What are regime-switching models and how are they applied to market risk?

Regime-switching models assume that financial markets alternate between distinct "regimes" or states — typically a calm/normal regime and a volatile/crisis regime — each governed by different statistical parameters.

The Basic Framework (Markov Regime-Switching)

The model assumes returns follow different distributions depending on the current state:

• State 1 (Normal): rₜ ~ N(μ₁, σ₁²) — e.g., mean = +0.04%, vol = 0.8%/day
• State 2 (Crisis): rₜ ~ N(μ₂, σ₂²) — e.g., mean = -0.15%, vol = 2.5%/day

Transitions between states follow a Markov chain with transition probabilities:

• P(stay in normal | currently normal) = 0.98
• P(switch to crisis | currently normal) = 0.02
• P(stay in crisis | currently crisis) = 0.90
• P(switch to normal | currently crisis) = 0.10

This means the normal regime is persistent (expected duration = 1/0.02 = 50 days) and the crisis regime is shorter but intense (expected duration = 10 days).

Why They're Better Than Standard Models

Standard GARCH models assume a single regime with smoothly evolving volatility. They tend to:

• React too slowly to regime changes (volatility creeps up gradually)
• Underestimate the probability of sudden jumps
• Produce VaR that's too low during calm periods transitioning to crisis

Regime-switching models capture the discontinuity — the abrupt shift from calm to crisis.

Practical Application

Alderton Capital uses a 2-state regime-switching model for its equity portfolio VaR. The model currently estimates a 78% probability of being in the normal regime. The blended 1-day 99% VaR is:

VaR = 0.78 × VaR_normal + 0.22 × VaR_crisis

This produces a higher VaR estimate than a single-regime model during transitional periods, providing a more conservative risk measure.

Limitations:

1. Regime identification is ex-post — by the time you know you're in a crisis, it may be too late
2. Overfitting — adding too many states creates instability
3. Estimation complexity — requires maximum likelihood with the Hamilton filter
4. Model risk — the true data-generating process may not follow discrete regimes

For the FRM exam, understand the conceptual advantage of regime switching over GARCH and be ready to calculate expected regime durations from transition probabilities. Explore our FRM market risk course for more advanced topics.