Consider the single-factor APT. Stocks A and B have expected returns of 12% and 14%, respectively. The risk-free rate of return is 5%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of
A) 0.67.
B) 0.93.
C) 1.30.
D) 1.69.

Question

Quizplus · Accepted Answer

The Arbitrage Pricing Theory (APT) posits that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors, plus an asset-specific factor. In the case of a single-factor model, the expected return can be simplified to: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). Given the information, we can solve for Stock A's beta by setting up the equations for both stocks and solving for the unknown beta of Stock A. For Stock B, we have: 14% = 5% + 1.2 * (Market Return - 5%). We can use this information to find the market premium, and then apply it to find Stock A's beta, which results in a beta of 0.93 when arbitrage opportunities are ruled out, indicating that Stock A is less sensitive to market changes than Stock B.

Consider the Single-Factor APT