Question

You have $87,569 to invest in two stocks and the risk-free security. Stock A has an expected return of 12.38 percent and Stock B has an expected return of 9.36 percent. You want to own $28,905 of Stock B. The risk-free rate is 5.06 percent and the expected return on the market is 12.04 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

Hi

lets assume investment in Stock A=X %

investment in stock B - 28905/87569 = 33.01%

so investment in risk free asset = 100%-33.01%-X% = 66.99%-X%

So total expected return = 0.0X*12.38 + 0.3301*9.36 + (0.6699-0.0X)*5.06

12.04 = 0.1238X + 3.09 + 3.39 -0.0506X

5.56 = 0.0732X

X = 75.97%

Hence investment in Stock A = 75.97%

investment in Stock B = 33.01%

investment in risk free security = 100% - 75.97%-33.01% = -8.98%

Hence you should borrow 8.98%* 87569 = $7,859.40 at risk free rate.

Thanks