The Temporal Price Relationship between S&P 500 Futures and the S&P 500 Index

This paper empirically examines the intraday price relationship between S&P 500 futures and the S&P 500 index using minute-to-minute data. Three-stage least-squares regression is used to estimate lead and lag relationships with estimates for expiration days of the S&P 500 futures compared with estimates for days prior to expiration. The results suggest that futures price movements consistently lead index movements by twenty to forty-five minutes while movements in the index rarely affect futures beyond one minute.     

The innovations of e-mini contracts and futures price volatility components: The empirical investigation of S&P 500 stock index futures

The effect of the initiation of e-mini stock index futures (ESIFs) on the volatility components of S&P 500 stock index futures is herein investigated. The study decomposes S&P 500 stock index-related observed volatilities into unobserved fundamental volatility and transitory noise and utilizes the decomposition to test two hypotheses: the “clientele factor hypothesis” and the “information adjustment hypothesis”. The first hypothesis proposes that the ESIFs attract more noisy traders who prefer trading the friendly-size futures contracts. The second one proposes that the innovations of ESIFs improve the information flow of the futures markets. Using a stochastic volatility model, the empirical results are consistent with both of our proposed hypotheses.     

DID BLACK MONDAY HAVE A PERMANENT EFFECT?

Black Monday caused an immediate disruption between index futures and stock markets, but it is not clear whether it had any lasting effects. Here we examine links between the markets that are sensitive to the liquidity shortages during Black Monday. By employing a tick-by-tick transactions data set of S&P 500 index futures trades and S&P 500 equity index we calculate the spot/futures basis and basis risk, the spot/futures lead/lag relation, and the bid-ask spread. Evidence suggests that Black Monday had little continuing effect. On high-volatility days, however, index arbitrage becomes more costly as prices are more sensitive to future trades.     

Index-futures arbitrage and the behavior of stock index futures prices

This article examines intraday transaction data for S&P500 stock index futures prices and the intraday quotes for theunderlying index. The data indicate that the futures price changesare uncorrelated and that the variability of these price changesexceeds the variability of price changes in the S&P 500index. This excess variability of the futures over the indexremains even after controlling for the nonsynchronous pricesin the index quotes, which induces auto-correlation in the indexchanges. We advance and examine empirically two hypotheses regardingthe difference between the futures price and its theoreticalvalue: that this 'mispricing' increases on average with maturity,and that it is path-dependent. Evidence supporting these hypothesesis presented.     

Pinning in the S&P 500 futures

We show that Standard & Poor's (S&P) 500 futures are pulled toward the at-the-money strike price on days when serial options on the S&P 500 futures expire (pinning) and are pushed away from the cost-of-carry adjusted at-the-money strike price right before the expiration of options on the S&P 500 index (anti-cross-pinning). These effects are driven by the interplay of market makers' rebalancing of delta hedges due to the time decay of those hedges as well as in response to reselling (and early exercise) of in-the-money options by individual investors. The associated shift in notional futures value is at least $115 million per expiration day.     

A further analysis of the lead-lag relationship between the cash market and stock index futures market

The intraday lead-lag relation between returns of the MajorMarket cash index and returns of the Major Market Index futuresand S&P 500 futures is investigated. Empirical results showstrong evidence that the futures leads the cash index and weakevidence that the cash index leads the futures. The asymmetriclead-lag relation holds between the futures and all componentstocks, including. those that trade in almost every five-minuteinterval. Evidence indicates that when more stocks move together(market-wide information) the futures leads the cash index toa greater degree. This suggests that the futures market is themain source of market-wide information.     

INTRADAY MARKET BEHAVIOR AND THE EXTENT OF FEEDBACK BETWEEN S&P 500 FUTURES PRICES AND THE S&P 500 INDEX

In this study we empirically examine the intraday lead/lag relation between S&P 500 futures prices and the S&P 500 index, and whether daily market characteristics are associated with changes in the relation. We estimate daily Geweke measures of feedback and regress time series of these measures on daily price volatility and volume characteristics. Results indicate that the contemporaneous price relation is substantive and that measures of contemporaneous feedback are positively associated with the daily range of the futures price. The primary implication is that the relation between cash and futures prices becomes stronger as futures price volatility increases. As volatility increases, information is being impounded at a faster rate so that futures and equity markets operate more closely as one market. Large futures price moves, by themselves, are not responsible for breakdowns in the stock-futures price relation.     

Price discovery on the S&P 500 index markets: An analysis of spot index,index futures,and SPDRs

This paper investigates the price discovery function in three S&P 500 index markets: the spot index, index futures, and S&P Depositary Receipts markets. Four hypotheses regarding market structure and security design are proposed to differentiate the price discovery function performed by the three index instruments. Using matched synchronous intraday trading data, Johansen's maximum likelihood estimator is employed to disclose the cointegration relationships among the three markets. Results indicate that the three price series are a cointegrated system with one long-run stochastic trend. Estimated coefficients of the vector error correction model suggest that price adjustment takes place in the spot index market and for SPDRs, but not in the futures market. When the common stochastic trend is decomposed, it is found that the futures market serves the dominant price discovery function. The leverage hypothesis and the uptick rule hypothesis explain its superior price discovery function.     

Index arbitrage and nonlinear dynamics between the S&P 500 futures and cash

We use a cost of carry model with nonzero transaction coststo motivate estimation of a nonlinear dynamic relationship betweenthe S&P 500 futures and cash indexes. Discontinuous arbitragesuggests that a threshold error correction mechanism may characterizemany aspects of the relationship between the futures and cashindexes. We use minute-by-minute data on the S&P 500 futuresand cash indexes. The results indicate that nonlinear dynamicsare important and related to arbitrage, and suggest that arbitrageis associated with more rapid convergence of the basis to thecost of carry than would be indicated by a linear model.     

S&P 500 Cash Stock Price Volatilities

S&P 500 stock return volatilities are compared to the volatilities of a matched set of stocks, after controlling for cross-sectional differences in firm attributes known to affect volatility. No significant difference in volatility is observed between 1975 and 1983—before the start of trade in index futures and index options. Since then, S&P 500 stocks have been relatively more volatile. The difference is statistically, but not economically, significant. The relative increase occurs primarily in daily returns and only to a lesser extent in longer interval returns. Other factors besides the start of derivative trade could be responsible for the small increase in volatility.     

Market uncertainty,expected volatility and the mispricing of S&P 500 index futures

An association between increased index futures mispricing and concurrent index volatility has been reported within several prior studies; in the present study, we argue that expected volatility over an arbitrage horizon also has an adverse effect on the ability and willingness of traders to engage in arbitrage, leading to greater and more persistent futures mispricing. Using the CBOE VIX and its innovation on the concurrent spot volatility as proxies for expected volatility, we present evidence of an increase in S&P 500 index futures mispricing with expected volatility. The impact of the VIX grows exponentially across the distribution of conditional mispricing levels, which suggests that the expectations of heightened future volatility become increasingly detrimental to arbitrage activities when the futures price deviations are enlarged; however, the influence of expected volatility is found to have been reduced during the global financial crisis period, a period during which concurrent volatility overwhelmingly dominated the magnitude of mispricing.     

The October 1987 S&P 500 Stock-Futures Basis

Five-minute changes in the S&P 500 index and futures contract are examined over a ten-day period surrounding the October 1987 stock market crash. Since nonsynchronous trading problems are severe in these data, new index estimators are derived and used. The estimators use the complete transaction history of all 500 stocks. Nonsynchronous trading explains part of the large absolute futures-cash basis observed during the crash. The remainder may be due to disintegration of the two markets. Even after adjustment for nonsynchronous trading, the index displays more autocorrelation than does the futures and the futures leads the index.     

OPTIMAL FUTURES HEDGE WITH MARKING-TO-MARKET AND STOCHASTIC INTEREST RATES

We investigate the effect of marking-to-market on an optimal futures hedge under stochastic interest rates. An intertemporal optimal hedge ratio that accounts for basis risk and marking-to-market is derived. This ratio includes all previous hedge ratios, with constant interest rates as special cases. In a preliminary empirical study using S&P 500 index futures contracts, we demonstrate that the futures-forward hedging differential is nontrivial, especially in risk-return optimization. We also show that the covariances between interest rates and spot and futures prices explain the differential: the larger the covariances are, the larger the differential will be.     

Commodity market financialization,herding and signals: An asymmetric GARCH R-vine copula approach

Institutional investors have significantly increased their exposure to commodity futures after 2004 in the process of commodity market financialization, raising questions about the risk-sharing and price-discovery functions of the market. We identify some symptoms of financialization through examining S&P500, JPM bond index, and 18 S&P GSCI excess return indices, employing ARMA-GARCH R-vine copula approach that can flexibly model high-dimensional multivariate asymmetric tail dependence. We discover three trends: an increased resemblance between the news impact curve of stocks and those of commodities; an increased bi-variate stock-commodity tail dependence; and an increased multivariate tail-dependence across all commodities. We also explore the market structural change underlying these symptoms using an augmented news impact curve. We suggest and provide evidence that herding, in addiction to leverage effect, explains the observed symptoms. The findings have profound implications for commercial hedgers and financial traders, and for regulators who are concerned about the functionalities of commodity futures market.     

Do economic statistics contain information to predict stock indexes futures prices and returns? Evidence from Asian equity futures markets

This research examines the impact of local and international market factors on the pricing of stock indexes futures in East Asian countries. The purpose of this paper is to present a study of the significant factors that determine the major stock indexes futures’ prices of Hong Kong, Malaysia, Singapore, South Korea and Taiwan. This study first investigates the relationships between Hang Seng Index Futures, KLCI Futures, SiMSCI Futures, KOSPI Futures, Taiwan Exchange Index Futures and local interest rates, dividend yields, local exchange rates, overnight S&P500 index and a newly constructed index, Asian Tigers Malaysia Index (ATMI). 11 years historical data of stock indexes futures and the economic statistics are studied; 10 years in-sample data are used for testing and developing the pricing models, and 1 year out-of-sample data is used for the purpose of verifying the predicted values of the stock indexes futures. Using simple linear regressions, local interest rates, dividend yields, exchange rates, overnight S&P500 and ATMI are found to have significant impact on these futures contracts. In this research, the next period close is predicted using simple linear regression and non-linear artificial neural network (ANN). An examination of the prediction results using nonlinear autoregressive ANN with exogenous inputs (NARX) shows significant abnormal returns above the passive threshold buy and hold market returns and also above the profits of simple linear regression (SLR). The empirical evidence of this research suggests that economic statistics contain information which can be extracted using a hybrid SLR and NARX trading model to predict futures prices with some degree of confidence for a year forward. This justifies further research and development of pricing models using fundamentally significant economic determinants to predict futures prices.

     

Intraday Price Discovery in the DJIA Index Markets

Abstract:  This paper explores the dynamics of price discovery between the Dow Jones Industrial Average (DJIA) index and its three derivative products: the DIAMOND exchange-traded fund (ETF), the floor-traded regular futures, and the electronically traded mini futures. Even though the American Stock Exchange is the primary listing exchange for the ETF, the analysis indicates that the electronically traded ETF on the Archipelago (ArcaEx) electronic communications network dominates the price discovery process for DIAMOND shares. The E-mini futures contribute the most to price discovery, followed by the ArcaEx DIAMOND. The DJIA index and regular futures contribute least to price discovery. The analysis is repeated using the derivatives of the S&P 500 index as a robustness check. The results indicate that multi-market trading ensures greater pricing efficiency. Informed traders favor electronic trading because of immediate and anonymous trade execution.     

Is the January effect still alive in the futures markets?

The January effect concerns the fact that small capitalization stocks have historically outperformed large capitalized stocks in January. We analyze evidence as to whether this anomaly can be exploited in the futures markets as a speculative investment or to add risk-adjusted value to portfolio performance. We find that the January effect is still alive in the futures markets on the Value Line minus S&P 500 spread trade, but that the marginal liquidity of the Value Line stock index futures contract has made it very risky to exploit the effect. Historically from 1982/3 to 2004/5, the trade has been profitable. This anomaly was also exploitable through a Russell 2000 minus S&P 500 spread trade from 1993/4 to 2004/5.

Futures and futures options with basis risk: theoretical and empirical perspectives

Under a no-arbitrage assumption, the futures price converges to the spot price at the maturity of the futures contract, where the basis equals zero. Assuming that the basis process follows a modified Brownian bridge process with a zero basis at maturity, we derive the closed-form solutions of futures and futures options with the basis risk under the stochastic interest rate. We make a comparison of the Black model under a stochastic interest rate and our model in an empirical test using the daily data of S&P 500 futures call options. The overall mean errors in terms of index points and percentage are ?4.771 and ?27.83%, respectively, for the Black model and 0.757 and 1.30%, respectively, for our model. This evidence supports the occurrence of basis risk in S&P 500 futures call options.     

Institutional Ownership and Changes in the S&P 500

Several recent articles have provided new evidence for the existence of price pressures by examining the price and volume effects associated with changes in the S&P 500. The present study extends this work by examining actual changes in institutional holdings following both additions to and deletions from the S&P 500. The results show that changes in institutional holdings in response to additions or deletions from the S&P 500 are positively correlated. In addition to providing further evidence for the existence of price pressure effects, the results also provide evidence of the very large institutional elasticities of demand for stock.     

An alternative approach to evaluating the agreement between financial markets

This research investigates that the price relationship between a stock index and its associated nearby futures markets can be explained by the cost-of-carry model using the concordance correlation (CC) coefficient in the US financial markets. The main purpose of this research is to confirm that the CC coefficient is an appropriate methodology to determine ex post arbitrage opportunities and to maximize ex ante arbitrage profits through the analysis of the price relationship derived from the cost-of-carry model. To increase the robustness of the results and to enable us to generalize our conclusions, this analysis is carried out in consideration of external uncertainty, including the marking-to-market procedure of futures contracts and the transaction cost on the stock index and its futures markets, under several assumptions related to the conditions of transactions. Examining transaction price data on the S&P 500 stock index and its futures markets shows that the CC coefficient gives a good result for ex ante arbitrage profits and is appropriate for analyzing the relationship between the observed stock index futures market price and its theoretical price derived from the cost-of-carry model.