How do Markov regime-switching models capture bull and bear markets?

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AcadiFi · Accepted Answer

Hamilton (1989) proposed that observed returns r_t follow one of K hidden regimes S_t in {1,...,K}, each with its own mean and variance: r_t | S_t = k ~ N(mu_k, sigma_k^2). The regime itself evolves as a first-order Markov chain governed by a K-by-K transition probability matrix P, where p_ij is the probability of moving from regime i to regime j. ```mermaid flowchart LR A[Bull Regime
low vol
positive mu] -->|p12| B[Bear Regime
high vol
negative mu] B -->|p21| A A -->|p11 stay| A B -->|p22 stay| B ``` At Brightmeadow, fitting a 2-state model on S and P 500 monthly returns might give mu1 = 0.9%, sigma1 = 3%, mu2 = -1.2%, sigma2 = 7%, with p11 = 0.97 and p22 = 0.85. That implies bull markets average roughly 33 months and bears roughly 7 months. The Hamilton filter recursively computes P(S_t = k | r_1,...,r_t), giving smoothed regime probabilities. These probabilities are strategic inputs for tactical allocation: when P(bear) exceeds 0.6, an AcadiFi-trained manager might cut equity beta and add volatility hedges. Key pitfalls: label switching during estimation, and overfitting with too many regimes. Stick with K = 2 or 3 unless BIC or likelihood ratio tests clearly favor more states. Also remember regimes are statistical constructs — they don't always align with NBER recessions.

How do Markov regime-switching models capture bull and bear markets?

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