Question

Greta has 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 9% per year, with a standard deviation of 23%. The hedge fund risk premium is estimated at 11% with a standard deviation of 38%. 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.

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.)

a-2. What is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answers as a decimal rounded to 4 places.)

Answer 1

a-1

Assuming weight is equally distributed.

Optimal asset allocation () =

here,

= Variance of S&P 500

= Variance of hedge fund

= Weight of S&P 500

= Weight of hedge fund

Corr_ab = Correlation between S&P 500 and hedge fund

Optimal asset allocation () = (23)²*0.50² + (38)²*0.50² + 2*23*0.50*38*0.50*0.30

= 529*0.25 + 1444*0.25 + 131.10

= 132.25 + 361 + 131.10

= 624.35

hence,  Optimal asset allocation () is 624.35

Standard deviation of portfolio () =

= 24.9870

a-2

E(r)_p =

here,

R_i = return on individual stock

W_i = Weight of individual stock

E(r)_p = 9*0.50 +11*0.50

= 4.50 + 5.50

= 10%

Hence, expected return on portfolio is 10%.