Question

In your portfolio, you have two stocks. You have a 50% investments in Stock A and 50% investment in Stock B. Stock A has a standard deviation of 25% and a beta of 1.2. Stock B has a standard deviation of 35% and a beta of 0.80. The correlation between Stock A and Stock B is 0.4. What is the standard deviation of your portfolio? (i) Less than 30% (ii) 30% (iii) More than 30% 2. What is the beta of your portfolio? 3. Which stock carries more risk if you want to keep a diversified portfolio?

Answer 1

1)

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

where x and y are the securities

Standard deviation of portfolio = ((0.5*0.25)^2 + (0.5*0.35)^2 + 2*0.5*0.5*0.25*0.35*0.4)^0.5

Standard deviation of portfolio = 0.2525 = 25.25%

Hence, (i) Less than 30%

2)

Beta of the portfolio = Weight of stock A*Beta of stock A + Weight of stock B*Beta of stock B

Beta of the portfolio = 0.5*1.2+0.5*0.8 = 1

Beta of the portfolio = 1

3)

Higher the standard deviation, higher is the risk of the stock. Since stock B has higher standard deviation, Stock B is more risky.