Question

You are considering investing $10,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 2% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 50% and 50%, respectively. X has an expected rate of return of 20%, and Y has an expected rate of return of 30%. The dollar values of your positions in X,Y, and Treasury bills would be ___,___ and ___, respectively, if you decide to hold a complete portfolio that has an expected return of 10%.

Answer 1

To hold a complete portfolio with an expected return of 10%, the dollar values of X, Y, and Treasury bills would be $5,000, $5,000, and $0 respectively.

Step-by-step explanation:

To determine the dollar values of your positions in X, Y, and Treasury bills, we can use the concept of the complete portfolio. Given that the optimal weights of X and Y in portfolio P are 50% each, and their expected returns are 20% and 30% respectively, we can calculate the dollar values as follows:

X = $10,000 * 0.5 = $5,000

Y = $10,000 * 0.5 = $5,000

Since Treasury bills have a risk-free rate of 2%, we can use the formula for the expected return of the complete portfolio to find the dollar value for Treasury bills:

Treasury Bills = ($10,000 - $5,000 - $5,000) / 0.02 = $0