2. Standard deviation of the portfolio with stock B is ____ % 3. Which stock wou

Question

2. Standard deviation of the portfolio with stock B is ____ %

3. Which stock would you add and why?

a. Add B because the portfolio is less risky when B is added.

b. Add A because the portfolio is less risky when A is added.

c. Add either one because both portfolios are equally risky.

You have a portfolio with a standard deviation of 27% and an expected return of 19%. You are considering adding one of the two stocks in the following table. If after adding the stock you will have 25% of your money in the new stock and 75% of your money in your existing portfolio, which one should you add? Standard deviation of the portfolio with stock A is %. (Round to two decimal places.)

Explanation / Answer

for two assets A and B

portfolio variance = wA^2 * vA^2 +wB^2 * vB^2 + 2 * wA * wB * covariance(A,B)

Covariance(A,B) = Sd(A) * Sd(B) * correlation(A,B)

where

wi = weight of asset i

vi = variance of asset i

sd(i) = standard deviation of asset i

standard deviation = sqrt(variance)

so.

1)
variance of portifolio with stock A

= 0.75^2 * 0.27^2 + 0.25^2 * 0.24^2 + 2 * 0.75 * 0.25 * 0.27 * 0.24 * 0.3

= 0.05189625

standard deviation of portifolio with stock A

= sqrt(0.05189625)

= 22.78%

2)
similarly

variance of portifolio with stock B

= 0.75^2 * 0.27^2 + 0.25^2 * 0.17^2 + 2 * 0.75 * 0.25 * 0.27 * 0.17 * 0.7

= 0.05486125

standard deviation of portifolio with stock B

= sqrt(0.05189625)

= 23.42%

3)

since standard deviation of portifolio is less with stock A , so it is less risky

hence choose stock A

so,

the correct choice is b

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