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%.