Question

You are considering investing $2,300 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 14%, and Y has an expected rate of return of 12%. To form a complete portfolio with an expected rate of return of 8%, 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. *No correlation given*

Multiple Choice

• 50%; 30%; 20%

• 43%; 26%; 17%

• 0%; 60%; 40%

• 26%; 46%; 28%

Answer 1

ANSWER: OPTION B 43%; 26%; 17%

(Answers are highlighted in grey)

Total Investment Value = $ 2300.

The portfolio consists of :

Return

Treasury bills 4%  

Risky portfolio P 13.2% (Refer Note 1)

To form a portfolio that gives a return of 8 %, we should find the weights for Treasury Bills and Portfolio P.

Let Weight of Treasury Bill be X.

So Weight of  Portfolio P = 1 - X

So,

4 * X + 13.2 (1 - X ) = 8

4X + 13.2 - 13.2X = 8

5.2 = 9.2X

X = 0.57

1 - X = 0.43

So, 43% of the amount should be invested in P

The proportion of X and Y out of the portfolio as a whole.

	X	Y
Optimal Weights (1)	0.60	0.40
Total Weight of P (2)	0.43	0.43
(1) * (2)	0.26	0.17

Note 1: portfolio P is constructed with two risky securities, X and Y.

	X	Y
Optimal Weights (1)	0.60	0.40
Expected Return (2)	0.14	0.12
(1) * (2)	0.084	0.048	0.132