Question

You have recently decided to invest your money in a bond fund. This fund has an expected return of 8%, and a standard deviation of 11%.

You have been considering investing in a fund that tracks the Russell 2000 index, which has an expected return of 15%, and a standard deviation of 17%.

The current T-Bill rate is 3%

You feel that the bond fund does not provide you with enough return, and you are uncomfortable with the risk of the Russell 2000 fund. Is there some combination of the Russell 2000 fund and T-Bills that you can use to increase your return, but keep your risk the same (as the bond fund)? If so describe the investment strategy.

Answer 1

Portfolio of the Investment = Combination of Russell 2000 fund & T-Bills

Risk of the portfolio or Standard deviation (SD) of portfolio = Standard deviation (SD) of bond fund i.e 11%

Formula to determine propostion of investment in Russell fund & T-Bills is

SD of portfolio^2 = (weight of Russell 2000 fund {consider it as"x"} ^2)*(SD of Russell 2000 fund^2)+(weight of T-Bills {consider it as"y"} ^2)*(SD of T-Bills^2)

(0.11)^2 = (x^2)*(0.17^2) + (y^2)*(0^2)

0.0121 = (x^2)*0.0289 ; x^2 = 0.0121/0.0289 ; x^2 = 0.4187 ; x = 64.7% whereas y =1-x = 100%-64.7% = 35.3%

To earn high return with same risk then invest 64.7% of investment in Russell 2000 fund balance in T-Bills, which is described below;

Security	Return	SD	Weight	Portfolio return	Portfolio SD
Russell 2000 fund	15%	17%	64.70%	9.71%	11.00%
T-Bills	3%	0%	35.30%	1.06%	0.00%
	100%	10.76%	11.00%