Question

Greta, an elderly investor, has a degree of risk aversion of A = 4 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 1-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 9% per year, with a SD of 18%. The hedge fund risk premium is estimated at 5% with a SD of 25%. 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 indeed zero, 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 4 places.)

Answer 1

	Risk premium	Standard Deviation()
S&P 500 (x)	9%	18%
Hedge Fund (y)	5%	25%
Correlation is 0

a1)

We can use the general formula to for estimating optimum weights of two portfolio (when correlation is 0) so that the portfolio variance is minimum

W_x = ²_y / ²_x + ²_y

= 0.18² / 0.18² + 0.25²

= 0.0324 / 0.0324 + 0.0625

=0.0324 / 0.0949

0.341412

W_y =  ²_x / ²_x + ²_y

= 0.25² / 0.18² + 0.25²

= 0.0625 / 0.0949

0.658588

Optimal Asset allocation

Weight of S&P 500 = 34.1412 %

Weight of Hedge fund = 65.8588%

a -2)

Expected risk premium on the portfolio

	Risk premium	Weight	Return or Risk premium(Premium * Weight)
S&P 500	9%	0.341412	0.03072708
Hedge Fund	5%	0.658588	0.0329294
		Overall Risk premium	0.06365648
		of the portfolio	or 6.3656 %