投资学第七版ch09课后答案

(t) 1 (f) 2 (t) 3 (t) 4 (t) 5 (t) 6 (f) 7 (t) 8 (f) 9 (t) 10 (t) 11 (f)

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AN INTRODUCTION TO ASSET PRICING MODELS

TRUE/FALSE QUESTIONS

One of the assumptions of Capital Market Theory is that lend at the risk-free rate.

investors can borrow or An assumption of Capital Market Theory is that buying or selling of assets entails no taxes, but entails significant transaction costs.

A risky asset is an asset with uncertain future returns, and uncertainty (or risk) is measured by the variance or standard deviation of returns.

The standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio. The Capital Market Line (CML) is the line from the intercept point that represents the risk-free rate tangent to the original efficient frontier. The market portfolio consists of all risky assets.

All portfolios on the CML are perfectly negatively correlated, which means that all portfolios on the CML are perfectly negatively correlated with the completely diversified market portfolio since it lies on the CML. Diversification reduces the unsystematic risk in a portfolio.

The Capital Asset Pricing Model (CAPM) is a technique for determining the expected risk on an asset.

Beta is a standardized measure of systematic risk.

Multifactor models of risk and return can be broadly grouped into models that use macroeconomic factors and models that use microeconomic factors.

Arbitrage Pricing Theory (APT) specifies the exact number of risk factors and their identity

MULTIPLE CHOICE QUESTIONS

(d)

1

(e)

2

(c)

3 (d) 4

(b) 5

Which of the following is not an assumption of the Capital Market Theory? a)b) All investors are Markowitz efficient investors. c) All investors have homogeneous expectations.

d) There are no taxes or transaction costs in buying or selling assets. e)

There are no risk-free assets.

All investors have the same one period time horizon.

The market portfolio consists of all a)b) New York Stock Exchange stocks. c)International stocks and bonds. d) Stocks and bonds.

e)

U.S. and non-U.S. stocks and bonds. Risky assets.

The separation theorems divides decisions on from decisions on . a)b) Lending, borrowing c) Risk, return

d) Investing, financing

e)

Risky assets, risk free assets Buying stocks, buying bonds

When identifying undervalued and overvalued assets, which of the following statements is false?

a) An asset is properly valued if its estimated rate of return is equal to its

b) required rate of return.

An asset is considered overvalued if its estimated rate of return is below its

c) required rate of return.

An asset is considered undervalued if its estimated rate of return is above its

d) required rate of return.

An asset is considered overvalued if its required rate of return is below its

e) estimated rate of return.

None of the above (that is, all are true statements)

Utilizing the security market line an investor would expect the stock's return to in a market that owning a stock with a beta of (-2) was expected to decline 10 percent. a)b) Rise or fall an indeterminate amount Rise by 20.0%

3

(d) 6

(e)

7

(a)

8

(a)

9

(d)

10

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c)d) e) Fall by 20.0% Rise by 10.2% Fall by 10.2% The Capital Market Line (CML) refers to the efficient formed by creating portfolios that a)b) Invest solely in the market portfolio M.

c) d) Lend at the risk free asset and invest in the market portfolio. Borrow at the risk free asset and invest in the market portfolio.

e) Lend and borrow at the risk free rate and invest in the market portfolio. Short sell the market portfolio.

As the number of stocks in a portfolio increases

a) The expected return of the portfolio increases because systematic risk

b) decreases.

The expected return of the portfolio increases because unsystematic risk

c) decreases.

The standard deviation of the portfolio increases because systematic risk

d) increases.

The standard deviation of the portfolio decreases because systematic risk

e) increases.

The standard deviation of the portfolio decreases because unsystematic risk

decreases.

The Security Market Line (SML) represents the relation between a)b) Risk and required return on an asset.

c)Systematic risk and required return on an asset. d) Risk and return on a diversified portfolio of assets. e)

Unsystematic risk and required return on an asset

Systematic risk and required return on a diversified portfolio of assets.

In a macro-economic based risk factor model the following factor would be one of many appropriate factors

a)b) c) Confidence risk. d) Maturity risk.

e) Expected inflation risk. Call risk.

Return difference between small capitalization and large capitalization stocks. In a multifactor model, confidence risk represents

a) Unanticipated changes in the level of overall business activity.

(b)

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(e)

12

b)c) d) Unanticipated changes in investors’ desired time to receive payouts. Unanticipated changes in short term and long term inflation rates.

Unanticipated changes in the willingness of investors to take on investment

e) risk.

None of the above. In a multifactor model, time horizon risk represents a)b) Unanticipated changes in the level of overall business activity.

c)Unanticipated changes in investors’ desired time to receive payouts. d)

Unanticipated changes in short term and long term inflation rates.

Unanticipated changes in the willingness of investors to take on investment e) risk.

None of the above.

In a micro-economic based risk factor model the following factor would be one of many appropriate factors

a)b) Confidence risk. c) Maturity risk.

d) Expected inflation risk. e) Call risk.

Return difference between small capitalization and large capitalization stocks.

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MULTIPLE CHOICE PROBLEMS

(b) 1

(b)

2

(b) 3

(c)

4

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Consider an asset that has a beta of 1.5. The return on the risk-free asset is 6.5% and the expected return on the stock index is 15%. The estimated return on the asset is 20%. Calculate the alpha for the asset. a)b) 19.25% c) 0.75% d)–0.75% e)

9.75% 9.0%

The table below provides factor risk sensitivities and factor risk premia for a three factor model for a particular asset where factor 1 is MP the growth rate in U.S. industrial production, factor 2 is UI the difference between actual and expected inflation, and factor 3 is UPR the unanticipated change in bond credit spread.

Risk Factor Risk Factor Sensitivity(β) Premium(λ) MP 1.76 0.0259 UI -0.8 -0.0432 UPR 0.87 0.0149

Calculate the expected excess return for the asset. a)b) 12.32% c) 9.32% d) 4.56% e) 6.32% 8.02%

The variance of returns for a risky asset is 25%. The variance of the error term, Var(e) is 8%. What portion of the total risk of the asset, as measured by variance, is unsystematic? a)b) 32% c) 8% d) 68% e)

25% 75%

An investor wishes to construct a portfolio consisting of a 40% allocation to a stock index and a 60% allocation to a risk free asset. The return on the risk-free

(b)

5

(d)

6

(d) 7

(b) 8

asset is 2% and the expected return on the stock index is 10%. The standard deviation of returns on the stock index 8%. Calculate the expected standard deviation of the portfolio. a)b) 5.2% c) 8.0% d) 3.2% e) 4.0% 1.2%

An investor wishes to construct a portfolio by borrowing 35% of his original wealth and investing all the money in a stock index. The return on the risk-free asset is 4.0% and the expected return on the stock index is 15%. Calculate the expected return on the portfolio. a)b) 18.25% c) 18.85% d) 9.50% e)

15.00% 11.15%

An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset. The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%. Calculate the expected return on the portfolio. a)b) 8.25% c) 16.50% d) 17.50% e)

9.75% 14.38%

A stock has a beta of the stock is 1.1. The risk free rate is 2.5% and the return on the market is 12%. The estimated return for the stock is 14%. According to the CAPM you should a)b) Sell because required return is 9.95%. c)Sell because required return is 16.5%. d) Buy because required return 11.5%. e)

Buy because required return is 12.95%. Short because it is undervalued.

Consider a risky asset that has a standard deviation of returns of 15. Calculate the correlation between the risky asset and a risk free asset. a)b) 1.0 0.0

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(a)

c) -1.0 d) 0.5 e) -0.5

9

The expected return for a stock, calculated using the CAPM, is 10.5%. The market return is 9.5% and the beta of the stock is 1.50. Calculate the implied risk-free rate. a) b) c) d) e) 10

7.50% 13.91% 17.50% 21.88% 14.38%

(d)

The expected return for a stock, calculated using the CAPM, is 25%. The risk free rate is 7.5% and the beta of the stock is 0.80. Calculate the implied return on the market. a) b) c) d) e)

7.50% 13.91% 17.50% 21.88% 14.38%

(c)

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The expected return for Zbrite stock calculated using the CAPM is 15.5%. The risk free rate is 3.5% and the beta of the stock is 1.2. Calculate the implied market risk premium. a) b) c) d) e)

5.5% 6.5% 10.0% 15.5% 12.0%

(d)

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Calculate the expected return for Express Inc. which has a beta of .69 when the risk free rate is.09 and you expect the market return to be .14. a) b) c) d) e)

0.05% 13.91% 10.92% 12.45% 14.25%

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS

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You expect the risk-free rate (RFR) to be 5 percent and the market return to be 9 percent. You also have the following information about three stocks.

CURRENT EXPECTED EXPECTED STOCK BETA PRICE PRICE DIVIDEND X 1.50 $ 22 $ 23 $ 0.75 Y 0.50 $ 40 $ 43 $ 1.50 Z 2.00 $ 45 $ 49 $ 1.00 (b) 13 What are the expected (required) rates of return for the three stocks (in the order

X, Y, Z)?

a) 16.50%, 5.50%, 22.00% b) 11.00%, 7.00%, 13.00% c) 7.95%, 11.25%, 11.11% d) 6.20%, 2.20%, 8.20% e) 15.00%, 3.50%, 7.30%

(a) 14 What are the estimated rates of return for the three stocks (in the order X, Y, Z)?

a) 7.95%, 11.25%, 11.11% b) 6.20%, 2.20%, 8.20% c) 16.50%, 5.50%, 22.00% d) 11.00%, 7.00%, 13.00% e) 15.00%, 3.50%, 7.30%

(e) 15 What is your investment strategy concerning the three stocks?

a) Buy stock Y, it is undervalued.

b) Buy stock X and Z, they are undervalued. c) Sell stocks X and Z, they are overvalued. d) Sell stock Y, it is overvalued. e) Choices a and c

USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS

Return forReturn for

Year GBC Market 1 25 12 2 10 13 3 5 17 4 -13 -15 5 11 -8 6 -20 9

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(a)

16 (e)

17 (b)

18 (d)

19

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Compute the beta for GBC Company using the historic returns presented above. a)b) 0.4255 c) 0.5929 d) 5.6825 e)

9.4163 0.3333

Compute the correlation coefficient between GBC and the Market Index. a)b) 0.4255 c)0.5929 d) 5.6825 e)

9.4163 0.3333

Compute the intercept of the characteristic line a)b) 0.4255 c) 1.013 d) 1.4385 e)

0.5875 0.5219

The equation of the characteristic line is a) RGBC + 1.013 = 0.4255(RMarket) b) RGBC = 1.013 - 0.4255(RMarket) c) RMarket = 1.013 + 0.4255(RGBC) d) RGBC = 1.013 + 0.4255(RMarket) e)

RMarket = 1.013 - 0.4255(RMarket)

CHAPTER 9

ANSWERS TO PROBLEMS

1 6.5 + 1.5(15 – 6.5) = 19.25%

alpha = 20 –19.25 = 0.75%

2

The table below shows the relevant calculations

Risk Factor Risk Factor Sensitivity(β)Premium(λ)(β)x(λ) MP 1.76 0.0259 0.0456 UI -0.8 -0.0432 0.0346 UPR 0.87 0.0149 0.013

Expected return 0.1232

3 8%/25% = 0.32. = 32% unsystematic. 4 0.4(0.08) = 0.032 or 3.2% 5 -0.35(4) + 1.35(15) = 18.85% 6 E(R)= 0.3(4.5) + 0.7(12) = 9.75%

7 E(R)= 2.5 + 1.1(12 – 2.5) = 12.95%. Buy the stock is undervalued. 8

The correlation between a risky asset and a risk-free asset is always zero.

9 10.5 = X + 1.5(9.5 – X). X = 7.5%. 10 25 = 7.5 + 0.8(X). X = 14.38%. Return on market = 14.38 + 7.5 = 21.88% 11 15.5 = 3.5 + 1.2(X). X = 10%. 12

k = .09 + .69 (.14 - .09) = .1245 = 12.45% For problems 13 - 15

STOCK REQUIRED ESTIMATED

EVALUATION X .05 + 1.50(.09 - .05) = 11% (23 - 22 + 0.75)/22 = 7.95% Overvalued

Y .05 + 0.50(.09 -.05) = 7% (43 - 40 + 1.50)/40 = 11.25% Undervalued Z .05 + 2.00(.09 - .05) = 13% (49 - 45 + 1.00)/45 = 11.11%

Overvalued

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For problems 16 – 19

The table below shows the relevant calculations.

(1) (2) (3) (4) (5) (6) (7) (8) GBC Market GBC Market (6) x (7)

22

(R-E(R ))R-E(R )R-E(R ) Year GBC Market (R-E(R ))

1 25 12 484.00 53.73 22.00 7.33 161.262 10 13 49.00 69.39 7.00 8.33 3 5 17 4.00 152.03 2.00 12.33 4 -13 -15 256.00 386.91 -16.00 -19.67 5 11 -8 .00 160.53 8.00 -12.67 6 -20 9 529.00 18.75 -23.00 4.33 Total 18 28 1386.00 841.33 Average 3.0000 4.67 Variance 277.20 168.27 Std. Dev. 16.65 12.97 Covariance Correlation 0.33

Beta 0.4255

16 Beta for GBC Computer is computed as follows:

Beta = Cov(GBC, Market)/ VarianceMarket

Beta = 18.40/82 = 0.2244 17 The correlation coefficient can be computed as follows: Correlation = Cov(GBC, Market)/(SDGBC x SD Market)

= 71.6/(16.65 x 12.97) = 0.33 Where:

SDGBC = [1386/5]1/2 SD = 16.65 Market = [841.33/5]1/2 = 12.97 Cov(GBC, Market) = 358/5 = 71.60 18

The alpha or intercept of the characteristic line is computed as follows: alpha = 3.0 - [(0.4255)(4.67)] = 1.013%

19 RGBC = 1.013 + 0.4255(RMarket)

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58.31 24.66 314.72-101.36-99.59 358.0071.60