Answer: 42.01 years.

## Explanation In the Gauss+ model, the half-life for a mean-reverting factor is calculated using the formula: \[\text{Half-life} = \frac{\ln(2)}{\alpha}\] Where: - \(\alpha\) is the mean reversion speed parameter - \(\ln(2)\) ≈ 0.6931 For the long-term factor, we use the parameter \(\alpha_l = 0.0165\) from the table. \[\text{Half-life} = \frac{\ln(2)}{\alpha_l} = \frac{0.6931}{0.0165} ≈ 42.01 \text{ years}\] **Step-by-step calculation:** 1. \(\ln(2) = 0.693147\) 2. \(\alpha_l = 0.0165\) 3. Half-life = \(0.693147 / 0.0165 = 42.01\) years This makes sense because: - A very small mean reversion speed (\(\alpha_l = 0.0165\)) indicates very slow mean reversion - Slow mean reversion results in a long half-life - The long-term factor is expected to have the longest half-life among the three factors (short-term, medium-term, and long-term) Therefore, the correct answer is **42.01 years**.

Author: LeetQuiz .