Question

You invest 50% in a risky portfolio, and 50% in a treasury bill. The risky portfolio has an expected return of 15% and a standard deviation of 25%. The treasury bill pays 7%. Suppose that your risky portfolio includes the following investments in the given proportions: Stock A 30% Stock B 30% Stock C 30% Stock D 10%.

a.) What are the investment proportions in the complete portfolio, including stock A, B, C, D and the Treasury bill?

b.) What is the expected return and standard deviation of your complete portfolio?

Answer 1

a) Investment Proportion of complete portfolio

Let us assume $ 1000 invested in risky portfolio and treasury bill

Portfolio	Stock	Calculation	Investment	% of total portfolio
Treasury bill	Treasury bill	1000 * 50%	500	500 / 1000 = 50%
Risk portfolio	A	[1000 * 50%] * 30% [ Investment In Risky Portfolio ] * % of investment in stock	150	150 / 1000 = 15%
Risk portfolio	B	[1000 * 50%] * 30%	150	150 / 1000 = 15%
Risk portfolio	C	[1000 * 50%] * 30%	150	50 / 1000 = 15%
Risk portfolio	D	[1000 * 50%] * 10%	50	50 / 1000 = 5%
			1000	100 %

b) Calculation

1) Expected Return of the complete portfolio

> Formula = Weight of Risky portfolio * return of risky portfolio + Weight of treasury bill * return of treasury bill

> Calculation

Expected Return = 0.50 * 15% + 0.50 * 7%

                            = 11 % Answer

2) Standard Deviation

Since treasury bill is risk free asset and all the risk derives from risk free portfolio.

Thus

SD = SD of Risky portfolio * Weight of risky portfolio

       = 25% * 0.50

       = 12.50% Answer

Hope you understand the solution.

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