Guide

Regime switching models in finance explained

Harbor Capital's balanced 60/40 sleeve held a fixed 60% equity weight through rising realized volatility in early 2020. A simple volatility-targeting overlay would have trimmed risk, but only after vol had already spiked — reactive, not anticipatory. Fitting a two-state Markov regime-switching model on monthly S&P 500 excess returns flagged a “high-volatility bear” state with filtered probability above 0.7 three weeks before the March drawdown trough. The sleeve cut equity to 48%, then re-expanded after filtered crisis probability fell below 0.35. Static policy would have drawn down 14.2%; the regime overlay limited peak-to-trough loss to 9.8% while preserving most of the subsequent rebound.

Financial markets do not behave like one stationary process. Bull runs, grinding bear markets, liquidity crises, and low-volatility carry regimes have different means, volatilities, and correlations. Regime switching models treat these as latent states governed by a Markov chain: the economy (or market) sits in an unobserved regime, and returns are drawn from regime-specific distributions. James Hamilton's 1989 econometric framework made this estimable; today allocators use regime filters alongside tactical asset allocation, risk parity, and macro overlays. This guide defines Markov switching, contrasts two-state and multi-state specifications, explains filtered and predicted probabilities, walks through the Harbor Capital refactor, compares regime models to GARCH and vol targeting, provides a technique decision table, common pitfalls, and a production checklist alongside our GARCH volatility guide and hidden Markov models guide.

Why stationary models break in portfolios

Classical mean-variance optimization and many factor regressions assume returns are drawn from a single distribution with fixed mean and variance. That assumption fails in practice: equity risk premia appear higher in calm expansions and vanish or invert in crises; correlations spike toward one when diversification is needed most; momentum and value factors rotate with macro states.

A single GARCH model captures volatility clustering but still models one continuous process. Regime switching adds discrete states — bull, bear, crisis — each with its own parameters. The Markov transition matrix encodes persistence: crisis regimes tend to stay crisis until probabilities shift. That persistence is what tactical allocators want when deciding whether a vol spike is noise or a state change.

What regime models estimate

State-dependent means — average excess return in each regime (often positive in bull, negative in bear).
State-dependent variances — crisis regimes carry multiples of calm-regime volatility.
Transition probabilities — probability of moving from state i to state j each period.
Filtered probabilities — P(regime = k | data through t), the real-time regime belief used for allocation rules.

Hamilton Markov switching: the workhorse specification

The standard univariate Hamilton model for excess returns r_t with K regimes is:

r_t = μ_{S_t} + σ_{S_t} ε_t, where S_t ∈ {1,…,K} follows a first-order Markov chain with transition matrix P, and ε_t ~ N(0,1).

Estimation uses the EM algorithm (Hamilton filter + Kim smoothing) to maximize the likelihood. Researchers typically start with K = 2 (calm vs stressed) or K = 3 (bull, sideways, bear). More states improve in-sample fit but overfit quickly on short samples; economic interpretability matters as much as log-likelihood.

Two-state vs three-state designs

Two-state (low/high vol): Simple crisis detector; good for vol-targeting triggers and equity de-risking. Often labels states by sorted variance.
Two-state (bull/bear): Separates positive-mean and negative-mean regimes; useful for trend timing but can flip late if means overlap.
Three-state: Bull, neutral, crisis — finer gradation for TAA bands; needs 20+ years of monthly data for stable estimates.
Multivariate switching: Joint modeling of equities, bonds, and commodities with regime-dependent correlation matrices — powerful but identification-heavy.

Filtered vs predicted probabilities in production

Allocators care about filtered probabilities ξ_t|t = P(S_t = k | r₁,…,r_t) because they use only information available at decision time. Predicted probabilities ξ_t|t−1 forecast next period's regime mix from today's beliefs and transition matrix — useful for scenario planning, not for same-bar reactions.

Common trading and allocation rules:

Threshold rule: If P(crisis | data) > 0.6, cut equity by X%; re-risk when P(crisis) < 0.35 for two consecutive months (hysteresis reduces whipsaw).
Probability-weighted blend: Target weight = sum over regimes of P(regime) times regime-optimal weight — smoother than hard switches.
Regime-conditional vol target: Scale gross exposure so portfolio vol equals policy band conditional on expected regime variance.

Pair regime signals with momentum or valuation overlays carefully: momentum often peaks entering crisis regimes; combining uncorrelated signals with explicit bounds avoids double-counting trend.

Harbor Capital regime overlay refactor

Harbor's 60/40 policy sleeve used quarterly rebalancing with a 5% band. After 2020, the investment committee asked whether a systematic crisis de-risking layer could complement existing vol targeting without discretionary macro calls.

Model spec — Two-state Markov switching on monthly U.S. equity excess returns (1990–present estimation window); states sorted by variance (calm vs high-vol stress).
Signal extraction — Filtered high-vol probability computed month-end; 2-month EMA smooth to reduce single-month noise.
Overlay rule — Linear equity haircut: reduce policy equity weight by up to 12 percentage points as smooth crisis probability rises from 0.4 to 0.85; floor at 45% equity; bonds fill the gap.
Backtest discipline — Expanding-window refit annually; out-of-sample 2005–2024; compared to static 60/40, vol targeting alone, and discretionary macro template in TAA guide.
Live deployment — Overlay activated 2019; March 2020 de-risk preceded full vol-target response by ~18 trading days in their implementation.

Outcome: Max drawdown improved 4.4 percentage points vs static policy over OOS window; CAGR fell 0.3% (insurance cost). Committee documented that regime models lag sharp V-reversals — re-risking rules must be explicit so the sleeve participates in recoveries.

Regime switching vs GARCH, vol targeting, and TAA

These tools overlap but answer different questions:

GARCH: Forecasts next-period conditional variance as a function of past shocks; continuous, no discrete states. Best for short-horizon vol forecasts and option pricing.
Volatility targeting: Scales exposure inversely to realized or forecast vol to hit a vol budget; reactive unless paired with forward-looking vol estimates.
Tactical asset allocation: Macro templates and signal stacks (momentum, yield curve, credit spreads) that tilt weights; may use regime labels as one input among many.
Regime switching: Estimates latent state probabilities from return dynamics; strong when means and volatilities shift together (crisis clusters).

Production stacks often layer them: regime filter for discrete de-risking, GARCH or EWMA for daily vol scaling within a regime, TAA for slower strategic tilts. Document precedence so rules do not fight each other.

Technique decision table

Approach	Detects	Best when	Watch out for
Two-state Markov (vol-sorted)	Calm vs crisis vol	Equity de-risking, crisis overlays on balanced portfolios	Late entry on gradual bears; label switching in estimation
Three-state Markov	Bull / neutral / bear	Graduated TAA bands, multi-asset sleeves with long history	Overfitting; unstable states on <20y samples
Multivariate switching	Regime-dependent correlations	Risk parity, multi-asset crisis hedging design	Parameter explosion; hard to validate OOS
GARCH(1,1)	Vol clustering	Daily vol forecasts, derivative hedging	No discrete crisis state; slow on level shifts
Vol targeting only	Realized vol vs target	CTA sleeves, simple risk budgets	Reactive; may overshoot in whipsaw
Macro TAA template	Yield curve, credit, momentum	Strategic tilts with economic narrative	Discretionary drift; multiple testing in backtests

Common pitfalls

In-sample regime labeling — States estimated on full sample then plotted historically is not OOS; use expanding or rolling refits.
Too many states — Four-plus regimes on monthly equity data rarely replicate; prefer parsimony.
Ignoring label switching — EM solutions are identified only up to permutation; enforce economic ordering (e.g., sort by variance) across refits.
Hard thresholds without hysteresis — P(crisis) crossing 0.5 monthly causes whipsaw; use entry/exit bands and smoothing.
Mixing frequencies — Monthly regime model driving daily leverage without bridge rules creates implementation gap.
Survivorship in backtests — Index series that exclude delisted names bias calm-regime means (see survivorship bias guide).
Confusing filtered and predicted probs — Reporting “we knew crisis was coming” using smoothed full-sample probabilities is misleading.
Single-asset regimes for global books — U.S. equity regimes may not map to EM or credit books; validate per sleeve.

Production checklist

Choose K (2 or 3) with economic justification before estimation.
Use monthly or weekly data consistently; align with rebalance cadence.
Estimate with Hamilton filter / EM; sort states by variance or mean for stable labels.
Validate with expanding-window OOS filtered probabilities since 2000.
Define entry/exit thresholds and hysteresis on filtered P(crisis).
Document interaction with vol targeting and TAA rules (precedence table).
Stress-test 2008, 2020, and 2022 paths; report max drawdown and recovery lag.
Refit annually or on 5-year rolling windows; monitor parameter drift.
Report insurance cost: CAGR sacrifice vs static policy for drawdown reduction.
Log live regime probabilities monthly for LP transparency.

Key takeaways

Regime switching models treat bull, bear and crisis periods as latent Markov states with distinct means and volatilities — more realistic than one stationary return distribution.
Filtered probabilities P(regime | data to date) drive allocation overlays; predicted probabilities forecast next period and serve scenario analysis.
Two-state vol-sorted models are the practical crisis detector; three-state specs need long histories and careful OOS validation.
Harbor Capital's refactor layered a Markov crisis overlay on 60/40 policy, improving drawdown at a modest CAGR cost versus static weights.
Combine regime filters with GARCH and vol targeting deliberately — document rule precedence to avoid conflicting de-risk signals.