Financial Risk Manager Part 1
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Q.230 Consider a single factor APT. Portfolio X has a beta of 1.2 and an expected return of 18%. Portfolio Y has a beta of 1.0 and an expected return of 14%. You are further provided with a risk-free rate of 6%. Assuming you wanted to exploit an arbitrage opportunity, you would take a short position in:
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A
Y and use the proceeds to take a long position in X.
B
Y and use the proceeds to take a long position in the risk-free asset.
C
X and use the proceeds to take a long position in Y.
D
X and use the proceeds to take a long position in the risk-free asset.
Explanation:
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%)
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