Question

1. You have decided to invest all your wealth in two mutual funds: A and

B. Their returns and risks are as follows:

• the mean returns are r˜_A = 15% and r˜_B = 11%
• the covariance matrix is

	rA	rB
rA	.04	.025
rB	.025	.032

You want your total portfolio to yield a return of 12%. What proportions of your wealth should you invest in A and B? What is the standard deviation of the return on your portfolio?

.

Answer 1

As the return of the portfolio is the weighted average return of the component assets. Let weight invested in A be w and that in B be (1-w). Then

So Return of this portfolio = w*15%+(1-w)*11% = 12%

=> w = 1/4 = 0.25 and (1-w) = 0.75

So, 25% must be invested in A and 75% in B to get 12% return

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient beltween returns of security i and security j

So, standard deviation of portfolio returns =sqrt (0.25^2*0.04+0.75^2*0.032+2*0.25*0.75*0.025)

=sqrt(0.029875)

=0.17284386 =17.2844%