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).
Calculate sample means:
Calculate deviations from means:
Sum the products: From the table provided: 0.0384 + 0.0164 + 0.0155 + 0.0050 + (-0.0067) + (-0.0084) + (-0.0058) = 0.0544
Divide by (n-1): Covariance = 0.0544 / (7-1) = 0.0544 / 6 = 0.009067 ≈ 0.01130 (rounded)
Key points:
Ultimate access to all questions.
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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