Research: Regime Shifts & Optimal Asset Allocation

In this note we pose a seemingly straightforward question: “Does optimal asset allocation vary across different regimes or state spaces over time?” The established consensus of expected annualised equity returns is pulled towards the historical mean. The principal weakness with this approach relates to an assumption surrounding constant expected returns. The constant expected return framework neglects to decipher the time-varying nature of asset returns. This heavy assumption contradicts the stochastic or random temperament of equity market probability distributions. Combined with recency bias[1], this framework may produce protracted periods of inferior expected returns. If equity risk dominates the majority of investor portfolios, a constant expected return framework implies latent under-estimation of portfolio risk. This relates to the smoothened profile of constant expected returns. A common trend emerges across the academic literature applicable to regime-shifting modelling, namely that the joint distribution of equity and fixed income returns pursue a dynamic, non-linear pattern. We advocate the benefits of focussing on time-varying expected returns. We use long-run historical data on security valuations and returns to assess return predictability. If the concept of time-varying returns appears plausible, then the onus should shift towards asset pricing models that capture the irregular characteristics of asset prices. We therefore utilise a regime-shifting Markov model to facilitate such analysis.

[1] Recency Bias describes a negative investor sentiment by-product of assigning high probability asset return outcomes with the most recent historical returns

In future articles we seek to explore whether regime shifts exist and if these individual state spaces exhibit common economic parameters. Can we distinguish between a secular generational regime and the normal business cycle? If so, what are the implications for asset allocation and investor preferences? This research will focus particular attention on the regime-shifting means, volatilities, cross-covariance’s and autocorrelations of specific asset returns across different regimes. We allow the states to be observable to investors who filter state probabilities from return distributions. The task here is to distinguish between these regimes through interpretation and analysis of the rate of change of our variables. Greater granularities of observations are secured by focussing on the rate of change. We cannot observe the state through the dependent variable. However through interpretation of the parameters we can identify specific state space characteristics through its rate of change.

[1] Recency Bias describes a negative investor sentiment by-product of assigning high probability asset return outcomes with the most recent historical returns

Economic time series often exhibit dramatic breaks in their behaviour as a consequence of financial crises, unforeseen government policy action or so-called “black swan” events. We consider how we might capture the consequences of a dramatic change in the behaviour of a single variable yt. Traditionally, the behaviour could be described with a simple 1st-order auto regression model. A probabilistic model is required governing the transition from St to St2. A Markov model is utilised as we do not observe St directly. Markov switching models assume that St is unobserved and follows a particular stochastic process namely an N-State Markov chain. The evolution of the Markov chain is described by their transition probabilities. We only infer its operation through the observed behaviour of yt. The parameters necessary to fully describe the probability law governing yt include the variance [σ2], the auto-regressive coefficients [φ], the intercepts c1 and the state transition probabilities P11, P22 . . . PNN. We can observe the probability of being in state j given the information set t and the vector of population parameters;

ξjt = Pr(St = j|Ωt : θ)

The process governing the underlying dynamics of the underlying regime is a 1st order Markov chain. Markov switching models seek to capture the asymmetry of economic activity (Hamilton, 1989), fat-tail events, non-linear probability distributions, time-invariant parameter estimation and time-varying asset premia across multiple business cycles/ regimes.

We specify a number of different probabilistic models including a Markov-switching Dynamic regression [MSDR], a Markov-switching Auto-regressive regression [MSAR], a Vector-autoregressive [VAR(p)] model with exogenous variables and a Markov-switching Vector-autoregressive Model [MS-VAR]


  • [MSDR] yt = µs + Xtα + Ztβs + εs
  • [MSAR] yt = µst + Xtα + Ztβst + θi,st (yt-i – µst-i – Xt-iα – Zt-iβst-i) + εst 
  • [VAR(p)] yt = AYt-1 + B0xt + µt


We estimate the parameters of our Markov-switching models through Maximum Likelihood.                                    We estimate θ by updating the conditional likelihood utilising a nonlinear filter. Following the Hamilton [1989] approach, we weigh the conditional densities by their individual probabilities to determine the marginal density of yt. The assets selected include the S&P500, Nikkei225, Gold and the 10 Year US Treasury return. The analysis is segmented across both the full 50 year sample period [1968-2019] and three specific regimes [1968-1983], [1984-2007] & [2008-2019]. The primary purpose of segmenting our sample period was to identify whether the parameters were indeed consistent across multiple regimes. We identify some common properties of regime-switching estimates and note a short selection of these here. In the interests of precision, two regimes have been selected. Whilst it may be difficult to identify the regimes against the standard means, the volatility (σ2) estimates offer some useful insights. We can legitimately assume that the regimes are ordered by the intrinsic nature of their volatility. Regime 1 or s1 is clearly a lower volatility regime whereby the second regime s0 captures a classical bear market scenario for asset returns. We have produced strong evidence supporting the negative risk-reward relationship between International equity markets and volatility. Lower volatility regimes which may [for simplicity] be categorised as “Bull markets”, consistently provide superior risk-adjusted returns for equities. The primary research question of this paper is to identify whether asset allocation may be optimised by investing in assets that consistently offer negative correlation features over different economic regimes. We find evidence supporting the theories that exposures to Gold offer attractive diversification benefits, particularly to equity investors. Across all four of the individual study sample periods monthly gold returns outperform during periods of excess volatility. It is interesting to note that Gold outperforms the S&P500 over the 50 year sample of monthly returns

We construct a robust framework upon which to classify our individual state spaces. Regimes classification is structured upon a combination of empirical evidence and proven economic principles. Regimes are classified in terms of factor exposures to economic growth, inflation and volatility. We construct a 2 x 2 factor model of Growth and inflation characterised by a four quadrant internal system. These internal regimes are classified by a combination of factors. The first order effects relate to the inter-relationship or covariance between growth and inflation. The second order effects constitute the policy response to this environment. The quantitative model chosen incorporates an equal blend of Prospect theory, Bayesian inference and financial history. The main research question is whether a model which utilizes these core inputs has the ability to consistently and accurately identify inflections in the performance of key factor exposures, across asset classes, 3-6 months ahead of the market consensus. The primary data signal relates to the rate of change of the underlying factor and whether it is either increasing or decreasing. The model is structured across a 2 x 2 factor model incorporating growth and inflation. This 2 x 2 factor model captures four distinctive regimes. These regimes are determined by the prevailing economic conditions. There is a third latent factor relating to government policy which is mapped in second derivative terms. A brief description of each regime is detailed below. Dynamic asset allocation seeks to capture enhanced investment opportunities through profitable sector pivots, factor exposures and optimal asset allocation. The research seeks to identify if the model has the capacity to accurately forecast which sectors investors should be purchasing. There are two core principles underpinning the composition of our regime classifications. These include an appreciation of (i) how the cyclical growth environment traverses’ other significant drivers of asset returns and (ii) the parameters that segment the regimes themselves. The core drivers of asset returns from a regime space perspective include volatility, growth expectations, the discount rate and inflation.


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