Answer: Y and use the proceeds to take a long position in X.

## Explanation This question involves Arbitrage Pricing Theory (APT) and identifying arbitrage opportunities. ### Step 1: Calculate the factor premium for each portfolio For Portfolio X: - Expected return = Risk-free rate + Beta × Factor premium - 18% = 6% + 1.2 × F - 12% = 1.2 × F - F = 10% For Portfolio Y: - Expected return = Risk-free rate + Beta × Factor premium - 14% = 6% + 1.0 × F - 8% = 1.0 × F - F = 8% ### Step 2: Identify the arbitrage opportunity Both portfolios should have the same factor premium in an efficient market, but we have: - Portfolio X: Factor premium = 10% - Portfolio Y: Factor premium = 8% This creates an arbitrage opportunity. Portfolio X is underpriced relative to its risk (offering higher expected return than justified by its beta), while Portfolio Y is overpriced. ### Step 3: Execute the arbitrage strategy To exploit this: - **Short Portfolio Y** (sell the overpriced asset) - **Use proceeds to buy Portfolio X** (buy the underpriced asset) This creates a zero-investment portfolio with positive expected return: - Short Y: -14% expected return - Long X: +18% expected return - Net expected return: 4% risk-free profit ### Why other options are incorrect: **B:** Shorting Y and buying risk-free asset would give negative expected return (6% - 14% = -8%) **C:** Shorting X and buying Y would give negative expected return (14% - 18% = -4%) **D:** Shorting X and buying risk-free asset would give negative expected return (6% - 18% = -12%)

Author: Tanishq Prabhu