Question

you decide to invest in a portfolio consisting of 18 percent Stock A, 36 percent Stock B, and the remainder in Stock C. Based on the following information, what is the variance of your portfolio? State of Economy Probability of State Return if State Occurs of Economy Stock A Stock B Stock C Recession .680 − 8.30% − 3.40% − 12.06% Normal .210 4.40% 17.80% 11.39% Boom .110 36.30% 38.56% 37.43%

Answer 1

Given the individual stock returns in different states of the economy, first calculate the total portfolio return in a given state. Total portfolio return can be calculated as the weighted sum of individual stock returns. For example, in the state of recession, total portfolio return would be:

= 0.18*8.3% + 0.36*3.4% + 0.46*12.06%

= 8.27%

Similarly portfolio returns in all three states can be calculated as shown below.

Then the next step is to calculate the mean portfolio return of these three states which is simply the sum of these returns weighted by the probability of state. Mean portfolio return is:

= 8.27%*0.68 + 12.44%*0.21 + 37.63%*0.11

= 12.37%

Now, variance can be calculated using the formula:

Where

• is the portfolio return in each of the three states
• is the mean portfolio return calculated above
• is the probability of each state

So, Variance = (8.27% - 12.37%)^2*0.68 + (12.44% - 12.37%)^2*0.21 + (37.63% - 12.37%)^2*0.11

which is equal to 0.0082