The Arbitrage Pricing Theory (APT) is a multifactor model of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macroeconomic factors, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. In this case, the expected return of a portfolio is calculated as the sum of the risk-free rate and the product of the portfolio’s beta and the factor premium. For portfolio X, the expected return is 18%, which equals 1.2F (where F is the factor premium) plus the risk-free rate of 6%. Solving for F gives us a factor premium of 10%. For portfolio Y, the expected return is 14%, which equals 1.0F plus the risk-free rate of 6%. Solving for F in this case gives us a factor premium of 8%. Since the factor premium for portfolio X is higher than that for portfolio Y, an arbitrage opportunity exists. By shorting portfolio Y (selling it) and using the proceeds to take a long position in portfolio X (buying it), you can exploit this arbitrage opportunity and earn a risk-free profit.

Choice B is incorrect. Selling Portfolio Y and using the proceeds to take a long position in the risk-free asset would not provide an arbitrage opportunity. This is because the expected return of Portfolio Y (14%) is higher than the risk-free rate (6%). Therefore, this strategy would result in a lower return rather than an arbitrage profit.

Choice C is incorrect. Shorting Portfolio X and using the proceeds to take a long position in Portfolio Y would not yield an arbitrage opportunity either. The expected return of Portfolio X (18%) exceeds that of Portfolio Y (14%), despite having a higher beta value, which indicates more