Question 13.4: In Example 13.3, what are the standard deviations on the two...
In Example 13.3, what are the standard deviations on the two portfolios?
To answer, we first have to calculate the portfolio returns in the two states. We will work with the second portfolio, which has 50 percent in Stock A and 25 percent in each of Stocks B and C. The relevant calculations can be summarized as follows:
| State of Economy | Probability of State of Economy | Rate of Return If State Occurs | |||
| Stock A | Stock B | Stock C | Portfolio | ||
| Boom | .40 | 10% | 15% | 20% | 13.75% |
| Bust | .60 | 8 | 4 | 0 | 5.00 |
The portfolio return when the economy booms is calculated as:
E(R_{P}) = .50 × 10% + .25 × 15% + .25 × 20% = 13.75%
The return when the economy goes bust is calculated the same way. The expected return on the portfolio is 8.5 percent. The variance is thus:
\sigma ^{2}_{P} = .40 × (.1375 − .085)² + .60 × (.05 − .085)²
= .0018375
The standard deviation is about 4.3 percent. For our equally weighted portfolio, check to see that the standard deviation is about 5.4 percent.