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# Expected Rate of Return and Stock variance and Standard Deviation

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1) Given the following data, What is the weight of security 1? Of security 2? 3? What is the expected return on the portfolio?

Security 1 ; \$5,000 invested; Expected return 7%
Security 2; \$7,000 invested; Expected return 9%
Security 3; \$9,000 invested; Expected return 12%

2) The expected possible outcomes for Roxy Stock are below; what is the expected standard deviation of Roxy Stock?

State Probability Return
Super Boom 10% 35%
Boom 15% 20%
Expansion 45% 15%
Recession 30% -5%

#### Solution Summary

The weight of three securities are calculated. After completing the calculation, the expected return of the portfolio is calculated. This solution also includes a calculation for variance of a stock based on the four different returns and the probability of the return. After completing the variance calculation, the standard deviation of the stock is calculated.

\$2.19

## Calculate the expected rate of return and standard deviation of expected returns of stocks when the probability distribution of expected return are given.

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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