Financial Risk Manager Part 1

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%)