Question

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40%, respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. If you decide to hold 25% of your complete portfolio in the risky portfolio and 75% in the Treasury bills, then the dollar values of your positions in X and Y, respectively, would be __________ and _________.

Answer 1

For X $150

For Y $100

Step-by-step explanation:

The computation of optimal weight of X and Y in risky portfolio is shown below:-

Risk portfolio = Complete portfolio × Weight of risky portfolio

= $1,000 × 25%

= $250

So, Optimal weight of X and Y in risky portfolio will be

For X in dollars = Risk portfolio × Optimal weight percentage of X

= $250 × 60%

= $150

For Y in dollars = Risk portfolio × Optimal weight percentage of Y

= $250 × 40%

= $100

Therefore for computing the Optimal weight of X and Y in risky portfolio we simply multiply the risk portfolio with optimal percentage of X and in the similar way of Y.