Suppose Stock X has a beta of
𝛽
𝑋
=
0.5
and Stock Y has a beta of
𝛽
𝑌
=
1.4
with respect to the single factor, M.

The single factor, M, has a return standard deviation of
𝜎
𝑀
=
0.2
.

Required:

Compute the covariance between Stock X and Stock Y.

Report your final answer as a decimal, rounded to four decimal places.
Example: if the result is 0.1234567, present it as 0.1235 (not 12.35%).
Keep at least six decimal places in all intermediate calculations before the final rounding.

Question

Suppose Stock X has a beta of 
𝛽
𝑋
=
0.5
 and Stock Y has a beta of 
𝛽
𝑌
=
1.4
 with respect to the single factor, M.

The single factor, M, has a return standard deviation of 
𝜎
𝑀
=
0.2
.

Required:

Compute the covariance between Stock X and Stock Y.

Report your final answer as a decimal, rounded to four decimal places.
Example: if the result is 0.1234567, present it as 0.1235 (not 12.35%).
Keep at least six decimal places in all intermediate calculations before the final rounding.

BlackTom AI · Accepted Answer

To approach this covariance problem, I’ll start by identifying the relationship between the two stocks and the common factor M. In a single-factor model, the covariance between two assets i and j is given by Cov(i,j) = beta_i * beta_j * Var(M).

First, extract the necessary inputs: beta_X = 0.5, beta_Y = 1.4, and the standard deviation of the factor M is sigma_M = 0.2. The variance of M is Var(M) = (sigma_M)^2 = (0.2)^2 = 0.04.

Next, multiply the betas to get the product beta_X * beta_Y = 0.5 * 1.4 = 0.7. This product captures how strongly the two assets co-move with the common factor.

Then scale this product by Var(M) to obtain the covariance: Cov(X,Y) = 0.7 * 0.04 = 0.028.

If you want to present the final answer with the required four-decimal formatting, you would express 0.028 as 0.0280.

Summary of the calculation steps in sequence: (1) compute Var(M) = 0.04, (2) compute beta product = 0.7, (3) compute Cov(X,Y) = 0.7 * 0.04 = 0.028, (4) format as 0.0280.

Common potential pitfalls to avoid: forgetting to square the sigma_M to obtain Var(M), or miscomputing the beta product, which would yield an incorrect covariance value. Ensuring the intermediate results are kept with enough precision (at least four decimals) helps prevent rounding errors before the final formatting.

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