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[Discussion] - 8 - Security Expected Return Standard Dev...

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Warm-up problems. Set A: {10%,20%,30%} Set B: {20%,30%,40%, } I am assuming that you familiar with basic statistical calculations 1. Calculate the mean of set A 2. Calculate the variance of set A 3. Calculate the standard deviation of set A and set B 4. Calculate the covariance of set A and set B 5. Calculate the correlation of set A and set B Diversification Problems/CAPM Formula for Beta Covariance (Market Return, Individual Stock Return) / Variance (Market Return) Capital Asset Pricing Model Individual Return = Risk Free Return + Beta * (Market Return – Risk Free Return ) Chapter 11, Problem 24: Fill in the blank. We want our portfolio to have a beta that perfectly follows the market. Asset Investment [$100 total] Beta A 20 .80 B 30 1.30 C 1.5 Risk-Free 1 = 0.8*20/100 + 1.30 * 30/100 + (X/100) * 1.5 . Solve for X to get the investment. 100 – 20 – 30 – X = Investment in risk free asset, which has a beta of 0. Chapter 11, problem 30: Fill in the blanks
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Unformatted text preview: Security Expected Return Standard Dev Correlation with market Beta A .1 .27 .85 B .14 .50 1.5 C .17 .7 .35 Market Portfolio .12 .2 Risk-Free .05 [A] The correlation of the market portfolio with itself is 1,the beat of a market portfolio is 1. [B] The risk free return has a standard deviation of 0, the correlation is 0, the beta is 0. [C] You can solve for the rest of the terms (correlation of A, standard deviation of B, beta of C): Beta = Variance(Return of Market, Return of Individual Stock) / (standard dev of market)^2 Correlation with Market = Variance(Return of Market, Return of individual stock)/[ (standard deviation of market) * (standard deviation of individual stock)] Chapter 11, Problem 30: Does security A’s expected return match up with the CAPM? Use the CAPM formula. Risk free return rate = 0.05, Market Return = 0. 12, Beta = 0.85. The two won't match....
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