Question

The following are estimates for two stocks. Stock Expected Return Beta firm-specific Standard Deviation A 0.14 0.68 0.28 B 0.20 1.38 0.41 The market index has a standard deviation of 0.22 and the risk-free rate is 0.05. Suppose that we were to construct a portfolio with proportions: Stock A 0.32 Stock B 0.45 The remaining proportion is invested in T-bills. Compute the standard deviation of the portfolio. Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Answer 1

We have the following information

	Stock A	Stock B	Market	T- Bill
Return	0.14	0.20		0.05
SD	0.28	0.41	0.22
Beta	0.68	1.38

Weight of Stock A = wA = 0.32

Weight of Stock B= wB = 0.45

Weight of T-Bill = 1-wA-wB = 0.23

cov(A,B) = r x SDA x SDB = Beta A x Beta B x SD(Market)^2

cov(A,B) = r x SDA x SDB = 0.68 X 1.38 X (22 X 22)

= 454.19

SD of portfolio = ( wA^2 x SDA^2 + wB^2 x SDB^2 + 2 x wA x wB x r x SDA x SDB )^0.5

= (0.32^2 x 28^2 + 0.45^2 x 41^2 + 2 x 0.32 x 0.45 x 454.19)^0.5

=(80.28 + 340.40 + 130.81)^0.5

=23.48%

= 0.2348

Therefore the SD of portfolio is 0.2348

answered by: anonymous