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.

类似问题

Which ONE of the following thalamic nuclei is targeted by the trigeminothalamic tract?

Which ONE of the following is disinhibited in the direct pathway of the basal ganglia motor loop

30. What is the main purpose of the lecture?

Section FChoose a, b or c as the best answer.29. Which statement is the speaker most likely to agree with?

28. 15-minute neighbourhoods provide residents with inexpensive ____ .

27. ____ % of global car ownership is in the U.S.A.

26. ____ % of American drivers use their cars for all journeys.

Section FQuestions 25 – 28. Complete the following sentences with ONE WORD OR A NUMBER from the lecture. 25. American ____ have built more car spaces than is legally required.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单