Question

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 6.6% per year, with a SD of 21.6%. The hedge fund risk premium is estimated at 11.6% with a SD of 36.6%. 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 returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

S&P
Hedge

a-2. What is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 2 places.)

Expected risk premium_________%

Answer 1

a-1

Here,

E[R1] = Risk Premium of S&P 500 = 6.60%

E[R2] = Risk Premium of Hedge Fund = 11.60%

σ[r1] = Std. Dev of returns of S&P 500 = 21.60%

σ[r2] = Std. Dev of returns of Hedge Fund = 36.60%

σ[r1, r2] = Covariance of returns of S&P 500 & Hedge Fund = ρ*σ[r1]*σ[r2] = 0.3*21.60%*36.60% = 0.024

w1 = 0.6129 = 61.29%

w2 = 1-w1 = 0.3871 = 38.71%

a-2 The calculation of the expected premium risk of the portfolio E[R(P)] is as follows:

E[R(P)] = w1*E[R1] + w2*E[R2] = 0.6129*6.60% + 0.3871*11.60% = 8.54%