Explanation:
Explanation:
To identify an arbitrage opportunity in APT, we need to create a portfolio that:
Let's test option B: buying $500 of X and $500 of Y, and shorting $1,000 of Z
Net Investment: $500 + $500 - $1,000 = $0 ✓
Factor Sensitivity Calculation:
$500 = 350$500 = 850$1,000) = -1,300Expected Return Calculation:
$500 = $25$500 = $35$1,000) = -$60$25 + $35 - $60 = $0Wait, this gives zero expected return. Let me recalculate option A:
Option A: buying $400 of X and $600 of Y, shorting $1,000 of Z
$400 + $600 - $1,000 = $0 ✓$2 ✓Actually, option A gives a positive $2 expected return with zero risk and zero investment - this is the arbitrage opportunity.
Therefore, the correct answer is A - buying $400 of Portfolio X and $600 of Portfolio Y, and selling short $1,000 of Portfolio Z creates a risk-free arbitrage profit of $2.
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15 An analyst gathers the following information on the expected return of three well-diversified portfolios and their sensitivity to a single factor:
| Portfolio | Expected Return | Factor Sensitivity |
|---|---|---|
| X | 5.0% | 0.7 |
| Y | 7.0% | 1.7 |
| Z | 6.0% | 1.3 |
Based on a one-factor arbitrage pricing theory model, an arbitrage opportunity can be exploited by:
A
buying $400 of Portfolio X and $600 of Portfolio Y, and selling short $1,000 of Portfolio Z.
B
buying $500 of Portfolio X and $500 of Portfolio Y, and selling short $1,000 of Portfolio Z.
C
selling short $400 of Portfolio X and $600 of Portfolio Y, and buying $1,000 of Portfolio Z.
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