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Markov Chain Trading Model

John Montgomery7 min read

Markov Chain Trading Model

The Markov Chain Trading Model is the simplest member of the Markov family applied to markets: a discrete-time, discrete-state Markov chain used to predict the next price state directly. Price action over a chosen period (a daily candle, an hourly bar, a monthly return) is first discretised into a small finite set of observed states — at minimum up / flat / down, and more commonly a handful of return-magnitude buckets such as the six-state D3-U3 scheme used by Aronsson Folkesson 2023 on the OMXS30 Index. A transition probability matrix P is then estimated by counting empirical transitions: P_ij = count(state i -> state j) / count(state i). To generate a signal, the trader reads the current state, takes that row of P, and predicts the most probable next state (or propagates the full state distribution forward via P^n). This is fundamentally different from its siblings — in a Hidden Markov Model Regime Detection and a Markov Regime-Switching Model the state is latent and inferred, whereas here the state is a directly observable, mechanically-defined function of price. The Markov chain trading model trades the chain itself; the others trade an inferred regime.

Markov Chain Trading Model [defines] First-Order Memory Assumption Markov Chain Trading Model [contradicts] Hidden Markov Model Regime Detection Aronsson Folkesson 2023 [proposes_model] Markov Chain Trading Model

Two assumptions do all the work, and both are fragile. The first is the first-order Markov property: the next state depends only on the current state. This deliberately throws away the price path, trend persistence, and any longer memory — an explicit modelling choice that Do Carmo 2017 frames as treating the market as “memoryless”. The second is time-homogeneity: the transition matrix is assumed constant over the estimation window. The model’s accuracy is therefore bounded by how well a single fixed matrix describes a market that visibly changes regime. The other discretionary lever — the State Definition Arbitrariness problem — is the choice of how many states and where to put the thresholds. Wilinski 2019 states the dilemma precisely: too few states and the chain almost always stays put (so it predicts nothing useful), too many states and each bucket has too few observations to estimate a reliable probability. There is no objective state definition, which opens a wide researcher degree of freedom and a direct channel for Overfitting in Quantitative Trading and Data-Snooping Bias.

First-Order Memory Assumption [causes] State Definition Arbitrariness State Definition Arbitrariness [supports] Overfitting in Quantitative Trading Wilinski 2019 [relates] State Definition Arbitrariness

On the central question — does direct Markov-chain price prediction produce a tradeable edge? — the academic evidence is weak and should be graded as such. Aronsson Folkesson 2023 tested first- and second-order chains on the OMXS30 Index and found a single chain performed no better than random chance; only a voting ensemble of ten chains using the six-state configuration reached an out-of-sample accuracy of 17.1% versus a 16.7% random benchmark — a fraction of a percentage point, with the aggregated up/down model actually scoring below its 50% benchmark on accuracy. The authors are candid that “it is not reasonable to expect that the simple prediction approach with Markov chains would considerably outperform random chance” and that the model carries a positive bias unsuitable for risk-averse investors. Do Carmo 2017 reports only that a Markov chain beats a Random Walk Benchmark on a reconstruction-error metric (error 0.35 vs 0.67 over 500 Monte Carlo runs) — an error comparison, not a profit-and-loss result, and with no trading simulation at all. Mettle et al 2024 uses the chain purely descriptively to rank five national markets by steady-state risk, again with no backtest. The one paper reporting actual profit, Wilinski 2019, obtains “good results” on the Calmar Ratio for EUR USD Currency Pair and WIG20 Index data — but those numbers come from a simulation whose window length, window count and interval count were optimised by machine learning on the same data, and the paper presents no out-of-sample, net-of-cost track record. None of the four studies clears the bar of Out-of-Sample Backtesting with Transaction Costs and Slippage deducted.

Aronsson Folkesson 2023 [compares_benchmark] Random Walk Benchmark Wilinski 2019 [reports_profitability] Calmar Ratio Do Carmo 2017 [compares_benchmark] Random Walk Benchmark Markov Chain Trading Model [contradicts] Buy-and-Hold Benchmark

The failure modes are well understood and they are structural, not incidental. The dominant one is the Non-Stationary Transition Matrix: a matrix estimated on one period systematically misforecasts the next because market dynamics shift with volatility regimes, news flow and structural breaks. Wilinski 2019 treats this as the headline problem and responds with a heterogeneous chain whose transition matrix is re-estimated over a rolling sequence of windows — an admission that the fixed-matrix model is not viable on its own. Aronsson Folkesson 2023 hits the same wall, noting that zero-probability rows force a fallback to a uniform (pure-chance) distribution, and that second-order chains did not beat first-order despite using more information — the extra states simply spread thin data even thinner. Three honest conclusions follow. First, simple discrete Markov-chain price prediction is at best marginally better than a Random Walk Benchmark on accuracy or error metrics, and that margin is far too small to be confidently profitable after Transaction Costs and Slippage. Second, the model has genuine descriptive value — steady-state distributions, hitting times and recurrence times characterise a market’s structure, which is closer to Regime Classification than to a tradeable signal. Third, any profitability claim from this model family should be treated as alleged until demonstrated out-of-sample, net of costs, against a buy-and-hold and random-walk baseline — a standard the surveyed literature does not meet.

Non-Stationary Transition Matrix [causes] Markov Chain Trading Model Wilinski 2019 [opposes] Non-Stationary Transition Matrix Markov Chain Trading Model [relates] Regime Classification Transaction Costs and Slippage [contradicts] Markov Chain Trading Model

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