Question

(CAPM and expected returns) a Given the following holding period retums, mh compute the average rums and the standad deviations for the Zemin Coporation and for the market b. If Zemin's beta is 1.32 and the risk-free rate is 7 percent, what would be an expected returs for an investor owning Zemin? (Note Because the precedng retus are based on montly daa, you wil reod to avuaire the retums to make them comparable with the risk-fhee rate. For smplicity, ycan convert from monthly to yealy reburs by muliplying the average monthly netumes by 12) c How does Zemin's historcal average etum compare with the etum you beleve you should expect based on the capital asset pricing model and the fim's systematic nsk? a Gven the hoidng period setus shown in the table, the average monthly etun for the Zemn Corporation is (Round to two decimal places) The standard deeviation for the Zemin Corporation s%(Roud to two decmal places) Given the halding period retuns shown in the table, the average morely reum for the maket is (Round to three decimal places) The standard deviation for the market is (Round to two decimal places) b. I Zemin's beta is 1.32 and the ssk-free rate is 7 pecent, the expected netum for an ivestor ouning Zemin is% Round to hwo decimal places) The average annual historical return for Zemin is (Round to two decimal places c. How doos Zomin's hstorical average retum compare with the return you beleve you should expect based on the captal asset pricing model and the im's systematic nisk? (Select from the drop down menu)

Answer 1

a). Average monthly return = sum of returns/number of months

Return for Zemin = (7%+5%+2%-4%+4%+2%)/6 = 2.67%

Market return = (5%+3%+0%-3%+1%+4%)/6 = 1.67%

Standard deviation ={ sum of [(monthly return - average return)^2]/n} ^0.5

Standard deviation for Zemin= {1/6*[(7%-2.67%)^2 + (5%-2.67%)^2 + (2%-2.67%)^2 + (-4%-2.67%)^2 + (4%-2.67%)^2 + (2%-2.67%)^2]}^0.5 = 3.45%

Market standard deviation = {1/6*[(5%-1.67%)^2 + (3%-1.67%)^2 + (0%-1.67%)^2 + (-3%-1.67%)^2 + (1%-1.67%)^2 + (4%-1.67%)^2]}^0.5 = 2.687%

b). Annual market return = monthly return*12 = 1.67%*12 = 20.00%

Zemin expected annual return (using CAPM) = risk-free rate + beta*(market return - risk-free rate)

= 7% + 1.32*(20%-7%) = 24.16%

c). Historical average return = monthly return*12 = 2.67%*12 = 32.00%

Expected return = 24.16%

Historical return is higher than the expected return by 32% - 24.16% = 7.84%