Chapter 12 - Dropbox 2.4

Problem 1: Calculating Returns

Suppose you bought a bond with an annual coupon of 7 percent one year ago for $970.  The bond sells for $940 today and has a standard $1000 face value.  The inflation rate last year was 3 percent.

a) What was your total dollar return on this investment over the past year?                                                                                   b) What was your total nominal rate of return on this investment over the past year?                                 c) What was your total rate of real return on this investment?

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Chapter 12 - Dropbox 2.4

Problem 2: Calculating Returns and Variability

Two alternative investments present the following expected returns:

Returns

Year

X

Y

1

15%

21%

2

26%

36%

3

7%

13%

4

-13%

-26%

5

11%

15%

a) Calculate the arithmetic average returns, the variances, and the standard deviations for both X and Y.                                                                                                                b) Which of these would you consider a superior investment?  Why?

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Chapter 12 - Dropbox 2.4

Problem 3: Risk Premiums

Large-company stocks and Treasury Bills produced the following historial returns:

Returns

Year

Stock

T-Bills

1970

3.94%

6.50%

1971

14.30%

4.36%

1972

18.99%

4.23%

1973

-14.69%

7.29%

1974

-26.47%

7.99%

1975

37.23%

5.87%

a) Calculate the arithmetic average returns for large-company stocks and T-Bills over this time period.                                                                                                            b) Calculate the standard deviation of the returns for large-company stocks and T-Bills over this period.                                                                                                                c) Calculate the observed risk premium in each year for the large-company stocks versus the T-Bills.  What was the average risk premium over this period?  What was the standard deviation for the risk premium over this period?                                                                                                                                                                                                                d) Is it possible for the risk premium to be negative before an investment is undertaken?  Can the risk premium be negative after the fact?  Explain.

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Chapter 13 - Dropbox 2.4

Problem 1: Calculating Expected Return

Based on the following information, calculate the expected return:

Probability of this State Occuring

Portfolio Return if State Occurs

State of Economy

Recession

10%

-18%

Normal

60%

11%

Boom

30%

26%

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Chapter 13 - Dropbox 2.4

Problem 2: Calculating Portfolio Beta

You own a stock portfolio invested 20 percent in Stock Q, 30 percent in Stock R, 35 percent in Stock S, and 15 percent in Stock T.  The betas for these four stocks are 0.84, 1.17, 1.08, and 1.36, respectively.

What is the portfolio beta?

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Chapter 13 - Dropbox 2.4

Problem 3: Using the Capital Asset Pricing Model (CAPM)

A stock has a beta of 1.15, the expected return on the market is 10.3 percent, and the risk-free rate is 3.8 percent.

What must investors' expected return on this stock be?

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