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.     

Volatility and cross correlation across major stock markets

Several papers have documented the fact that correlations across major stock markets are higher when markets are more volatile—this is done by comparing unconditional correlations over sub-periods or by using conditional correlations that are time varying. In this paper we examine the relation between correlation and variance in a conditional time and state varying framework. We use a switching ARCH (SWARCH) technique that does two things. One, it enables us to model variance as state varying. Two, a bivariate SWARCH model allows us to go from conditional variance to state varying covariances and correlations and hence test for differences in correlations across variance regimes. We find that the correlations between the U.S. and other world markets are on average 2 to 3.5 times higher when the U.S. market is in a high variance state as compared to a low variance regime. We also find that, compared to a GARCH framework, the portfolio choices resulting from our SWARCH model lead to higher Sharpe ratios.     

Earnings quality and the heterogeneous relation between earnings and stock returns

We adopt a heterogeneous regime switching method to examine the informativeness of accounting earnings for stock returns. We identify two distinct time-series regimes in terms of the relation between earnings and returns. In the low volatility regime (typical of bull markets), earnings are moderately informative for stock returns. But in high volatility market conditions (typical of financial crisis), earnings are strongly related to returns. Our evidence suggests that earnings are more informative to investors when uncertainty and risk is high which is consistent with the idea that during market downturns investors rely more on fundamental information about the firm. Next, we identify groups of firms that follow similar regime dynamics. We find that the importance of accounting earnings for returns in each of the market regimes varies across firms: certain firms spend more time in a regime where their earnings are highly relevant to returns, and other firms spend more time in a regime where earnings are moderately relevant to returns. We also show that firms with poorer accrual quality have a greater probability of belonging to the high volatility regime.     

Are the gains from international portfolio diversification exaggerated? The influence of downside risk in bear markets

The fundamental rationale for international portfolio diversification is that it expands the opportunities for gains from portfolio diversification beyond those that are available through domestic securities. However, if international stock market correlations are higher than normal in bear markets, then international diversification will fail to yield the promised gains just when they are needed most. We evaluate the extent to which observed correlations to monthly returns in bear, calm and bull markets are captured by three popular bivariate distributions: (1) the normal, (2) the restricted GARCH(1,1) of J. P. Morgan’s RiskMetrics, and (3) the Student-t with four degrees of freedom. Observed correlations during calm and bull markets are unexceptional compared to these models. In contrast, observed correlations during bear markets are significantly higher than predicted. Higher-than-normal correlations during extreme market downturns result in monthly returns to equal-weighted portfolios of domestic and international stocks that are, on average, more than two percent lower than those predicted by the normal distribution. If the extent of non-normality during bear markets persists over time, then a US investor allocating assets into foreign markets might want to allocate more assets into foreign markets with near-normal correlation profiles and avoid markets with higher-than-normal bear market co-movements.     

Cross‐region and cross‐sector asset allocation with regimes

Cross‐region and cross‐sector asset allocation decisions are one of the most fundamental issues in international equity portfolio management. Equity returns exhibit higher volatilities and correlations, and lower expected returns, in bear markets compared to bull markets. However, static mean–variance analysis fails to capture this salient feature of equity returns. We accommodate the nonlinearity of returns using a regime switching model across both regions and sectors. The regime‐dependent asset allocation potentially adds value to the traditional static mean–variance allocation. In addition, optimal allocation across sectors provide greater benefits compared to international diversification, which is characterized by higher returns, lower risks, lower correlations with the world market and a higher Sharpe ratio.     

Size,value and momentum in stock returns: evidence from India

This paper examines the effects of size, value and momentum on the cross-sectional relation between expected returns and risk in the Indian stock market. We find that the conditional Carhart four-factor model empirically describes the variation of cross-section of return better than the unconditional model. When size, book-to-market and momentum effects are controlled in the conditional model, the positive relation of market beta, book-to-market and momentum with expected returns remains economically and statistically significant. However, this evidence is found to be subject to characteristics of test portfolios. The expected returns are sensitive to changes in predictive macroeconomic variables.     

Benefits of diversifying investments into emerging markets with time-varying correlations: An Australian perspective

Australian investors can reduce their overall portfolio risk by diversifying into equities from other markets. Emerging markets have attracted significant interest because of their low correlations with Australian equity market returns; however, a number of studies have indicated that correlations between equity returns are increasing over time, so using unconditional estimates of correlations in a portfolio optimization model can result in the selection of a portfolio that may not be optimal.We use an Asymmetric Dynamic Conditional Correlation GARCH model to estimate time-varying correlations and include these correlation estimates in the portfolio optimization model. The assets used for portfolio construction comprise seven emerging market indices that are available to foreign investors. This study finds that, despite increasing correlations, there are still potential benefits for Australian investors who diversify into international emerging markets.     

A Cross-Sectional Empirical Test of a Dual-State Multi-Factor Pricing Model

During empirical testing of the Capital Asset Pricing Model an assumption is typically made that risk is intertemporally constant. However, prior research finds that risk changes over time. We empirically test a conditional dual-state cross-sectional model allowing risk to change through prior identification of different market and economic states. We examine relationships between returns and conditional market and economic-factor betas, size, book-to-market equity, and earnings-price ratios. We find that relationships shift across regimes, suggesting the importance of a conditional, as opposed to unconditional, model. Relationships also change in January.     

Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

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.     

Performance aspects of Greek bond mutual funds

This paper examines the performance characteristics of Greek bond funds and the impact of fund flows on portfolio returns. The evidence shows that on average bond funds do not offer risk-adjusted profits exceeding the returns of the benchmark index, which is in consistence with the US and international evidence. Returns before fees are slightly superior to the returns of the benchmark index, but when fees are considered they lag considerably. The security selection and market timing skills of fund managers are also tested using both an unconditional and a conditional model to test for the impact of public information variables. We also find that fund flows impact negatively on market timing.     

Moments of multivariate regime switching with application to risk-return trade-off

We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.     

Conditional Properties of Hedge Funds: Evidence from Daily Returns*

Using daily returns on a set of hedge fund indices, we study (i) the properties of the indices' conditional density functions and (ii) the presence of asymmetries in conditional correlations between hedge fund indices and other investments and between hedge fund indices themselves. We use the SNP approach to obtain estimates of conditional densities of hedge fund returns and then proceed to examine their properties. In general, a nonparametric GARCH(1,1) model appears to provide the best fit for all strategies. We find that the conditional third and fourth moments are significantly affected by changes in the current volatility of returns on hedge fund indices. We examine changes in the conditional probability of tail events and report significant changes in the probability of extreme events when the conditioning information changes. These results have important implications for models of hedge fund risk that rely on probability of tail events. We formally test for the presence of asymmetries in conditional correlations to determine if there is contagion between hedge funds and other investments and between various hedge fund indices in extreme down markets versus extreme up markets. We generally do not find strong evidence in support of asymmetric correlations.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Do large-cap exchange-traded funds perform better than their small-cap counterparts in extreme market conditions?

This study proposes a new threshold model that differentiates between the size and sign-dependent responses of large- and small-cap exchange-traded funds (ETFs) to changes in extreme market conditions. The asymmetric returns in extreme upsides, extreme downsides, and “in-between” markets are estimated using three sets of betas. Findings support the notion that small-cap ETFs in all seven countries fall more in extreme downturns than they rise in extreme upturns. By contrast, six out of nine large-cap ETFs climb up in upside more than they fall in downswing. Therefore, investors should be cautious when assigning excessive weights to small-cap ETFs in their portfolio.     

Time-varying market,interest rate,and exchange rate risk premia in the US commercial bank stock returns

This paper examines the role of market, interest rate, and exchange rate risks in pricing a sample of the US Commercial Bank stocks by developing and estimating a multi-factor model under both unconditional and conditional frameworks. Three different econometric methodologies are used to conduct the estimations and testing. Estimations based on nonlinear seemingly unrelated regression (NLSUR) via GMM approach indicate that interest rate risk is the only priced factor in the unconditional three-factor model. However, based on ‘pricing kernel’ approach by Dumas and Solnik [(1995). J. Finance 50, 445–479], strong evidence of exchange rate risk is found in both large bank and regional bank stocks in the conditional three-factor model with time-varying risk prices. Finally, estimations based on the multivariate GARCH in mean (MGARCH-M) approach where both conditional first and second moments of bank portfolio returns and risk factors are estimated simultaneously show strong evidence of time-varying interest rate and exchange rate risk premia and weak evidence of time-varying world market risk premium for all three bank portfolios, namely those of Money Center bank, Large bank, and Regional bank.     

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reportedevidence of two types of asymmetries in the joint distributionof stock returns. The first is skewness in the distributionof individual stock returns. The second is an asymmetry in thedependence between stocks: stock returns appear to be more highlycorrelated during market downturns than during market upturns.In this article we examine the economic and statistical significanceof these asymmetries for asset allocation decisions in an out-of-samplesetting. We consider the problem of a constant relative riskaversion (CRRA) investor allocating wealth between the risk-freeasset, a small-cap portfolio, and a large-cap portfolio. Weuse models that can capture time-varying moments up to the fourthorder, and we use copula theory to construct models of the time-varyingdependence structure that allow for different dependence duringbear markets than bull markets. The importance of these twoasymmetries for asset allocation is assessed by comparing theperformance of a portfolio based on a normal distribution modelwith a portfolio based on a more flexible distribution model.For investors with no short-sales constraints, we find thatknowledge of higher moments and asymmetric dependence leadsto gains that are economically significant and statisticallysignificant in some cases. For short sales-constrained investorsthe gains are limited.     

Conditioning Information and European Bond Fund Performance

In this paper we evaluate the performance of European bond funds using unconditional and conditional models. As conditioning information we use variables that we find to be useful in predicting bond returns in the European market. The results show that, in general, bond funds are not able to outperform passive strategies. These findings are robust to whatever model (unconditional versus conditional and single versus multi‐index) we use. The multi‐index model seems to add some explanatory power in relation to the single‐index model. Furthermore, when we incorporate the predetermined information variables, we can observe a slight tendency towards better performance. This evidence is consistent with previous studies on stock funds and comes in support of the argument that conditional models might allow for a better assessment of performance. However, our results suggest that the impact of additional risk factors seems to be greater than the impact of incorporating predetermined information variables.     

Stock market correlations during the financial crisis of 2008–2009: Evidence from 50 equity markets

Using data from 50 equity markets we examine conditional and unconditional correlations around two major banking events during the financial crisis of 2008–09. To measure the value of covariance information on the augmented DCC model used in the study, a portfolio in-sample estimation is performed. We show that by taking into account the change in the level of variance in high volatility periods, the estimates of the conditional covariance are more efficient in capturing the dynamics of the stock markets variance. Furthermore, in a two-asset allocation framework, the model consistently generates relatively low portfolio variances, implying substantial benefits in portfolio diversification.