Question 13.3: Suppose we have the following projections for three stocks: ...
Suppose we have the following projections for three stocks:
| State of Economy | Probability of State of Economy | Returns If State Occurs | ||
| Stock A | Stock B | Stock C | ||
| Boom | .40 | 10% | 15% | 20% |
| Bust | .60 | 8 | 4 | 0 |
We want to calculate portfolio expected returns in two cases. First, what would be the expected return on a portfolio with equal amounts invested in each of the three stocks? Second, what would be the expected return if half of the portfolio were in A, with the remainder equally divided between B and C?
Based on what we’ve learned from our earlier discussions, we can determine that the expected returns on the individual stocks are (check these for practice):
E(R_{A}) = 8.8%
E(R_{B}) = 8.4%
E(R_{C}) = 8.0%
If a portfolio has equal investments in each asset, the portfolio weights are all the same. Such a portfolio is said to be equally weighted. Because there are three stocks in this case, the weights are all equal to 1/3. The portfolio expected return is thus:
E(R_{P}) = (1/3) × 8.8% + (1/3) × 8.4% + (1/3) × 8% = 8.4%
In the second case, verify that the portfolio expected return is 8.5 percent.1