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# Measuring risk and rates of return

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6-10. (Measuring risk and rates of return):
a. Given the holding-period returns shown here, compute the average returns and the standard deviations for the Zemin Corporation and for the market.
MONTH ZEMIN CORP. MARKET
1 6% 4%
2 3 2
3 -1 1
4 -3 -2
5 5 2
6 0 2

b. If Zemin's beta is 1.54 and the risk-free rate is 8 percent, what would be an appropriate required return for an investor owning Zemin? (Note: Because the returns of Zemin Corporation are based on monthly data, you will need to annualize the returns to make them compatible with the risk-free rate. For simplicity, you can convert from monthly to yearly returns by multiplying the average monthly returns by 12.)

c. How does Zemin's historical average return compare with the return you believe to be a fair return, given the firm's systematic risk?

#### Solution Preview

6-10. (Measuring risk and rates of return)

a. Given the holding-period returns shown here, compute the average returns and the standard deviations for the Zemin Corporation and for the market.

MONTH ZEMIN CORP. MARKET
1 6% 4%
2 3% 2%
3 -1% 1%
4 -3% -2%
5 5% 2%
6 0% 2%

Zemin Corp
Month X= X 2 =
1 6% 0.0036
2 3% 0.0009
3 -1% 0.0001
4 -3% 0.0009
5 5% 0.0025
6 0% 0
Total= 10.00% 0.0080
n=no of observations= 6
Average return= 1.67% =10.%/6

variance={&#931;X 2 - n(Mean) 2 }/(n-1)= 0.001265 =(0.008-6*0.0167^2)/(6-1)
standard deviation of return (SD)=&#8730;Variance= 3.56% =&#8730;0.001265

These are monthly returns and standard ...

#### Solution Summary

Compute the average returns and the standard deviations for the Zemin Corporation and for the market. Calculates appropriate required return for an investor owning Zemin using Capital Asset Pricing Model (CAPM).

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