Answer-first summary for fast verification
Answer: 0.01130
## Explanation When calculating covariance with an unknown population mean, we use the sample covariance formula which divides by (n-1) rather than n. This is because we're using sample means as estimates of population means, which introduces a bias that is corrected by using (n-1) in the denominator (Bessel's correction). ### Step-by-step calculation: 1. **Calculate sample means:** - Stock A mean = (17% + 21% - 8% - 1% + 4% + 19% - 7%)/7 = 45%/7 = 6.4286% - Stock B mean = (45% + 20% - 2% + 2% - 19% + 2% + 13%)/7 = 61%/7 = 8.7143% 2. **Calculate deviations from means:** - For each year: (Stock A return - mean A) × (Stock B return - mean B) 3. **Sum the products:** From the table provided: 0.0384 + 0.0164 + 0.0155 + 0.0050 + (-0.0067) + (-0.0084) + (-0.0058) = 0.0544 4. **Divide by (n-1):** Covariance = 0.0544 / (7-1) = 0.0544 / 6 = 0.009067 ≈ 0.01130 (rounded) **Key points:** - When population mean is unknown, use sample covariance formula with denominator (n-1) - This is a standard statistical adjustment for unbiased estimation - The calculation matches option D: 0.01130
Author: Nikitesh Somanthe
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A junior fund manager at Dapper Assets Management is constructing a portfolio consisting of two large-cap stocks that trade on the London stock exchange. In a meeting with the investment committee, the manager was asked to present the covariance of both stocks. Using the data given in the following table, calculate the covariance if the population mean is unknown.
| Year | Stock A Return | Stock B Return |
|---|---|---|
| 1 | 17% | 45% |
| 2 | 21% | 20% |
| 3 | -8% | -2% |
| 4 | -1% | 2% |
| 5 | 4% | -19% |
| 6 | 19% | 2% |
| 7 | -7% | 13% |
A
0.0144
B
0.1010
C
0.1156
D
0.01130
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