Answer-first summary for fast verification
Answer: 0.0003765
**Step-by-step calculation:** 1. **Calculate expected returns:** - E(R_A) = 0.4 × 0.12 + 0.35 × 0.10 + 0.25 × 0.08 = 0.048 + 0.035 + 0.02 = 0.103 - E(R_B) = 0.4 × 0.18 + 0.35 × 0.15 + 0.25 × 0.12 = 0.072 + 0.0525 + 0.03 = 0.1545 2. **Calculate covariance using formula:** Cov(A,B) = Σ P(s) × [R_A - E(R_A)] × [R_B - E(R_B)] 3. **Calculate for each state:** - **Boom:** 0.4 × (0.12 - 0.103) × (0.18 - 0.1545) = 0.4 × 0.017 × 0.0255 = 0.0001734 - **Normal:** 0.35 × (0.10 - 0.103) × (0.15 - 0.1545) = 0.35 × (-0.003) × (-0.0045) = 0.000004725 - **Slow:** 0.25 × (0.08 - 0.103) × (0.12 - 0.1545) = 0.25 × (-0.023) × (-0.0345) = 0.0001984 4. **Sum the contributions:** Cov(A,B) = 0.0001734 + 0.000004725 + 0.0001984 = 0.0003765 **Key points:** - Covariance measures how two variables move together - Positive covariance (0.0003765) indicates that stocks A and B tend to move in the same direction - Options A (0.103) and C (0.1545) are the expected returns, not the covariance - Option B (0.0001734) is only the contribution from the Boom state, not the total covariance
Author: Nikitesh Somanthe
Ultimate access to all questions.
No comments yet.
A renowned economist has calculated that the Canadian economy will be in one of 3 possible states in the coming year: Boom, Normal, or Slow. The following table gives the returns of stocks A and B under each economic state.
| State | Probability(state) | Return for stock A | Return for stock B |
|---|---|---|---|
| Boom | 40% | 12% | 18% |
| Normal | 35% | 10% | 15% |
| Slow | 25% | 8% | 12% |
Which of the following is closest to the covariance of the returns for stocks A and B?
A
0.103
B
0.0001734
C
0.1545
D
0.0003765