Managing extreme risks in tranquil and volatile markets using conditional extreme value theory

Financial risk management typically deals with low-probability events in the tails of asset price distributions. To capture the behavior of these tails, one should therefore rely on models that explicitly focus on the tails. Extreme value theory (EVT)-based models do exactly that, and in this paper, we apply both unconditional and conditional EVT models to the management of extreme market risks in stock markets. We find conditional EVT models to give particularly accurate Value-at-Risk (VaR) measures, and a comparison with traditional (Generalized ARCH (GARCH)) approaches to calculate VaR demonstrates EVT as being the superior approach both for standard and more extreme VaR quantiles.     

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.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

Conditional Heteroskedasticity and Global Stock Return Distributions

This paper investigates conditional return distribution characteristics for seven developed markets (DMs) and eight emerging markets (EMs). With the exception of Germany and Japan, the behavior of monthly returns of DM sample countries is similar to that of the U.S. In contrast, EM returns exhibit a substantially greater degree of serial correlation and a higher incidence of autoregressive conditional heteroskedasticity (ARCH) in monthly data. Aggregation of returns into two- and three-month holding periods decreases the significance of the ARCH effects. However, there are cross-sectional differences in the rate at which ARCH effects become insignificant. The findings of ARCH in monthly returns sample data is attributed to differences in the rate at which information arrives and is transmitted into prices in each market.     

An Assessment of Empirical Model Performance When Financial Market Transactions are Observed at Different Data Frequencies: An Application to East Asian Exchange Rates

This paper compares the performance of alternative models of east Asian exchange rates at different data frequencies. Selected models employ different specifications of the conditional variance and the conditional error distribution. Conditional variance specifications include: homoscedasticity, GARCH, LGARCH, and EGARCH. Conditional error distribution specifications include normal and Student t. The best exchange rate model specification is clearly conditional on data frequency. Higher frequency (daily, weekly) data commonly exhibit characteristics that demand more sophisticated estimation methods than analysts commonly employ. These characteristics generally vanish at lower (monthly, quarterly) frequencies. Overall we find significant benefit from accommodating heteroscedasticity and leptokurtic properties of the conditional distribution as data frequency increases. Using a likelihood ratio test we compare the relative gain from addressing heteroscedasticity (through use of GARCH models) versus accommodation of leptokurtosis. This comparison suggests that the gains from correct specification of the conditional distribution dominate those obtained from addressing problems of heteroscedasticity.     

MARKET MODEL CORRECTED FOR GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY AND THE SMALL FIRM EFFECT

Prior studies show that heteroscedasticity and serial correlation are present in the market model. In this paper I estimate the market model parameters under generalized autoregressive conditional heteroscedastic processes. Employing daily stock rate of return data from the Center for Research in Security Prices for 1985 through 1989, excluding October 1987 and October 1989, I show that previous estimates of beta coefficients are overstated significantly, suggesting model improvements are needed to take these problems into account. The efficiency of the market model parameters is significantly improved across all firms during the period investigated.     

Size,time-varying beta,and conditional heteroscedasticity in UK stock returns

The purpose of this study is to examine the relationship between firm size and time-varying betas of UK stocks. We extend the Schwert and Seguin (1990)(Journal of Finance 45, 1120–1155) methodology by explicitly modeling conditional heteroscedasticity in the market model residual returns. Our results show that the time-varying coefficient is not statistically significant for both small and large firm stock indexes. We also find that accounting for GARCH effects in the Schwert-Seguin market model yields beta estimates that are markedly differently from those when conditional heteroscedasticity is ignored. Event studies that ignore conditional heteroscedasticity may bias the abnormal returns of small and large firms, thereby leading to a different conclusion regarding the significance of an information event.     

Evaluating the Forecast Accuracy of Emerging Market Stock Returns

This paper analyzes the forecast performance of emerging market stock returns using standard autoregressive moving average (ARMA) and more elaborated autoregressive conditional heteroskedasticity (ARCH) models. Our results indicate that the ARMA and ARCH specifications generally outperform random walk models. Models that allow for asymmetric shocks to volatility are better for in-sample estimation (threshold autoregressive conditional heteroskedasticity for daily returns and exponential generalized autoregressive conditional heteroskedasticity for longer periods), and ARMA models are better for out-of-sample forecasts. The results are valid using both U. S. dollar and domestic currencies. Overall, the forecast errors of each Latin American market can be explained by the forecasts of other Latin American markets and Asian markets. The forecast errors of each Asian market can be explained by the forecasts of other Asian markets, but not by Latin American markets. Our predictability results are economically significant and may be useful for portfolio managers to enter or leave the market.     

Determinants of returns and volatility of Chinese ADRs at NYSE

This paper examines the determinants of returns and of volatility of the Chinese ADRs as listed at NYSE. Using an autoregressive conditional heteroskedasticity (ARCH) model and data from 16 April 1998 through 30 September 2004, we find that Hong Kong stock market (underlying market), US stock market (host market), and local (Shanghai A and B) markets all are important determinants of returns of the Chinese ADRs. However, the underlying Hong Kong market has the most significant impact on mean returns of the ADRs. In terms of the determinants of the conditional volatility of the ADRs returns, only shocks to the underlying markets are significant. These results are consistent with [Kim, M., Szakmary, A.C., Mathur, I., 2000. Price transmission dynamics between ADRs and their underlying foreign securities. Journal of Banking and Finance 24, 1359–1382] who find that the most influential factor in pricing the ADRs in Japan, UK, Sweden, The Netherlands and Australia is their underlying shares. Implications of the results for investors are discussed.     

Conditional sovereign CDS in market basket risk scenario: A dynamic vine-copula analysis

This study examines the sensitivity of sovereign CDS markets in G7 and BRICS, which is conditional on a joint market basket risk scenario consisting of crude oil, gold, stock indices, exchange rates, freight indices, and copper prices. By compare the conditional and unconditional sovereign CDS returns using dynamic Vine-Copula model, we find that: 1) The conditional sovereign CDS returns will be less than (greater than) the unconditional ones, when scenario settings is at upper (lower) quantile level. Extreme scenario risk level settings (e.g., 1% or 99%) do not always make a significant difference between conditional and unconditional sovereign CDS. 2) Major black swan evens have significant impact on the difference between the conditional and unconditional sovereign CDS, but such an impact is short-lived especially in G7 countries. 3) Taking into account of the covariate effects, the conditional risk scenarios of sovereign CDS are heterogeneous across countries, down- and up-ward tail as well risk factors associated with the market basket.     

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.     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

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 Efficiency of Conditional Heteroskedasticity Models

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.     

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.     

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.     

The quality of market volatility forecasts implied by S&P 100 index option prices

This study examines the performance of the S&P 100 implied volatility as a forecast of future stock market volatility. The results indicate that the implied volatility is an upward biased forecast, but also that it contains relevant information regarding future volatility. The implied volatility dominates the historical volatility rate in terms of ex ante forecasting power, and its forecast error is orthogonal to parameters frequently linked to conditional volatility, including those employed in various ARCH specifications. These findings suggest that a linear model which corrects for the implied volatility's bias can provide a useful market-based estimator of conditional volatility.     

Smooth Transition ARCH Models: Estimation and Testing

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.     

Return predictability in African stock markets

This paper models weekly index returns adjusted for thin trading as a nonlinear autoregressive process with conditional heteroscedasticity to investigate the weak-form pricing efficiency of 11 African stock markets. Specifically, the use of the EGARCH-M model allows us to capture how conditional volatility affects the pricing process without imposing undue restrictions on the parameters of the conditional variance equation. On the basis of such a robust model, we are able to reject the evidence in prior studies that the Nigerian stock market is weak-form efficient. On the other hand, we confirm extant results that the markets in Egypt, Kenya, and Zimbabwe are efficient while that of South Africa is not weak-form efficient. We also generate new results, which point to the efficiency of the stock markets in Mauritius and Morocco, while the markets in Botswana, Ghana, Ivory Coast, and Swaziland are not consistent with weak-form efficiency.     

VOLATILITY FORECASTS,TRADING VOLUME,AND THE ARCH VERSUS OPTION‐IMPLIED VOLATILITY TRADE‐OFF

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored. We find that if trading volume was low during period t?1 relative to the recent past, ARCH is at least as important as options for forecasting future stock market volatility. Conversely, if volume was high during period t?1 relative to the recent past, option‐implied volatility is much more important than ARCH for forecasting future volatility. Considering relative trading volume as a proxy for changes in the set of information available to investors, our findings reveal an important switching role for trading volume between a volatility forecast that reflects relatively stale information (the historical ARCH estimate) and the option‐implied forward‐looking estimate.