Answer: 33%

## Explanation This question involves mean reversion in correlation modeling. The key components are: - **Long-run mean correlation (μ)**: 32% or 0.32 - **Current correlation (April 2014)**: 36% or 0.36 - **Regression equation**: Y = 0.24 - 0.75X ### Step 1: Identify the mean reversion rate The regression equation Y = 0.24 - 0.75X represents an AR(1) process where: - Y = correlation at time t - X = correlation at time t-1 The general form of an AR(1) process is: \[ \rho_t = \alpha + \beta \rho_{t-1} \] Where: - α = μ(1 - β) (long-run mean times (1 - mean reversion parameter)) - β = mean reversion parameter From the regression: α = 0.24, β = -0.75 ### Step 2: Calculate the expected correlation for May 2014 Using the AR(1) model: \[ \rho_{May} = \alpha + \beta \times \rho_{April} \] \[ \rho_{May} = 0.24 + (-0.75) \times 0.36 \] \[ \rho_{May} = 0.24 - 0.27 \] \[ \rho_{May} = -0.03 \] This gives -3%, which doesn't make sense for correlation. Let me reconsider. ### Step 3: Alternative interpretation The regression might be in a different form. Let's use the mean reversion formula: \[ E[\rho_{t+1}] = \mu + \beta(\rho_t - \mu) \] Where β is the mean reversion parameter. From the regression: Y = 0.24 - 0.75X This suggests that when X (previous correlation) increases by 1, Y (current correlation) decreases by 0.75, indicating strong mean reversion. Using the mean reversion formula: \[ E[\rho_{May}] = 0.32 + (-0.75) \times (0.36 - 0.32) \] \[ E[\rho_{May}] = 0.32 + (-0.75) \times 0.04 \] \[ E[\rho_{May}] = 0.32 - 0.03 \] \[ E[\rho_{May}] = 0.29 \] This gives 29%, which is not among the options. Let me try another approach. ### Step 4: Correct calculation The regression Y = 0.24 - 0.75X can be rewritten as: \[ \rho_t = 0.24 - 0.75 \rho_{t-1} \] For May 2014 (using April 2014 correlation): \[ \rho_{May} = 0.24 - 0.75 \times 0.36 \] \[ \rho_{May} = 0.24 - 0.27 \] \[ \rho_{May} = -0.03 \] This is clearly wrong for correlation. Let me check if the regression parameters need adjustment. ### Step 5: Final correct approach The regression Y = 0.24 - 0.75X suggests that when correlation is at its long-run mean of 32%, the predicted value should be 32%: \[ 0.32 = 0.24 - 0.75 \times 0.32 \] \[ 0.32 = 0.24 - 0.24 \] \[ 0.32 = 0 \] This doesn't hold. The correct interpretation is that the mean reversion rate is 0.75, and the calculation should be: \[ Expected\ correlation = Long-run\ mean + Mean\ reversion\ rate \times (Current - Long-run) \] \[ = 0.32 + 0.75 \times (0.36 - 0.32) \] \[ = 0.32 + 0.75 \times 0.04 \] \[ = 0.32 + 0.03 \] \[ = 0.35 \] **Therefore, the expected correlation for May 2014 is 35%, which corresponds to option C.** This makes sense because with strong mean reversion (75%), the correlation moves significantly back toward the long-run mean of 32% from the current level of 36%.