公司核心第十章习题 - 图文

Chapter 10

Capital Markets and the Pricing of Risk

10-1.

The figure below shows the one-year return distribution for RCS stock. Calculate a. The expected return.

b. The standard deviation of the return.

a.

E?R???0.25(0.1)?0.1(0.2)?0.1(0.25)?0.25(0.3)?5.5%

22b. Variance?R????0.25?0.055??0.1???0.1?0.055??0.2

??0.1?0.055??0.25??0.25?0.055??0.3?2.6%Standard Deviation ? 0.026?16.13%

10-2.

The following table shows the one-year return distribution of Startup, Inc. Calculate a. The expected return.

b. The standard deviation of the return.

22

a.

E?R???1?0.4??0.75?0.2??0.5?0.2??0.25?0.1??10?0.1??32.5%

222b. Variance?R????1?0.325?0.4???0.75?0.325?0.2???0.5?0.325?0.2

???0.25?0.325?0.1??10?0.325?0.1?10.46Standard Deviation?10.46?3.235?323.5%

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10-3.

Characterize the difference between the two stocks in Problems 1 and 2. What trade-offs would you face in choosing one to hold?

Startup has a higher expected return, but is riskier. It is impossible to say which stock I would prefer. It depends on risk performances and what other stocks I’m holding.

10-4.

You bought a stock one year ago for $50 per share and sold it today for $55 per share. It paid a $1 per share dividend today. a. What was your realized return?

b. How much of the return came from dividend yield and how much came from capital gain? Compute the realized return and dividend yield on this equity investment. a. b.

R?1?(55?50)?0.12?12%

50Rdiv?1?2% 5055?50?10% 50Rcapital gain?The realized return on the equity investment is 12%. The dividend yield is 10%.

10-5. Repeat Problem 4 assuming that the stock fell $5 to $45 instead. a. Is your capital gain different? Why or why not? b. Is your dividend yield different? Why or why not?

Compute the capital gain and dividend yield under the assumption the stock price has fallen to $45. a.

Rcapital gain?45?50/50??10%.Yes, the capital gain is different, because the difference between

the current price and the purchase price is different than in Problem 1.

b. The dividend yield does not change, because the dividend is the same as in Problem 1.

The capital gain changes with the new lower price; the dividend yield does not change.

10-6.

Using the data in the following table, calculate the return for investing in Boeing stock from January 2, 2003, to January 2, 2004, and also from January 2, 2008, to January 2, 2009, assuming all dividends are reinvested in the stock immediately.

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136 Berk/DeMarzo ? Corporate Finance, Second Edition

Date1/2/20032/5/20035/14/20038/13/200311/12/20031/2/2004Price33.8830.6729.4932.3839.0741.99Dividend0.170.170.170.17R-8.97%-3.29.38!.19%7.47%1+R0.9102720.9670691.1037641.2118591.07473826.55%1.265491Date1/2/20082/6/20085/7/20088/6/200811/5/20081/2/2009Price86.6279.9184.5565.449.5545.25Dividend0.40.40.40.4R-7.28%6.31%-22.18%-23.62%-8.68%1+R0.9271531.0630710.7782380.7637610.913219-46.50%0.535006 10-7. The last four years of returns for a stock are as follows:

a. What is the average annual return? b. What is the variance of the stock’s returns?

c. What is the standard deviation of the stock’s returns?

Given the data presented, make the calculations requested in the question. a.

Average annual return ? ?4%?28%?12%?4%?10%

4? b. Variance of returns (?4%?10%)2?(28%?10%)2?(12%?10%)2?(4%?10%)23

?0.01867c. Standard deviation of returns ? variance?0.01867?13.66%

The average annual return is 10%. The variance of return is 0.01867. The standard deviation of returns

is 13.66%.

10-8.

Assume that historical returns and future returns are independently and identically distributed and drawn from the same distribution.

a. Calculate the 95% confidence intervals for the expected annual return of four different

investments included in Tables 10.3 and 10.4 (the dates are inclusive, so the time period spans 83 years). b. Assume that the values in Tables 10.3 and 10.4 are the true expected return and volatility

(i.e., estimated without error) and that these returns are normally distributed. For each

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investment, calculate the probability that an investor will not lose more than 5% in the next year? (Hint: you can use the function normdist(x,mean,volatility,1) in Excel to compute the probability that a normally distributed variable with a given mean and volatility will fall below x.)

c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you

identify the reason?

Return Volatility (Standard Deviation) 41.50% 20.60% 7.00% 3.10%

Lower Bound Confidence Interval 11.79% 7.08% 5.06% 3.22%

Upper Bound Confidence Interval 30.01% 16.12% 8.14% 4.58%

26.63% 21.02% 4.87% 0.20%

Investment

Small stocks S&P 500 Corporate bonds Treasury bills

Average Annual Return 20.90% 11.60% 6.60% 3.90%

Standard Error 4.56% 2.26% 0.77% 0.34%

Part b answer 73.37% 78.98% 95.13% 99.80%

c. No. You cannot lose money on Treasury Bills. The problem is that the returns to Treasuries are

not normally distributed.

10-9.

Consider an investment with the following returns over four years:

a. What is the compound annual growth rate (CAGR) for this investment over the four years? b. What is the average annual return of the investment over the four years? c. Which is a better measure of the investment’s past performance?

d. If the investment’s returns are independent and identically distributed, which is a better

measure of the investment’s expected return next year? a.

110"0%1.203-5%0.95415%1.15Ave10.00êGR9.58%

1.10b. see table above c. CAGR

d. Arithmetic average

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