# Calculating mean, variance and standard deviation of returns

1. Suppose a stock had an initial price of $86 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $94.

2. You have observed the following returns on Crash-n-Burn Computer's stock over the past five years: 13 percent, -8 percent, 16 percent, 16 percent, and 10 percent.

a. What was the arithmetic average return on Crash-n-Burn's stock over this five-year period?

b-1 What was the variance of Crash-n-Burn's returns over this period?

b-2 What was the standard deviation of Crash-n-Burn's returns over this period?

3. Suppose you bought a 4.4 percent coupon bond one year ago for $850. The bond sells for $900 today.

a. Assuming a $1,000 face value, 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. If the inflation rate last year was 1.5 percent, what was your total real rate of return on this investment?

4. You find a certain stock that had returns of 18 percent, −7 percent, 25 percent, and 18 percent for four of the last five years. The average return of the stock over this period was 14.48 percent.

a. What was the stock's return for the missing year?

b. What is the standard deviation of the stock's return?

5. You have observed the following returns on Crash-n-Burn Computer's stock over the past five years: 13 percent, -8 percent, 16 percent, 16 percent, and 10 percent. Suppose the average inflation rate over this period was 1.5 percent and the average T-bill rate over the period was 5.0 percent.

a. What was the average real return on Crash-n-Burn's stock?

b. What was the average nominal risk premium on Crash-n-Burn's stock

6. A stock has a beta of 1.85 and an expected return of 14 percent. A risk-free asset currently earns 3.4 percent.

a. What is the expected return on a portfolio that is equally invested in the two assets?

b. If a portfolio of the two assets has a beta of 0.74, what are the portfolio weights?

c. If a portfolio of the two assets has an expected return of 8 percent, what is its beta?

d. If a portfolio of the two assets has a beta of 3.70, what are the portfolio weights

7. You own a portfolio that is 38 percent invested in Stock X, 24 percent in Stock Y, and 38 percent in Stock Z. The expected returns on these three stocks are 12 percent, 18 percent, and 14 percent, respectively. What is the expected return on the portfolio?

8. You own a stock portfolio invested 35 percent in Stock Q, 30 percent in Stock R, 20 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are 0.79, 1.17, 1.18, and 1.35, respectively. What is the portfolio beta?

Consider the following information:

Rate of Return If State Occurs

State of Probability of

Economy State of Economy Stock A Stock B

Recession 0.20 0.05 − 0.18

Normal 0.55 0.08 0.11

Boom 0.25 0.13 0.28

a. Calculate the expected return for the two stocks.

b. Calculate the standard deviation for the two stocks

9. You have $19,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 12 percent and Stock Y with an expected return of 11.5 percent. If your goal is to create a portfolio with an expected return of 11.80 percent, how much money will you invest in Stock X and Stock Y?

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#### Solution Summary

Solutions to given problems depict the steps to find weighted beta, average return, standard deviation of returns and variance.

Corporate Finance

Calculating the variance and standard deviation:

Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara's

investment.

Probability Return

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Boom 0.1 25.00%

Good 0.4 15.00%

Level 0.3 10.00%

Slump 0.2 -5.00%

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Zero coupon bonds:

Diane Carter is interesting in buying a five-year zero coupon bond whose face value is $1,000. She understands that the market interest rate for similar investment is 9 percent. Assume annual coupon payments. What is the current value of this bond?