You have $89048 to invest in two stocks and the risk-free security. Stock A has an expected return of 12.08 percent and Stock B has an expected return of 9.44 percent. You want to own $30284 of Stock B. The risk-free rate is 3.88 percent and the expected return on the market is 11.67 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.)
Total Investment = $89,048
Investment in Stock B = $30,284
Weight of Stock B = Investment in Stock B / Total
Investment
Weight of Stock B = $30,284 / $89,048
Weight of Stock B = 0.3401
Let weight of risk-free security be x
Weight of Stock A = 1 - Weight of Stock B - Weight of Risk-free
Security
Weight of Stock A = 1 - 0.3401 - x
Weight of Stock A = 0.6599 - x
Expected Return of Portfolio = Weight of Stock A * Expected
Return of Stock A + Weight of Stock B * Expected Return of Stock B
+ Weight of Risk-free Security * Expected Return of Risk-free
Security
0.1167 = (0.6599 - x) * 0.1208 + 0.3401 * 0.0944 + x * 0.0388
0.1167 = 0.0797 - x * 0.1208 + 0.0321 + x * 0.0388
x * 0.0820 = -0.0049
x = -0.0598
Weight of Risk-free Security = -0.0598
Investment in Risk-free Security = -0.0598 * $89,048
Investment in Risk-free Security = -$5,325.07
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