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Page 1: Investments, Levy and Post

Instructor’s Problem Set

Investments

Haim LevyThierry Post

© Pearson Education Limited 20051

Page 2: Investments, Levy and Post

ISBN 0 273 68511 2

© Pearson Education Limited 20052

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Chapter 1 Introduction

MULTIPLE CHOICE QUESTIONS

1. Which of the following is not a basic component of the investment process?A. investor characteristicsB. investment vehiclesC. strategy developmentD. strategy monitoringE. All of the above are basic components of the investment process.

© Pearson Education Limited 20053

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Chapter 1 Introduction

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. E

© Pearson Education Limited 20054

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Chapter 1 Introduction

OPEN QUESTIONS

1. “Following the investment process allows investors to identify an optimal portfolio and stick with it indefinitely.”

Do you agree with this statement? Why or why not?

Answer:The statement is false. The investment process is dynamic and never-ending. Investor characteristics change as time passes. For example, older investors tend to be more risk-averse than younger investors. Even if one can identify an optimal portfolio at a given point in time, the portfolio’s characteristics may change over time. Suppose an investor determines that his or her optimal asset allocation is 30% cash, 50% bonds, and 20% stocks. If stocks subsequently perform very well, their values will increase, causing stocks to represent more than 20% of the investor’s wealth. As investor characteristics, economic factors, and market factors change, it will be necessary for investors to adjust their investment strategies. The processes of strategy development, implementation, and monitoring go on continuously.

© Pearson Education Limited 20055

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Chapter 2 Bonds, Stocks and Other Securities

MULTIPLE CHOICE QUESTIONS

1. Which type of risk is faced by holders of corporate bonds that can be considered non-existent by holders of government bonds?A. foreign exchange rate riskB. inflation rate riskC. market riskD. default risk

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Chapter 2 Bonds, Stocks and Other Securities

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. D

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Chapter 2 Bonds, Stocks and Other Securities

OPEN QUESTIONS

1. Explain what is meant by the following statement:

“The ownership of the firm is residual in nature."

Answer:This statement refers to the fact that common shareholders receive what is left over after all other claims on the firm have been provided.

2. Describe the differences between financial assets and physical assets for each of the following characteristics.a. Divisibilityb. Marketabilityc. Holding period

Answer:a. An asset is divisible if you can buy and sell small portions of it. Financial assets are easily

divisible, while most physical assets (such as factories) are not.b. An asset is marketable (or liquid) if it can quickly and easily be sold for cash without

affecting its value. Most physical assets (such as houses) are illiquid. Financial assets typically are more marketable than physical assets, even though some financial assets (such as stocks) are much more liquid than others (such as stamps).

c. Those who purchase physical assets usually intend to hold them for a long time, because such assets are not expected to provide cash flows until some time has passed. In contrast, investors who buy financial assets often plan to hold them for only a very short time.

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Chapter 3 Security Markets

MULTIPLE CHOICE

1. You purchase shares with a market price of $60 when the initial margin requirement is 80%. The maintenance margin is 30%. What is the highest price that will trigger a margin call?A. $8B. $ 12C. $ 17D. $ 24E. $ 48

2. Which type of underwriting arrangement requires the underwriter to buy the entire new issue from the issuing corporation at a predetermined price, and absorb all unsold shares for his own account at this price?A. firm commitment B. best effortC. standby commitmentD. contractual offeringE. rights issue

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Chapter 3 Security Markets

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2. A

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Chapter 3 Security Markets

OPEN QUESTIONS

1. What is margin trading, and why is it considered risky?

Answer:Trading on margin refers to an investor buying securities by first borrowing a portion of the funds needed from his or her broker. By borrowing, the investor can take a larger position than otherwise would be possible. This “leverage” magnifies the possible positive, and negative, returns the investor faces.

2. Suppose you purchase 500 shares of ABC Company common stock at $75 per share by borrowing funds from your broker. Your initial margin is 65%, the maintenance margin 55%.

a. How much of your own money will you have to provide?b. What is the price at which you would begin to receive a margin call?

Answer:a. Based on the information given and the notation from the chapter, N = 500, P = $75, IM = 0.65, and MM = 0.55. You buy 500 ∙ $75 = $37,500 worth of common stocks and the 65% margin means you have to provide 0.65 ∙ 37,500 = $24,375.

You can also use Equation 3.1 to arrive at this number:

From Equation 3.1 we observe

IM ∙ (N ∙ P) = N ∙ P – B

Thus, the amount initially provided equals IM ∙ (N ∙ P) = 0.65 ∙ (500 ∙ $75) = $24,375.

b. The margin call price is based on Equation 3.2, which is

3. The price (P’), below which you will be called for the maintenance margin can be expressed without the amount borrowed (B). Develop and explain this formula.

Answer:From equation 3.2’ we have

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Chapter 3 Security Markets

However, Equation 3.1 is

And solving for the loan balance we have

B = N ∙ P – IM ∙ (N ∙ P) = N ∙ P ∙ (1 – IM)

Substituting B for our result here, we have

P’ =

Dividing all terms by N, we have

P’ =

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Chapter 4 Institutional Investors

MULTIPLE CHOICE QUESTIONS

1. Which type of fund is most likely to invest in high-grade commercial paper?A. equity fundB. bond fundC. balanced fundD. money market mutual fund E. index fund

2. A mutual fund owns securities with a market value of $9,000,000, has 500,000 shares outstanding, owes its employees $200,000, and has a 3% load charge. The net asset value per share is:A. $18.00B. $18.90C. $16.85D. $17.60E. $18.48

3. The current market value of all securities held by a fund less any liabilities, divided by the number of shares outstanding is the:A. book valueB. net asset valueC. market valueD. net profitE. share price

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Chapter 4 Institutional Investors

MULTIPLE CHOICE QUESTIONS: ANSWERS

2. D2. D3. B

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Chapter 4 Institutional Investors

OPEN QUESTIONS

1. The ABC Fund, a closed-end fund, consists of three securities – 1,000 shares of Security A, which is currently trading for $35; 2,000 shares of Security B, which is trading for $45; and 3,000 shares of Security C, which is trading for $55. What is its NAV if the fund has $87,000 in net liabilities and 10,000 shares outstanding?

Answer:NAV = [1,000($35) + 2,000($45) + 3,000($55) – $87,000]/10,000

= [$35,000 + $90,000 + $165,000 – $87,000]/10,000= $203,000/10,000 = $20.30

2. Why must open-end funds keep more cash on hand than closed-end funds?

Answer:Open-end funds must be ready at all times to repurchase shares from the public, so the funds must keep some cash on hand at all times. If they did not, they would be forced to sell assets every time investors redeemed their shares and would incur significant transaction costs.Closed-end funds do not have to be concerned with day-to-day liquidity needs because such funds do not allow investors to redeem shares.

3. Can mutual funds be sold at a discount? At a premium? Explain.

Answer:Mutual fund shares are priced at net asset value and may be sold at an offer price that includes a load. Mutual funds do not trade at a premium or discount from NAV, as do closed-end funds.

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Chapter 5 Security Regulation and Investment Ethics

MULTIPLE CHOICE QUESTIONS

1. Which of the following created the Securities and Exchange Commission?A. Securities Act of 1933B. Glass-Steagall Banking Act of 1933C. Securities Exchange Act of 1934 D. Securities Acts Amendments of 1975E. Employee Retirement Income Security Act of 1974

2. Which of the following statements about corporate governance is wrong?A. Corporate governance is important because it is the framework through which

shareholders can be assured of legal compliance.B. Corporate governance is a method of controlling the corporation.C. Corporate governance establishes the appropriate ethical conduct of the corporation.D. Corporate control usually rests with the CEO, who is elected by the common shareholders.E. With the increasing concentration of shares held by large institutional investors, the role of

active corporate governance on the part of the shareholders will increase.

3. Which of the following statements about churning is wrong?A. Churning is buying and selling excessive amounts for a client.B. It is difficult to prove in most cases whether churning has occurred or whether the broker

is pursuing some sort of investment strategy.C. Churning is illegal under SEC rules as well as the rules of all major exchanges.D. The courts have used the ratio of commissions to invested equity to determine whether

excessive trading exists.E. Churning is unethical but not unlawful.

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Chapter 5 Security Regulation and Investment Ethics

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2. D3. E

OPEN QUESTIONS

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Chapter 5 Security Regulation and Investment Ethics

1. A broker recommends several changes to your portfolio. You make several changes a month based on your broker’s recommendations. At the end of six months your portfolio returns are exceeded by your commission costs. Has your broker acted illegally?

Answer:The broker may be guilty of churning, which is illegal under SEC Rule 10b-5. To prove churning, the courts have used three tests to determine whether excess trading existed: 1. Annualized turnover ratio (how frequently securities are traded).2. Ratio of commissions to invested equity.3. The proportion of commissions derived by the broker from the account in question

compared with all other accounts handled by that broker

2. What are the differences between regulations and ethics?

Answer:Regulations are rules established by governments for the purpose of identifying unacceptable behavior. Ethics embodies the ideals we should strive for and how we should behave. A behavior that is unacceptable based on ethical standards may be found acceptable by existing regulations.

3. Describe a situation in which a corporate manager’s behavior is unethical but not unlawful.

Answer:An example would be a CEO nominating people who are dependent on him or her to the board of directors, which determines his or her compensation. This action is clearly unethical but not unlawful.

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Chapter 6 Rates of Return

MULTIPLE CHOICE QUESTIONS

1. Which of the following should be used when estimating the average performance across different securities for one period of time?

A. geometric averageB. arithmetic average C. compound averageD. complex average

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Chapter 6 Rates of Return

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B

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Chapter 6 Rates of Return

OPEN QUESTIONS

1. The table below provides a history of stock prices and dividends for Bismal Company stock. Compute the after-tax return to an investor who buys 100 shares of Bismal stock on January 1 and sells the stock on December 31. Assume the tax rate on ordinary income is 20% and the tax rate on capital gains income is 28%.

Date DividendMarket Price When Dividend Is Received

January 1 $36January 15 $0.85 $42April 15 0.85 $42July 15 0.85 $44October 15 0.85 $40December 31 $40

Answer:

Using the linking method:

Date Market Price When Dividend Is Received

Dividend Interim Period

After-tax

After-tax

Interim Rate of Return

Time-Weighted Rate of Return

1-Jan $36 15-Jan $42 $0.85 1 18.37% 18.37%15-Apr $42 0.85 2 1.4571 20.091415-Jul $44 0.85 3 6.219 27.56

15-Oct $40 0.85 4 –7.7000 17.737931-Dec $40 5 –2.0000 15.3831

The return for interim periods 1 through 4 is:

R1 = [42 – 36 + 0.85(1 – 0.28)]/36 = 18.3667%.

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Chapter 6 Rates of Return

R2 = [42 – 42 + 0.85(1 – 0.28)]/42 = 1.4571%.

R3 = [44 – 42 + 0.85(1 – 0.28)]/42 = 6.2190%.

R4 = [40 – 44 + 0.85(1 – 0.28)]/44 = –7.7000%.

The after-tax rate of return for interim period 5 is:

R5 = [40 – 40 – (40 – 36)(0.20) + (0)(1 – 0.28)]/40 = –2.0000%.

The after-tax return for the year is

(1.183667)(1.014571)(1.062190)(0.923000)(0.980000) – 1 = 15.3830%.

2. Describe three different ways indexes can be constructed.

Answer:

Indexes can be constructed using the price-weighted, value-weighted, or equally-weighted methods. The price-weighted index weights its component securities by their market price, whereas the value-weighted index weights its component securities on their equity value. The equally-weighted index weights each security equally.

3. The following tab1e shows the NYSE composite index over a recent 15-year period:

End of NYSEYear Composite1988 156.261989 195.011990 180.491991 229.441992 240.211993 259.081994 250.941995 329.511996 392.301997 511.191998 595.811999 650.302000 656.872001 589.802002 472.872003 646.40

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Chapter 6 Rates of Return

A. Ignoring dividends, calculate the simple annual rates of return.

B. Calculate the arithmetic average of the annual rates of return.

C. Calculate the geometric average of the annual rates of return.

D. Compare your answers in Parts b and c. How do you account for the difference between these averages?

Answer:

A. The interim rates of return are based on Equation 6.1 and are given in the following table:

End of NYSE Interim

Year CompositeRate of Return

1988 156.261989 195.01 0.24801990 180.49 -0.07461991 229.44 0.2711992 240.21 0.0471993 259.08 0.0781994 250.94 -0.03141995 329.51 0.311996 392.30 0.19051997 511.19 0.3031998 595.81 0.1661999 650.30 0.0912000 656.87 0.0102001 589.80 -0.1022002 472.87 -.1982003 646.40 0.367

B. The arithmetic average of these 15 rates of return is:

= (0.2480 - 0.0746 + 0.271 + 0.047 + 0.078 - 0.0314 + 0.31 + 0.1905 + 0.303 + 0.166

+ 0.091 + 0.010 – 0.102 – 0.198 + 0.367)/15 = 1.6755/15 = 0.1117 or 11.17%

C. The geometric average of these 15 rates of return is:

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Chapter 6 Rates of Return

D. The difference in the averages is due to the variability of rates of return. When there is novariability, the averages are identical.

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Chapter 7 Fundamentals of Portfolio Analysis

MULTIPLE CHOICE QUESTIONS

1. Which of the following statements about risk is correct?A. If all investors were risk averse, there would be no positive risk premium.B. The variance of return is a measure of the dispersion around the mean and is used as a

measure of risk.C. Risk-neutral investors are willing to pay a higher price for an asset whose variance

increases.D. Investors are risk averse when they ignore an asset’s variance and only consider the asset’s

expected return.E. Most investors are risk neutral.

2. An analyst developed the following probability distribution of potential rates of return for Stock Z under three scenarios and later revised the expected rate of return for each scenario:

Original Expected Revised ExpectedScenario Probability Rate of Return Rate of Return1 0.20 0.20 0.2102 0.50 0.30 0.3103 0.30 0.50 0.525

If the original variance of the expected rate of return was 0.0124, Stock Z’s revised standard deviation of expected return will be:A. 0.1050.B. 0.1114.C. 0.1141.D. 0.1169.

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Chapter 7 Fundamentals of Portfolio Analysis

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B2. D

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Chapter 7 Fundamentals of Portfolio Analysis

OPEN QUESTIONS

1. Given the following information, calculate the E(R), variance, and standard deviation.

State of economy Probability Mutual fund Common stock Certificate of depositWeak growth 33% 8% 6% 7%Moderate growth 33% 10% 12% 7%Strong growth 33% 12% 15% 7%

Expected return ____ ____ ____Standard deviation ____ ____ ____

Answer: Mutual fund

Probability HPR P(HPR) [HPR-E(R)]2 P[HPR-E(R)]2

33% 8% 2.64% (8 – 9.9)2 1.191333% 10% 3.30% (10 – 9.9)2 0.003333% 12% 3.96% (12 – 9.9)2 1.4553

E(R) = 9.90 Variance 2 = 2.6499 Standard deviation = 1.6279

Common stock

33% 6% 1.98% (6 – 10.89)2 7.891033% 12% 3.96% (12 – 10.89)2 0.406633% 15% 4.95% (15 – 10.89)2 5.5744

E(R) = 10.89% Variance 2 = 13.5060Standard deviation = 3.6751

Certificate of deposit

33% 7% 2.31% (7 – 7)2 033% 7% 2.31% (7 –7)2 033% 7% 2.31% (7 -7)2 0

E(R) = 6.93% , Round to 7% Variance 2 = 0 Standard deviation = 0

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Chapter 7 Fundamentals of Portfolio Analysis

Note that the certificate of deposit has 0 variance and standard deviation, meaning no risk.

2. Next year a security will yield $90 with a probability of ½ and $110 with a probability of ½. An investor is willing to pay $80 for this asset today. The risk-free interest rate is 15%.a. Is this investor a risk seeker or a risk averter?b. What is the risk premium?

Answer:a. The rates of return are ($901$80) - 1 = 0.125 and ($110/$80) - 1 = 0.375. The expected rate

of return is E(R) = ½ * (12.5%) + 1/2 * (37.5%) = 25% and because this expected return exceeds the riskless interest rate, we know that this investor is a risk averter.

b. The risk premium is equal to the expected return less the riskless rate or 25% - 15% = 10%.

3. Answer Question 24 assuming that the investor is ready to pay $95 for this asset.

Answer: a. In this case, the rates of return are ($90/$95) - 1 = -0.053 and ($110/$95) - 1 = 0.1579. The

expected rate of return is E(R) = ½ * (-5.3%) + ½ * (15.79%) = 5.245% and because this expected return does not exceed the riskless interest rate, we know that this investor is a risk seeker.

b. The risk premium is equal to the expected return less the riskless rate or 5.25% - 15.0% = -9.75%.

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Chapter 8 Mean-Variance Analysis

MULTIPLE CHOICE QUESTIONS

1. Which of the following is not a variable in the calculation of the variance of a portfolio?A. the correlations between assetsB. the variance of each assetC. the expected return of each assetD. the proportion invested in each assetE. the covariances between assets

2. The correlation between Compaq and Pfizer is:A. 0.19B. 0.46C. 0.51D. 0.64E. 0.38

3. The variance of the portfolio, composed of 25% invested in Compaq and 75% invested in Pfizer, is:A. 12.33B. 13.94C. 152D. 144E. 176

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Chapter 8 Mean-Variance Analysis

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2. C3. C

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Chapter 8 Mean-Variance Analysis

OPEN QUESTIONS

1. Describe an asset's risk when held with other assets in a portfolio.

Answer:The variance of the returns on the asset is the measure of risk of that asset when an investor holds only one asset. However, when the investor holds more than one risky asset, the risk of an individual asset is a function not only of its own variance but also of its degree of dependency on the other assets in the portfolio.

2. Calculate the correlation of Stock C with Stock D.

State of Economy Probability Stock C Stock D

Excellent 0.4 20% 0%Wonderful 0.6 0% 10%

Answer:We must first calculate C,D, C, and D. These calculations, in turn, require us to compute E(RC) and E(RD).E(RC) = 0.4(20%) + 0.6(0%) = 8%. E(RD) = 0.4(0%) + 0.6(10%) = 6%. 2

C = 0.4(0.20 – 0.08)2 + 0.6(0 – 0.08)2 = 0.0096. 2

D = 0.4(0 – 0.06)2 + 0.6(0.10 – 0.06)2 = 0.0024. C,D = 0.4(0.20 - 0.08)(0 - 0.06) + 0.6(0 - 0.08)(0.10 - 0.06) = -0.0048. C,D = –0.0048/(0.0096)1/2(0.0024)1/2 = –1. The assets are perfectly negatively correlated.

3. The probability distributions of returns for Stock A and Stock B are given below:

State of

Economy Probability Stock A Stock B

Bad 0.2 –5% 0% OK 0.3 0% 15% Good 0.5 10% 30%

a. Calculate the expected returns for Stock A and Stock B.b. Calculate the correlation of Stock A with Stock B.c. Portfolio Q is formed by investing 80% in Stock A and 20% in Stock B. Calculate the expected return and standard deviation of Portfolio Q.

Answer:

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Chapter 8 Mean-Variance Analysis

a. E(RA) = 0.2(–5%) + 0.3(0%) + 0.5(10%) = 4%. (RB) = 0.2(0%) + 0.3(15%) + 0.5(30%) = 19.5%.b. A,B = 0.2(–0.05 – 0.04)(0 – 0.195) + 0.3(0 – 0.04)(0.15 – 0.195) + 0.5(0.10 – 0.04) (0.30 – 0.195) = 0.0072. Calculate variances: 2

A = 0.2(–0.05 – 0.04)2 + 0.3(0 – 0.04)2 + 0.5(0.10 – 0.04)2 = 0.0039. 2

B = 0.2(0 – 0.195)2 + 0.3(0.15 – 0.195)2 + 0.5(0.30 – 0.195)2 = 0.013725. Calculate correlation: A,B = 0.0072/(0.0039)1/2(0.013725)1/2 = 0.984.c. E(RQ) = 0.8(4%) + 0.2(19.5%) = 7.1%.

2Q = 0.22(0.0039) + 0.82(0.013725) + 2(0.2)(0.8)(0.0072) = 0.011244.

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Chapter 9 Portfolio Diversification

MULTIPLE CHOICE QUESTIONS

1. Total risk decrease as the: A. number of stocks in the portfolio decreases B. correlation between the returns of the securities in the portfolio decreases C. correlation between the returns of the securities in the portfolio increases D. number of different industries in the portfolio decreases E. number of stocks in the same industry increases

2. Diversification is most effective when security returns are: A. negatively correlated B. positively correlated C. low D. high E. uncorrelated

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Chapter 9 Portfolio Diversification

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B2. A

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Chapter 9 Portfolio Diversification

OPEN QUESTIONS

1. Explain the statement: “A little diversification goes a long way.”

Answer:

In general, the greater the number of securities in a portfolio, the lower the portfolio’s variance. However, as the number of securities increases, the incremental contribution to the reduction in the portfolio’s variance becomes smaller and smaller. Therefore, the greatest gain is achieved by diversifying in a relatively few securities

2. Why do most mutual funds hold hundreds of stocks, while it can be shown that about 90% of the maximum potential benefit from diversification (when considering typical U.S. stocks) is achieved with a portfolio composed of twelve to eighteen securities?

Answer:

First of all, although the benefit from including more stocks in the portfolio diminishes, the benefit is still positive. An individual investor who faces large information and transaction costs cannot study/trade hundreds of stocks. For a large mutual fund, however, the information and transaction costs per $1 invested is so small that it is still worthwhile to increase the number of assets in the portfolio and enjoy the little ensuing benefit from risk reduction.Second, large funds cannot concentrate on a limited number of stocks without their buying and selling greatly affecting the price of those securities.

3. “Investors with less than $100,000 should stick with mutual funds because of diversification benefits.” Evaluate this statement.

Answer:

While it is true that mutual funds will provide the benefits of diversification, these benefits are not free. The cost of diversification through mutual funds can be anything between 1% and 3% per annum. The extra diversification benefits a mutual fund can provide to small investors must outweigh these costs in order to be worthwhile.

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Chapter 10 The Capital Asset-Pricing Model

MULTIPLE CHOICE QUESTIONS

1. An investor invests 40% of her wealth in a risky asset with an expected rate of return of 15% and a standard deviation of 20%. The rest of her wealth is invested in the risk-free asset, which yields 6%. What are the expected return and standard deviation of her portfolio?

A. E(R) = 8.0%, = 12%B. E(R) = 9.6%, = 8% C. E(R) = 9.6%, = 12%D. E(R) = 11.4%, = 12%

2. No matter how large the number of stocks in the portfolio is, the risk that cannot be diversified away is the:A. company-specific riskB. unsystematic riskC. systematic riskD. unique riskE. both a and b

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Chapter 10 The Capital Asset-Pricing Model

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B2. C

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Chapter 10 The Capital Asset-Pricing Model

OPEN QUESTIONS

1. Suppose investors can borrow and lend at the risk-free rate of 7%. Joyce Zoot wants the expected return of her total portfolio to be 15%. Her financial planner has told her that this will require her to invest some of her money in the risk-free asset and the rest in a risky asset (asset A) that has an expected return of 30%. With this investment plan, the risk of Joyce’s complete portfolio will be 20%. What is the standard deviation of Portfolio P?

Answer:

Use Equation 10.2. The expected return of Joyce’s portfolio will be 15% if

15% = wr(7%) + (1 – wr)(30%).

Solving,

wr = 0.652 and (1 – wr) = 0.348.

Now use Equation 10.3 to solve for the standard deviation of asset A:

0.20 = (1 – wr)A = 0.348A. Solving, A = 57.5%.

2. Regressing returns for Stock A against returns for the market portfolio yielded the following results: Stock A’s alpha is 2%, Stock A’s beta is 2, and the standard deviation of Stock A’s returns is 40%. The standard deviation of the market’s returns is 10%.

A. Where does Stock A’s characteristic line intercept the vertical axis?

B. What is the slope of Stock A’s characteristic line?

C. What is the systematic risk of Stock A?

D. What is the unique risk of Stock A?

Answer:

A. Alpha is the intercept for the characteristic line ( = 0.02).

B. Beta is the slope of the characteristic line ( = 2).

C. Using Equation 10.8, the systematic risk is 2i2

m = 22(0.10)2 = 0.04.

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Chapter 10 The Capital Asset-Pricing Model

E. Using Equation 10.8, the unique risk is 2i - 2

i2m = 0.402 – 22(0.10)2 = 0.16 – 0.04 =

0.12.

3. A portfolio that is invested 5/9 in Stock A and 4/9 in Stock B has an expected return of 20%.

Stock A Stock BExpected Return

Not available 28%

Variance 0.0484 0.0324Beta 0.6 1.5

What are the risk-free rate and the expected return on the market?

Answer:

The beta of the portfolio is the weighted average of the betas of Stock A and Stock B:

p = (5/9)(0.6) + (4/9)(1.5) = 1.

Since the beta of the portfolio is the same as the market’s beta, the portfolio’s expected return (20%) must be equal to the market’s expected return.

Additionally, the capital asset pricing model must hold for all assets in equilibrium. For Stock B, we have

28% = r + 1.5(20% – r). Solving, r = 4%.

To check these results we can use CAPM to solve for Stock A’s expected return:

E(RA) = 4% + 0.6(20% – 4%) = 13.6%,

and calculate the portfolio’s expected return as the weighted average of the expected returns of Stock A and Stock B:

E(Rp) = (5/9)(13.6%) + (4/9)(28%) = 20%.

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Chapter 11 Arbitrage Pricing Theory

MULTIPLE CHOICE QUESTIONS

1. Which of the following statements about the single index model (SIM) is correct?A. The SIM requires more computations to solve for the mean-variance efficient set.B. The SIM can decompose risk into its systematic component and unsystematic component.C. The SIM claims that both the systematic and unsystematic risks can be diversified away.D. The SIM assumes that a firm's specific news is dependent on another firm's specific news.E. Statements a and d are both correct.

2. Which of the following statements is false?A. The single index model was developed to reduce the computational problems in calculating

the efficient frontier.B. The APT was developed as an alternative to the CAPM.C. With the single index model, risk can be broken down into systematic and unsystematic

components.D. With large portfolios, systematic risk can be virtually eliminated.E. The single index model assumes that returns are generated by a single factor and firm-

specific factors.

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Chapter 11 Arbitrage Pricing Theory

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B2. D

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Chapter 11 Arbitrage Pricing Theory

OPEN QUESTIONS

1. Why does the single index model (SIM) reduce the amount of computations?

Answer:The SIM assumes that a firm's specific news is independent of another firm's specific news. In statistical terms, this assumption implies that Cov. (ei, ej) = 0, where ei is the firm i's specific news. Also, the deviation from the line for ei is assumed to be independent of the common factor. With these assumptions, the covariance of these two stocks is reduced to:

Cov. (Ri, Rj) = ijI2

Thus, the investor only needs to estimate the betas for each stock rather than all possible covariances.

2.a. According to the APT, if i 0, this implies that the ith stock has no unsystematic risk.

Evaluate this assertion.b. According to the APT, if i 0, this implies that the rate of return on the ith stock must be

equal to the risk-free rate. Evaluate this assertion.

Answer:a. This assertion is false i 0 implies that the stock has no systematic risk. Recall with APT

and when i 0, we have , and so only unsystemic risk remains.b. This assertion is also false. If i 0, this implies that the expected rate of return is zero. However, for large portfolios when , this assertion is true, but not for individual assets. Again, by APT, returns are generated by

and when i 0, we have

and the possibility of different outcomes due to being a random variable.

3. There are three stocks with the following parameters:Stock A Stock B Stock C

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Chapter 11 Arbitrage Pricing Theory

Mean return 10% ? 20%

Beta 1 4 2

a. What should be the mean return on Stock B to avoid arbitrage?b. Find the value of a0 and a1 in the linear equation E(Ri) a0 a1i.

Answer:

a. We need to find the mean rate of return that will make the slope of the SML the same regardless of which securities are used. The slope of the line based on stock A and C is

We need to find the mean rate of return such that the slope will be 10% when using stock B. Thus, we need to solve for

Solving for ?, we find 40%. Thus, the mean of stock B must be 40% or we are not in equilibrium. The intercept must be zero in order to maintain a slope of 10%.

b. From above we have and .

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Chapter 12 Efficient Markets: Theory and Evidence

MULTIPLE CHOICE QUESTIONS

1. Which of the following statements is true?I. In a strong form efficient market, it is possible for fundamental analysts to earn

abnormal returns consistently.II. In a strong form efficient market, it is possible for technical analysts to earn

abnormal returns consistently.III. In a strong form efficient market, asset allocation is useless.A. I onlyB. I and II onlyC. III onlyD. I, II, and IIIE. neither I, nor II, nor III

2. If the market is perfectly efficient, which of the following statements is false?A. Prices will fluctuate randomly around their true value.B. Security prices reflect all publicly available information.C. Smaller firms tend to outperform larger firms on a risk-adjusted basis.D. An average mutual fund does not outperform the market as a whole.E. Both technical analysis and fundamental analysis are economically worthless.

3. A random walk occurs when: A. stock prices respond slowly to new informationB. the stock price level is randomC. past information is useful in predicting future pricesD. stock price changes are random but predictableE. future price changes are uncorrelated with past price changes

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Chapter 12 Efficient Markets: Theory and Evidence

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. E2. C3. E

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Chapter 12 Efficient Markets: Theory and Evidence

OPEN QUESTIONS

1. Describe three forms of the efficient market theory (EMT).

Answer:There are three forms of the efficient market theory: weak, semi strong, and strong EMT. According to the weak form of the EMT, today’s stock prices reflect all information about the historical prices of the stock. The semi strong form of the EMT states that prices reflect all relevant publicly available information. The strong form states that current prices reflect all publicly and privately available information.

2. Define anomaly and describe four common types of anomalies.

Answer:A market anomaly is any event that can be exploited to produce abnormal profits. There are four categories of anomalies: seasonal, event, firm, and accounting anomalies. Firm anomalies are anomalies that result from firm-specific characteristics, such as the size effect. Seasonal anomalies are anomalies that depend solely on time, such as the January effect. Event anomalies are price changes that occur after some easily identified event, such as a listing announcement. Accounting anomalies are changes in stock prices that occur after the release of accounting information, such as an earnings announcement.

3. Noodles McSpirkle is a crackpot who has developed an asset pricing model. Like generally accepted pricing models, Noodles’ model predicts a relationship between risk and expected return. However, Noodles’ model uses something called Zarumba (represented by the variable Z in Noodles’ writings) as a risk measure. No one but Noodles understands how to calculate Zarumba, but Noodles claims to have proven that, for any stock, E(R) = 3Z. The following table provides data for five stocks, including actual return, Zarumba, and beta.

Stock Zarumba Beta Actual Return

A 0.08 2.00 32.0%B 0.24 1.75 32.0C 0.07 1.20 24.0D 0.04 0.50 12.0E 0.03 0.25 8.5

a. For each stock, calculate the expected return according to Noodles’ model and the CAPM. The expected return on the market is 20%, and the risk-free rate is 4%.

b. For each stock, use both pricing models to determine whether or not the stock earned an abnormal return.

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Chapter 12 Efficient Markets: Theory and Evidence

c. What does this problem reveal about the real-world difficulties of determining whether or not the market is efficient?

Answer:a. Noodles’ model predicts that E(R) = 3Z. The expected return for Stock A is simply 3(8%) =

24%. Calculations for the rest of the stocks follow the same pattern.The CAPM predicts that E(R) = r + [E(RM – r]. The expected return for Stock A is 4% + 2(20% – 4%) = 36%. Calculations for the rest of the stocks follow the same pattern. The following table contains expected returns for each stock as predicted by each model.

Expected ReturnStock Noodles’ Model CAPM

A 24% 36.0%B 72 32.0C 21 23.2D 12 12E 9 8

b. An abnormal return is equal to actual return minus expected return. Whether or not a stock earned an abnormal return depends on the expected return, which depends on the pricing model used.The following table compares actual returns with expected returns and indicates whether abnormal return is positive, negative, or zero.

Expected Return ABNORMAL RETURN

StockNoodles’ Model CAP

M

Actual Return

Noodles’ Model CAPM

A 24% 36.0% 32.0% Positive Negative

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Chapter 12 Efficient Markets: Theory and Evidence

B 72 32.0 32.0 Negative ZeroC 21 23.2 24.0 Positive PositiveD 12 12 12.0 Zero ZeroE 9 8 8.5 Negative Positive

c. In principle, we can test whether or not the market is efficient by comparing actual returns with expected returns. If the market is efficient, actual returns should exceed expected returns exactly as often as actual returns fall short of expected returns.This problem demonstrates that such a test of market efficiency actually tests two propositions at once because it presupposes that the researcher has accurately measured expected return. If the test shows that abnormal returns tend to be positive, we cannot be sure if the finding results because the expected return was incorrect or because the market is not efficient. For Stock B, using CAPM to calculate expected return suggests that the market is efficient, while Noodles’ model suggests that it is not.

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Chapter 13 Interest Rates and Bond Valuation

MULTIPLE CHOICE QUESTIONS

1. Which of the following statements is true?A. According to the unbiased expectations hypothesis, the yield curve will be flat if

expected future short-term rates exceed current short-term rates.B. According to the unbiased expectations hypothesis, long-term rates are equal to

expected future short-term rates.C. According to the liquidity preference hypothesis, the term structure is usually

downward sloping.D. According to the market segmentations hypothesis, interest rates for long-

maturity bonds are independent from interest rates for short-maturity bonds.

2. Which of the following is the best measure of a discount bond’s total expected return?A. current yieldB. yield to callC. capital gains yieldD. yield to maturity E. coupon yield

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Chapter 13 Interest Rates and Bond Valuation

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. D2. D

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Chapter 13 Interest Rates and Bond Valuation

OPEN QUESTIONS

1. If interest rates rise, will individuals save more or less? Explain your answer.

Answer: The relationship between the amount people save and interest rates is not immediately apparent. First, an increase in interest rates may cause people to save more because this will afford greater consumption. This effect is known as the substitution effect. Second, an increase in interest rates may actually imply a decrease in savings because you have to save less now in order to achieve a fixed level of consumption in the future. This is known as the income effect. Finally, there is a wealth effect, which asserts that an increase in interest rates implies an increase in current wealth level (for a example, if you held a bond portfolio and the interest rates goes up from 8% to 10 %, the value of your portfolio goes down and your wealth is going down). The final results depend on the strength of these conflicting forces.

2. “If the yield to maturity is zero, no matter what the maturity is, the par value of the bond must be equal to its market value.” Evaluate this statement. Is there a specific type of bond for which this is true?

Answer: This statement is not true for any bond with annual coupons larger than zero (C>0). Suppose we have a bond with one year to maturity, with a par value of $1000 and an annual coupon of C=$100. If y=0, then by Equation (), we have

which is greater than Par = $1000. This statement is true only if the annual coupon is zero because then the sum of the future coupons is zero, and the price will equal the par value (because there is no discounting).

3. “If the yield curve is flat, then all forward rates must be equal to zero.” Evaluate this statement. Demonstrate your answer with a numerical example.

Answer: This statement is not true. If the yield curve is flat, all the forward rates are equal to the spot rate. If the spot rate is 8% and the yield curve is flat. The expected rate for next year will also be 8%. By the formula for the relationship between forward rates and spot rates we see

or 8%

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Chapter 14 Bonds—Analysis and Management

MULTIPLE CHOICE QUESTIONS

1. What is the duration of a 5-year zero-coupon bond?A. 4.5B. 5.0 C. 5.5D. The answer cannot be determined without more information.

2. Which of the following is an income immunization strategy that selects only bonds whose coupon and principal payments occur exactly when cash is required?A. cash matching strategy B. duration matching strategyC. horizon matching strategyD. contingent immunization strategy

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Chapter 14 Bonds—Analysis and Management

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. B2. A

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Chapter 14 Bonds—Analysis and Management

OPEN QUESTIONS

1. Several immunization strategies were discussed in this chapter. Rank cash matching, duration matching, and horizon matching from the least flexible to the most flexible. Explain your rankings.

Answer:The least flexible is cash matching, which requires each year’s cash flow to be matched exactly. The most flexible is duration matching, where the duration of the assets is matched with the duration of the liabilities. In between these two strategies is horizon matching, which requires cash matching for the first several years and duration matching thereafter.

2. Suppose you owned four different bonds with the following characteristics. What is the duration of the bond portfolio?

Bond Market Value of Holdings

Duration

A $14,327 1.27 yearsB $56,490 8.74 yearsC $19,467 5.66 yearsD $37,592 6.72 years

Answer:From Equation 14.5, the duration of a portfolio is a weighted average of the durations of the individual bonds where the weights are determined by the market value of the bonds. In this case, the total market value of the holdings isMV 14,327 56,490 19,467 37,592 127,876The weights for each bond areBond A:

Bond B:

Bond C:

Bond D:

Thus, the duration of the bond portfolio isD 0.1120(1.27) 0.4418(8.74) 0.1522(5.66) 0.2940(6.72) 6.84 years

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Chapter 14 Bonds—Analysis and Management

3. There are five bonds, each of which has a duration of 4 years. Your holding period is 2 years. ‘By diversifying between these four bonds, you can reduce the portfolio duration to 2 years.’ Assuming you cannot short sell, do you agree with this statement? Defend your answer.

Answer:This statement is not true. Recall from Equation 14.5 that

where wi = MVi / MV

MVi is the market value of the portfolio holdings of bond iMV is the market value of the total bond portfolioDi is the duration of bond i.

So long as wi is positive (thus, assuming you cannot short sell), the only possible value of D is four years. That is,

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Chapter 15 Stocks—Valuation and Selection

MULTIPLE CHOICE QUESTIONS

1. Which of the following is not a problem encountered when implementing DDMs?A. Using DDMs to identify undervalued stocks is useful only if the mispricing of

stocks is corrected in the market.B. DDMs assume that the discount rate is constant over time.C. Theoretical DDMs relate future cash flows to price, but future cash flows are

unknown today.D. DDMs have little practical value because they value stocks assuming infinite

cash flows and investors’ investment horizons are always finite.

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Chapter 15 Stocks—Valuation and Selection

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. D

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Chapter 15 Stocks—Valuation and Selection

OPEN QUESTIONS

1. Using the constant-growth DDM, prove that the dividend growth rate, g, is equal to the stock’s expected capital gains yield.

Answer:Begin by expressing P1 as a function of d2:P1 = d2/(k – g) = d1(1 + g)/(k – g).But d1/(k – g) = P0, so P1 = P0(1 + g).If we isolate g, we see that1 + g = P1/P0

g = P1/P0 – 1 = (P1 – P0)/P0, which is the expected capital gains yield.

2. Cyclops Company’s stock is expected to pay a $0.25 dividend 1 year from today. Analysts believe that thereafter dividends will grow at a constant rate of 1% per year. The return on the market is forecast to be 12%, and the risk-free rate is 4%. The beta of Cyclops’s stock is 0.2. What is the value of Cyclops’s stock?

Answer:The required return is given by the CAPM: k = 4% + 0.2(12% – 4%) = 5.6%.Cyclops is a constant-growth company, soP0 = $0.25/(0.056 – 0.01) = $5.43.

3. “If a dividend discount model indicates that a stock is undervalued, investors should buy the stock.” Is this statement always true, only sometimes true, or never true? Carefully justify your answer.

Answer:The statement is only sometimes true and reflects the reality that investors must be very careful when interpreting the results of an analysis based on a DDM. If the DDM indicates that the stock is undervalued, it does not guarantee that it will soon be correctly valued. In fact, the stock could become more undervalued before turning around, creating losses for investors unwilling or unable to wait for the mispricing to be corrected.Also, investors must be confident of the inputs used to draw the conclusion that the stock is mispriced. The problems for this chapter have demonstrated how sensitive the model’s value estimate is to the magnitude of its parameters. It is possible that the market price of the stock is correct and that the analyst’s estimate of true value is incorrect.

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Chapter 16 Financial Statement Analysis

MULTIPLE CHOICE QUESTIONS

1. Sometimes when a company purchases a new asset, the full cost of the asset is not recorded on the company’s income statement as an expense; instead, the asset is depreciated, and the cost of the asset is spread out over several years. Which basic accounting concept requires this treatment?A. matching B. historical costC. conservatismD. consistency

2. Which of the following best matches costs with revenues during an inflationary period?A. LIFO B. FIFOC. average cost methodD. all three methods match revenues with costs equally well

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Chapter 16 Financial Statement Analysis

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. A2. A

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Chapter 16 Financial Statement Analysis

OPEN QUESTIONS

1. An investment analyst has identified the following information about J.L. Manufacturing:

Total Costs ($)Inventory on January 1 10,000 units @ $25 250,000Purchases in January 5,000 units @ $29 145,000Purchases in April 5,000 units @ $35 175,000Purchases in November 4,000 units @ $40 160,000Total available for sale 24,000 units 730,000Inventory on December 31 4,000 units

What are the value of the ending inventory and the cost of goods (COGS) sold by the FIFO, LIFO, and average cost method? Which method is preferred for tax purposes?

Answer:FIFO method , the ending inventory is4.000 * 40 = $160.000COGS is 730.000 – 160.000 = $570.000

LIFO method , the ending inventory is4.000 * 25 = $100.000COGS is 730.000 – 100.000 = $630.000

Average cost method, the average cost is730.000/24.000 = $30,42The ending inventory is4.000 * 30,42 = $121.680COGS is 730.000 – 121.680 = $608.320The LIFO method gives the highest COGS. Hence, it will produce the lowest taxable profits, so it is preferred for tax reasons.

2. Suppose you are given the following information regarding Galactoca, Inc.:

Net Income $100 millionDepreciation $20 millionStock Repurchases $10 millionInvestments on New Project $30 million

Based solely on these figures, what is the net cash flow for this period?

Answer: The statement of cash flow is given in the following table:

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Chapter 16 Financial Statement Analysis

Millions

Operating ActivitiesNet Income $100Depreciation $20Net Cash $120Investing ActivitiesInvestments -$30Net Cash -$30Financing ActivitiesStock Repurchases -$10Net Cash -$10Net Change in Cash $80

3. A firm’s current liabilities were $50 million, and its current assets were $60 million. The firm has $40 million of inventory.

a. What is the current ratio?b. What is the quick ratio?

Answer:a. The current ratio is current assets divided by current liabilities or $60/$50 =

1.2.b. The quick ratio is cash and near equivalents divided by current liabilities or ($60 - $40)/50 = 0.4

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Chapter 17 Macroeconomic Analysis

MULTIPLE CHOICE QUESTIONS

1. Gross domestic product consists of all of the following exceptA. consumption.B. investment.C. budget deficit. D. net trade.

2. All of the following are goals of fiscal policy exceptA. maximizing GDP growth.B. maximizing employment.C. maintaining stable prices.D. controlling the money supply.

3. Which of the following is not a variable in the calculation of the equation of the international Fisher relationship?A. domestic nominal rate of interestB. foreign inflation rateC. foreign exchange rateD. domestic real rate of interestE. domestic inflation rate

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Chapter 17 Macroeconomic Analysis

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2 D3. C

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Chapter 17 Macroeconomic Analysis

OPEN QUESTIONS

1. The government of Smallvia recently reported that its GDP for the year was $8 billion. Consumption during the period was $1,5 billion, investment was $2 billion, and government spending was $3 billion. What was Smallvia’s net trade for the period?

Answer:Using Equation 17.1,GDP = C + I + G + (X – M)where (X – M) is net trade. Gives 8 = 1,5 + 2 + 3 + (X – M)for Smallvia (in billions of dollars). Solving,(X – M) = $1,5 billion.

2. Can an investor use macroeconomic data to predict stock returns?

Answer:Yes. For example, Lettau and Ludvigson (2001a) show that the consumption-to-wealth ratio is a powerful leading indicator for excess returns on aggregate stock market indexes. Note that predicting excess returns does not mean we can earn systematic abnormal risk-adjusted returns. That is, it does not yield abnormal risk-adjusted returns if the predicted price change reflects only a change in risk or risk premiums.

3. What is the purchasing power parity?

Answer:The purchasing power parity is the relationship between two countries'

inflation rates and their foreign exchange rates. This parity is used to estimate exchange rates based on expected inflation rates. If a country has a high inflation rate, its currency is expected to depreciate.

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Chapter 18 Technical Analysis

MULTIPLE CHOICE QUESTIONS

1. Which of the following statements about the candlestick chart is false?a. If the opening price is above the closing price, then the real body is shaded dark.b. There are two parts of the candlestick line: the real body and the shadows.c. The candlestick chart was developed in the United States, and became popular

in Japan and other countries.d. The candlestick chart is based on a day’s opening, high, low, and closing prices.e. The candlestick chart is similar in many ways to the bar chart in that it maps the

price movement over time.

2. Which of the following statements about technical analysis is false? a. Technical analysts believe that financial prices reflect investors’

attitudes, which at times may not be entirely rational.b. Technical analysis assumes that security prices react quickly to new

information.c. Technical analysis contradicts the weak form of the EMT.d. Technical analysts believe that by studying historical market data, clues

will be found regarding the future direction of security prices.e. Technical analysts believe that their analysis enables them to beat the

market consistently.

3. Which of the following statements is false?a. Odd-lot trading is typically done by small investors who, technical

analysts believe, are usually wrong.b. One basic tenet of the Dow Theory is that no additional information is

needed for the stock market outside of data on stock indexes.c. Point-and-figure charts attempt to identify reversals in the direction of

stock prices without consideration of time.d. The real body of the candlestick line is the broad part consisting of the

difference between the highest price and lowest price.e. The Dow Theory claims that a bear market is established when both the

Dow Jones Industrial Average and the Dow Jones Transportation Average are moving down.

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Chapter 18 Technical Analysis

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2. B3. D

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Chapter 18 Technical Analysis

OPEN QUESTIONS

Questions 1 through 3 use the following data for Acme Company:

Day Close High Low Open1 $51.06 $52.63 $51.00 $51.382 51.63 52.94 51.00 51.003 50.69 50.88 50.00 51.004 51.88 53.19 51.38 51.815 52.13 54.25 52.00 52.756 53.56 54.25 52.44 54.197 54.25 54.25 51.00 53.888 53.69 57.44 53.69 57.259 56.75 57.00 55.38 56.44

10 56.94 61.44 56.50 60.2511 61.00 61.00 57.81 57.8812 57.63 58.88 57.25 58.6313 59.31 60.25 57.81 58.7514 59.06 59.06 56.06 57.4415 57.63 58.69 57.00 57.00

1. Create a bar chart for Acme Company.

Answer:The bar chart for Acme Company is:

2. Create a candlestick chart for Acme Company.

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Chapter 18 Technical Analysis

Answer:The candlestick chart for Acme Company is:

3.a. Calculate the 3-day moving average closing stock price for Acme Company.b. Graph the moving average and daily closing prices on the same chart. Use a

bar chart to represent closing prices and a line to represent the moving average.c. Suppose a technical analyst bought the stock the first time the closing price

exceeded the 3-day moving average and sold the stock the first time the closing price fell below the 3-day moving average, repeating this strategy as often as possible. Calculate the profit or loss for this strategy for the 15-day period.

Answer:a. The moving

average is calculated as

in Exhibit 18-11.

© Pearson Education Limited 2003

DAY

CloseThree-Day

Total (A)Three-Day Simple

Moving Average (A/3)

1 $51.062 51.633 50.69 $153.38 $51.134 51.88 154.20 51.405 52.13 154.70 51.576 53.56 157.57 52.527 54.25 159.94 53.318 53.69 161.50 53.839 56.75 164.69 54.90

10 56.94 167.38 55.7911 61.00 174.69 58.2312 57.63 175.57 58.5213 59.31 177.94 59.3114 59.06 176.00 58.6715 57.63 176.00 58.67

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Chapter 18 Technical Analysis

b. The moving average chart for Acme Company is:

c. The strategy leads to the following transactions.

Day Transaction Profit4 Buy at $51.888 Sell at $53.69 $1.819 Buy at $56.75

12 Sell at $57.63 $0.8814 Buy at $59.0615 Sell at $57.63 –$1.43

Total Profit $1.26Over the 15-day period, the investor would earn a profit of $1.26 per share (ignoring transaction costs).

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Chapter 19 Futures, Options and Other Derivatives

MULTIPLE CHOICE QUESTIONS

1. Which of the following actions will close a short position in a put option?A. buying a call with the same strike price, expiration, and underlying assetB. selling a call with the same strike price, expiration, and underlying assetC. buying a put with the same strike price, expiration, and underlying assetD. selling a put with the same strike price, expiration, and underlying asset

2. A plain vanilla swap is also known as aA. standard swap.B. conventional swap.C. fixed for floating swap. D. contractual swap.

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Chapter 19 Futures, Options and Other Derivatives

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. C2. C

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Chapter 19 Futures, Options and Other Derivatives

OPEN QUESTIONS

1. What is the difference between European-style options and American-style options?

Answer: The distinction between American and European style options involves the date when the contract can be exercised, and has nothing to do with geographic location. European-style options can be exercised only on specific dates. American-style options, in contrast, can be exercised any time on or before the expiration date of the contract. The holder of an American option has the freedom to decide when, if ever, the option contract will be exercised, as long as it is before the expiration date.

2. Straddles and strangles are related strategies involving 2 options, refer to section 19.6 for details.

a. Draw a pay-off diagram for a straddle.b. Do the same for a strangle. Explain why this strategy is ‘a bet on volatility’, and

even more so than a straddle.

Answer:a. Payoff diagram for a long straddle. A long straddle requires buying both a single

put and call on the same asset, with the same exercise price and expiration date.

b. Payoff diagram for a long strangle. The investor buys a call and a put, but the call has a higher exercise price (XH). This results in an area where the movement of the stock price between XL and XH doesn’t change the profit or loss, allowing for higher price volatility. With strangle the downside risk is less, then with a straddle.

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Chapter 19 Futures, Options and Other Derivatives

The payoff diagrams for short straddles and strangles and constructed in a similar way, using short positions in options.

3. Use the following data for parts a through e.

Option Strike Price Option Price/ShareCall A $25 $2Put A 30 13 Call B 20 4Put B 15 2Call C 10 13Put C 20 3

a. If the underlying stock is priced at $20, which of the options is in-the-money? Out-of-the-money? At-the-money?

b. Calculate the intrinsic value of each option.c. Calculate the time value of each option.d. If an investor bought all six options and the stock price was $30 at the options

expiration date, what would be the investor’s gain/loss on each option share?e. Do part d for each option contract.

Answer:a. In-the-money: Put A and Call C

Out-of-the-money: Call A and Put BAt-the-money: Call B and Put C

b. Intrinsic values:Call A = $0Put A = 30 – 20 = $10Call B = 20 –20 = $0Put B = $0Call C = 20 – 10 = $10Put C = 20 – 20 = $0

c. Time value = price – intrinsic valueCall A = 2 – 0 = $2

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Chapter 19 Futures, Options and Other Derivatives

Put A = 13 – 10 = $3Call B = 4 – 0 = $4Put B = 2 – 0 = $2Call C = 13 – 10 = $3Put C = 3 – 0 = $3

d. Gain/loss per shareCall A = 30 – 25 – 2 = $3Put A = 0 – 13 = – $13Call B = 30 – 20 – 4 = $6Put B = 0 – 2 = – $2Call C = 30 – 10 – 13 = $7Put C = 0 – 3 = – $3

e. Gain/loss per contractCall A = 3 (100) = $300 Put A = – 13 (100) = – $1,300Call B = 6 (100) = $600Put B = – 2 (100) = – $200 Call C = 7 (100) = $700Put C = – 3 (100) = – $300

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Chapter 20 Derivatives Valuation

MULTIPLE CHOICE QUESTIONS

1. According to put-call parity, which one of the following is true?a. Buying a call and selling a put is equivalent to buying stock and

borrowing PV(X). b. Buying a call and selling a put is equivalent to selling stock and lending

PV(X).c. Selling a call and buying a put is equivalent to selling stock and

borrowing PV(X).d. Selling a call and buying a put is equivalent to buying stock and lending

PV(X).

2. Which of the following is inversely related to the value of a call option?a. the value of the underlying assetb. the strike price of the call option c. the risk-free rate of interestd. the call option’s time to expiratione. the volatility of the underlying asset’s price

3. Which of the following is not a necessary assumption for the Black-Scholes option pricing model?

a. The market is frictionless.b. Investors are price takers.c. Short selling is allowed, with full use of the proceeds.d. Borrowing and lending both occur at the continuously compounded risk-

free rate.e. All investors have the same expectation of St.

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Chapter 20 Derivatives Valuation

MULTIPLE CHOICE QUESTIONS: ANSWERS

1. A2. B3. E

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Chapter 20 Derivatives Valuation

OPEN QUESTIONS

1. Suppose the standard deviation is 30%, S0 $100, X $100, r 5%, q = 3% and t 1/2. Calculate the Black-Scholes call and put option prices.

Answer:

d1= = = 0.1532

d2= 0.1532 – (0.3 ) = -0.0589

so that N(d1) = 0.56089 and N(d2) = 0.47652

Call = 100e-(0.03*0.5) * 0.56089 – 100e-(0.05*0.5) * 0.47652 = 55.2539– 46.4755 = 8.78Put = 100e-(0.05*0.5) * [1- 0.47652] – 100e-(0.03*0.5) * [1- 0.56089] = 51.0555 – 43.2573 = 7.80

2. Explain intuitively why the upper boundary for the price of a European put option is p0  X / (1 + r)t.

Answer:A put option gives its holder the right to sell the underlying asset for $X. Therefore, the put is most valuable when the underlying asset is worthless. In other words, the maximum possible payoff for a put option is $X, but the payoff will not be received until the option expires. The put can never be worth more than the present value of its maximum payoff.

3. Use put-call parity to prove that an at-the-money call option on a given stock must cost more than an at-the-money put option on the same stock. Assume the options have the same maturity and strike price.

Answer:Put-call parity gives the relationship among a call and a put with the same expiration date and strike price, the strike price, and the price of the underlying asset (Equation 20.8):

. Rearranging, .

If the call and the put are both at the money, then S = X and

, so c0 p0 > 0.

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Chapter 21 Risk Management

OPEN QUESTIONS

1. Consider a portfolio consisting of $10 million invested in the S&P 500 and $5 million invested in US Treasury bonds. The S&P 500 has an expected return of 14 percent and a standard deviation of 16 percent. The Treasury bonds have an expected return of 9 percent and a standard deviation of 4 percent. The correlation between the S&P 500 and the US Treasury bonds is 0.2 percent. All figures are stated on an annual basis.

a. Find the 99% VaR for one day. b. Suppose the correlation rises to 0.4 percent. Find the VaR for one day, and

explain the difference with section a of this question.

Answer:

a.

The 99% VaR is $ 242,972.84

b.

The 99% VaR is $ 248,621.83 which is higher than the VaR calculated with section a. This comes from the fact that the standard deviation of the portfolio rises through the increase of the correlation between the S&P 500 and the US Treasury bonds.

2. An investor has a bond with a value of $100 and this bond’s initial credit rating is BBB, in the table below the value of the bond is given depending on the credit rating the bond has on a certain moment (these figures are made up).

Credit Rating Bond Value ($) Transition Probability (%)

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Chapter 21 Risk Management

AAA 111.76 0.02AA 109.75 0.33A 105.53 5.95BBB 103.40 86.93BB 100.96 5.30B 93.84 1.17CCC 84.98 0.12Default 56.43 0.18

a. Calculate the best possible outcome and the worst possible outcome.

b. What is the recovery rate?

Answers:a. The best possible outcome is an upgrade to AAA, in this case the value of the

bond rises from $103.40 to $111.76, and this is a gain of $8.36. The worst possible outcome is of course default. This would result in a loss of $46.97 ($103.40 – $56.43).

b. The recovery rate is a substantial amount of the principal that may still be recovered in case of default. As you can see in the table in the second column, the recovery rate is 56.43 %.

3. Briefly explain main similarities and differences between stress-testing approach and Extreme Value Theory.

Answer:

Both stress testing and EVT are meant to supplement the VaR analysis. Stress-testing involves VaR estimations at significant fluctuations of key variables. EVT describes the behavior of the left-tail of the return distribution. In case of stress-testing the VaR model is extended, but its assumptions are not changed. EVT models a fat tail anew and does not necessarily follow the same model assumptions that were used to compute VaR.

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Chapter 22 Performance Evaluation

OPEN QUESTIONS

1. What is the problem caused by survivorship bias within data sets on mutual fund performance?

Answer:

Most of the data sets employed for mutual fund performance evaluation include the past records of all mutual funds currently in existence. Hence, when a fund merges or gets liquidated (ceases to exist), its past performance is deleted from the database. This because today’s investors are not interested in the records of funds that no longer exists. Thus, if mutual funds with bad performance are taken of the market, their bad records are deleted from the data set as well. Therefore, the average performance of the surviving funds will overstate the success of the mutual fund industry as a whole (including the liquidated funds).

2. What basic problems should one take into account when using performance analysis?

Answer:

The four basic problems when using performance evaluation are: the fact that performance evaluation is a historical exercise by its very nature, and the link between past performance and future performance may be weak; the fact that theory provides little guidance in the selection of the appropriate set of risk factors to be used to correct for risk; difficulties in estimating the risk and return characteristics of individual securities; and difficulties in estimating the return distribution for portfolios due to changes in the composition of a portfolio, and the lack of timely information on this composition.

3. Use Equations 22.3 and 22.4 to prove that Jensen’s performance index will indicate that a portfolio beat the market if, and only if, Treynor’s performance index indicates that the portfolio beat the market.

Answer:

We want to show that any portfolio that beats the market according to Jensen’s performance index must have 1) a positive value for Jensen’s index and 2) a value for Treynor’s index that exceeds the value of Treynor’s index for the market. Equation 22.4 shows that Jensen’s index is positive if, and only if,

0

Thus,

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Chapter 21 Risk Management

The left side of this inequality is Treynor’s index for the portfolio (Equation 22.3). The right side of this inequality is Treynor’s index for the market (remember that the market’s beta is 1). We see that Jensen’s index is greater than zero if and only if Treynor’s index for the portfolio is greater than Treynor’s index for the market.

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