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 5.2% per year, with a SD of 20.2%. The hedge fund risk premium is estimated at 10.2% with a SD of 35.2%. 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. What should be Greta’s capital allocation, assuming a correlation of 0? (Please use this fomula:           E(rc) = rf + σc ([E(rp)-rf])/σ)

B. How would this change, qualitatively, if the correlation were positive?

Answer 1

a. As seen from the table below, Risk adjusted return is highest when the portfolio is comprised of S&P 500 only.

b. If the correlation were positive, we could choose an optimal allocation of the portfolio based on Capital Market line formation.

				Assume
		Risk premium	Std Dev	Risk free return	Expected Return
	S&P 5oo	5.20%	20.20%	5%	10.20%
	Hedge fund	10.20%	35.20%	5%	15.20%
		Correlation Coefficient		0
			Portfolio std dev	Portfolio expected return	Risk adjusted Return
S&P 500	w1	0.1	34%	14.70%	0.44
Hedge Fund	w2 = 1-w1	0.2	32%	14.20%	0.44
		0.3	31%	13.70%	0.45
		0.4	29%	13.20%	0.45
		0.5	28%	12.70%	0.46
		0.6	26%	12.20%	0.47
		0.7	25%	11.70%	0.47
		0.8	23%	11.20%	0.48
		0.9	22%	10.70%	0.49
		1	20%	10.20%	0.50