# 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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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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