Answer-first summary for fast verification
Answer: 0.0003765
## Covariance Calculation Explanation To calculate the covariance between stocks A and B, we use the formula: **Cov(A, B) = Σ P(s) × [R_A – E(R_A)] × [R_B – E(R_B)]** ### Step 1: Calculate Expected Returns **E(R_A) = Σ P(s) × R_A** - Boom: 0.4 × 0.12 = 0.048 - Normal: 0.35 × 0.10 = 0.035 - Slow: 0.25 × 0.08 = 0.020 - **E(R_A) = 0.048 + 0.035 + 0.020 = 0.103** **E(R_B) = Σ P(s) × R_B** - Boom: 0.4 × 0.18 = 0.072 - Normal: 0.35 × 0.15 = 0.0525 - Slow: 0.25 × 0.12 = 0.030 - **E(R_B) = 0.072 + 0.0525 + 0.030 = 0.1545** ### Step 2: Calculate Covariance Components | State | P(s) | [R_A – E(R_A)] | [R_B – E(R_B)] | P(s) × [R_A – E(R_A)] × [R_B – E(R_B)] | |---------|------|----------------|----------------|----------------------------------------| | Boom | 0.40 | 0.12 - 0.103 = 0.017 | 0.18 - 0.1545 = 0.0255 | 0.4 × 0.017 × 0.0255 = **0.0001734** | | Normal | 0.35 | 0.10 - 0.103 = -0.003 | 0.15 - 0.1545 = -0.0045 | 0.35 × (-0.003) × (-0.0045) = **0.000004725** | | Slow | 0.25 | 0.08 - 0.103 = -0.023 | 0.12 - 0.1545 = -0.0345 | 0.25 × (-0.023) × (-0.0345) = **0.00001984** | ### Step 3: Sum the Components **Cov(A, B) = 0.0001734 + 0.000004725 + 0.00001984 = 0.0003765** Therefore, the covariance between stocks A and B is **0.0003765**, which corresponds to option D.
Author: Tanishq Prabhu
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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?
A
0.103
B
0.0001734
C
0.1545
D
0.0003765
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