit analysis - character, capacity,
collateral, and covenants}.
Credit enhancements: Third party guarantees and letter of credit (LOC) issued by banks.
Medium-term note (MTN) versus corporate bonds: Offered continuously to investors.
Unlike corporate bonds, investors can choose the maturity and coupon of MTN. With the help
of a derivative wrapper, they can embed options, change currency, link the return to equity
index, etc. MTN + Derivatives = Structured notes.
Commercial paper (CP): Short-term promissory notes with a maturity of less than 270 days.
CP programs allow for rollover, but the issuer is exposed to the risk of the market drying up.
Direct paper sold by issuer. Dealer paper sold by agents. Little secondary market trading.
Asset-backed securities: Created from the cash flows from assets other than mortgages,
e.g. consumer loans and trade receivables.
International bonds: Foreign bonds {e.g. Yankees are issued by non-US firms in the US}.
Eurobonds {sold to investors outside the country of denomination, e.g. JPY denominated
bond sold in London}. Global bonds {sold in Yankee and Eurobond market}. Sovereign debt
{issued by various governments. Ideal for investors diversifying abroad. Withholding tax is a
key concern}.
SS14_RA1-D Yield spreads
Fed’s monetary tools: Open market operations {buying Treasuries in the repo market »
injects money into markets » lowers Fed Funds rate}. Discount rate {lowering this rate
makes it more attractive for banks to borrow money from Fed}. Reserve requirements
{lower required reserve ratio » more funds available for lending; used rarely}. Verbal
persuasion {used often}.
Risks inherent in US Treasuries: Interest rate risk {very low for T-bills, very high for T-bonds}.
Portfolio of Treasuries exposed to yield curve risk and reinvestment risk. No credit or liquidity
risk.
Treasury yield curve: Graph of yields of on-the-run Treasuries versus maturity. Typically
upward sloping (normal), but can be downward sloping (inverted) or flat. Two problems: (1)
Yields of on-the-run Treasuries are lowered by demand in repo market, and (2) Different
coupons and reinvestment risk makes yields non-comparable.
Term structure of interest rates: Graph of zero coupon yields versus maturity. Solves
problem of Treasury yield curve.
Absolute yield spread = Yield of bond - Yield of reference bond.
Relative yield spread = Absolute yield spread / Yield of the reference bond. Better basis for
comparison over time than absolute spread.
Yield ratio = Yield of bond / Yield of reference bond.
Bond market sectors in the US: Government. Agencies. Munis. Corporate. Mortgage-backed.
Asset-backed.
Intermarket spread: Yield spread for same maturity and different sectors.
Intramarket spread: Yield spread for different maturities and same sector.
Credit spread tends to widen when the economy enters a recession and narrow when
economy is booming.
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The revision guide for the CFA® Level I exam
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Impact of embedded options: Call option increases reinvestment risk and yield spread
must be higher to compensate. Put option is favorable towards investors - reduces yield
spread. The yield spread of Agency MBS is primarily due to prepayment risk.
Option-adjusted spread excludes the risk due to the embedded option, while the nominal
spread does not, making an option-adjusted spread a superior measure to compare returns.
Lack of liquidity can increase yield spread, even of off-the-run Treasuries.
Impact of tax-exemption: Munis trade at low yields (even negative yield spread) because
their income is tax exempt.
After-tax yield = Pre-tax yield x (1 - Marginal tax rate of investor).
Tax-equivalent yield = Tax-exempt yield / (1 - Marginal tax rate of investor).
Impact of technical factors: Yield spreads rise if there is a glut in supply of bonds.
The yields spreads of sovereign bonds over US Treasuries are “nominal” since the currencies
may be different and the spreads are simply differences in two yields.
SS14_RA2 Alternative Bond Issues
Certificates for automobile receivables (CARs): Backed by auto loans. Short maturities (<
5 years) shortened further by amortization & prepayments.
Credit card receivables: Backed by credit card loans. Trustee of credit card ABS retains
principal payments and reinvests them into more receivables during a lock out period.
Investors have a trigger option to force redemption during lock out period if the loss rate on
loans rises.
US corporate bond market: Dominated by utilities, followed by industrials, transportation
and financial firms. Longer-term bonds have call provisions.
Japanese corporate bond market: Dominated by banks.
German corporate bond market: Dominated by banks.
SS15: Debt Investments: Analysis and Valuation
SS15_RA1-A Principles of bond valuation
Valuation process: (1) Estimate the expected cash flows. (2) Determine the appropriate
discount rates. (3) Calculate sum of present values {= Sum[Cash flow in period t/(1 +
Discount rate)^t]}.
Cash flow estimation can be complicated by embedded options {callable or convertible
bonds} or by variable coupons.
Appropriate discount rate: Ideally, each cash flow should be valued using the spot rate
corresponding to its maturity.
Bond price is inversely related to discount rate.
Pull to par: As time passes, the price of a bond trading at a premium will fall back to par and
the price of a bond trading at a discount will rise to par.
Value of a zero-coupon bond = Par / (1 + Yield/2)^(2 x Years to maturity).
Full price of a bond between coupon payments = Sum[Cash flow in period t/(1 + Discount
rate)^(t-1+w)], where w = Days remaining until next coupon / Total days in coupon period.
Accrued interest = Coupon x (1 - w). Clean price = Full price - Accrued coupon.
Deficiency of traditional approach to valuation: Each cash flow is unique. Valuing all cash
flows of a security using a single discount rate is incorrect.
Arbitrage-free valuation: Cash flows are valued using the spot rate corresponding to their
maturity. More accurate than the traditional approach.
Stripping: If a dealer finds Treasury coupon bonds trading at a lower price than Treasury
strips, he can make a riskless (arbitrage) profit by buying coupon bond and selling strips.
Reconstitution: If a dealer finds Treasury coupon bonds trading at a higher price than
Treasury strips, he can make an arbitrage profit by buying strips and selling coupon bonds.
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The revision guide for the CFA® Level I exam
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SS15_RA1-B Measures of yield
Total return = Coupon interest payments + Reinvestment income + Capital gain/loss.
Reinvestment income: The income from the reinvestment of coupons until final maturity.
Very significant for securities held over several years.
Current yield = Annual coupon / Price.
Yield to maturity: IRR of an investment in the bond. Discount rate that equates the PV of all
expected cash flows from bond to its full price.
Bond-equivalent yield (BEY): Discount rate calculated using six-monthly periods and
annualized by multiplying by two.
Yield to call: Values bond on the basis that it will be called on first call date.
Cash flow yield: Based on cash flows that include an assumption regarding prepayment rate.
Used for MBS that have monthly payments.
Cash flow yield = [(1 + Monthly yield)^6 - 1] x 2.
Assumptions and limitations of yield: (1) Security will be held to maturity, and (2) All
intermediate cash flows will be reinvested at the same rate as yield.
Higher term to maturity » Higher reinvestment risk.
Higher coupon rate » Higher reinvestment risk.
Annual pay versus semi-annual pay: Many non-US governments and corporate bonds that
pay annual coupons.
Annual pay yield = (1 + BEY/2)^2 - 1.
BEY = [(1 + Annual-pay yield)^0.5 - 1] x 2.
Discount margin measure for a floater: Assume that the reference rate will not change from
its current value. Determine the margin over the reference rate that makes the present value
of cash flows equal to market price of floater.
T-bill yield = (1 - Settlement price) x (360 / Days remaining to maturity).
Limitations of nominal spread: (1) Does not account for term structure of interest rates (noarbitrage
pricing). (2) Ignores affect of embedded options.
Zero-volatility spread (Z-spread): Spread over the entire Treasury spot rate curve.
Accounts for the term structure of interest rates, but ignores the affect of embedded options.
Difference between Z-spread and nominal spread is greatest for amortizing bonds, for longterm
high-coupon bonds, and for steep yield curves.
Option-adjusted spread (OAS): Spread over entire Treasury spot rate curve after
accounting for embedded options. OAS is highly dependent on the model used to calculate
the spread and the assumption for interest rate volatility. Higher interest rate volatility
assumed » Lower OAS.
Option cost = Z-spread - OAS. For option-free bonds OAS = Z-spread.
Nominal spread may be misleading in the case of securities with embedded options. Buy
securities with largest OAS for a given duration.
Bootstrapping: Process of calculating spot rates from coupon bond yields.
Forward rate from period 1 to period 2 = (1 + z2)^2 / (1 + z1) – 1.
SS15_RA1-C Measurement of interest rate risk
Full valuation: Recalculate the value of all securities after a change in interest rates. Works
well for periodic reports but impractical for managing risk of large portfolio.
Parametric approach: Relies on a simple measure like duration to estimate response of
portfolio to parallel shifts in yield curve.
Price yield relationship of option-free bonds: Price is inversely related to yield. Price
sensitivity depends on maturity and coupon. For small changes in yield, the price change is
same whether yield moves up or down. For large changes in yield, the price increase for a fall
in yield is greater than the price decrease for a similar rise in yield, i.e. the price yield curve is
convex.
Positive convexity: The decrease in an option-free bond’s price due to a rise in yield is
lower than the increase for an equal fall in yield. This results a positive adjustment to the
duration-based estimate of price change whether yield goes up or down.
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The revision guide for the CFA® Level I exam
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Embedded options can dramatically change the price-yield profile. At high yields the profiles
of these bonds are similar, but at low yields price of callable/prepayable securities grows
slower with a fall in yield than the price of option-free bonds {price compression}.
Negative convexity: For callable and prepayable securities, at low levels of yield, the price
increase for a given fall in yield is less than the price decrease for an equal rise in yield.
Duration of a bond = Percentage change in price for a 100 basis point change in yield = (V_
- V+) / (2 x Vo x dy).
Modified duration versus effective duration: No difference in case of option-free bonds.
However in bonds with embedded options, modified duration does not account for change in
cash flows due change in interest rates, while effective duration does.
Macaulay duration: Weighted average number of years remaining to receive the present
value of a bond.
Macaulay duration = Modified duration x (1 + BEY/2).
Price value of a basis point (PVBP) = Duration x Price / 10,000.
Effective convexity = (V_ + V+ - 2 x Vo) / (2 x Vo x dy^2).
Approximate bond price change (using duration) = -1 x Duration x dy.
Contribution of convexity: Convexity x dy^2.
Approximate bond price change (using duration and convexity
= -1 x Duration x dy + Convexity x dy^2.
SS15_RA2 Term structure of interest rates
Yield curve is typically upward sloping (normal), but it can be downward sloping (inverted) or
flat.
Expectations hypothesis: Term structure of interest rates results from the market’s
expectations of future interest rates. If the market expects inflation and consequently interest
rates to be higher in future periods, it will expect higher forward rates leading to an upward
sloping yield curve. This theory fails to account for why term structure of interest rates is
upward sloping more often than downward sloping.
Liquidity preference theory: Investors demand a premium for investing in long-term bonds
to compensate for higher risk. Borrowers are willing to pay the extra yield since short-term
debt that needs to be rolled over exposes them to refinancing risk.
Market segmentation theory: Various borrowers and lenders have preferred maturity
ranges based on their objectives. These preferences are fixed. Thus the market is divided
into distinct maturity segments, in which interest rates are determined by the demand and
supply of loanable funds. If there is a shortage of loanable funds in the short term and excess
in the long term, then short-term rates will be high and long-term rates will be low.
SS15_RA3 DCF Applications
Bank discount yield (BDY) = (Dollar discount / Face value) x (360 / Days to maturity).
Holding period yield (HPY) = (P2 + I - P1) / P1. Where P1 and P2 are the purchase and
sale/redemption price respectively and I is the interest earned.
Effective annual yield (EAY) = [(P2 + I) / P1]^(365 / Days to maturity) - 1.
Money market yield (MMY) = [(P2 + I - P1) / P1] x (360 / Days to maturity).
EAY = (1 + HPY) ^(365 / Days to maturity) – 1.
MMY = HPY x (360 / Days to maturity).
MMY = (360 x BDY) / (360 - Days to maturity x BDY).
Price zero-coupon bond with N years remaining = F / (1 + Y/2)^(2 x N). Alternatively, use
the TVM function on a bond calculator with PMT=0.
Yield of zero-coupon bond = (F / P)^[1 / (2 x N)] - 1.
Arbitrage-free valuation: Each individual cash flow is valued by discounting it at a spot rate
corresponding to its maturity.
Price of a security = Sum[Cash flow t / (1 + Spot rate t)^t].
Price of coupon bond: Use the TVM functions on a bond calculator.
Arbitrage: If the sum of the PVs of cash flows is more than the price of the security, then buy the
security and sell the cash flows individually, and vice versa.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 39
SS16: Derivative Investments
SS16_RA1-A Introduction to derivatives
Derivatives are financial contracts or securities whose payoff depends on underlying assets
or indices.
Forwards: Contracts that set the terms for some future transaction between two parties, who
both have the obligation to fulfill their part of the bargain.
Futures: Standardized forward contracts purchased or sold on derivatives exchanges.
Options: Contracts that give their owners the right, but not the obligation, to conduct a
transaction in the future, whose terms are set in the option contract.
Swaps: Contracts for the exchange of two or more sets of cash flows between two parties.
Futures versus forwards: Forwards are negotiated privately in the OTC market, so they can
be customized, do not have any margin requirements and do expose the parties to credit risk.
Futures are standardized, exchange-traded contracts that are more liquid and so cheaper
than forwards. Futures buyers and sellers must deposit a margin with the exchange/clearing
house. Futures have near-zero credit risk.
Arbitrage: The opportunity to make a risk-free profit without any investment.
No-arbitrage: The whole basis of derivatives and their valuation rests upon the condition that
the markets function well and there are no persistent arbitrage opportunities.
Derivatives applications: Speculation {they are cheap, precise and offer high leverage, and
long/short positions are available}. Hedging {again long/short positions are available, lower
cost and more convenient}. Arbitrage {more liquid, trade close to their true value and require
less capital}.
Complete market: Investors can obtain any and all identifiable payoffs by trading securities
in the market. Difficult in traditional cash-based markets, possible with the help of derivatives.
SS16_RA1-B Futures markets
Futures buyer has a long position on underlying asset. Futures seller has a short position.
Futures buyer profits if asset price rises, while futures seller profits if asset price falls.
Hedging: To reduce a long exposure {e.g. investor holding a stock portfolio, firm mining gold,
farmer with wheat in the field}, you would sell futures. To reduce a short exposure {e.g. airline
that needs to buy oil, importer who needs to buy foreign currency}, you would buy futures.
Speculation: If you believe prices will rise buy futures. If you think they will fall, sell futures.
Open interest = Outstanding long positions + Outstanding short positions.
Trading volume: Number of contracts executed in a given day. When a party buys a future it
generates one unit of trading volume. If the party then closes out by selling the contract, it
generates another unit of trading volume.
Benefits of futures: (1) Price discovery (by creating a highly liquid and transparent market)
and (2) Hedging. Regulation and speculation are required for smooth functioning of futures
market, but are not considered to be benefits.
Futures contracts: Standardized by the quality of the underlying asset, notional amount, tick
size {smallest unit by which futures price can change}, tick value {dollar value of one tick},
expiration, delivery terms, and margin requirements.
Initial margin: Amount that must be deposited at the time of opening a futures position.
Maintenance margin: Level to which a margin account may fall before a request for
additional funds (a margin call) is made.
Variation margin = Initial margin - Equity balance in margin account. Must be deposited
upon the receipt of a margin call to bring the margin account back to the required level.
Closing futures positions: Offset {buy a contract to close a short position and sell a
contract to close a long position, most common}.#! Delivery {any contract outstanding at
expiration settled by physical delivery of asset. Cash settlement {many financial futures do
not allow physical delivery and instead require cash settlement}. Exchange for physicals
(EFP) {two traders with opposite side of a contract conduct the transaction and ask exchange
to cancel their positions}.
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The revision guide for the CFA® Level I exam
page 40
SS16_RA1-C Introduction to the options market
Option buyer has the right to buy or to sell the underlying asset but no obligation to do so.
Option seller (writer) has no right, but an obligation to complete the trade required by the
option contract.
Call option: Gives its holder the right to purchase an asset at the strike price.
Put option: Gives its holder the right to sell an asset at the strike price.
American versus European: American-style options can be exercised at any time up to the
expiration date. European-style options can only be exercised on the expiration date. Since
American-style gives more flexibility, it can be more expensive than European-style in some
(but not all) cases. Both options have the same value on the expiration date.
Settlement: Physically-settled or cash-settled.
Option value: Call option is in-the-money if current asset price > strike price, and out-of-themoney
if current asset price < strike price. Put option is in-the-money if current asset price <
strike price, and out-of-the-money if current asset price > strike price.
Margins: Option buyer must pay option premium upfront {100% initial margin}. Option seller
must deposit option premium x 1.2.
SS16_RA1-D Option payoffs and strategies
Long call: Limited downside {call buyer can lose the premium if asset price < strike price}.
Unlimited upside {Profit = Asset price - Strike price - Premium}.
Short call: Limited upside {call buyer can keep the premium if asset price < strike price}.
Unlimited downside {Loss = Asset price - Strike price - Premium}.
Long put: Limited downside {call buyer can lose the premium if asset price > strike price}.
Unlimited upside {Profit = Strike price - Asset price - Premium}.
Short put: Limited upside {call buyer can keep the premium if asset price > strike price}.
Limited downside {Loss = Strike price - Asset price - Premium}.
Covered call: An investor buys the stock and sells a call on the stock. Results in a profile like
a short put option with limited upside potential and unlimited downside risk. Suitable for an
investor who already owns the stock, wants to keep it, but does not believe that it will rise
spectacularly. Consequently, he is happy to collect the premium by selling the call option.
Portfolio insurance: An investor who holds the stock buys a put on the stock. Results in a
profile that looks like a call on the stock with unlimited upside and limited downside. The put
protects the investor from a steep fall in stock price, but at the cost of the option premium.
SS16_RA1-E Introduction to the swaps market
Swap: A financial contract that involves the exchange of cash flows between two firms.
Interest rate swap (plain vanilla): One party pays interest coupons based on a fixed rate
and the other pays coupons based on LIBOR that sets for the period. Payments are
exchanged on a net basis and there is no exchange of notional value.
Pay-fixed swap: We pay fixed rate and receive floating rate.
Receive-fixed swap: We receive fixed rate and pay floating rate.
Currency swap: Notional amounts and payments on the two sides are denominated in
different currencies. The basic swap in this category involves the exchange of LIBOR-based
payments in US dollars and fixed rate payments in a foreign currency.
A borrower who has floating rate liabilities and is concerned about a rise in interest rates
should enter into a pay-fixed swap to fix its cost of debt.
A borrower who has fixed rate liabilities and is concerned about a fall in interest rates should
enter into a receive-fixed swap to convert its debt into floating rate.
Advantages of swaps over capital markets: Lower transaction costs. Quick and
anonymous execution in OTC markets with no regulations, and anonymity.
Swaps versus futures: Swaps can be customized and do not require any margin payments,
but they do create a lot of credit risk. Futures are more liquid and so cheaper. They do
require margin but do not create any credit risk. Swaps are mainly used by large firms and
institutional investors for hedging. Futures are used for both hedging and speculation by
individuals as well as institutional investors.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 41
SS17: Alternate Investments
SS17_RA1 Real estate investments
Determinants of value: Demand factors {demographics, psychographics, availability of
mortgage financing, economic base of community}. Supply {availability of similar properties}.
Property {restrictions on use, location, quality, structural damage, property management}.
Property transfer process {inefficient market - rewards good research, marketing, contract
negotiation and lease improvements}.
Real estate valuation: Cost approach {cost of rebuilding property at today's prices}.
Comparative sales approach {relative to selling price of comparable properties}. Income
approach {Value = Net operating income / Market capitalization rate}. Appraisal approach
{professional real estate appraiser estimates the value}.
Net operating income (NOI) = Gross rental income x (1 - Vacancy rate) - Collection losses -
Operating expenses including insurance and property taxes.
After-tax cash flows = NOI - Mortgage interest and principal payments – Taxes.
Taxes = (NOI - Mortgage interest payments - Depreciation) x Marginal tax rate.
NPV = Sum[After-tax cash flows / (1 + Return required by investor)]. If NPV > 0 investor
should consider the investment subject to other non-financial factors.
Leverage: Using debt financing to buy property leverages up the investment. When return
from property rises above cost of debt, the return on equity rises rapidly - positive leverage.
When return from property falls below the cost of debt, return on equity falls rapidly - negative
leverage.
REITs: Closed end investment companies. Costs - management fees. Benefits - diversified
and liquid.
Equity REITs: Invest directly in properties.
Mortgage REITs: Make loans mortgaged by property. Receive priority over equity investors.
Hybrid REITs: Combination of equity and mortgage REITs.
SS17_RA2 Professional Asset Management
Investment company: Pools funds from several investors to construct a diversified portfolio
containing stocks, bonds, etc. Management fee ranges from ¼ to 1 percent of portfolio value
each year.
Net asset value (NAV) = Total market value of asset portfolio / Number of outstanding
shares.
Closed-end investment companies raise their funds via an IPO of irredeemable stock that
can be traded in the secondary market. Although the NAV of stocks is published daily, the
stock price may deviate significantly from NAV.
Open-end investment companies continue to issue and redeem shares after IPO. Shares are
not exchange traded. Bid and offer prices are only available from the company.
Load of an open-ended funds: The investment company may impose a 7-8 percent sales
charge/front load, making offering price = NAV / (1 + % load). In addition, the company may
deduct up to 0.75% p.a. for marketing and distribution under 12b-1 plan, and ¼% - 1% for
investment management.
SS17_RA3 Venture Capital
Benefits for entrepreneurs: Equity capital. Management advice provided by VC. Positive
signal sent to market.
Benefits for investors: Ability of VCs to structure deals for upside potential with some
downside protection. Resolution of agency conflicts with entrepreneurs. Diversification
benefits.
Agency conflicts: Entrepreneur depends on the continued financial and managerial support
of the VC. The VC commits time, managerial input and capital. Investors rely on the abilities
of the VC to invest in risky business. The entrepreneur has only one business project, while
the VC has many. The investment dilutes entrepreneur's stake and may lead to a loss of
motivation. Entrepreneurs may be resistant to share control with the VC. The VC may ignore
investors once the VC fund has been fully subscribed.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 42
Controlling agency conflicts: The entrepreneur needs to keep the VC interested in his
venture. The VC needs to keep the entrepreneur motivated to protect the investment by
keeping the right to dismiss the managers and the entrepreneur. Investors need to keep the
VC motivated with participation in the profits and limiting the life of the VC fund.
Venture capital record: VCs in the US have generated average returns of 10 - 20 percent.
Huge variability between ventures - the best ones generate returns of 40-50%, a third lose
money and 10-17% are complete write-offs.
Factors affecting VC return: (1) Stage of the venture {seed investment returns are low
compared to early stage and later stage}. (2) Capital/IPO market. (3) Real asset markets. (4)
Flow of funds into venture capital {too much money is chasing investments drives down
returns}
Diversification benefits: The VC has low correlations with bonds and blue-chip stocks.
Higher correlations with small cap stocks.
International VC is still relatively new. Mostly merchant capital rather than venture capital).
Hampered by underdeveloped legal systems/enforceability of contracts and lack of active
IPO markets/exit route.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 43
SS18: Capital Market Theory: Basic Concepts
SS18_RA1-A Investment Setting
Nominal RFR = (1 + Real RFR) x (1 + Expected inflation rate) – 1.
Expected inflation rate: Changes significantly based on market expectations.
Real risk-free rate = T-bill yield - Expected inflation. Does not change much over time.
Expected return from investment = Nominal RFR + Risk premium.
Risk premium: Compensates investors for taking risks inherent in the stock (business,
financial, liquidity, and exchange rate).
Securities market line: A straight line that shows the return that can be expected in the
market for each level of systematic risk. Expressed as an equation the SML becomes CAPM.
Movement along SML: As the level of systematic risk of a specific investment rises and falls,
it will move up and down along the SML.
Change of slope of SML: The slope of the SML is the market risk premium. As the risk
perception rises, the slope will increase and the SML will rotate counter-clockwise about the
RFR, and vice versa.
Parallel shifts in SML: As inflation expectations in the market rise, the entire SML shifts
upwards, and vice versa.
SS18_RA1-B Asset Allocation Decision
Individual investor life cycle has four phases.
Accumulation: Early career, low net worth, needs to keep funds liquid for purchase of car,
house, etc.
Consolidation: Mid-to-late career, income exceeds expenses to allow the build up of
investments, long-term horizons, relative highest risk-taking ability.
Spending: High net worth, but liquidation of investment begins to fund expenses that are
higher than income.
Gifting: Parallel and following spending. Tax planning important in passing wealth to heirs
and causes.
Four-step portfolio management process: (1) Write policy statement {investor's objectives
and constraints}. (2) Develop the investment strategy {policy statement + capital market
environment}. (3) Construct the portfolio {allocate the funds according to strategy}. (4)
Monitor and update {according to changes in the investor's objectives or constraints and
changes in market}.
Investment objectives: Return requirement, income requirement, risk tolerance.
Investment constraints: Liquidity needs, time horizon, tax concerns, legal and regulatory
factors (for institutions) and unique needs and preferences (e.g. ethical investing).
Asset allocation: (1) Select asset classes. (2) Assign weights to each asset class. (3) Define
allowable range for deviation in weights. (4) Select specific investments. Empirical studies
show that 85 - 95% of return comes from steps (1) and (2).
SS18_RA1-C Selecting Investments in a Global Market
Why invest globally? (1) Investing abroad increases choice. (2) Non-US securities may
have higher rates of return. (3) Diversification benefits due to low correlation with US
securities.
The evidence: The proportion of the US market in the world capital markets has fallen from
53% in 1969 to 42% in 1998. It is still falling. World equity markets have a low correlation and
bond markets have an even lower one. Correlations fall even further when all returns stated
in USD.
Effect of exchange rate movement: A major factor in determining the final returns. If local
currency strengthens the USD returns will be enhanced, and if the local currency weakens
the USD returns will be worse.
CFA® Level I - 2003
The revision guide for the CFA® Level I exam
page 44
SS18_RA1-D Introduction to Portfolio Management
Markowitz portfolio theory: Investors base investment decisions on expected risk and
return, and higher returns to lower returns and lower risk to higher risk.
Markowitz’s efficient frontier: Curve connecting the portfolios that offer the highest return at
each level of total risk.
Correlation between two assets 1 and 2 = Cov_12 / (StdDev_1 x StdDev_2).
Expected return of a two asset portfolio = w1 x E(R1) + w2 x E(R2).
Variance of a two asset portfolio = w1^2 x Var_1 + w2^2 x Var_2 + 2 x w1 x w2 x StdDev_1 x
StdDev_2 x Correlation_12.
SS18_RA1-E Introduction to Asset Pricing Models
Capital market theory: Introducing the risk-free asset with zero variance and zero covariance
with other assets into the Markowitz framework.
Capital market line (CML): Straight line joining risk-free asset with the market portfolio on
the return versus variance (total risk) graph. Tangential to the efficient frontier. Investors are
only fully invested in the market at the point of tangency. To the left of this point, they lend out
a part of their portfolio at the risk-free rate. To the right, they borrow additional funds at the
risk-free rate and invest them in the market portfolio.
Total risk = Systematic risk + Unsystematic risk. Systematic risk cannot be diversified.
Unsystematic risk can be diversified. The market only pays the investor for systematic risk
since large investors can diversify away the unsystematic risk.
Securities market line: A straight line that shows the return that can be expected in the
market for each level of systematic risk. Expressed as an equation, the SML becomes
CAPM.
Contrast CML and SML: CML shows the expected return versus total risk. Useful for
indicating the highest return possible at each level of risk for a fully diversified portfolio. SML
shows the expected return versus systematic risk. Useful for determining the expected return
of a security given its beta.
Relative value (alpha) = Expected return from the asset - Required return indicated for the
level of systematic risk by SML. Assets with alpha = 0 {expected return on SML} are correctly
value, those with alpha > 0 {expected return below SML} are overvalued, and those with
alpha < 0 {expected return above SML} are undervalued.
Capital asset pricing model (CAPM): E(Ri) = RFR + Beta x (RM - RFR).
Characteristic line: Linear regression line of historical returns of an asset against the market
portfolio. Slope of this line is the beta of the asset.
Arbitrage pricing theory (APT): Relaxes some of the restrictive assumptions made by
CAPM {quadratic utility functions, normally distributed returns, existence of a market portfolio
that is held by all investors}. CAPM has only one factor (beta), but APT can have several. A
disadvantage is that APT does not specify these factors.
Expected return using APT = RFR + B1 x F1 + B2 x F2 + … + Bn x Fn. This reverts to CAPM
when only one factor (market risk) is used.