# Expected rate of return and standard deviation of return

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.

This question has the following supporting file(s):

• problemset.xls
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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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Pushkal Kumar Pandey, MBA

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Active since 2003

BTech, IIT Delhi
MTech, IIT Delhi
MBA, IIM Bangalore

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Extracted Content from Question Files:

• problemset.xls

PROBLEM SET #1

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, K x hat, equals 12%).
I calculated 16% for stock X (the instructor said I should have 12%) where did I go wrong?
16%

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% = Standdev of X
4% =standdev of Y

CV is STDV/Expected Return, but because both of my calculations are wrong, I know I won't get the right answer.

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?
How do I set this one up?

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
to be 20 percent per year". Explain what is wrong with this calculation.

Not sure2
X Y

Mean 14.38 Mean 17.93
Standard Error 6.92 Standard Error 8.49
Median 12.00 Median 20.00
Mode #N/A Mode #N/A
Standard Deviation 15.48 Standard Deviation 18.99
Sample Variance 239.52 Sample Variance 360.67
Kurtosis 0.27 Kurtosis (0.75)
Skewness 0.95 Skewness 0.51
Range 38.10 Range 45.35
Minimum (0.10) Minimum (0.35)
Maximum 38.00 Maximum 45.00
Sum 71.90 Sum 89.65
Count 5.00 Count 5.00

Now Calculate the
less risky than