FIN 300 & FIN302 – Homework Assignment #3
Due by 11.59pm on March 21
This homework assignment is to be submitted electronically via Canvas. If you feel that a
question misses essential information, make a reasonable assumption and clearly state that
assumption.
No late homework will be accepted. You are allowed to – and I encourage you to – work
together on homework assignments. However, you must hand in your own individual
homework. Photocopies (or any other form of copies such as pictures taken of someone
else’s homework) are unacceptable. You must show how you obtained all your answers.
Homework assignments are graded pass (1) / fail (0): to pass, you have to attempt 100% of the
homework assignment.
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Chapter 11 Problems
#1. Consider the return behavior of the following two stocks:
State of Economy Probability of State Return on Stock A Return on Stock B
Recession .25 -4.0% 7%
Normal .60 7.2% 8.2%
Boom .15 13.4% 9.4%
(a) Calculate the expected return on each stock.
(b) Calculate the standard deviation of the return on each stock.
(c) Calculate the covariance and correlation of returns between the two stocks.
#2. Return to the data above in problem #1
(a) Suppose an investor formed a portfolio by placing $1,000 in Stock A and $1,000 in Stock B.
What are the portfolio weights (percentages) invested in A and B? Calculate the expected return
and standard deviation of this portfolio.
(b) Suppose an investor formed a portfolio by placing $1,500 in Stock A and $500 in Stock B.
What are the portfolio weights (percentages) invested in A and B? Calculate the expected return
and standard deviation of this portfolio.
#3. An investor places 60% of his funds in Stock I and 40% of his funds in Stock J. The
expected return on Stock I is 5% and the expected return on Stock J is 10%. The standard
deviation of returns for Stock I is 10% and for Stock J is 20%.
(a) What is the expected return of the investor’s portfolio?
(b) What is the variance of the investor’s portfolio assuming the correlation between the returns
of I and the returns of J is +1.0?
(c) What is the variance of the investor’s portfolio assuming the correlation between the returns
of I and the returns of J is +.5?
#4. You manage a risky portfolio with an expected return of 17% and a standard deviation of 27%.
The T-bill rate is 7%.
a. Your client chooses to invest 70% of her savings in your fund and 30% in a T-bill money market
fund. What is the expected value and standard deviation of the rate of return of your client's
portfolio?
b. Suppose that your risky portfolio includes the following investments in these proportions:
Stock A: 27%
Stock B: 33%
Stock C: 40%
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What are the investment proportions in your client's overall portfolio including the position in T-
bills?
c. Suppose your client decides to invest in your portfolio a proportion y of her total investment
budget so that the overall portfolio will have an expected rate of return of 15%.
i. What is the proportion y?
ii. What are your client's investment proportions in your three stocks and the T-bill fund?
iii. What is the standard deviation of the return on your client's portfolio?
d. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected
return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation
will not exceed 20%.
i. What is the investment proportion y?
ii. What is the expected rate of return on the overall portfolio?
#5. The stock of Business Adventure sells for $40 a share. Its likely dividend payout and end-of-
year price depends on the state of the economy by the end of the year as follows:
Dividend Stock Price
Boom $2.00 $50.00
Normal Economy $1.00 $43.00
Recession $0.50 $34.00
(a) Calculate the expected holding period return and standard deviation of the holding period
return. All three scenarios are equally likely.
(b) Calculate the expected return and standard deviation of a portfolio half invested in Business
Adventures and half in Treasury bills. The return on bills is 4%.
#6. An industrial firm has a beta of 1.4. Based on historical data you estimate the market risk
premium to be 8.5% and the current risk-free rate is 5%. Using the CAPM, what is the expected
return on the stock for this industrial firm?
#7. Are the following data consistent with the CAPM model? Explain.
Portfolio Expected Return Beta
Risk-free securities .10 0
Market Portfolio .18 1.0
Security A .16 1.5
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Chapter 13 Problems
#8. Mitsubishi Inc., is a levered firm with a debt-to-equity ratio of 0.25. The beta of common
stock is 1.15, while the beta of debt is 0.3 (the company’s debt is not risk-free). The market-risk
premium is 10 percent and the risk-free rate is 6 percent. The corporate tax rate is 35 percent.
Assume the CAPM holds. What is this firm's rWACC?
#9. Pacific Cosmetics is evaluating a project to produce a perfume line. Pacific currently does
not produce any body scent products. Pacific Cosmetics is an all-equity firm.
(a) Should Pacific Cosmetics use its stock beta to evaluate the project?
(b) How should Pacific Cosmetics compute the beta to evaluate the project?
#10. A firm currently has $50 million in stock and $50 million in bonds and the beta on the
firm’s stock is currently estimated to be 1.0. The company’s debt is risk-free, therefore the beta
of debt is zero. If the firm changes its capital structure so that is has $25 million in stock and $75
million in bonds, what will the new beta on the firm’s stock be? There are no taxes.
