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Simplicity versus Complexity: A Comparative Analysis of HMM and HSMM for Regime-Based Asset Allocation

John Montgomery4 min read

Baitinger & Hoch 2024

Eduard Baitinger (FERI Trust GmbH) and Leonard Hoch (Bocconi University) released “Simplicity versus Complexity: A Comparative Analysis of HMM and HSMM for Regime-Based Asset Allocation” as SSRN Working Paper No. 4796238 in April 2024. The paper sets up a controlled contest within the regime-switching family: the standard Hidden Markov Model versus the more elaborate Hidden Semi-Markov Model. The HSMM relaxes the HMM’s most criticised structural assumption — that a regime’s duration is implicitly geometric, because exit probability is constant each period — by attaching an explicit sojourn distribution (Poisson or Gamma) to each state. In principle this lets the HSMM capture more stylised facts of equity returns, which is the usual argument for adopting it. Baitinger & Hoch ask whether that theoretical richness translates into better investment outcomes.

The central finding is a clean caution against complexity. The HSMM does outperform the HMM in-sample, exactly as its richer parameterisation predicts — but “this advantage largely disappears in out-of-sample applications.” The authors conclude that the simpler HMM “may be equally suitable for regime-based investment strategies.” Two further results undercut common complexity-chasing in the same direction: strategies built on daily data outperform those built on monthly data, and increasing the number of hidden states does not necessarily improve investment-strategy performance. The paper explicitly frames itself as challenging “the perceived necessity of employing complex models in the construction of regime-based investment strategies.”

This is the vault’s most direct empirical evidence on State-Count Selection and on overfitting risk inside the HMM family itself. The pattern — extra parameters buy in-sample fit that does not survive out-of-sample — is the textbook signature of Overfitting in Quantitative Trading. It generalises the Dacco and Satchell 1999 message from “knowing the true model does not help if you misclassify” to “fitting a richer model does not help, because the extra flexibility is spent on in-sample noise.” It also tempers the marketing instinct to equate a more sophisticated state-space (semi-Markov durations, more regimes) with a better trading model: the added structure is an in-sample artefact unless it demonstrably survives genuine out-of-sample testing. The daily-beats-monthly result is consistent with Bulla et al. 2010, whose after-cost edge depends on the granularity of daily regime calls.

A caveat on this note’s own evidence base: the full SSRN PDF is gated, so the public record is the complete posted abstract plus the working paper’s stated conclusions. Per-configuration Sharpe ratios, the exact in/out-of-sample split, and whether transaction costs are charged are inside the gated text and are recorded here as unclear rather than guessed. The headline finding — complexity does not pay out-of-sample — is stated unambiguously in the abstract and is consistent enough with the broader regime-switching literature to be treated as credible cautionary evidence, but it is graded alleged at the note level pending sight of the full results, and no independent replication exists.

Profitability grade — negative. Within the vault’s grading scheme this is negative/cautionary evidence: the paper demonstrates that a leading route to “better” regime models — added model complexity, more states, semi-Markov durations — is in-sample overfitting whose advantage does not persist out-of-sample. It is not a profitability claim for any strategy; it is direct evidence that complexity in this model family fails the out-of-sample test, which argues for parsimony rather than for sophistication as the path to anything tradeable.

Baitinger & Hoch 2024 [supports] State-Count Selection Baitinger & Hoch 2024 [supports] Overfitting in Quantitative Trading Hidden Semi-Markov Model [contradicts] Regime-Based Asset Allocation Baitinger & Hoch 2024 [relates] Dacco and Satchell 1999

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