Regime switching in the relationship between equity returns and short-term interest rates in the UK

This paper examines the relationship between UK equity returns and short-term interest rates using a two regime Markov-Switching EGARCH model. The results suggest one high-return, low variance regime within which the conditional variance of equity returns responds persistently but symmetrically to equity return innovations. In the other, low-mean, high variance, regime equity volatility responds asymmetrically and without persistence to shocks to equity returns. There is evidence of a regime dependent relationship between shorter maturity interest rate differentials and equity return volatility. Furthermore, there is evidence that events in the money markets influence the probability of transition across regimes.     

How asymmetric is U.S. stock market volatility?

This paper explores differences in the impact of equally large positive and negative surprise return shocks in the aggregate U.S. stock market on: (1) the volatility predictions of asymmetric time-series models, (2) implied volatility, and (3) realized volatility. Following large negative surprise return shocks, both asymmetric time-series models (such as the EGARCH and GJR models) and implied volatility predict an increase in volatility and, consistent with this, ex post realized volatility normally rises as predicted. Following large positive return shocks, asymmetric time-series models predict an increase in volatility (albeit a much smaller increase than following a negative shock of the same magnitude), but both implied and realized volatilities generally fall sharply. While asymmetric time-series models predict a decline in volatility following near-zero returns, both implied and realized volatility are normally little changed from levels observed prior to the stable market. The reasons for the differences are explored.     

The predictive power of the implied volatility of options traded OTC and on exchanges

This paper investigates the efficiency of stock index options traded over-the-counter (OTC) and on the exchanges in Hong Kong and Japan. Our findings suggest that implied volatility is superior to either historical volatility or a GARCH-type volatility forecast in predicting future volatility in both the OTC and exchange markets. This paper is also one of the first to compare the predictive power of the implied volatility of stock index options traded OTC to that of exchange-traded stock index options. Our evidence suggests that the OTC market is more efficient than the exchanges in Japan, but that the opposite is true in Hong Kong.     

Asymmetric risk premium in value and growth stocks

There are two competing explanations for the existence of a value premium, a rational market risk explanation, whereby value stocks are inherently more risky than growth stocks, and a market over-reaction hypothesis, where agents overstate future returns on growth stock. Using asymmetric GARCH-M models this paper tests the predictions of the two hypotheses. Specifically, examining whether returns exhibit a positive (negative) risk premium resulting from a negative (positive) shock and the relative size of any premium. The results of the paper suggest that following a shock, volatility and expected future volatility are heightened, leading to a rise in required rates of return which depresses current prices. Further, these effects are heightened for value stock over growth stock and for negative shocks over positive shocks. Thus, in support of the rational risk interpretation, with a volatility feedback explanation for predictive volatility asymmetry.     

Confidence building on Euro convergence: Evidence from currency options

We study the evolution of investor confidence in 1992-1998 over the chance of individual currencies to converge to the Euro, using data on currency option prices. Convergence risk, which may reflect uncertainty over policy commitment as well as exogenous fundamentals, induces a level of implied volatility in excess of actual volatility. This volatility wedge should gradually decrease as confidence grows over time as convergence policy is maintained, and the risk of a reversal is progressively resolved. Empirically, we indeed find a positive volatility wedge which declines over time only for currencies involved in the Euro convergence process. The wedge and other convergence risk measures are correlated with both exogenous fundamentals and proxies for policy commitment uncertainty. We also find that the wedge responds to policy shocks in an asymmetric fashion, suggesting that policy risk is resolved at different rates after negative and positive shocks. Finally, we estimate a regime-switching model of convergence uncertainty, using data on interest rates, currency rates, and currency option prices. The results confirm the time-varying and asymmetric nature of convergence risk, and indicate that investors demand a risk premium for convergence risk.     

Looking for risk premium and contagion in Asia-Pacific foreign exchange markets

This article tests pure contagion effects among four Asian foreign exchange markets, namely, Japan, Hong Kong, Singapore, and Taiwan during the 1997 Asian crisis. A conditional version of international capital asset pricing model (ICAPM) in the absence of purchasing power parity (PPP) is used to control for economic fundamentals or systematic risks. The empirical results show strong contagion effects in both conditional means and volatilities of those markets after systematic risks have been accounted for. Specifically, the contagion-in-mean effects are mainly driven by the past return shocks in Hong Kong, Singapore, and Taiwan. As for contagion in volatility, the lead/lag relationships appear to be multidirectional among Japan, Singapore, and Taiwan, but between Hong Kong and Singapore, and between Hong Kong and Taiwan, they are unidirectional, with Hong Kong playing the dominant role in generating negative volatility shocks. In addition, the conditional ICAPM with asymmetric multivariate general autoregressive conditional heteroscedastic in mean (MGARCH(1,1)-M) structure is able to explain/predict on average 17.28% of the return variations in those markets. Therefore, this study provide a further evidence that the time-varying risk premium is a very strong candidate in explaining the predictable excess return puzzle [Lewis, K. K. (1994). Puzzles in international financial markets. NBER Working Paper No. 4951] since the risk premia founded in this article are not only statistically significant but also economically significant.     

Ex Ante Stock Market Return Volatility Implied by the OEX Option Premium

Previous empirical evidence suggests that stock return volatility expectations change over time, but the existing models of time-varying variance lack a theoretical structure that is rigorously linked to the efficient markets dividend discount model. This paper develops and tests such a model. The conditional forecast variance of the return on the stock market portfolio is expressed as a linear combination of the adjusted conditional forecast variance of the interest rate and the dividend growth rate. An empirical test using the implied variance of the S&P 100 index option provides evidence that supports the model's predictions.     

Firm size and volatility analysis in the Spanish stock market

Using Spanish stock market data, this paper examines volatility spillovers between large and small firms and their impact on expected returns. By using a conditional capital asset pricing model (CAPM) with an asymmetric multivariate GARCH-M covariance structure, it is shown that there exist bidirectional volatility spillovers between both types of companies, especially after bad news. After estimating the model, a positive and significant price of risk is obtained. This result is consistent with the volatility feedback effect, one of the most popular explanations of the asymmetric volatility phenomenon, and explains why risk premiums are much more sensitive to negative return shocks coming from the whole market or other related markets.     

Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions

Financial returns typically display heavy tails and some degree of skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using recent generalizations of the asymmetric Student-t and exponential power distributions to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial return volatility and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distributions are used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide evidence for the usefulness of the general distributions in improving fit and prediction of downside market risk of financial assets. Constrained versions, corresponding with distributions used in the previous literature, are also estimated in order to provide a comparison of the performance of different conditional distributions.     

A behavioural explanation to the asymmetric volatility phenomenon: Evidence from market volatility index

This study examines how the behavioural explanations, in particular loss aversion, can be used to explain the asymmetric volatility phenomenon by investigating the relationship between stock market returns and changes in investor perceptions of risk measured by the volatility index. We study the behaviour of India volatility index vis‐à‐vis Hong Kong, Australia and UK volatility index, and provide a comprehensive comparative analysis. Using Bai‐Perron test, we identify structural breaks and volatility regimes in the time series of volatility index, and investigate the volatility index‐return relation during high, medium and low volatility periods. Regardless of volatility regimes, we find that volatility index moves in opposite direction in response to stock index returns, and contemporaneous return is the most dominating across the four markets. The negative relation is strongest for UK followed by Australia, Hong Kong and India. Second, volatility index reacts significantly different to positive and negative returns; negative return has higher impact on changes in volatility index than positive return across the markets over full‐sample and sub‐sample periods. The asymmetric effect is stronger in low volatility regime than in high and medium volatility periods for all the markets except UK. The strength of asymmetric effect is strongest for Hong Kong and weakest for India. Finally, negative returns have exponentially increasing effect and positive returns have exponentially decreasing effect on the changes in volatility index.     

Cross-section of option returns and volatility

We study the cross-section of stock option returns by sorting stocks on the difference between historical realized volatility and at-the-money implied volatility. We find that a zero-cost trading strategy that is long (short) in the portfolio with a large positive (negative) difference between these two volatility measures produces an economically and statistically significant average monthly return. The results are robust to different market conditions, to stock risks-characteristics, to various industry groupings, to option liquidity characteristics, and are not explained by usual risk factor models.     

Theory and evidence on the dynamic interactions between sovereign credit default swaps and currency options

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.     

The relationship between stock returns and volatility in international stock markets

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

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.     

Modeling structural changes in the volatility process

GARCH-type models have been very successful in describing the volatility dynamics of financial return series for short periods of time. However, the time-varying behavior of investors, for example, may cause the structure of volatility to change and the assumption of stationarity is no longer plausible. To deal with this issue, the current paper proposes a conditional volatility model with time-varying coefficients based on a multinomial switching mechanism. By giving more weight to either the persistence or shock term in a GARCH model, conditional on their relative ability to forecast a benchmark volatility measure, the switching reinforces the persistent nature of the GARCH model. The estimation of this benchmark volatility targeting or BVT-GARCH model for Dow 30 stocks indicates that the switching model is able to outperform a number of relevant GARCH setups, both in- and out-of-sample, also without any informational advantages.     

The relationship between risk and expected return in Europe

We employ MIDAS (mixed data sampling) to study the risk–expected return trade-off in several European stock indices. Using MIDAS, we report that in most indices there is a significant positive relationship between risk and expected return. This strongly contrasts with the result we obtain when we employ both symmetric and asymmetric GARCH models for conditional variance. We also find that asymmetric specifications of the variance process within the MIDAS framework improve the relationship between risk and expected return. As an additional application, we analyze the extent to which European stock markets are integrated, which is a particularly relevant issue, especially following the launch of the Euro in January 1999. Finally, we propose a bivariate MIDAS specification to test the pricing significance of the hedging component within an intertemporal risk–return trade-off with multiple European market indices.     

Modeling the time varying volatility of housing returns: Further evidence from the U.S. metropolitan condominium markets

This study extends the literature on modeling the volatility of housing returns to the case of condominium returns for five major U.S. metropolitan areas (Boston, Chicago, Los Angeles, New York, and San Francisco). Through the estimation of ARMA models for the respective condominium returns, we find volatility clustering of the residuals. The results from an ARMA‐TGARCH‐M model reveal the absence of asymmetry in the conditional variance. Dummy variables associated with the housing market collapse unique to each metropolitan area were statistically insignificant in the conditional variance equation, but negative and statistically significant in the mean equation. Condominium markets in Los Angeles and San Francisco exhibit the greatest persistence to volatility shocks.     

Risk and the January effect

We use a time-series GARCH framework with the conditional variance/covariance as proxies for systematic risk to reexamine the proposition by Rozeff and Kinney (1976) and Rogalski and Tinic (1986) that the January effect may be a phenomenon of risk compensation in the month. We find no clear evidence that either conditional volatility or unconditional volatility in January is predominantly higher across the sampling years. Hence, against the proposition, the January effect is not due to risk per se. Rather, we find strong evidence that the January effect is due to higher compensation for risk in the month. This may be possible if investors have an increasing RRA utility function. Although many studies find that volatility tends to be higher in January, we find it to be period-specific and mostly in value-weighted return series, but not in equal-weighted return series. This is true both for the unconditional and conditional return volatility.     

Stock returns,trading volume,and volatility: The case of African stock markets

The presence of the African Stock Markets (ASMs) in the global frontier markets indices confirms their global portfolio diversification role. This study investigates the asymmetric and intertemporal causality among the stock returns, trading volume, and volatility of eight ASMs. Results based on the linear model reveal that return generally Granger cause trading volume. However, evidence from the quantile regression shows that lagged trading volume has a negative causal effect on returns at low quantiles and positive causal effects at high quantiles. This evidence is consistent with volume-return equilibrium models, disposition and overconfidence models, and information asymmetry models. The positive causal effects of volatility on volume support the dispersion of beliefs model. In contrast, intertemporal evidence of contemporaneous and lagged causal relationships from trading volume to volatility supports the mixture of distribution hypothesis, sequential information acquisition hypothesis, and dynamic efficient market hypothesis. Volume-return and return-volume causality dynamics are quantile-specific and therefore driven by market conditions. However, the volume-volatility causality is dependent on volatility regimes. The linear model results confirm how model misspecification can distort and even reverse empirical evidence relative to nonlinear models.