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Week 12Chapter 20 + 21

CHAPTER 20 PROBLEM 1Based on the historical returns in Figure 20.2, calculate the

mean and standard deviation of return in dollars for an equally

weighted portfolio of French and German stocks. Calculate the

Sharpe index for this portfolio using the historical mean on U.S.

T-bills as the risk-free rate.

2FINS3616 Peter Kjeld Andersen

CHAPTER 20 PROBLEM 3The MSCI world stock market index in Figure 20.2 had a mean

annual return of 11.3% and a standard deviation of 17%.

Meanwhile, dollar returns to a globally diversified bond

portfolio had a mean of 8.4 and a standard deviation of 10.8%.

The correlation between these two indices was 0.360. Calculate

the mean and standard deviation of an equally weighted

portfolio of global stocks and bonds. Also, calculate the Sharpe

index for this stock-bond portfolio using the historical 6.8% U.S.

T-bill rate.

3FINS3616 Peter Kjeld Andersen

CHAPTER 20 PROBLEM 5Suppose expected returns in the U.S. and Germany are 10% and

20% respectively. Standard deviations are also 10% and 20%

respectively. Calculate the standard deviation of an equally

weighted combination of the two assets under the following

four cases:

I. Perfect positive correlation

II Perfect negative correlationII. Perfect negative correlation

III. Zero correlation

IV. A correlation of 0.3

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CHAPTER 20 PROBLEM 7Suppose you calculated a Sharpe index for every security in the

world over the most recent year. Are any of these securities

likely to exhibit performance (measured as excess return per

unit of risk) that is superior to that of the world market

portfolio? Why or why not?

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CHAPTER 20 PROBLEM 9The Philippine stock market in Makati rises 12% in Philippine

pesos. During the same period, the peso rises from

$0.0425/Peso to $0.0440/Peso. By how much does the

Philippine stock market rise in U.S. dollars?

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CHAPTER 20 PROBLEM 11How much of the return variance on a foreign stock investment

is likely to come from variations in the foreign stock market and

how much from variation in the exchange rate? What are the

proportions for a foreign bond investment?

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CHAPTER 20 PROBLEM 13You are planning for retirement and must decide on the inputs

to use in your asset allocation decision. Knowing the benefits of

international portfolio diversification, you want to include

foreign stocks and bonds in your final portfolio. What statistics

should you collect on the worlds major debt and equity

markets? Can you trust that the future will be like the past?

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CHAPTER 21 PROBLEM 1Calculate the equity required return under each of the

following, assuming the CAPM holds:

I. The risk-free rate is 8%, beta is 1.5, and the market risk

premium is 8.5%.

II. The risk-free rate is 4%, beta is 1.2, and the market riskII. The risk free rate is 4%, beta is 1.2, and the market risk

premium is 8.5%.

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CHAPTER 21 PROBLEM 3As a security analyst for the London branch of Merrill Lynch, you

have identified the following factors and factor sensitivities for

British Petroleum (BP):

Prod Prod Oil Oil Spot SpotE[r] F F F= + + +Factors and factor sensitivities are as follows:

FACTORS BETAS

FProd Changes in world industrial production Prod = +1.50

F Change in crude oil pricesOil = 0.80FOil Change in crude oil prices

FspotChange in the value of GBP against a basket of

foreign currenciesSpot = +0.01

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g

CHAPTER 21 PROBLEM 3BPs expected return if all factors are equal to their expectation i 14%is = 14%.

A. All else constant, is British Petroleums share price likely to go up or down with an increase in world industrial production? With an increase in crude oil prices? With an increase in the value of the pound?

B. What is the expected return on BP stock in a year when world industrial production is 2% above the expectation, oil prices rise unexpectedly by 10%, and the spot rate (S/f) goes down by 5%?

C. If BP stock rises by 4% during this period, by how much does BP over- or underperform its expectation?

11FINS3616 Peter Kjeld Andersen

CHAPTER 21 PROBLEM 5As a security analyst for the New York branch of Deutsche Bank,

you have identified the following factors and factor sensitivities

for Amazon.com (AMZN):

M M Z Z D DE[r] F F F= + + + This is basically Fama & French

Factors and factor sensitivities are as follows:

FACTORS BETAS

FmMarket Factor

(Rm Rf)F = +1.00

FZFirm Size Factor

(small minus large stock returns)Z = +0.10

FRelative Financial Distress D = +0.05

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FD (value minus growth stock returns)D

CHAPTER 21 PROBLEM 5Amazons expected return if all factors are equal to their

expectation is = 10%.

A. What is Amazons expected return in a year when each

factor is 1% lower than its expectation?

B. If Amazon.coms stock price rises by 12% during this period,B. If Amazon.com s stock price rises by 12% during this period,

by how much does Amazon.com over- or under-perform its

expectation?expectation?

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CHAPTER 21 PROBLEM 7The regional directors of a major investment bank are discussing

strategies for their respective countries.

A. As a director of North American investment strategy based

on momentum to your foreign colleagues.

B. As director of European investments, do you think such aB. As director of European investments, do you think such a

momentum-base strategy will work in your markets? Why or

why not?why not?

C. As director of Latin American investments, do you think a

momentum-based strategy will work in your markets? Why

or why not?

14FINS3616 Peter Kjeld Andersen