Problem. Suppose there is a risk free asset in the economy that gives a return o

Question

Problem. Suppose there is a risk free asset in the economy that gives a return of r = 1 percent, and that market returns are given by the following table: Market Probability Return 0.3 0.3 0.4 ear ormal Bull 2% There are two available securities, call them A and B, with the following returns under the different market conditions: SecurityBear |Normal Bull -5% | 4% | 13% -6% 3% 20% (a) Explain what alpha and beta measure in one sentence each (b) What are the expected returns of the market and each security? What are the excess returns? (c) What is the variance of the market? (d) What are the covariances of each security with the market? (e) What is the calculated beta for each security?

Explanation / Answer

Alpha is a measure of excess return of an investment by comparing and evaluting with the return of benchmark index or market index using a mathematical model.

Beta is a meaure of volatility of a stock or systematic risk that can not be eliminated by effective portfolio diversification.

B) Expected Returns of the Market and Each security

Expected Return = Probability * Expected Return

Expected Return of Market = ((0.3 (-1%)) + (0.3(2%) )+(0.4(5%)) = 0.023

Expected Return of Security A = 0.3(-5%) +0.3(4%) +0.4(13%) = 0.049

Expected Return of Security B = 0.3(-6%) +0.3(3%) +0.4(20%) = 0.071

Variance of the Market

Rm R-Rm (R-Rm)2 Proba *(R-Rm)2

-0.01 (-0.01) - (0.023) = -0.033 0.001089 0.0003267

0.02 (0.02 )  - (0.023) = -0.003   0.000009 0.0000027

0.05 ( 0.05) - ( 0.023) = 0.027 0.000729   0.0002916

Variance = (0.0003267 +0.0000027+0.0002916) = 0.000621

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