Can VAR models capture regime shifts in asset returns? A long-horizon strategic asset allocation perspective

It is often suggested that through a judicious choice of predictors that track business cycles and market sentiment, simple vector autoregressive (VAR) models could produce optimal strategic portfolio allocations that hedge against the bull and bear dynamics typical of financial markets. However, a distinct literature exists that shows that nonlinear econometric frameworks, such as Markov switching (MS), are also natural tools to compute optimal portfolios in the presence of stochastic good and bad market states. In this paper we examine whether simple VARs can produce portfolio rules similar to those obtained under MS, by studying the effects of expanding both the order of the VAR and the number/selection of predictor variables included. In a typical stock-bond strategic asset allocation problem, we compute the out-of-sample certainty equivalent returns for a wide range of VARs and compare these measures of performance with those typical of nonlinear models for a long-horizon investor with constant relative risk aversion. We conclude that most VARs cannot produce portfolio rules, hedging demands, or (net of transaction costs) out-of-sample performances that approximate those obtained from equally simple nonlinear frameworks. We also compute the improvement in realized performance that may be achieved adopting more complex MS models and report this may be substantial in the case of regime switching ARCH.     

Can Linear Predictability Models Time Bull and Bear Real Estate Markets? Out-of-Sample Evidence from REIT Portfolios

A recent literature has shown that REIT returns contain strong evidence of bull and bear dynamic regimes that may be best captured using nonlinear econometric models of the Markov switching type. In fact, REIT returns would display regime shifts that are more abrupt and persistent than in the case of other asset classes. In this paper we ask whether and how simple linear predictability models of the vector autoregressive (VAR) type may be extended to capture the bull and bear patterns typical of many asset classes, including REITs. We find that nonlinearities are so deep that it is impossibile for a large family of VAR models to either produce similar portfolio weights or to yield realized, ex-post out-of-sample long-horizon portfolio performances that may compete with those typical of bull and bear models. A typical investor with intermediate risk aversion and a 5-year horizon ought to be ready to pay an annual fee of up to 5.7 % to have access to forecasts of REIT returns that take their bull and bear dynamics into account instead of simpler, linear forecast.     

Can Markov switching models predict excess foreign exchange returns?

This paper merges the literature on technical trading rules with the literature on Markov switching to develop economically useful trading rules. The Markov models’ out-of-sample, excess returns modestly exceed those of standard technical rules and are profitable over the most recent subsample. A portfolio of Markov and standard technical rules outperforms either set individually, on a risk-adjusted basis. The Markov rules’ high excess returns contrast with mixed performance on statistical tests of forecast accuracy. There is no clear source for the trends, but permitting the mean to depend on higher moments of the exchange rate distribution modestly increases returns.     

<Emphasis Type="Italic">K</Emphasis>-fold cross validation performance comparisons of six naive portfolio selection rules: how naive can you be and still have successful out-of-sample portfolio performance?

Recent research reports that optimal portfolio selection models often perform worse than equal-weight naive diversification in out-of-sample testing. This paper extends this line of inquiry by comparing the out-of-sample performance of the equal-weight naive strategy to the out-of-sample performance of five alternative naive strategies, each of which derives from a simple heuristic that does not require any optimization. Out-of-sample portfolio performance is assessed by mean, standard deviation, skewness, and Sharpe ratio; k-fold cross validation is used as the out-of-sample testing mechanism. The results indicate that the proposed naive heuristic rules exhibit strong out-of-sample performance, in most cases superior to the equal-weight naive strategy. These findings are consequential for at least two reasons: first, if these simple heuristic-based rules outperform the equal-weight naive strategy, then by transitivity they can outperform the mean–variance- and shortfall-optimal portfolio rules that have been shown in the literature to be inferior to the equal-weight naive rule, which further emphasizes the out-of-sample fragility of “optimal” methods; and second, among naive diversification strategies, some appear more robust in out-of-sample testing than others, hence the proposed methods may be useful when forming mixed portfolio selection models wherein a naive strategy is combined with an optimal strategy to improve performance.     

Economic and financial crises and the predictability of U.S. stock returns

We argue that the use of publicly available and easily accessible information on economic and financial crises to detect structural breaks in the link between stock returns and macroeconomic predictor variables improves the performance of simple trading rules in real time. In particular, our results suggest that accounting for structural breaks and regime shifts in forecasting regressions caused by economic and financial crises has the potential to increase the out-of-sample predictability of stock returns, the performance of simple trading rules, and the market-timing ability of an investor trading in the U.S. stock market.     

Testing for negative expected market return premia

This paper tests the hypothesis that the expected return premium on the market portfolio is always non-negative. A violation of this lower bound restriction provides evidence against a broad class of risk-based equilibrium models in favor of bubble behavior. Our tests utilize information variables, identified in prior literature, that predict time variation in market return premia. We employ out-of-sample forecasts and bootstraps generated with parameters that are consistent with non-negativity but closest to the estimated parameters. We find statistically reliable evidence against non-negativity for the excess return on the value-weighted market index. The most negative out-of-sample prediction was −2.01% in September 1973.     

How good can heuristic-based forecasts be? A comparative performance of econometric and heuristic models for UK and US asset returns

This paper systematically investigates the sources of differential out-of-sample predictive accuracy of heuristic frameworks based on internet search frequencies and a large set of econometric models. The volume of internet searches helps gauge the degree of investors’ time-varying interest in specific assets. We use a wide range of state-of-the-art models, both of linear and nonlinear type (regime-switching predictive regressions, threshold autoregressive, smooth transition autoregressive), extended to capture conditional heteroskedasticity through GARCH models. The predictor variables investigated are those typical of the literature featuring a range of macroeconomic and market leading indicators. Our out-of-sample forecasting exercises are conducted with reference to US, UK, French and German data, both stocks and bonds, and for 1- and 12-months-ahead horizons. We employ several forecast performance metrics and predictive accuracy tests. Internet-search-based models are found to perform better than the average of all of the alternative models. For several country-asset-horizon combinations, particularly for UK bond returns, our heuristic models compare favourably with sophisticated econometric methods. The heuristic models are also shown to perform well in forecasting realized volatility. The baseline results are supported by several extensions and robustness checks, such as using alternative search keywords, controlling for Fama–French and Cochrane–Piazzesi factors, and implementing heuristic-based trading strategies.     

The Effect of Market Regimes on Style Allocation

We analyse time-varying risk premia and the implications for portfolio choice. Using Markov Chain Monte Carlo (MCMC) methods, we estimate a multivariate regime-switching model for the Carhart (1997) four-factor model. We find two clearly separable regimes with different mean returns, volatilities, and correlations. In the High-Variance Regime, only value stocks deliver a good performance, whereas in the Low-Variance Regime, the market portfolio and momentum stocks promise high returns. Regime-switching induces investors to change their portfolio style over time depending on the investment horizon, the risk aversion, and the prevailing regime. Value investing seems to be a rational strategy in the High-Variance Regime, momentum investing in the Low-Variance Regime. An empirical out-of-sample backtest indicates that this switching strategy can be profitable, but the overall forecasting ability for the regime-switching model seems to be weak compared to the iid model.     

Dealing with financial instability under a DSGE modeling approach with banking intermediation: A predictability analysis versus TVP-VARs

In the dynamic stochastic general equilibrium (DSGE) literature there has been an increasing awareness on the role that the banking sector can play in macroeconomic activity. We present a DSGE model with financial intermediation as in Gertler and Karadi (2011). The estimation of shocks and of the structural parameters shows that time-variation should be crucial in any attempted empirical analysis. Since DSGE modelling usually fails to take into account inherent nonlinearities of the economy, we propose a novel time-varying parameter (TVP) state-space estimation method for VAR processes both for homoskedastic and heteroskedastic error structures. We conduct an exhaustive empirical exercise to compare the out-of-sample predictive performance of the estimated DSGE model with that of standard ARs, VARs, Bayesian VARs and TVP-VARs. We find that the TVP-VAR provides the best forecasting performance for the series of GDP and net worth of financial intermediaries for all steps-ahead, while the DSGE model outperforms the other specifications in forecasting inflation and the federal funds rate at shorter horizons.     

Are CDS spreads predictable? An analysis of linear and non-linear forecasting models

This paper investigates the forecasting performance for CDS spreads of both linear and non-linear models by analysing the iTraxx Europe index during the financial crisis period which began in mid-2007. The statistical and economic significance of the models' forecasts are evaluated by employing various metrics and trading strategies, respectively. Although these models provide good in-sample performances, we find that the non-linear Markov switching models underperform linear models out-of-sample. In general, our results show some evidence of predictability of iTraxx index spreads. Linear models, in particular, generate positive Sharpe ratios for some of the strategies implemented, thus shedding some doubts on the efficiency of the European CDS index market.     

Industry return predictability,timing and profitability

This paper aims to investigate the predictability of Australian industrial stock returns. Several identified economic variables are found to contain significant predictive power over industry portfolio returns in a Bayesian dynamic forecasting model. The Bayesian updating process was also applied in an investigation of out-of-sample prediction, timing ability and the profitability of an investment strategy of industry-rotation. When the predictor variables are employed in out-of-sample analysis, the predictive power is superior to the naïve prediction. The timing ability and profitability associated with predictability are also economically significant. When the industry momentum is examined, the results show that a group-rotation strategy can enhance the portfolio performance.     

Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.     

Return predictability and intertemporal asset allocation: Evidence from a bias-adjusted VAR model

Within a VAR based intertemporal asset allocation model we explore the effects on return predictability and optimal asset allocation of adjusting VAR parameter estimates for small-sample bias. We apply a simple and easy-to-use analytical bias formula instead of bootstrap or Monte Carlo bias-adjustment. Regarding return predictability we show that bias-adjustment in the multivariate setup can yield very different results than in the univariate case. Furthermore, bias-correcting the VAR parameters has both quantitatively and qualitatively important effects on the optimal portfolio choice. For intermediate values of risk-aversion, the intertemporal hedging demand for bonds and stocks is heavily affected by the bias-correction. Utility calculations also show large effects of bias-adjustment, both in-sample and out-of-sample.     

The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.     

A Markov regime switching approach for hedging energy commodities

This paper estimates constant and dynamic hedge ratios in the New York Mercantile Exchange oil futures markets and examines their hedging performance. We also introduce a Markov regime switching vector error correction model with GARCH error structure. This specification links the concept of disequilibrium with that of uncertainty (as measured by the conditional second moments) across high and low volatility regimes. Overall, in and out-of-sample tests indicate that state dependent hedge ratios are able to provide significant reduction in portfolio risk.     

Timing and diversification: A state-dependent asset allocation approach

Abstract

The influence of changing economic environment leads the distribution of stock market returns to be time-varying. A conditionally optimal investment hence requires a dynamic adjustment of asset allocation. In this context, this paper examines the improvement in portfolio performance by simulating portfolio strategies that are conditioned on the Markov regime switching behaviour of stock market returns. Including a memory effect eliminates the empirical shortcoming of discrete state models, namely that they produce a standard and an extreme state in stock returns. So far, this has prevented the regimes from being used as a valuable conditioning variable. Based on a discrete state indicator variable, is presented evidence of considerable performance improvement relative to the static model due to optimal shifting between aggressive and well diversified portfolio structures.     

Financial turbulence,systemic risk and the predictability of stock market volatility

This paper adds a novel perspective to the literature by exploring the predictive performance of two relatively unexplored indicators of financial conditions, i.e. financial turbulence and systemic risk, over stock market volatility using a sample of seven emerging and advanced economies. The two financial indicators that we utilize in our predictive setting provide a unique perspective on market conditions, as they relate directly to portfolio performance metrics from both volatility and co-movement perspectives and, unlike other macro-financial indicators of uncertainty, or risk, can be integrated into diversification models within forecasting and portfolio design settings. Since the data for the two predictors are available at a weekly frequency, and our focus is to produce forecasts at the daily frequency, we use the generalized autoregressive conditional heteroskedasticity-mixed data sampling (GARCH-MIDAS) approach. The results suggest that incorporating the two financial indicators (singly and jointly) indeed improves the out-of-sample predictive performance of stock market volatility models over both the short and long horizons. We observe that the financial turbulence indicator that captures asset price deviations from historical patterns does a better job when it comes to the out-of-sample prediction of future returns compared with the measure of systemic risk, captured by the absorption ratio. The outperformance of the financial turbulence indicator implies that unusual deviations in not only asset returns, but also in correlation patterns play a role in the persistence of return volatility. Overall, the findings provide an interesting opening for portfolio design purposes, in that financial indicators, which are directly associated with portfolio diversification performance metrics, can also be utilized for forecasting purposes, with significant implications for dynamic portfolio allocation strategies.     

Prospect theory–based portfolio optimization: an empirical study and analysis using intelligent algorithms

The behaviourally based portfolio selection problem with investor’s loss aversion and risk aversion biases in portfolio choice under uncertainty is studied. The main results of this work are: developed heuristic approaches for the prospect theory model proposed by Kahneman and Tversky in 1979 as well as an empirical comparative analysis of this model and the index tracking model. The crucial assumption is that behavioural features of the prospect theory model provide better downside protection than traditional approaches to the portfolio selection problem. In this research the large-scale computational results for the prospect theory model have been obtained for real financial market data with up to 225 assets. Previously, as far as we are aware, only small laboratory tests (2–3 artificial assets) have been presented in the literature. In order to investigate empirically the performance of the behaviourally based model, a differential evolution algorithm and a genetic algorithm which are capable of dealing with a large universe of assets have been developed. Specific breeding and mutation, as well as normalization, have been implemented in the algorithms. A tabulated comparative analysis of the algorithms’ parameter choice is presented. The prospect theory model with the reference point being the index is compared to the index tracking model. A cardinality constraint has been implemented to the basic index tracking and the prospect theory models. The portfolio diversification benefit has been found. The aggressive behaviour in terms of returns of the prospect theory model with the reference point being the index leads to better performance of this model in a bullish market. However, it performed worse in a bearish market than the index tracking model. A tabulated comparative analysis of the performance of the two studied models is provided in this paper for in-sample and out-of-sample tests. The performance of the studied models has been tested out-of-sample in different conditions using simulation of the distribution of a growing market and simulation of the t-distribution with fat tails which characterises the dynamics of a decreasing or crisis market.     

Stock return expectations in the credit market

In this paper we compute long-term stock return expectations (across the business cycle) for individual firms using information backed out from the credit derivatives market. Our methodology builds on previous theoretical results in the literature on stock return expectations and, empirically, we demonstrate a close relationship between credit-implied stock return expectations and future realized stock returns. We also find stock portfolios selected based on credit-implied stock return forecasts to beat equally- and value-weighted portfolios of the same stocks out-of-sample. Contrary to many other studies, our expectations/predictions are made at the individual stock level rather than at the portfolio level, and no parameter estimations using historical stock price- or credit spread observations are needed.