Math Problem Statement
Greta has risk aversion of A = 3 when applied to return on wealth over a 1-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 12% with a standard deviation of 35%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Required: a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation?
Solution
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Math Problem Analysis
Mathematical Concepts
Portfolio Theory
Expected Return
Portfolio Variance
Utility Maximization
Formulas
Portfolio Expected Return: E[R_p] = w_SP * E[R_SP] + w_HF * E[R_HF]
Portfolio Variance: σ_p^2 = w_SP^2 * σ_SP^2 + w_HF^2 * σ_HF^2 + 2 * w_SP * w_HF * σ_SP * σ_HF * Corr(SP, HF)
Utility Function: U = E[R_p] - (A/2) * σ_p^2
Theorems
Modern Portfolio Theory
Mean-Variance Optimization
Suitable Grade Level
Undergraduate - Finance/Economics
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