Question

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 returnsof 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.)

Answer 1

a) Average return = sum of holding period returns/number of months
For Zemin = ( 6 +3 + 1 – 3 + 5 + 0)/6 = 2%
For the market = (4 + 2 – 1 – 2 + 2 + 2)/6 = 1.17%
Standard deviation = {(return in month t – average return)2 + {return on month n – average return)2}1/2
No. of months -1 no. of months -1
For Zemin = {(6-2)/5) 2 + (3 – 2)/5) 2 + (1-2)/5)2 + (-3-2)/5)2 + (5-2)/5)2 }1/2
= {0.64 + 0.04 + 0.04 + 1 + 0.36}1/2
= {2.08]1/2
= 1.44
For the market = {(4-1.17)/5) 2 + (2-1.17)/5)2 + (-1-1.17)/5)2 + (-2-1.17)/5)2 + (2-1.17)/5)2 + (2-1.17)/5)2}1/2
= {0.32 + 0.028 + 0.188 + 10.05 + 0.028 + 0.028}1/2
= {1.642}1/2
= 1.28


B) K j = k r f + ß j (k m – k r f) where
K j = the required rate of return.
K r f = the risk free rate.
? j = beta
K m = expected return for the market.
Monthly market rate = 1.17%
Annual market rate = 1.17 × 12 = 14.04%
K j = 8 + 1.54 (14.04 – 8)
= 17.3%