An investor is considering investing in a small-cap stock fund and a general bon

Question

An investor is considering investing in a small-cap stock fund and a general bond fund.    The correlation between the returns of the two funds is 0.10. The returns and standard deviations are given in the following table.

Expected Annual Return

Standard Deviation of Returns

Emerging Markets stock fund

28%

40%

Global Equities Fund

16%

21%

If the investor requires a portfolio return of 23 percent, what should the percentage invested in each fund be? Show your calculations.

What is the standard deviation of a portfolio constructed according to the weights computed in part A? Show your calculations.

Expected Annual Return

Standard Deviation of Returns

Emerging Markets stock fund

28%

40%

Global Equities Fund

16%

21%

Explanation / Answer

Part - A

Set us assume W is the weight in emerging market stcok fund and 1-W is weight in Global Equities fund since the total weight should be 1.

Hence 0.28*W + 0.16*(W-1) = 0.23,

Solving we get W = w1 = weight in emrging markets fund = 0.5833 or 58.33% and

1-W = w2 = weight in global market fund = 0.4167 or 41.67%

Part -2

Portfolio Std. deviation is sqrt( w1^2 * sd1^2 + w2^2*sd2^2 + 2*w1*w2*corr(1,2)*sd1*sd2)

= sqrt (0.5833^2*0.4^2 + 0.41677^2*0.21^2 + 2*0.4*0.21*0.1*0.5833*0.4167)

= 0.2573

Hence portfolio Std. Dev is 0.2573 or 25.73%

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