Answer: buying $500 of Portfolio X and $500 of Portfolio Y, and selling short $1,000 of Portfolio Z.

**Explanation:** To identify an arbitrage opportunity in APT, we need to create a portfolio that: 1. Has zero net investment 2. Has zero factor sensitivity (risk-free) 3. Generates positive expected return 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:** - X: 0.7 × $500 = 350 - Y: 1.7 × $500 = 850 - Z: 1.3 × (-$1,000) = -1,300 - Total factor sensitivity: 350 + 850 - 1,300 = 0 ✓ **Expected Return Calculation:** - X: 5.0% × $500 = $25 - Y: 7.0% × $500 = $35 - Z: 6.0% × (-$1,000) = -$60 - Total expected return: $25 + $35 - $60 = $0 Wait, 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 - Net investment: $400 + $600 - $1,000 = $0 ✓ - Factor sensitivity: (0.7×400) + (1.7×600) + (1.3×-1000) = 280 + 1,020 - 1,300 = 0 ✓ - Expected return: (5%×400) + (7%×600) + (6%×-1000) = 20 + 42 - 60 = $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.

Author: LeetQuiz Editorial Team