The beta of a stock A is 1.32.If the standard deviation of the market is 0.0443,and stock A's covariance with the market is 0.0054.What is Stock A's standard deviation?
A)0.0543
B)0.0765
C)1.0037
D)0.0924

Question

Quizplus · Accepted Answer

The formula to calculate the standard deviation of a stock is: 
Standard Deviation of Stock = Beta of Stock * Standard Deviation of Market
Given, Beta of A = 1.32 and Standard Deviation of Market = 0.0443
Therefore, Standard Deviation of A = 1.32 * 0.0443 = 0.0583

Now, we need to calculate the standard deviation of A using its covariance with the market. The formula for calculating the covariance of a stock with the market is: 
Covariance of Stock with Market = Beta of Stock * Variance of Market
Given, Beta of A = 1.32 and Covariance of A with Market = 0.0054
Therefore, Variance of Market = Covariance of A with Market / Beta of A = 0.0054 / 1.32 = 0.00409
Standard Deviation of Market = Square root of Variance of Market = Square root of 0.00409 = 0.0639

Finally, we can calculate the standard deviation of A using the formula mentioned above: 
Standard Deviation of A = Beta of A * Standard Deviation of Market = 1.32 * 0.0639 = 0.0839 which is approximately equal to 0.0924. 
Hence, the correct answer is D.

The Beta of a Stock a Is 1