Treat regimes as latent probabilities whose allocation value must be reproduced with filtered signals, realistic execution, out-of-sample evidence, and precommitted governance.
A two-state model infers probabilities with limited memory
In a Markov-switching model, a latent state s_t takes one of several categories and observed returns follow a state-conditional distribution. Transition probability p_ij links the prior state s_(t-1) to the current state s_t. [1] These are modeling assumptions: the market does not arrive labeled low volatility or high volatility. If p_11 equals 0.95 in a homogeneous two-state model, the conditional expected duration is 1/(1-0.95), or twenty periods. That is not 95% economic certainty, a forecast of return, or evidence that parameters will remain stable. States can differ in mean, volatility, correlation, tails, liquidity, or other measurements, and their numeric labels are arbitrary until ordered by a stated parameter. For an allocation decision at t, report the filtered probability produced with information available by t. A smoothed probability uses later observations to revise the historical state and cannot be used as though it were known at the trade date. [6] Record data vintage, timestamp, return convention, estimation window, initialization, parameter constraints, software, random seed where applicable, state-ordering rule, and probability cutoff. The key point is that a state is an uncertain inference under a specific model, not an observed fact or command.
Table 1. Two-state inference| Current state | Next low | Next high | Constraint |
|---|
| Low | p11 | p12 | p11+p12=1 |
| High | p21 | p22 | p21+p22=1 |
| Duration | 1/(1-p11) | 1/(1-p22) | Under model |
| Decision | Filtered probability | Filtered probability | No future |
Latent
A regime is inferred under a model; it is not an observed market label.
HMMs and rolling thresholds answer different questions
A Hidden Markov Model combines the likelihood of the latest observation, a transition matrix, and the previous filtered probabilities. A rolling threshold compares a trailing statistic with a cutoff. The HMM depends on the number of states, emission distribution, initialization, optimizer, constraints, training window, and convergence; different starts can reach local optima or assign isolated outliers to a separate state. A threshold is transparent but its 12- or 26-week lookback and a 20% annualized cutoff are parameters, not universal defaults. Annualizing weekly volatility by the square root of 52 embeds a sampling and scaling convention that must be stated and tested. A probabilistic output is not automatically accurate, and a faster binary response is not automatically useful. Compare both methods on the same point-in-time observations, decision dates, execution lag, cost model, and objective. Hysteresis, minimum dwell time, or two cutoffs can reduce switching but add parameters; specify them before evaluation. Confirmation with a second signal is not independent when both signals are transformations of the same returns. Worked example: a 51% filtered high-volatility probability and a 20.1% threshold reading should remain uncertain near their boundaries rather than being rewritten as two confirmations. Evaluate calibration, false positives, false negatives, delay, and action cost—not merely label agreement.
Table 2. Method controls| Method | Input | Parameter | Failure |
|---|
| HMM | Returns/variables | States/distribution | Local optimum |
| Threshold | Rolling statistic | Window/cutoff | Whipsaw |
| Hysteresis | Two cutoffs | Bands | Lag |
| Confirmation | Another measure | Dependence | False confidence |
No future
A decision backtest uses filtered probability, never a posterior smoothed state.
The published 2020–2025 regime timeline is not reproducible
The prior article describes weekly S&P 500 regimes from January 2020 through May 2025, including pandemic, inflation, regional-bank, and later policy episodes, but does not provide the exact total-return series, vendor and version, trading calendar, missing-data treatment, return code, fit schedule, training sample, estimated parameters, seed, software version, convergence results, filtered probabilities, classification cutoff, or machine-readable timestamps. Therefore those dates cannot be presented as an audited AIBROKER analysis. A macro narrative attached after the event can sound reasonable without proving that the model classified it using information available then. Reproduction requires a versioned input artifact; deterministic return construction; rolling or expanding estimation performed separately at every decision date; parameters estimated only inside that window; filtered—not smoothed—probabilities; predeclared state ordering and action cutoff; and an output file containing signal timestamp, availability timestamp, decision, and later realized outcome. [6] Preserve failed fits and restarts rather than silently substituting the final successful model. Compare the result with raw realized volatility and an unconditioned base rate as diagnostics, not as post-hoc proof. Decision rule: until that artifact exists and independently reproduces, the 2020–2025 episode table is an illustrative research hypothesis and must not support a trading or allocation claim.
Table 3. 2020–2025 evidence| Claim | Required | Missing | Status |
|---|
| Series | Total return/version | Yes | Unaudited |
| HMM | Fit/seed/parameters | Yes | Unaudited |
| Labels | Filtered/cutoff | Yes | Unaudited |
| Events | Ex-ante rule | Yes | Narrative |
Missing artifact
The 2020–2025 timeline lacks enough evidence for reproduction.
The quoted regime-aware 60/40 performance also fails the evidence gate
The prior comparison also quotes approximately 6.4% annualized return and -18.7% maximum drawdown for static 60/40 versus 6.1% and -14.9% for a regime-aware version from 2020–2025. It omits exact equity and bond proxies, total-return treatment, start and end dates, initial weights, intraweek timing, signal availability, execution lag, rebalance method, cash return, borrowing, distributions, spread, impact, turnover calculation, tax, code, and output series. Those numbers fail the performance-evidence gate and must not be evidence that regime allocation reduced drawdown. [5] A valid test fixes an implementable static benchmark and the adaptive rule before the evaluation sample; executes at prices actually available after the signal; includes all costs and constraints; and attributes the difference to equity, bonds, cash, timing, and implementation. Report exact observations, confidence intervals or resampling uncertainty, multiple subperiods, worst switches, time out of market, turnover, capacity, and sensitivity to one reasonable change at a time. Scenario analysis must distinguish an overlay that scales gradually from an all-or-nothing switch. One short window dominated by a few shocks cannot establish a stable pattern. What most investors miss is that a lower historical drawdown can be a result of favorable signal timing discovered in sample rather than a reproducible control.
Table 4. Performance evidence| Quoted metric | Static | Regime | Problem |
|---|
| Return | ~6.4% | ~6.1% | No proxies/code |
| Drawdown | ~-18.7% | ~-14.9% | No series |
| Volatility | ~9.8% | ~8.7% | No convention |
| Turnover | Low | Higher | No costs |
Unaudited performance
The quoted 60/40 numbers cannot support a drawdown claim.
Five failures: lag, whipsaw, label switching, tails, and structural change
Regime systems fail in at least five distinct ways. Lag means the estimator recognizes stress after the damaging move. Whipsaw means noisy boundary crossings generate turnover and tax without persistent change. Label switching means numerical state identities reverse across fits unless ordered consistently. Thin or Gaussian emissions can understate fat tails and allocate crisis observations poorly. Structural change means transition rates, correlations, inflation sensitivity, liquidity, or the stock-bond relationship moves outside the training domain. A first-order, constant-transition Markov assumption can itself be wrong. Diagnose detection delay, switch count, state occupancy, convergence, parameter drift, probability calibration, tail residuals, correlation and liquidity exposures, and performance by fit vintage. Use multiple predeclared starts, constrained estimation where justified, heavier-tailed alternatives, out-of-sample calibration, and sensitivity to state count and window. Do not choose the variant with the best full-sample Sharpe ratio. False alarms and missed transitions have different financial costs, and the allocation rule must state both. The uncomfortable implication is that the model can appear most confident precisely when an omitted mechanism makes its historical state definitions least relevant.
Table 5. Failure diagnostics| Failure | Diagnostic | Cost | Response |
|---|
| Lag | Detection delay | Initial loss | Explicit lag |
| Whipsaw | Switch count | Cost/tax | Tested bands |
| Label switch | Parameters | Interpretation | Order states |
| Drift | Calibration | Wrong model | Revalidate |
Model risk
Distribution, states, and transitions can fail during the shock that matters.
A regime probability is a governed input, never an allocation order
A high-volatility label does not authorize buying, selling, or de-risking. Define in advance which probability enters the rule, signal availability and lag, maximum allocation change, step size, frequency, hysteresis, rebalance bands, turnover cap, tax and liquidity constraints, override authority, incident response, rollback, and conditions for revalidation. A 60% probability versus 40% matters only if a pretested rule translates that difference into a net benefit that survives uncertainty. For an investor near a spending goal, funding and horizon can dominate the model; for a concentrated or leveraged portfolio, exposure controls may bind regardless of the label. Compare signal calibration with the unconditional base rate and document disagreement among genuinely different inputs. If probabilities oscillate, estimation fails, or observations leave the training domain, retain the policy allocation and open a review rather than improvising. Checklist: confirm point-in-time input, filtered probability, valid fit, independent data health, executable price, estimated cost, current policy band, affected tax lots, authorized action, and rollback evidence. The regime signal changes capital only through a previously approved and bounded decision rule.
Table 6. Deployment gate| Gate | Evidence | Failure | Decision |
|---|
| Point in time | Filtered plus lag | Smoothed | Reject |
| Execution | Prices/costs | Impossible close | Recalculate |
| Robustness | OOS/sensitivity | One period | Do not deploy |
| Governance | Caps/rollback | Ad hoc action | Policy first |
Governance
A label changes capital only through a prevalidated and bounded rule.
The decisive gate is net out-of-sample performance without future data
A regime model passes only when versioned code reproduces signals without future data, estimates parameters inside each historical window, executes after a realistic lag at obtainable prices, accounts for turnover, spread, impact, financing, tax where relevant, and capacity, and improves a feasible alternative on data not used for model or rule selection. [6] Evaluate net return, drawdown, expected shortfall or tail loss, volatility, turnover, time in each state, false-switch cost, implementation shortfall, parameter stability, and goal-relevant outcomes. Preserve every tried state count, distribution, window, threshold, and action mapping; adjust inference and skepticism for multiple research attempts. Use nested or otherwise properly separated selection and evaluation when choices are data-driven. An overlay with gradual caps can reduce model risk but is not inherently superior to a switch or static allocation. Reject deployment when the conclusion disappears under a reasonable seed, start, window, cost, proxy, lag, or period. Practical takeaway: fragility is evidence against implementation, not an invitation to optimize until the result returns. Publish the reproducible artifact and limitations before any performance number or allocation recommendation.
Net
Turnover, tax, spread, and impact belong inside the test.
Reject
Sensitivity to seed, window, cost, or period is a reason not to deploy.
Related analysis
Regime DetectionHidden Markov ModelVolatility RegimeAsset Allocation
Sources & Further Reading
- Ang, A., & Bekaert, G. (2002). International asset allocation with regime shifts. Review of Financial Studies, 15(4), 1137-1187. Source
- AQR Capital Management. Research on regime-aware allocation and defensive positioning. Source
- S&P Dow Jones Indices. S&P 500 index facts and methodology resources.
- Federal Reserve Economic Data (FRED). S&P 500 index series and related market data.
- Federal Reserve Bank of St. Louis. Market data and series documentation.
- Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2), 357–384. Source