Risk Measurement Summary

Problem 6-10a
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 Mean = 6 + 3 + -1 + -3 + 5 + 0 = 10/6 = 1.6
Market Mean = 4 +2 +1 + -2 + 2 + 2 = 9/6 = 1.5
Zemin Corp Standard Deviation 6 -1.6 ^ = 19.36 3 -1.6 ^ = 1.96
-1 -1.6 ^ = 5.2
-3 – 1.6 ^ =9.2 5 -1.6 ^ = 11.56
47.28/5 = √9.45=3.56
Market Deviation
4 - 1.5 ^ = 6.25
2 – 1.5 ^= 0.25
1 – 1.5 ^ = 0.55
-2 – 1.5 ^ = 7
2 -1.5 ^ = 0.25
14.3/5 = √2.86= 1.97
Problem 6-10b 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.)

Zemin’s Annualized return:= (Zemin Corp deviation * 12)= 42.72%

Market’s Annualized Return: = (market deviation * 12) = 23.64%

Expected return = Risk Free Rate + Beta (Market Rate – Risk Free Rate)
Where Market Rate= Market Annual Return

Appropriate Required Return = 8+1.54(23.64 - 8) = 32.09%

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?

When comparing historic average return of Zemin with the fair return of the firm, CAPM can be instrumental