Consider the one-factor APT.The standard deviation of returns on a well-diversified portfolio is 18%.The standard deviation on the factor portfolio is 16%.The beta of the well-diversified portfolio is approximately __________.
A)0.80
B)1.13
C)1.25
D)1.56
E)none of the above

Question

Quizplus · Accepted Answer

The one-factor APT model is given by the equation:

E(Ri) = Rf + biF1

where:
E(Ri) = expected return on security i
Rf = risk free rate
bi = sensitivity of security i to the factor
F1 = the factor return

The standard deviation of returns on the well-diversified portfolio is:

σp = sqrt(σ^2e + bi^2σ^2f + 2biCov(ef))

where:
σe = standard deviation of idiosyncratic risk
σf = standard deviation of factor returns
Cov(ef) = covariance between idiosyncratic risk and the factor

Given that the portfolio is well-diversified, we can assume that σe is relatively small, so we can simplify the equation to:

σp = biσf

Therefore, we can calculate the beta of the well-diversified portfolio as:

bi = σp / σf = 18% / 16% = 1.125

So the closest answer choice is B: 1.13.

Consider the One-Factor APT