Assume that the economy can experience high growth, normal growth, or recession.
ID: 1227359 • Letter: A
Question
Assume that the economy can experience high growth, normal growth, or recession. Under these conditions, you expect the following stock market returns for the coming year: State of the Economy Probability Return High Growth 0.2 60% Normal Growth 0.7 18% Recession 0.1 2% a. Compute the expected value of a $1,000 investment over the coming year. If you invest $1,000 today, how much money do you expect to have next year? What is the percentage expected rate of return? Instructions: Enter dollar values rounded to the nearest whole dollar and percentages rounded to the nearest tenth (1 decimal place). The expected value is $ 1248 and the expected rate of return is 24.8 %. b. Compute the standard deviation of the percentage return over the coming year. Standard deviation = %. c. If the risk-free return is 7 percent, what is the risk premium for a stock market investment? Risk premium = 17.8 %.
Explanation / Answer
The expected value of $ 1000 invested = 0.2 X0.6 X $ 1000 + 0.7 X 0.18 X $ 1000 + 0.1 X 0.02 X $ 1000
The expected value of $ 1000 invested = $ 248
The money expected is $ 1248
Percentage expected rate of return = (248 X 100) / 1000
Percentage expected rate of return = 24.80 %
Average return =( 0.2 X 0.6 + 0.7 X 0.18 + 0.1 X 0.02) / 3
Average return = 8.26 %
Variance =[ (0.6 - 0.0826)2 + ( 0.18 - 0.0826)2 + ( 0.02 - 0.0826)2 ] / 3
Variance = (0.267 + 0.009486 + 0.003918 ) / 3
Variance = 0.09346
SD = 30.57 %
Security's risk premium = Security expected return - risk free return
Security's risk premium = 24.80- 7
Security's risk premium = 17.80 %
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