An economic evaluation of stock–bond return comovements with copula-based GARCH models

Owing to their importance in asset allocation strategies, the comovements between the stock and bond markets have become an increasingly popular issue in financial economics. Moreover, the copula theory can be utilized to construct a flexible joint distribution that allows for skewness in the distribution of asset returns as well as asymmetry in the dependence structure between asset returns. Therefore, this paper proposes three classes of copula-based GARCH models to describe the time-varying dependence structure of stock–bond returns, and then examines the economic value of copula-based GARCH models in the asset allocation strategy. We compare their out-of-sample performance with other models, including the passive, the constant conditional correlation (CCC) GARCH and the dynamic conditional correlation (DCC) GARCH models. From the empirical results, we find that a dynamic strategy based on the GJR-GARCH model with Student-t copula yields larger economic gains than passive and other dynamic strategies. Moreover, a less risk-averse investor will pay higher performance fees to switch from a passive strategy to a dynamic strategy based on copula-based GARCH models.     

Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach

To analyze the intertemporal interaction between the stock andbond market returns, we assume that the conditional covariancematrix follows a multivariate GARCH process. We allow for asymmetriceffects in conditional variances and covariances. Using dailydata, we find strong evidence of conditional heteroskedasticityin the covariance between stock and bond market returns. Theresults indicate that not only variances, but also covariancesrespond asymmetrically to return shocks. Bad news in the stockand bond market is typically followed by a higher conditionalcovariance than good news. Cross asymmetries, that is, asymmetriesfollowed from shocks of opposite signs, appear to be importantas well. Covariances between stock and bond returns tend tobe relatively low after bad news in the stock market and goodnews in the bond market. A financial application of our modelshows that optimal portfolio shares can be substantially affectedby asymmetries in covariances. Moreover, our results show sizablegains due to asymmetric volatility timing.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.     

Analyzing hedging strategies for fixed income portfolios: A Bayesian approach for model selection

During the recent European sovereign debt crisis, returns on EMU government bond portfolios experienced substantial volatility clustering, leptokurtosis and skewed returns as well as correlation spikes. Asset managers invested in European government bonds had to derive new hedging strategies to deal with changing return properties and higher levels of uncertainty. In this environment, conditional time series approaches such as GARCH models might be better suited to achieve a superior hedging performance relative to unconditional hedging approaches such as OLS. The aim of this study is to test innovative hedging strategies for EMU bond portfolios for non-crisis and crisis periods. We analyze single and composite hedges with the German Bund and the Italian BTP futures contracts and evaluate the hedging effectiveness in an out-of-sample setting. The empirical analysis includes OLS, constant conditional correlation (CCC), and dynamic conditional correlation (DCC) multivariate GARCH models. We also introduce a Bayesian composite hedging strategy, attempting to combine the strengths of OLS and GARCH models, thereby endogenizing the dilemma of selecting the best estimation model. Our empirical results demonstrate that the Bayesian composite hedging strategy achieves the highest hedging effectiveness and compares particularly favorable to OLS during the recent sovereign debt crisis. However, capturing these benefits requires low transactions cost and efficiently functioning futures markets.     

The empirical risk–return relation: A factor analysis approach

Existing empirical literature on the risk–return relation uses relatively small amount of conditioning information to model the conditional mean and conditional volatility of excess stock market returns. We use dynamic factor analysis for large data sets, to summarize a large amount of economic information by few estimated factors, and find that three new factors—termed “volatility,” “risk premium,” and “real” factors—contain important information about one-quarter-ahead excess returns and volatility not contained in commonly used predictor variables. Our specifications predict 16–20% of the one-quarter-ahead variation in excess stock market returns, and exhibit stable and statistically significant out-of-sample forecasting power. We also find a positive conditional risk–return correlation.     

Asymmetric volatility and risk in equity markets

It appears that volatility in equity markets is asymmetric:returns and conditional volatility are negatively correlated.We provide a unified framework to simultaneously investigateasymmetric volatility at the firm and the market level and toexamine two potential explanations of the asymmetry: leverageeffects and volatility feedback. Our empirical application usesthe market portfolio and portfolios with different leverageconstructed from Nikkei 225 stocks. We reject the pure leveragemodel of Christie (1982) and find support for a volatility feedbackstory. Volatility feedback at the firm level is enhanced bystrong asymmetries in conditional covariances. Conditional betasdo not show significant asymmetries. We document the risk premiumimplications of these findings.     

Hedging with Chinese metal futures

This paper evaluates different hedging strategies for aluminum and copper futures contracts traded at Shanghai Futures Exchange. In addition to usual candidates such as the traditional regression hedge ratio and the hedging strategy constructed from bivariate fractionally integrated generalized autoregressive conditional heteroskedasticity (BFIGARCH) model, two advanced specifications are proposed to account for impacts of the basis on market volatility and co-movements between spot and futures returns. Empirical results suggest that the basis has asymmetric effects and optimal hedging strategy constructed from the asymmetric BFIGARCH model tends to produce the best in-sample and out-of-sample hedging performance.     

Bond risk premia and realized jump risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R² of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high-frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40%. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.     

Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets

We estimate a flexible affine model using an unbalanced panel containing S&P 500 and VIX index returns and option prices and analyze the contribution of VIX options to the model’s in- and out-of-sample performance. We find that they contain valuable information on the risk-neutral conditional distributions of volatility at different time horizons, which is not spanned by the S&P 500 market. This information allows enhanced estimation of the variance risk premium. We gain new insights on the term structure of the variance risk premium, present a trading strategy exploiting these insights, and show how to improve S&P 500 return forecasts.     

Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.     

Asymmetric Correlation and Volatility Dynamics among Stock, Bond, and Securitized Real Estate Markets

We apply a multivariate asymmetric generalized dynamic conditional correlation GARCH model to daily index returns of S&P500, US corporate bonds, and their real estate counterparts (REITs and CMBS) from 1999 to 2008. We document, for the first time, evidence for asymmetric volatilities and correlations in CMBS and REITs. Due to their high levels of leverage, REIT returns exhibit stronger asymmetric volatilities. Also, both REIT and stock returns show strong evidence of asymmetries in their conditional correlation, suggesting reduced hedging potential of REITs against the stock market downturn during the sample period. There is also evidence that corporate bonds and CMBS may provide diversification benefits for stocks and REITs. Furthermore, we demonstrate that default spread and stock market volatility play a significant role in driving dynamics of these conditional correlations and that there is a significant structural break in the correlations caused by the recent financial crisis.     

Modeling Corporate Bond Returns

We propose a conditional factor model for corporate bond returns with five factors and time-varying factor loadings. We have three main empirical findings. First, our factor model excels in describing the risks and returns of corporate bonds, improving over previously proposed models in the literature by a large margin. Second, our model recommends a systematic bond investment portfolio whose high out-of-sample Sharpe ratio suggests that the credit risk premium is notably larger than previously estimated. Third, we find closer integration between debt and equity markets than found in prior literature.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

The Dynamic and Dependence of Takaful and Conventional Stock Return Behaviours: Evidence from the Insurance Industry in Saudi Arabia

This paper investigates the dynamics of volatility in the stock market using competing univariate GARCH specifications. Moreover, it provides a study of the pairwise correlation pattern of stock returns for a wide range of Saudi Arabian insurance business lines by using a dynamic DCC-GARCH model. Our results show that volatility responds asymmetrically to shocks with a persistence of variance in the stock return data, supporting the presence of irrational behaviour as well as the effectiveness of a cross-market diversification strategy. Finally, we reach a point at which, between every two-business line stock returns, there is a dynamic conditional correlation.     

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.     

Model-driven statistical arbitrage on LETF option markets

In this paper, we study the statistical properties of the moneyness scaling transformation, which adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the discrepancy between the IV smiles for levered and unlevered ETF options. We construct bootstrap uniform confidence bands which indicate that the implied volatility smiles are statistically different after moneyness scaling has been performed. An empirical application shows that there are trading opportunities possible on the LETF market. A statistical arbitrage type strategy based on a dynamic semiparametric factor model is presented. This strategy presents a statistical decision algorithm which generates trade recommendations based on comparison of model and observed LETF implied volatility surface. It is shown to generate positive returns with a high probability. Extensive econometric analysis of the LETF implied volatility process is performed including out-of-sample forecasting based on a semiparametric factor model and a uniform confidence bands' study. These provide new insights into the latent dynamics of the implied volatility surface. We also incorporate Heston stochastic volatility into the moneyness scaling method for better tractability of the model.     

A Conditional Assessment of the Relationships between the Major World Bond Markets

This paper uses a bivariate GARCH framework to examine the lead‐lag relations and the conditional correlations between 10‐year US government bond returns and their counterparts from the UK, Germany, and Japan. We find that while mean and volatility spillovers exist between the major international bond markets, they are much weaker than those between equity markets. The results also indicate that the correlations between the US and other major bond market returns are time varying and are driven by changing macroeconomic and market conditions. However, in contrast to the finding that the benefits of international diversification in equity markets evaporate during high‐stress periods, we find that the benefits of diversification across major government bond markets do not decrease during periods of extremely high bond market volatility or following extremely negative US and foreign bond returns.     

Multivariate FIAPARCH modelling of financial markets with dynamic correlations in times of crisis

This paper applies the vector AR-DCC-FIAPARCH model to eight national stock market indices' daily returns from 1988 to 2010, taking into account the structural breaks of each time series linked to the Asian and the recent Global financial crisis. We find significant cross effects, as well as long range volatility dependence, asymmetric volatility response to positive and negative shocks, and the power of returns that best fits the volatility pattern. One of the main findings of the model analysis is the higher dynamic correlations of the stock markets after a crisis event, which means increased contagion effects between the markets. The fact that during the crisis the conditional correlations remain on a high level indicates a continuous herding behaviour during these periods of increased market volatility. Finally, during the recent Global financial crisis the correlations remain on a much higher level than during the Asian financial crisis.     

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.     

The generalized asymmetric dynamic covariance model

In this paper we extend the ADC model of Kroner and Ng [1998. Review of Financial Studies 11, 817–844] such that it allows for cross-asymmetries in conditional volatility. That is, the model allows for asymmetries in covariances after shocks of opposite signs. We find evidence for significant cross-asymmetries in the conditional volatility in stock and bond markets.