You are considering investing $1,700 in a complete portfolio. The complete portf

Question

You are considering investing $1,700 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 75% and 25% 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

Portfolio returns are the weighted average returns of individual securities.

Therefore reurns from portfolio P

= 75% in X and 25% in Y

= 13 * 75% + 10 * 25%

= 12.25%

Returns from risk free securities = 4%

Let required investment in risk free securites be X, investment in risky securities is 1-X

Required returns = 7%

=> X *4% + (1-X) * 12.25 = 7

4X + 12.25 -12.25X = 7

8.25X = 5.25

X = 63.64%

Investment in risk free securities = 1700 * 63.64% = $ 1,082

Investment in risky Securities = 1700 - 1082 = $ 618

Investment in X = 618 * 75% = $ 464

Investment in Y = 618 * 25% = $ 154

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