Explanation:
The unbiased estimate of sample covariance is calculated using the formula:
Where:
Let's calculate step by step:
Year 1: (0.18 - 0.146)(0.32 - 0.138) = (0.034)(0.182) = 0.006188
Year 2: (0.13 - 0.146)(0.22 - 0.138) = (-0.016)(0.082) = -0.001312
Year 3: (0.04 - 0.146)(0.00 - 0.138) = (-0.106)(-0.138) = 0.014628
Year 4: (0.30 - 0.146)(0.10 - 0.138) = (0.154)(-0.038) = -0.005852
Year 5: (0.08 - 0.146)(0.05 - 0.138) = (-0.066)(-0.088) = 0.005808
Sum of products: 0.006188 - 0.001312 + 0.014628 - 0.005852 + 0.005808 = 0.01946
Unbiased covariance: σ_AB = (1/4) × 0.01946 = 0.004865
Therefore, the unbiased estimate of the sample covariance is 0.004865, which corresponds to option D.
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A quantitative analyst is constructing a stock selection algorithm that will be employed in making intraday trades and uses the annual returns of two utility stocks, stock A and stock B, to test the model's capacity to capture dependence between stock returns. The 5 years of annual returns data for each stock used in the test are shown in the following table:
| Year | Return of stock A (Rₐ) | Return of stock B (R_b) |
|---|---|---|
| 1 | 0.18 | 0.32 |
| 2 | 0.13 | 0.22 |
| 3 | 0.04 | 0.00 |
| 4 | 0.30 | 0.10 |
| 5 | 0.08 | 0.05 |
The analyst estimates that the sample means of the returns of stock A (μₐ) and stock B (μ_b) are 0.146 and 0.138, respectively. What is the unbiased estimate of the sample covariance of stocks A and B?
A
0.003828
B
0.003892
C
0.004785
D
0.004865
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