Question

The returns of three stocks are random variables (R1, R2, R3). The mean returns of three stocks are (10%, 5%, 3%). The covariance (in percentage term2 ) is given by

	stock1	stock2	stock3
stock1	8	0.6	0.01
stock2		5
stock3			1

If you have allocated 20% of your assets in stock 1, 10% in stock 2 and the rest in stock 3, what is the mean return on your asset? The standard deviation?

Answer 1

The mean returns of three stocks are 10%, 5%, 3%

Their allocation are in the ratio 20 % : 10 % : 70 % = 0.2 : 0.1 : 0.7

Thus mean return on asset = 0.2 x 10 % + 0.1 x 5 % + 0.7 x 3 % = 4.6 %

Variance of all stocks in this ratio

= Var(1) x 0.2 + Var(2) x 0.1 + Var(3) x 0.7 + 2Cov(1,2) x 0.2 x 0.1 + 2Cov(2,3) x 0.1 x 0.7 + 2Cov(3,1) x 0.7 x 0.2

= 8 x 0.2 + 5 x 0.1 + 1 x 0.7 + 2 x 0.6 x 0.2 x 0.1 + 2 x 0 x 0.1 x 0.7 + 2 x 0.01 x 0.7 x 0.2

= 2.8268

Hence standard deviation = square root of variance = 1.68 %