Question

You have a portfolio with a standard deviation of 26% and an expected return of 18%.

You are considering adding one of the two stocks in the following table. If after adding the stock you will have 20% of your money in the new stock and 80% of your money in your existing? portfolio, which one should you? add?

	expected return	standard deviation	correlation with your portfolios return
stock a	13%	24%	0.4
stock b	13%	17%	0.6

Standard deviation of the portfolio with stock A is __%?

Standard deviation of the portfolio with stock B is __%?

which stock would you add to your portfolio?

Answer 1

Standard deviation of portfolio =

let x be current portfolio, y be the new portfolio a or b

a. Std dev with stock A = (0.8^2 *.26^2 + 0.2^2*0.24^2 + 2*0.8*0.2*0.4*0.24*.26)^0.5

= (0.05356)^0.5 = 23.14%

Expected return = = (0.8*18% + 0.2*13%) = 17%

b. Std dev with portfolio B =(0.8^2 *0.26^2 + 0.2^2*0.17^2 + 2*0.8*0.2*0.6*0.17*.26)^0.5

=(0.05291)^0.5 = 23%

Expected return = (0.8*18% + 0.2*13%) = 17%

Since the expected returns are same, and standard deviation of portfolio is lower with Stock B

Ans = Stock B