Question

You have $84,174 to invest in two stocks and the risk-free security. Stock A has an expected return of 13.34 percent and Stock B has an expected return of 9.55 percent. You want to own $26,193 of Stock B. The risk-free rate is 4.84 percent and the expected return on the market is 11.97 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

Amount available to invest = $84174

investment in stock B = $26193

=> Weight of stock B in portfolio Wb = investment in B/total investment = 26193/84174 = 0.3112

Expected return on stock A Ra = 13.34%

Expected return on stock B Rb = 9.55%

Risk free rate Rf = 4.81%

expected return on market Rm = 11.97%

Since portfolio's return = market return

=> Portfolio return E(r) = 11.97%

Let weight of risk free asset be W

=> Weight of stock A = 1 - W - 0.3112 = 0.6888 - W

So, expected return on a portfolio is weighted return on its asset

=> E(r) = Wa*Ra + Wb*Rb + Wf*Rf

=> 11.97 = (0.6888-W)*13.34 + 0.3112*9.55 + W*4.84

=> 11.97 = 9.19 - 13.34W + 2.97 + 4.84W

=> W = (12.16 - 11.97)/(13.34-4.84) = 0.0224

So, weight of risk free asset = 0.0224

=> Investment in risk free-security = W*total investment = 0.0224*84174 = $1887.87