Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study

Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.     

Asymmetric mean-reversion and contrarian profits: ANST-GARCH approach

This paper investigates the time-series evidence of asymmetric reverting patterns in stock returns that is attributable to “contrarian profitability.” Using asymmetric nonlinear smooth-transition (ANST) GARCH(M) models, we find that, for monthly excess returns of US market indexes over the period of 1926:01–1997:12, negative returns on average reverted more quickly, with a greater reverting magnitude, to positive returns than positive returns revert to negative returns. The results are quite consistent when the models are implemented not only for the different sample periods, such as 1926:01–1987:09 and 1947:01–1997:12, but also for portfolios with different characteristics, such as different firm-size portfolios and Fama–French risk-adjusted factor portfolios. We interpret the asymmetrical reversion as evidence of stock market overreaction.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

Evidence of psychological barriers in the conditional moments of major world stock indices

This study investigates the existence of psychological barriers in the Dow Jones Industrial Average, the S&;P 500, and six foreign stock indices. It is believed by many in the investment community that index levels that are multiples of 100 serve as barriers, and that markets may resist crossing these barriers. Although return dynamics in the neighborhood of barrier points are not identical for all series studied, we find aberrations in the conditional means and variances consistent with psychological barriers. In five of the eight indices studied, conditional mean returns are significantly higher after crossing a barrier as part of an upward move, while only two series exhibit significant mean effects after crossing a barrier as part of a downward move. In seven of the eight series studied, we find significant conditional variance effects coincident with a barrier crossing. In addition, most series exhibit evidence of autoregressive conditional heteroskedastic (ARCH), generalized ARCH (GARCH), and leverage effects.     

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.     

Some extensions of the CAPM for individual assets

There is ample evidence that stock returns exhibit non-normal distributions with high skewness and excess kurtosis. Experimental evidence has shown that investors like positive skewness, dislike extreme losses and show high levels of prudence. This has motivated the introduction of the four-moment capital asset pricing model (CAPM). This extension, however, has not been able to successfully explain average returns. Our paper argues that a number of pitfalls may have contributed to the weak and conflicting empirical results found in the literature. We investigate whether conditional models, whether models that use individual stocks rather than portfolios and whether models that extend both the moment and factor dimension can improve on more traditional static, portfolio-based, mean–variance models. More importantly, we find that the use of a scaled coskewness measure in cross-section regression is likely to be spurious because of the possibility for the market skewness to be close to zero, at least for some periods. We provide a simple solution to this problem.     

Is the ex‐ante equity risk premium always positive? Evidence from a new conditional expectations model

We model the conditional risk premium by combining principal component analysis and a statistical learning technique, known as boosted regression trees. The method is validated through various out‐of‐sample tests. We apply the estimates to test the positivity restriction on the risk premium and find evidence that the risk premium is negative in periods of low corporate and government bond returns, high inflation and downward‐sloping term structure. These periods are linked with changes in business cycles; the states when theories predict the existence of negative risk premium. Based on the evidence, we reject the conditional capital asset pricing model and raise a question over the practice of imposing the positive risk premium constraint in predictive models.     

Are there nonlinearities in short‐term interest rates?

The present paper investigates the characteristics of short‐term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short‐term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short‐term interest rate. Out‐of‐sample forecasting performance of one‐factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.     

The Effect of Money Shocks on Interest Rates in the Presence of Conditional Heteroskedasticity

Most current empirical work finds no evidence that money shocks lower interest rates. We show that these nonresults are mainly due to a failure to model the conditional heteroskedasticity of interest rates. Autoregressive conditional heteroskedasticity (ARCH) models find a significant liquidity effect where ordinary least squares (OLS) models do not. The existence of a liquidity effect is found using different models and sample periods when ARCH models are used in estimation, but never when OLS is employed.     

An examination of alternative CAPM-based models in UK stock returns

We evaluate the performance of unconditional and conditional versions of seven stochastic discount factor models in UK stock returns between January 1975 and December 2001. We find that the conditional four-moment capital asset pricing model (CAPM) has the best performance among the models we consider in terms of the lowest [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591–607] distance measure and explaining the time-series predictability of industry portfolio excess returns. Conditional models also do a better job than unconditional models. However we find that the superior performance of the conditional four-moment CAPM, and conditional models in general, arises in part due to overfitting the data.     

Measuring and Testing the Impact of News on Volatility

This paper defines the news impact curve which measures how new information is incorporated into volatility estimates. Various new and existing ARCH models including a partially nonparametric one are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented which emphasize the asymmetry of the volatility response to news. Our results suggest that the model by Glosten, Jagannathan, and Runkle is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high.     

Mean-variance cointegration and the expectations hypothesis

The present paper sheds further light on a well-known (alleged) violation of the expectations hypothesis of the term structure (EHT): the frequent finding of unit roots in interest rate spreads. We show that the EHT implies (i) that the nonstationarity stems from the holding premium, which is hence (ii) cointegrated with the spread. In a stochastic discount factor framework, we model the premium as being driven by the integrated variance of excess returns. Introducing the concept of mean-variance cointegration, we actually find cointegration relations between the conditional first and second moment of US bond data.     

Risk premia in international equity markets revisited

Recent evidence suggests that global equity markets are becoming more risky. We develop a model to explain risk premia in international equity markets. The model is then used to investigate the changing nature of conditional risk premia and their effect on unconditional global risk. Using this model we find that the increase in international variance and covariance of realized excess returns can be attributed to systematic variations in global risk premia correlated across markets as well. Understanding this additional source of increased global correlation is important. These results have interest both for practitioners and for those interested in modeling global asset prices.     

The predictability of returns on equity REITs and their co-movement with other assets

Recent evidence suggests that the variation in the expected excess returns is predictable and arises from changes in business conditions. Using a multifactor latent variable model with time-varying risk premiums, we decompose excess returns into expected and unexpected excess returns to examine what determines movements in expected excess returns for equity REITs are more predictable than all other assets examined, due in part to cap rates which contain useful information about the general risk condition in the economy. We also find that the conditional risk premiums (expected excess returns) on EREITs move very closely with those of small cap stocks and much less with those of bonds.     

There is a risk-return trade-off after all

This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.     

Can analysts predict rallies better than crashes?

We use the copula approach to study the structure of dependence between sell-side analysts’ consensus recommendations and subsequent security returns, with a focus on asymmetric tail dependence. We match monthly vintages of I/B/E/S recommendations for the period January–December 2011 with excess security returns during six months following recommendation issue. Using a mixed Gaussian–symmetrized Joe–Clayton copula model we find evidence to suggest that analysts can identify stocks that will substantially outperform, but not underperform relative to the market, and that their predictive ability is conditional on recommendation changes.     

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.     

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.     

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.