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Consider an economy with 3 uncorrelated risky assets and a riskless asset. The CAPM is assumed to hold. The economy is populated by three
Consider an economy with 3 uncorrelated risky assets and a riskless asset. The CAPM is assumed to hold. The economy is populated by three mean-variance investors, A, B, and C, with risk aversion coefficient given by YA 1.0, B = 2.0, and c = 4.0. We obtained data on the portfolio holdings of the three investors, but we have some missing values, as shown in the table below: Investor A Asset 1 40% Asset 2 Asset 3 Investor B 30% Investor C 20% a) Solve for the portfolio of all investors, including the exposure to the risk-free asset. What is the leverage of investor A? b) Suppose the beta of company 1 is B = 0.80 and all companies have the same volatility. Compute the beta of the companies 2 and 3. c) Suppose the market return is 5% and the risk-free rate is zero. Given the market betas computed in (b), solve for the expected return on all companies. d) Given the expected returns computed in (c), solve for the variance of returns. e) Suppose the wealth-weighted aggregate risk aversion is equal to 2.0. Using the asset-pricing theory discussed in class, solve for the market variance. Discuss how the market variance can be lower than the variance of each individual firm.
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