Question

You have $82762 to invest in two stocks and the risk-free security. Stock A has an expected return of 11.42 percent and Stock B has an expected return of 9.84 percent. You want to own $33805 of Stock B. The risk-free rate is 4.46 percent and the expected return on the market is 12.13 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the risk-free security? Answer to two decimals. (Hint: A negative answer is OK - it means you borrowed (rather than lent or invested) at the risk free rate.)

Answer 1

Solution: -

Weight of stock B in portfolio = 33805/82762 = 0.4085

We want return = 12.13%

Therefore share in our return of B = 12.13*0.4085 = 4.955%

Now the return from stock A amd risk free security

= 12.13 - 4.955 = 7.175%

Let the share of risk free be x therefore share of A be (1-x)

Now(1- x)*11.42% + x*4.46% = 7.175%

= 11.42% - 0.1142x + 0.0446x = 7.175%

= 4.245% = 0.0696x

Therefore x = 60.99%

Now it means invest in risk free = (82762 - 33805) *60.99%

= $48957*60.99% = 29859 approx