Consider the one-factor APT.The standard deviation of return on a well-diversified portfolio is 20%.The standard deviation on the factor portfolio is 12%.The beta of the well-diversified portfolio is approximately _________.
A) 0.60
B) 1.00
C) 1.67
D) 3.20

Question

Quizplus · Accepted Answer

The one-factor APT model assumes that the return of an asset is generated by a single macroeconomic factor. The formula for the APT model is:

Ri = Rf + βiF + εi

where Ri is the return on asset i, Rf is the risk-free rate, βi is the sensitivity of asset i to the factor portfolio, F is the factor portfolio, and εi is the idiosyncratic risk.

Given that the standard deviation of the well-diversified portfolio is 20%, the idiosyncratic risk can be assumed to be small, which means that most of the risk comes from the systematic factor (F).

Using the formula for the variance of the well-diversified portfolio:

σ^2p = β^2σ^2F

where σ^2p is the variance of the well-diversified portfolio and β is the asset's beta, we can solve for β:

β = σp/σF = 20%/12% = 1.67

Therefore, the beta of the well-diversified portfolio is approximately 1.67.

Consider the One-Factor APT