Question

Consider the one-factor APT. The variance of the return on the factor portfolio is 0.08.
The variance of the return on the Asset A is 0.01. The beta of Asset A is:
A. At least 0.125
B. At most 0.125
C. At least 0.354
D. At most 0.354

Answer 1

Beta of a security can be calculated as: (standard deviation of the security/standard deviation of the factor)*correlation between security and factor.

Given that variance of security= 0.01; So, standard deviation of security= square root of (0.01)= 0.1

Given that variance of factor= 0.08; So, standard deviation of factor= square root of (0.08)= 0.2828

On substituting in the formula of Beta, we get Beta= (0.1/0.2828)*correlation= 0.354* correlation

We know that correlation ranges between (-1,1). So, Beta will lie between (-0.354,0.354). It means atleast -0.354 and atmost 0.354.

So, among the given options, Beta of asset A is atmost 0.354 (Option D).