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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.

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= &#931;= 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= &#931;= 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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