Calculating Returns and Standard Deviations [LO1] Based on the following information, calculate the expected return and standard deviation for the two stocks:
Introduction:
Expected return refers to the return that the investors expect on a risky investment in the future. Standard deviation refers to the variation in the actual returns from the expected returns.
To determine: The standard deviation of Stock A.
Answer to Problem 7QP
The standard deviation of Stock A is 4.49 percent.
Explanation of Solution
Given information:
Stock A’s return is 4 percent when the economy is in a recession, 9 percent when the economy is normal, and 17 percent when the economy is in a boom. The probability of having a recession is 15 percent, the probability of having a normal economy is 55 percent, and the probability of having a booming economy is 30 percent.
The formula to calculate the expected return on the stock:
The formula to calculate the standard deviation of the stock:
Compute the expected return on Stock A:
“R1” refers to the returns during the recession. The probability of having a recession is “P1”. “R2” is the returns in a normal economy. The probability of having a normal economy is “P2”. “R3” is the returns in a booming economy. The probability of having a booming economy is “P3”.
Hence, the expected return on Stock A is 10.65 percent.
Compute the standard deviation of Stock A:
“R1” refers to the returns during the recession. The probability of having a recession is “P1”. “R2” is the returns in a normal economy. The probability of having a normal economy is “P2”. “R3” is the returns in a booming economy. The probability of having a booming economy is “P3”. The expected return on Stock A “E(R)” is 10.65 percent.
Hence, the standard deviation of Stock A is 4.49 percent.
To determine: The standard deviation of Stock B.
Answer to Problem 7QP
The standard deviation of Stock B is 13.92 percent.
Explanation of Solution
Given information:
Stock B’s return is (17 percent) when the economy is in a recession, 12 percent when the economy is normal, and 27 percent when the economy is in a boom. The probability of having a recession is 15 percent, the probability of having a normal economy is 55 percent, and the probability of having a booming economy is 30 percent.
The formula to calculate the expected return on the stock:
The formula to calculate the standard deviation of the stock:
Compute the expected return on Stock B:
“R1” refers to the returns during the recession. The probability of having a recession is “P1”. “R2” is the returns in a normal economy. The probability of having a normal economy is “P2”. “R3” is the returns in a booming economy. The probability of having a booming economy is “P3”.
Hence, the expected return on Stock B is 12.15 percent.
Compute the standard deviation of Stock B:
“R1” refers to the returns during the recession. The probability of having a recession is “P1”. “R2” is the returns in a normal economy. The probability of having a normal economy is “P2”. “R3” is the returns in a booming economy. The probability of having a booming economy is “P3”. The expected return on Stock B “E(R)” is 12.15 percent.
Hence, the standard deviation of Stock B is 13.92 percent.
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