Expected rate of return and standard deviation of return
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1. Stocks X and Y have the following probability distributions of expected future returns:
PROBABILITY X Y Rate of return Y Rate of return X
10% -10% -35% -4% -1%
20% 20% 0% 0% 4%
40% 12% 20% 8% 5%
20% 20% 25% 5% 4%
10% 38% 45% 5% 4%
a. Calculate the expected rate of return, khat, for Stock Y (expected return for Stock X, Kx hat, equals 12%).
b. Calculate the standard deviation of expected returns for Stock X. (that for Stock Y is 20.35%). Now Calculate the
coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than
Stock X? Explain.
2. Shalit Corporation's 2002 sales were $12 million. Sales were $6 million 5 years earlier (in 1997).
a. To the nearest percentage point, at what rate have sales been growing?
b. Suppose someone calculated the sales growth for Shalit Corporation in part a as follows:
"Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so dividing 100 percent by 5, we find the growth rate
to be 20 percent per year". Explain what is wrong with this calculation.
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Solution Summary
The solutions shows steps to calculate the expected rate of return and standard deviation of expected returns of stocks when the probability distribution of expected return are given.
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1. Stocks X and Y have the following probability distributions of expected future returns:
PROBABILITY X Y Rate of return Y Rate of return X
10% -10% -35% -4% -1%
20% 20% 0% 0% 4%
40% 12% 20% 8% 5%
20% 20% 25% 5% 4%
10% 38% 45% 5% 4%
14% 16%
a. Calculate the expected rate of return, khat, for Stock Y (expected return for Stock X, Kx hat, equals 12%).
I calculated 16% for stock X (the instructor said I should have 12%) where did I go wrong?
16%
Your answer is correct for X ( to be more accurate it is 15.6%)
PROBABILITY Y Probability * Y
10% -35% -3.50%
20% 0% 0.00%
40% 20% 8.00%
20% 25% 5.00%
10% 45% 4.50%
Expected return=Average= Σ= 14.00%
PROBABILITY X Probability * X
10% -10% -1.00%
20% 20% 4.00%
40% 12% 4.80%
20% 20% 4.00%
10% 38% 3.80%
Expected return=Average= Σ= 15.60%
b. Calculate the standard deviation of expected returns for Stock X. (that for Stock Y is 20.35%). Now Calculate the ...
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