Concept explainers
Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two stocks.
To determine: The expected return of Stock A and Stock B.
Introduction:
Expected return refers to the return that the investors expect on a risky investment in the future.
Answer to Problem 7QP
The expected return of Stock A is 11.20 percent.
The expected return of Stock B is 18.40 percent.
Explanation of Solution
Given information:
Stock A’s rate of return is 2 percent when the economy is in a recession, 10 percent when the economy is normal, and 15 percent when the economy is in a boom.
Stock B’s rate of return is −30 percent when the economy is in a recession, 18 percent when the economy is normal, and 31 percent when the economy is in a boom.
The probability of having a recession is 10 percent, the probability of having a normal economy is 50 percent, and the probability of having a booming economy is 40 percent.
The formula to calculate the expected return on the stock:
Where,
R1 refers to the rate of returns during the recession economy,
Rn refers to the rate of returns for “n” number of items,
P1 refers to the probability of having a recession economy,
Pn refers to the probability of having “n” number of economy.
Compute the expected return on Stock A:
Hence, the expected return on Stock A is 0.1120 or 11.20 percent.
Compute the expected return on Stock B:
Hence, the expected return on Stock B is 0.1840 or 18.40 percent.
To determine: The standard deviation of Stock A and Stock B.
Introduction:
Standard deviation refers to the variation in the actual returns from the expected returns.
Answer to Problem 7QP
The standard deviation of Stock A is 3.87 percent.
The standard deviation of Stock B is 17.26 percent.
Explanation of Solution
Given information:
Stock A’s rate of return is 2 percent when the economy is in a recession, 10 percent when the economy is normal, and 15 percent when the economy is in a boom.
Stock B’s rate of return is −30 percent when the economy is in a recession, 18 percent when the economy is normal, and 31 percent when the economy is in a boom.
The probability of having a recession is 10 percent, the probability of having a normal economy is 50 percent, and the probability of having a booming economy is 40 percent.
The formula to calculate the standard deviation of the stock:
Compute the standard deviation of Stock A:
Hence, the standard deviation of Stock A is 0.0387 or 3.87 percent.
Compute the standard deviation of Stock B:
Hence, the standard deviation of Stock B is 0.1726 or 17.26 percent.
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Chapter 11 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
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