Question

You have $1M to invest. You want to maximize returns subject to a portfolio standard deviation of 11%. Assume the S&P500 index is the market portfolio (m), and that it has an expected return of 9% and a standard deviation of 15%. The risk free rate is 3%.

(a) Consider investing in a combination of m and rf. Given your willingness to accept a standard deviation of 11%, what is the expected return on your portfolio?

You are now contemplating a different portfolio. You have done some research and discovered an exciting investment opportunity – a hedge fund X which exploits new and non-standard data to gain an investment edge. Fund X has a beta of 0.4, standard deviation of 27%, and you expect that it will generate an alpha of 2.6%.

(b) Given your estimates of alpha and beta, what is the expected return on fund X?

Answer 1

	Market Portfolio=Asset 1,Risk Free Investment=Asset 2
	Return of asset1=R1=9%
	Return of asset2=R2=3%
	Standard deviation of asset 1=S1=15%
	Standard deviation of asset 2=S2=0%
	Covariance(1,2)=Corr(1,2)*S1*S2=0	67.32
	w1=Investment in asset 1
	w2=Investment in asset 2
	Portfolio Return
	w1*R1+w2*R2=w1*9+w2*3			……..Equation (1)
	Vp=Portfolio Variance=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)
	Portfolio Variance=(w1^2)*(15^2)+(w2^2)*(0^2)+2*w1*w2*0
	Vp=Portfolio Variance=(w1^2)*225……………Equation (2)
	Portfolio Standard Deviation=Square root of Variance
	If Portfolio standard deviation is 11%
	Expected Portfolio Return	7.40%
	Weight of Market Portfolio=	73.40%
b	Beta of Fund X	0.4
	Alpha of Fund X	2.60%
	Expected return of fund X=
	Risk Free Rate+Beta*(9-Risk free rate)+Alpha
	Expected Return of Fund x	8.00%	(3+0.4*(9-3)+2.6