Dynamic hedge ratio for stock index futures: application of threshold VECM

This study represents one of the first papers in stock-index-futures arbitrage literature to investigate the effects of arbitrage threshold on stock index futures hedging effectiveness by using threshold vector error correction model (hereafter threshold VECM). Moreover, in contrast to prior studies focusing on examining case studies involving mature stock markets, this study not only adopts US S&P 500 stock market as the sample but also adds an analysis of one emerging stock market, Hungarian BSI and examines the differences between them. Finally, this investigation employs a rolling estimation process to examine the impact of arbitrage threshold behaviours on the setting of futures hedging ratio. The empirical findings of this study are consistent with the following notions. First, arbitrage behaviour reduces co-movement between futures and spot markets and increases the volatility of both futures and spot markets. Second, this article denotes the outer regime of futures-spot market for the case of Hungarian BSI (US S&P 500) as a crisis (an unusual) condition. Moreover, arbitrage threshold behaviours make remarkable (unremarkable) shift on optimal hedge ratio between two different market regimes for the case of Hungarian BSI (US S&P 500). Finally, the framework involving regime-varying hedge ratio designed in this study provides a more efficient futures hedge ratio design for Hungarian BSI stock market, but not for US S&P 500 stock market.     

Crossing of Psychological Price Levels: The Price Dynamics and Interaction between S&P500 Index and Index Futures

The authors provide fresh evidence on the nonfundamental-driven price dynamics and interaction between index and index futures by examining the price movements of the S&P500 index and index futures surrounding the crossing of the 00 psychological barriers and 52-week highs and lows. In contrast to the extant evidence that futures leads in fundamental-driven price movements, the authors show the dominance of the crossing in the index in continuing the price trend after the crossing. Even when synchronized crossings occur, the index rises more than the index futures during upward crossings, whereas the index futures falls more than the index during downward crossings. While volatility is significantly reduced before upward crossings, but not for downward crossings, it is significantly higher during the crossing, and significantly lower after the crossings in both markets. These findings have clear practical implications for index arbitrageurs, investors, and regulators.     

Which types of commodity price information are more useful for predicting US stock market volatility?

This study aims to investigate which types of commodity price information are more useful for predicting US stock market realized volatility (RV) in a data-rich word. The standard predictive regression framework and monthly RV data are used to explore the RV predictability of commodity futures for the next-month RV on S&P 500 spot index. We utilize principal component analysis (PCA) and factor analysis (FA) to extract the common factors for each type and all types of commodity futures. Our results indicate that the futures volatility information of grains and softs has a significant predictive ability in forecasting the RV of the S&P 500. In addition, the FA method can yield better forecasts than the PCA and average methods in most cases. Further analysis shows that the volatility information of grains and softs exhibits higher informativeness during recessions and pre-crises. Finally, the forecasts of the five combination methods and different out-of-sample periods confirm our results are robust.     

Realized volatility transmission: The role of jumps and leverage effects

This paper is the first to employ a multivariate extension of the LHAR–CJ model for realized volatility of Corsi and Renó (2012) considering continuous and jump volatility components and leverage effects. The model is applied to financial (S&P 500), commodity (WTI crude oil) and forex (US$/EUR) intraday futures data and allows new insights in the transmission mechanisms among these markets. Besides significant leverage effects, we find that the jump components of all considered assets do not contain incremental information for the one-step ahead realized volatility. The volatility of S&P 500 and US$/EUR exchange rate futures exhibits significant spillovers to the realized volatility of WTI. Moreover, decreasing equity prices appear to increase volatility in other markets, while strengthening of the US$ seems to calm down the crude oil market.     

Correlations and volatility spillovers across commodity and stock markets: Linking energies,food, and gold

This paper employs a VAR-GARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 2000 to 2011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets.     

Market moves and the information content of option prices

In this paper we estimate risk-neutral returns distributions using the prices of options written on S&P 500 index futures and investigate whether or not specific characteristics of the returns distributions might be useful information for the purpose of predicting changes in market direction. The key distributional characteristics we focus on are skewness, kurtosis, and the probability weight in the extreme tails of the implied risk-neutral returns distributions. We find that, with one possible exception, the characteristics we considered are unlikely to improve a trader's ability to predict market moves.     

Market overreaction and investment strategies

We investigated the overreaction of the Korean market in response to shocks in the US stock market, and analysed the dynamic relationship between these two markets since 1996. We found that the KOSPI 200 index futures overreacted to the S&P 500 index returns during the period from 2000 to 2009 when the Korean market was in its growth stage. As the Korean market matured and the KOSPI 200 overnight futures were introduced in 2009, the overreaction disappeared. When investors employed the Kelly model or Value-at-Risk to exploit the overreaction, their trading strategies produced significant profits during the growth stage even after considering transaction costs and risk, but the profits attenuated once the overnight futures market was launched in 2009.     

Score-driven Markov-switching EGARCH models: an application to systematic risk analysis

We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.

Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC).     

Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.     

THE LEAD–LAG RELATION BETWEEN THE S&P500 SPOT AND FUTURES MARKETS: AN INTRADAY-DATA ANALYSIS USING A THRESHOLD REGRESSION MODEL

In this paper we examine the lead–lag interaction between the futures and spot markets of the S&P500 using the threshold regression model on intraday data. The use of threshold variables to model the changes in the regression structure with respect to different market conditions enables us to investigate the lead–lag interaction in a data-based approach and avoid stratifying the data arbitrarily. Using the basis as the threshold variable, we find that the short-selling restrictions in the spot market reduce the effect of the spot index as the leading variable. To study the effect of market-wide information on the interaction between the spot and futures markets, we use the coefficient of determination in the regression of the S&P500 on the Morgan–Stanley Composite Index-US and the Major Market Index as the threshold variable. We find that the lead effect of the futures market over the spot market is stronger when there is more market-wide information. On the other hand, the lead effect of the cash market over the futures market is weaker when there is more market-wide information. In addition, we also use the lagged 45-min return of the spot market as the threshold variable. We find that the lead effect of the spot market is stronger in periods of directionless trading than in periods of good or bad markets.     

Forecasting the S&P 500 index volatility

This study introduces a new pre-differencing transformation for the AR1MA model for forecasting S&P 500 index volatility. The out of sample forecasting performance of the ARIMA model using the new pre-differencing transformation is compared with the out of sample forecasting performance of the mean reversion model and the GARCH model. The ARIMA model using the new pre-differencing transformation introduced in this study is found to be superior to both the mean reversion model and the GARCH model in forecasting monthly S&P 500 index volatility for the forecast comparison periods used in this study.     

Markov regime-switching Beta-t-EGARCH

We suggest a Markov regime-switching (MS) Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model for U.S. stock returns. We compare the in-sample statistical performance of the MS Beta-t-EGARCH model with that of the single-regime Beta-t-EGARCH model. For both models we consider leverage effects for conditional volatility. We use data from the Standard Poor’s 500 (S&P 500) index and also a random sample that includes 50 components of the S&P 500. We study the outlier-discounting property of the single-regime Beta-t-EGARCH and MS Beta-t-EGARCH models. For the S&P 500, we show that for the MS Beta-t-EGARCH model extreme observations are discounted more for the low-volatility regime than for the high-volatility regime. The conditions of consistency and asymptotic normality of the maximum likelihood estimator are satisfied for both the single-regime and MS Beta-t-EGARCH models. All likelihood-based in-sample statistical performance metrics suggest that the MS Beta-t-EGARCH model is superior to the single-regime Beta-t-EGARCH model. We present an application to the out-of-sample density forecast performance of both models. The results show that the density forecast performance of the MS Beta-t-EGARCH model is superior to that of the single-regime Beta-t-EGARCH model.     

Calendar anomalies in cash and stock index futures: International evidence

This paper examines calendar anomalies (day-of-the-week and monthly seasonal effects) in cash and stock index futures returns. We consider daily data from FTSE100 (UK), FTSE/ASE-20 (Greece), S&P500 (US) and Nasdaq100 (US) spot and future indexes over the period 2004–2011. We employ a Regime-Switching specification which allows us to distinguish between different regimes corresponding to high and low volatile periods. The results show differences in the seasonal patterns in cash and futures indexes due to the existence of basis risk. Calendar effects are also conditioned to the market situation. During a low volatile situation these calendar effects tend to be positive, but these effects turn negative if the market is under a high volatile period. These findings are recommended to financial risk managers dealing with futures markets.     

Modeling volatility and conditional correlations between socially responsible investments,gold and oil

Socially responsible investing (SRI) is one of the fastest growing areas of investing. While there is a considerable literature comparing SRI to various benchmarks, very little is known about the volatility dynamics of socially responsible investing. In this paper, multivariate GARCH models are used to model volatilities and conditional correlations between a stock price index comprised of socially responsible companies, oil prices, and gold prices. The dynamic conditional correlation model is found to fit the data the best and used to generate dynamic conditional correlations, hedge ratios and optimal portfolio weights. From a risk management perspective, SRI offers very similar results in terms of dynamic conditional correlations, hedge ratios, and optimal portfolio weights as investing in the S&P 500. For example, SRI investors can expect to pay a similar amount to hedge their investment with oil or gold as investors in the S&P 500 would pay. These results can help investors and portfolio managers make more informed investment decisions.     

Value of hedge and expected returns

We demonstrate how it is possible to generate value for an investor with a hedge attached to the buy-and-hold strategy of an S&P 500 index fund. We study the S&P 500 index portfolio (not including dividends) and the value-weighted S&P 500 index portfolio (including dividends) of the Center for Research in Securities Prices for 1967:01–2011:12, using the capacity utilization and the unemployment rates in real time to determine if a hedge position should be initiated or closed. A hedge is initiated if the capacity utilization, the unemployment rate or a combination of the two signals a contraction in the real economy. The hedge position is closed if it signals otherwise an expansion. We use utility gains (Campbell and Thompson 2008), the manipulation-proof performance measure (MPPM) statistics (Ingersoll et al. 2007) and the P-Sharpe ratio (Bailey and López de Prado 2012) to evaluate the performance of a particular hedge strategy. The empirical results show that there are infinitely many hedges that can generate positive utility gains, higher MPPM statistics and higher P-Sharpe ratios.     

Investment performance of shorted leveraged ETF pairs

We analyze investment strategies involving triple-leveraged and inverse triple-leveraged ETF pairs by simulating daily returns over a 48-year period. Our results show that many such strategies significantly outperform the S&P 500 on a risk-adjusted basis. For example, when shorting the bear triple-leveraged ETF and the bull triple-leveraged ETF in a 2:1 proportion (while going long Treasuries), we find that the average annual Sharpe ratio is more than four times higher than for the S&P 500 and that the strategy outperforms the S&P 500 in 43 of the 48 years. Our results are robust to variations in bear/bull proportions, rebalance thresholds, and underlying parameters.     

Using the Haar wavelet transform in the semiparametric specification of time series

Using theoretical arguments for nonparametric wavelet estimation, we devise regression-based semiparametric wavelet estimators to dissect linear from nonlinear effects in a time series. The wavelet estimators localize in both time and frequency so that distortion due to outliers is lessened. Our regression-based approach also lends itself to ease of replication, clarity, flexibility, timeliness and statistical validity. We demonstrate the efficacy of the approach via rolling regressions on time series of quarterly U.S. GDP growth rates, monthly Hong Kong/ U.S. exchange rates, weekly 1-month commercial interest rates and daily returns on the S&P 500.     

QARMA-Beta-t-EGARCH versus ARMA-GARCH: an application to S&P 500

Statistical performance and out-of-sample forecast precision of ARMA-GARCH and QARMA-Beta-t-EGARCH are compared. We study daily returns on the Standard and Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 for period May 2006 to July 2010. Competing models are estimated for periods before and during the US financial crisis of 2008. Out-of-sample point and density forecasts are performed for periods during and after the US financial crisis. The results provide evidence of the superior in-sample statistical and out-of-sample predictive performance of QARMA-Beta-t-EGARCH.     

Exploring what stock markets tell us about GDP in theory and practice

This paper explores the stock market-GDP relationship from basic theory to simple empirics to better understand what stock market movements tell us about underlying GDP in real time. We present a simple theoretical model to make key relationships clear, then explore US GDP and US stock market (S&P 500) performance through a range of analytical tools from visual inspection to correlations, regressions, counting and extreme value calculations to a few illustrative narrative investigations. We find that the S&P 500 is weakly correlated with real GDP as well as with vintage GDP releases contemporaneous, but more strongly and statistically significantly with one lag as theory predicts. We also find that the S&P 500 is more closely related both contemporaneously and with a lag to final, revised GDP numbers - only known months later - than to vintage GDP estimates, suggesting that stock market trends are informative about true GDP.     

The links between international parity conditions and Granger causality: a study of exchange rates and prices

This article provides a simple equilibrium model of a futures market. Since the futures market is a zero sum game, some firms will, in equilibrium, end up being ‘speculators’ who bet against ‘hedgers’. We show it is firms that have high initial capital and/or poor production opportunities that are the most likely candidates to bet against the hedgers. In equilibrium, these groups earn a premium in order to provide this insurance so that speculating increases value. We also provide some results that imply an inverted U shaped relationship between trading volume and the level of futures prices. Empirical evidence from the S&P futures contract provides strong empirical support for this theoretical result.