Question

You wish to invest in two hedge funds: Eldorado and Shangrila. The expected return on the Eldorado hedge fund is 12% and the standard deviation of this return is 16%. The expected return on the Shangrila hedge fund is 20% and its standard deviation is 25%. The covariance between returns on the Eldorado fund and Shangrila fund is 80(%)^2. What percentage of your wealth should you invest in each of these two funds to earn 18% expected return on your portfolio? What is the standard deviation of the portfolio in part (a) above? If the beta of Eldorado is 2.5 and the beta of Shangrila is 3.4, what is the beta of your portfolio in (a)?

Answer 1

a).

Expected Return of a 2 stock portfolio is a weighted average of individual returns. It is calculated as (w1*r1)+((1-w1)*r2)

So, 18%= (w1*12%)+((1-w1)*20%

0.18= 0.2-0.08w1

w1= 0.02/0.08

w1= 25% and 1-w1= 75%

So, To get an expected return of 18%, we should invest 25% in Eldorado hedge fund and 75% in Shangrila hedge fund.

Standard deviation of a 2 stock portfolio is calculated as sqrt((w1^2*sd1^2)+(w2^2*sd2^2)+(2*w1*w2*C12)); where w is weight of the stock, sd is standard deviation of the stock and C12 is the Covariance between stock 1 and stock 2.

So, Standard deviation= sqrt((0.25^2*0.16^2)+(0.75^2*0.25^2)+(2*0.25*0.75*0.008))

sqrt(0.03976)

= 19.94%

Beta of a 2 stock portfolio is a weighted average of individual stocks in the portfolio.

So, Beta of Portfolio= (0.25*2.5)+(0.75*3.4)

= 3.175