You are considering investing $1,800 in a complete portfolio. The complete portf

Question

You are considering investing $1,800 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 4% 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 13%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 7%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively.

Explanation / Answer

The risky portfolio using X and Y has expected return of

E(rp) = 0.60 *0.15 + 0.40 * 0.12 = 0.09 + 0.048 = 0.138 or 13.8%.

E(rc) = W * 5% + (1-W)*13.8% - 9%

=0.05W + 0.138-0.138W-0.09

0.088W = 0.048

W = 0.048/0.088 = 0.545.

So, 0.454 will be the risk portfolio or 45% of risky portfolio.

Weight of X in the complete portfolio is 0.60 * 45% = 27%.

Weight of Y in the complete portfolio is 0.40 * 45% = 18%.

Hence, answer is 45%, 27%, 18%.

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