Financial Risk Manager Part 1
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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?
Other
Community
NNikitesh
A
0.103
B
0.0001734
C
0.1545
D
0.0003765
Explanation:
Step-by-step calculation:
-
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
-
Calculate covariance using formula: Cov(A,B) = Σ P(s) × [R_A - E(R_A)] × [R_B - E(R_B)]
-
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
-
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
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