Financial Risk Manager Part 1

Explanation

For an AR(1) model of the form:

$Y_t = c + \phi Y_{t-1} + \epsilon_t$

Where:

• c = intercept = 0.24
• φ = AR parameter = 0.65
• ε_t = white noise error term

The mean-reverting level (long-term mean) of the time series is calculated as:

$\text{Mean-reverting level} = \frac{c}{1 - \phi}$

Substituting the given values:

$\text{Mean-reverting level} = \frac{0.24}{1 - 0.65} = \frac{0.24}{0.35} = 0.6857$

This means the time series will tend to revert to approximately 0.69 over the long term.

Key Points:

• The mean-reverting level represents the long-term equilibrium value that the time series tends to approach
• For an AR(1) model, this is calculated as intercept divided by (1 - AR parameter)
• The result 0.6857 rounds to 0.69, which matches option A
• This calculation assumes the time series is stationary (|φ| < 1)