Question

You have a portfolio with a standard deviation of24%and an expected return of16%. You are considering adding one of the two stocks in the following table. If after adding the stock you will have25%of your money in the new stock and75%of your money in your existing portfolio, which one should you add? Standard deviation of the portfolio with stockAis \%. (Round to two decimal places.) Standard deviation of the portfolio with stock B is \%. (Round to two decimal places.)

Answer 1

The formula to calculate the portfolio standard deviation when adding a new stock is:

σp = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρ12σ1σ2)

where σp is the new portfolio standard deviation, w1 and w2 are the weights of the existing portfolio and the new stock, σ1 and σ2 are the standard deviations of the existing portfolio and the new stock, and ρ12 is the correlation coefficient between the two.

We are given:

Existing portfolio: σ1 = 24%, E(r1) = 16%, w1 = 0.75

Stock A: σ2 = 30%, E(r2) = 14%, w2 = 0.25

Stock B: σ2 = 18%, E(r2) = 20%, w2 = 0.25

For stock A:

σp = √(0.75^2×0.24^2 + 0.25^2×0.3^2 + 2×0.75×0.25×(-0.5)×0.24×0.3) = 26.2%

The correlation coefficient ρ12 is assumed to be -0.5, which means the two stocks have a negative correlation.

For stock B:

σp = √(0.75^2×0.24^2 + 0.25^2×0.18^2 + 2×0.75×0.25×0.3×0.24×0.18) = 22.1%

Therefore, if Kaylyn wants to minimize the portfolio risk, she should add stock B to her portfolio.