用另一个公式算？

问题如下：

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:

The analyst estimates that the sample means of the returns of stock A (μ_A) 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?

选项：

A.

0.003828

B.

0.003892

C.

0.004785

D.

0.004865

解释：

D is correct. Using the formula for the sample covariance estimator but dividing by n-1 for an unbiased estimate, we get

𝜎_𝐴𝐵=1/(𝑛−1)Σ(𝑅_𝐴,𝑖−𝜇_𝐴)∗(𝑅_𝐵,𝑖−𝜇_𝐵)

Which is expanded as

1/4[(0.18−0.146)(0.32−0.138)+(0.13−0.146)(0.22−0.138)+(0.04−0.146)(0.00−0.138)+(0.30−0.146)(0.10−0.138)+(0.08−0.146)(0.05−0.138)]=(14)∗(0.01946)=0.004865

A is incorrect. This is the result when the two means are switched in the summation formula and the multiplier used is 1/5.

B is incorrect. This is the result when the multiplier used is 1/5 instead of 1/(5-1).

C is incorrect. This is the result when the two means are switched in the summation formula.