CAPM Given the following holding-period returns, , compute the average returns a

Question

CAPM Given the following holding-period returns, , compute the average returns and the standard deviations for the Sugka Corporation and for the market. If Sugita's beta is 1.39 and the risk free rate is 6 percent, what would be an expected return for an investor owning Sugita? (Note-Because the preceding returns are based on monthly data, you will need to annualize the returns to make them comparable with the risk free rate For simplicity, you can convert from monthly to yearly returns by multiplying the average ninthly returns by 12.) How does Sugita's historical average return compare with the return you should expect based on the Capital Asset Pricing Model and the firm's systematic risk? Given the holding period returns shown in the table the average monthly return for the Sugita Corporation is % (Round to two decanal places.)

Explanation / Answer

a. Computation of Average returns & Standard deviation Month Sugita Corp.% % - Av. (Diff)^2 Market% % - Av. (Diff)^2 1 2.4 -0.2 0.04 1.2 -1.17 1.3689 2 -0.8 -3.4 11.56 3 0.63 0.3969 3 -1 -3.6 12.96 2 -0.37 0.1369 4 1 -1.6 2.56 1 -1.37 1.8769 5 7 4.4 19.36 5 2.63 6.9169 6 7 4.4 19.36 2 -0.37 0.1369 Total 15.6 Variance= 65.84 14.2 Variance= 10.8334 Average Return 2.6 2.37 2.60% Standard deviation=Sq.rt.of Variance = 8.11 3.29 ie. 8.11% ie. 3.29% b. Expected return would be Risk-free rate+ Beta(Market return-risk-free rate) Here, risk-free rate=6% ie. 0.06                    beta=1.39 Market return = 2.37/month ie. 2.37*12= 28.44 ie. 0.2844 So, Expected return =0.06+1.39(0.2844-0.06) ie. 0.371916 ie. 37.19% c. Historical average 2.60% Av.Return to be expected 37.19/12= 3.10 As the av.return to be expected is more than the historical average the asset is likely to earn more reurns & also more risky as the greater standard deviation suggests.

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