TOWARD AN EARLY WARNING SYSTEM OF FINANCIAL CRISES: WHAT CAN INDEX FUTURES AND OPTIONS TELL US? ABSTRACT

Transcription

1 TOWARD AN EARLY WARNING SYSTEM OF FINANCIAL CRISES: WHAT CAN INDEX FUTURES AND OPTIONS TELL US? ABSTRACT This research develops an early warning system (EWS) for equity market crises based on multinomial logit models and variables relating to the information content of index futures and options. We show that the information impounded in S&P 500 futures and options are useful as leading indicators of financial crises. The current literature is absent of such studies. Results reveal that models estimated with futures and put options significantly improve the medium-term predictability of equity market crises. Variables that consistently provided information of an impending crisis include: the VIX, open interest, dollar volume, and put option prices. Keywords: Financial crises; S&P 500 options and futures; Early Warning System (EWS); multinomial logit models JEL classification: G01; G12 1

2 1. INTRODUCTION Can the prediction of financial crises be improved? This question is addressed often in existing literature, particularly following the spike in currency crises in the late 1990s. Several authors have developed and modified early warning system (EWS) models, and demonstrated success in the prediction of currency crises. 1 Surprisingly, a relatively sparse literature exists on forecasting equity market crises for the purpose of providing early signals of market declines. The current paper addresses this void in the literature. We accomplish this by exploring the information content of index futures and options, with the purpose of developing an EWS of financial crises. A considerable body of literature reports that options and/or futures markets tend to lead equity markets in terms of information arrival. 2 In addition, several researchers show that option volumes, option open interest, and implied volatility (VIX) exhibit predictive power on very short-term equity price movement. 3 There are reasons to believe that derivative markets may provide information in developing an early warning system (EWS) for equity markets. For example, Black (1975) argues that higher financial leverage offered by derivatives attracts greater participation by informed traders. Greater leverage implies greater risk and therefore increases the incentives for information dissemination and price discovery. Easley et al. (1998), and Pan and Poteshman (2006) present empirical evidence of information-based trading in option markets. The evidence presented in these studies indicates that derivative markets are more informative than equity markets. If an early warning system (EWS) model incorporates information revealed from derivative markets, it should be able to provide early signals of equity market crises. In two related papers, Bates (1991) and Rappoport and White (1994) document that the equity market crashes in 1987 and 1929 were expected. Bates (1991) reports unusually high 1 For example, please see Kaminsky et al. (1998), Berg and Pattillo (1999), Burkart and Coudert (2002), Kumar et al. (2003), and Bussiere and Fratzscher (2006). 2 Please see, Manaster and Rendleman (1982), Diltz and Kim (1996), Kawaller et al. (1987), Stoll and Whaley (1990), Chan (1992), Fleming et al. (1996), Pizzi et al. (1998), and Kavussanos et al. (2008). 3 See, Easley et al. (1998), Pan and Poteshman (2006), and Chung et al. (2011). 2

3 prices of out-of-money (OTM) put options on the S&P 500 futures a year prior the 1987 crash. In his jump-diffusion option pricing model, the parameters implied by option prices indicate that a market crash was expected dating back to October Examining the 1929 crash, Rappoport and White (1994) treat brokers loans as options offered to investors. They document a sharp increase in interest premium, margin requirements on brokers loans, and implied volatility on options prior to the 1929 market crash. In a paper most related to the current research, Coudert and Gex (2008) show that risk aversion indicators, including the implied volatility of the S&P 500 options (VIX), are good leading indicators of equity market crises. Although these studies have documented the predictability of equity market crises using information obtained from derivatives, they do not comprehensively examine the information impounded in index futures and options markets on the prediction of subsequent equity market crises. The current research employs a multinomial logit model to test the forecasting power of several derivative market indicators on the probability of a financial crisis. We employ variables from the two most active index derivatives in the U.S., the S&P 500 futures (SP) and the S&P 500 options (SPX), to test the predictability of financial crises from 1997 to In the multinomial logit model, we include the following variables as suggested by existing literature: Open interest, dollar volume, option price, option effective spread, and the implied volatility on S&P 500 options (VIX). This study tests several model specifications to understand the marginal contribution of each explanatory variable in the prediction of a financial crisis. The empirical results support the notion that index futures and options lead equity markets. The in-sample performance shows that the best futures and option models have very similar performance characteristics, both successfully predicting the majority of financial crises within the sample period. Overall, the best performing model using put option variables correctly identifies 86.6% of observations and 69.2% of crisis months. The results of this paper demonstrate that information contained in index futures and options is useful as leading indicators of financial turmoil. This research contributes to the financial crisis literature in that the EWS 3

4 model that utilizes the information content of index futures and options can forecast equity market crises over a one-year horizon, which is absent in most of prior literature. The remainder of the paper is organized as follows. Section 2 reviews literature, Section 3 describes data and methodologies, Section 4 discusses our empirical results, and Section 5 concludes. 2. LITERATURE REVIEW This section reviews the current literature on early warning system (EWS) models to predict financial crises. We then motivate our variable selection with a review of the literature on the informational content contained in options and futures markets. 2.1 Studies on early warning system models The current state of predicting financial crisis is much better than a random guess. A number of studies have developed early warning system models based on data from a variety of countries. Examples of this research include: Kaminsky et al. (1998), Berg and Pattillo (1999), Burkart and Coudert (2002), Kumar et al. (2003), Bussiere and Fratzscher (2006), Distinguin et al. (2006), and Coudert and Gex (2007). Kaminsky et al. (1998) propose and test a signals approach which combines several macroeconomic variables as leading indicators to predict currency crises. They show that a EWS based on leading macroeconomic indicators crossing a pre-specified threshold level is useful in the prediction of currency crises. 4 Berg and Patillo (1999) dispute the success rate of Kaminsky et al. s (1998) EWS and claim that its success is likely due to better data fit from in-sample estimations. Using Kaminsky et al. s (1998) signals approach to develop a forecast for the 1997 Asian currency crisis, Berg and 4 These leading indicators include: international reserves, the real exchange rate, domestic credit, public sector credit, domestic inflation, trade balance, exports, money growth, real GDP growth, the fiscal deficit, and equity prices. 4

5 Patillo (1999) show that out-of-sample performance from Kaminsky et al. s (1998) approach is not superior to a simple probit-based model. In a departure from the signals approach, Burkart and Coudert (2002) employ Fisher s classical discriminant analysis to identify currency crises in 15 emerging countries. To identify currency crises, they include capital controls, contagion dummies, and a banking sector weakness indicator in their set of explanatory variables. The performance of their model is impressive, as they claim to have correctly predicted four out of five currency crises in their sample period. Kumar et al. (2003) and Distinguin et al. (2006) employ binomial logit models to predict currency crashes and banking crises, respectively. The results of both papers argue for the use of a binomial discrete dependent variable approach to forecast financial crises. However, Bussiere and Fratzscher (2006) argue that an early warning system model based on a binomial discrete dependent variable is subject to a post-crisis bias because it does not distinguish crisis and postcrisis periods. Applying a multinomial logit model, Bussiere and Fratzscher (2006) show a significant improvement of forecasting currency crises. In a recent paper related to the current research, Coudert and Gex (2007) employ a modified logit and a multinomial logit models using seven well-known risk aversion indicators. They document that the majority of these risk aversion indicators are good indicators of currency crises, and all of them predict well for equity market crises. Most of the early warning system models use macroeconomics variables as leading indicators to predict currency crises. In contrast to the majority of existing literature, the current research employs the information revealed in derivative markets to predict equity market crises within a multinomial logit model over a one-year forecasting horizon. The next section reviews and summarizes the linkages between equity and derivative markets to motivate our variable selection. 5

6 2.2 Information content of options and futures variables Information content of options/futures price (return) Voluminous literature examines the lead-lag relationship between option and the underlying equity prices (returns). However, results remain inconclusive. Several studies document that option markets lead the equity markets [e.g., Manaster and Rendleman (1982); Diltz and Kim (1996)]. Manaster and Rendleman (1982) show that the implied stock prices computed from the Black-Scholes option pricing model contain information about future movements of observed stock prices. Diltz and Kim (1996) report that changes in current stock prices adjust to lagged changes in option-implied stock prices for up to two days. There is also evidence that equity markets lead the option markets [e.g., Stephan and Whaley (1990); Chan et al. (1993); Finucane (1999)]. Stephan and Whaley (1990) find that price changes and trading volume in the stock market lead the option market by as much as fifteen minutes. Chan et al. (1993) argue that the results obtained by Stephan and Whaley (1990) are induced by infrequent trading of options. Finucane (1999) takes a new sampling approach of using variable-length intervals. He shows that stock quotes tend to lead option quotes for a few seconds to less than six minutes. As to studies on futures markets, the preponderance of the empirical evidence demonstrates that futures returns lead cash index returns [e.g., Kawaller et al. (1987); Stoll and Whaley (1990); Chan (1992); Fleming et al. (1996); Pizzi et al. (1998)]. Kawaller et al. (1987), Stoll and Whaley (1990), Chan (1992), and Pizzi et al. (1998) provide strong evidence that returns on S&P 500 futures significantly lead cash index returns. In a comprehensive analysis of the S&P 100 and 500 futures, options, and spot markets, Fleming et al. (1996) find that index futures and option returns lead equity index returns, and that index futures lead index option markets. Their empirical evidence is consistent with the trading cost hypothesis that price discovery occurs first in the lowest-cost markets. 6

7 International evidence confirms that futures prices (returns) lead equity prices (returns) [e.g., Tang et al. (1992); Abhyankar (1998); Ryoo and Smith (2004); Kavussanos et al. (2008)]. These studies report a bi-directional causal relationship between index futures prices (returns) and index prices (returns), with strong evidence of the feedback effect from index futures prices (returns) to cash index prices (returns) in Hong Kong, U.K., South Korea, and Greece Information content of volume and open interest The informational role of options/futures volume and open interest has been researched extensively in literature. For example, volumes and open interest have been used to examine information arrival in options/futures and equity markets, to predict equity/option price movements, to predict future price volatility, and to investigate the existence of informed trading regarding corporate events. Most related to the current research are studies that use volume to examine the lead-lag relationship between options/futures and equity markets [e.g., Anthony (1988); Chakravarty et al. (2004)]. Anthony (1988) reports the lead of call options to the underlying shares with one-day lag by examining the flow of information through trading volumes. Investigating the relative contribution of option and stock markets to price discovery, Chakravarty et al. (2004) document that option markets are more informative when the option volume is higher and effective spread is narrower relative to those of the stock markets. Bessembinder et al. (1996) examine the relations between information, divergence of opinions, and trading activity of S&P 500 futures. They confirm a positive relationship between information flow and trading volume in the spot and futures markets. The preponderance of empirical evidence documents that option volumes have predictive power for future stock price movement in the short-run [e.g., Easley et al. (1998); Pan and Poteshman (2006)]. The multimarket trading model of Easley et al. (1998) implies that particular types of options trading contain information for future stock price changes. Aggregating the option volume of positive news (i.e. buying a call or selling a put) and of negative news (i.e. 7

8 selling a call or buying a put), Easley et al. (1998) find bi-directional results: Stock prices lead option volumes by twenty to thirty minutes, but option volumes affect stock price changes much more rapidly. Pan and Poteshman (2006) also document that positive and negative signals conveyed from options volumes exhibit predictive power of future equity price movement. Pan and Poteshman (2006) find that stocks with low put-call ratios (i.e. positive signals) outperform those with high put-call ratios (i.e. negative signals) by more than 40 basis points on the next day and more than 1% over the next week. A related strand of research explores the relationship between option/futures volume, open interest, and equity price volatility [e.g., Bessembinder and Seguin (1992); Sarwar (2005)]. In an analysis of S&P 500 futures, Bessembinder and Seguin (1992) partition futures volumes and open interest into expected and unexpected components. They find that equity volatility is negatively related to anticipated volumes and open interest, while positively related to unexpected components. Sarwar (2005) examines relations between trading volume of S&P 500 options and price volatility of the S&P 500 index. Sarwar (2005) documents bi-directional feedback effects between option volume and future price volatility. Significant research also explores the information role of option volume and open interest surrounding corporate events [e.g., Amin and Lee (1997); Jayaraman et al. (2001); Cao et al. (2005); Roll et al. (2010)]. Amin and Lee (1997) and Roll et al. (2010) report an increase in option volume or in the options/stock trading volume ratio (O/S) prior to earnings announcement dates. Roll et al. (2010) conclude that part of the options trading in the pre-announcement period is information-based trading. Jayaraman et al. (2001) and Cao et al. (2005) investigate trading activities in option markets surrounding the announcement of a merger, acquisition, or takeover. Jayaraman et al. (2001) report a significant increase in volume and open interest for out-of-the-money options with maturity of less than 60 days prior to the rumor of a takeover. Cao et al. (2005) show that call-volume imbalance is highly predictive of the next-day equity returns in the pre- 8

9 announcement period. Evidence from these studies indicates that option traders participate in dissemination of information of major corporate events Information content of implied volatilities Most relevant literature explores the information role of option implied volatility and examines its relationship with equity returns, future realized volatility, and stock market crashes. The evidence of a positive relationship between implied volatility and equity returns has been presented in Giot (2005) and Banerjee et al. (2007). In an analysis of VIX and S&P 100 index, Giot (2005) documents a positive relationship between VIX and future market index returns. In a similar study, Banerjee et al. (2007) find that future portfolio returns are positively significantly related to both VIX levels and innovations for portfolios sorted by beta, size, and book-to-market equity. Recent research has demonstrated the superior predictive power of implied volatility on future realized volatility and returns. In a study of the 1997 Hong Kong stock market crash, Fung (2007) finds that implied volatility performs better than volume, open interest, and arbitrage basis of index futures in forecasting the future realized volatility. Chung et al. (2011) show that the information embedded in VIX options significantly improves the predictive power on the returns, volatility, and density of the S&P 500 index. Research on the topic of implied volatility and financial crises is investigated in papers following the 1929 and the 1987 equity market crashes [e.g., Rappoport and White (1994); Schwert (1990); Bates (1991)]. Rappoport and White (1994) examine the 1929 crash, and treat brokers loans as options offered to investors. They document a sharp increase in interest premium, margin requirements on brokers loans, and implied volatility on options prior to the 1929 market crash. Schwert (1990) and Bates (1991) also report that the implied volatility of options rose significantly during the 1987 equity market crash. In a study on the stock volatility behavior from 1885 to 1988, Schwert (1990) shows that the implied volatility of call options on 9

10 the S&P 500 index rose significantly during the 1987 stock market crash, and did not decline until March Bates (1991) documents that the implied volatility estimated from a jumpdiffusion model rose significantly a few months prior the crash in October 1987 and jumped to a 50% annual rate during the equity market crash. The existing evidence suggests a positive relationship between the implied volatility and the probability of financial crises. The vast literature reviewed above illustrates the general relationship and short-term dynamics between variables relating to futures/options and equity markets. In the current research, we focus on the medium-term (i.e. 1-year) prediction of equity market crises using an early warning system model that incorporates the information flow from index futures and options markets to equity markets. 3. DATA AND METHODOLOGIES 3.1 Data The Standard and Poor s 500 futures (SP) and options (SPX) are chosen as the study sample for this research. The sample period selected is from January 2, 1997 to December 31, S&P 500 futures and options are the most active index derivatives traded on Chiago Merchantile Exchange (CME) and Chicago Board Options Exchange (CBOE), respectively. 5 The daily data for S&P 500 futures (SP) and options (SPX) are obtained from Norma's Historical Data and Market Data Express at CBOE, respectively. Both datasets contain closing price, expiration date, total volume, and open interest. The exercise price, and last bid and asked prices are only available for options contracts. S&P 500 index prices and the historical data on CBOE Volatility Index (VIX) were obtained from Market Data Express dataset and CBOE s website, respectively 6. 5 According to the statistics released by CME and CBOE in 2011, the total trading volumes of S&P 500 futures and S&P 500 options account for 86% and 61.71% of total equity index futures and options traded on CME and CBOE, respectively. 6 The old VIX data computed using the new methodologies are also available on CBOE: 10

11 VIX measures the expected near-term stock market volatility based on the S&P 500 s option prices. 7 The following criteria are imposed to filter the options data: Options must have trading volume, open interest, closing price higher than or equal to $0.125, and at least 7 days to maturity. 8 This study excludes LEAPS (Long Term Equity AnticiPation Security) options from the sample as LEAPS often have different characteristics than standard options. The initial screen yields a total of 657,409 daily options observations in the sample, 273,030 of which are call options, while 384,379 of which are put options. We do not filter the futures data because the minimum futures price over the sample period is $ and the nearest maturity of futures contracts dominate trading in each month. The sample of futures data contains 27,778 daily observations. The daily futures and options data are converted to monthly frequencies to obtain the key variables for analysis: Open interest, total dollar volume, average daily closing price of options, and average daily option effective spread. Existing literature documents that these variables contain information about future equity prices and/or contribute to price discovery. A logarithmic transformation is applied to open interest and total dollar volume following existing literature. Please refer to Table 1 for variable definitions. Out-of-the-money (OTM) options offer the greatest leverage to investors. Informed traders should enjoy higher profit from trading OTM options. Thus, we would expect more information to be revealed from the trading of OTM options. 9 Indeed, Bates (1991) documents that the prices of OTM put options on S&P 500 futures became unusually high relative to those of 7 The original VIX was computed based on at-the-money S&P 100 index (OEX) option prices. From September 22 in 2003, COBE changed its methodology of computing the VIX by incorporating more information of implied volatility from a wide range of strike prices. The new VIX is based on S&P 500 index option (SPX) prices. 8 Aït-Sahalia and Lo (1998) document that options with low price and low trading volume are unreliable. Sarwar (2005) also remove S&P 500 options with price less than $.125 from the sample to examine the relationship between option volume and price volatility. 9 Chakravarty, Gulen, and Mayhem (2004) provide evidence that price discovery is greater for out-of-themoney options than at-the-money options. 11

12 OTM calls during the year prior to the 87 s crisis. The theoretical implied price of an OTM put indicates that an OTM put at that time should trade at a discount relative to an OTM call. Motivated by this empirical evidence, we explore the informational role of OTM puts for predicting financial crises in addition to call, put, and all options in the sample. Following the majority of literature, the ratio of strike to spot prices of less than or equal to 0.95 is used to classify the out-of-the-money (OTM) put options. 10 As a preliminary examination of the options data, we compute the put-call ratios of open interest and dollar volume to see whether more put options trade before and during a financial crisis. 3.2 Methodology Following Patel and Sarkar (1998) and Coudert and Gex (2008), we use the ratio in order to identify a financial crisis month. Patel and Sarkar (1998) define as the ratio of an index level at month t to the maximum of an index level for the period up to month t. Coudert and Gex (2008) set 24 months as a rolling period in calculating the research follows Coudert and Gex s (2008) method to calculate the ratio. The current as well as the corresponding crisis indicator. (Eq. 1) where is the S&P 500 index level in month t. A low value of indicates a larger price decline in the index level over a 24-month period. The ratio is capped at 100%. A ratio of 100% indicates that the index level in that month rises to the maximum value in the rolling 24-month period. The ratio is then translated to an equity market crisis indicator if is less than two standard deviations below its mean value For example, please see Fleming et al. (1996) for classifying moneyness of options. 11 Patel and Sarker (1998) document that in the beginning of a market crash, the equity price index falls to two standard deviations below the mean value of for developed markets, which is about a 20 12

13 (Eq. 2) where is the standard deviation of. To derive statistics in a large sample, we calculate the mean value and the standard deviation of for the first month in the sample period (1997:01) from the whole sample period, and add an additional month at a time to the sample in calculating these two statistics in each of the following months. We employ Coudert and Gex (2008) method to eliminate double counting the same crisis over a 12-month period. This study uses a multinomial logit model to examine the information content of index futures and options for prediciting financial crises. Bussiere and Fratzscher (2006) and Coudert and Gex (2008) document the superiority of multinomial logit models over binomial models in the prediction of financial crises. The dependent variable,, in the multinomial logit model comprises three discrete values (0, 1, and 2) for three outcomes: the normal, pre-crisis, and post-crisis periods, respectively. The classification of the discrete values for the dependent variable is constructed based on the crisis indicator. The pre-crisis period ( ) includes 12 months before and the onset of a crisis (i.e. 13 months in total), while the post-crisis period ( ) consists of 11 months following the onset of a crisis. Other months are considered the normal period ( ). (Eq. 3) Figure 1 displays the ratio over the sample period from January of 1997 to December of Consistent with the results in existing financial crisis literature, the ratio fell sharply during the periods of dot.com bubbles and the recent subprime mortgage crisis. The periods shaded gray in Figure 1 represent the two pre-crisis periods over the sample period: August of 2001 to August of 2002, and January of 2008 to January of percent relative decline in the price index. Coudert and Gex (2008) use two standard deviations below the mean value of as the threshold value. 13

14 [Figure 1 here] The predicted probabilities of the multinomial logit model are formulated as: (Eq. 4) where is the dependent variable, is a matrix of explanatory variables, is the transpose of a row vector,, of parameters, denotes the logistic cumulative distribution function, and k=1 or 2 denotes a pre or post-crisis period, respectively. We form various combinations of the explanatory variables in the multinomial logit models for S&P 500 futures (SP) and options (SPX), and examine their performance for predicting a financial crisis. 12 The followings are the specifications of futures models:, and where is a 1x4 vector of parameters, is a 3Tx4 matrix, each element in matrix is a Tx1 vector, is a vector of ones, is a vector of zeros, the scalar explanatory variable at month t is defined in Table 1, and T in the current study is 156 months. The options models are specified as:, and 12 A combination which may result in multicollinearity because of high correlations among explanatory variables is avoided. The average daily futures price across futures contracts in a month,, is not included in the model specification because it does not improve the estimation results. The log difference between (or and its lag is not included in the model specification for the same reason. 14

15 where is a 1x6 vector of parameters, is a 6Tx6 matrix, each element in matrix is a Tx1 vector, the scalar explanatory variable at month t is defined in Table 1, is a vector of ones, is a vector of zeros, and T in the current study is 156 months. Prior research documents a positive relationship between implied volatility and equity market crashes [e.g., Schwert (1990); Bates (1991); Rappoport and White (1994)]. Therefore, the coefficient on VIX,, is expected to be positively signed in the pre-crisis period. Existing literature does not offer a clear guidance of the relationship between a financial crisis and open interest, or volume/dollar volume. Bessembinder and Seguin (1992) report that equity volatility is negatively related to anticipated volumes and open interest, while positively related to unexpected components in futures markets. An equity market crisis is likely to be associated with higher price volatility. If the majority of the increase in the open interest or volume in options and futures is unexpected during a down market, an increase of open interest or volume will raises the chances of having a financial crisis. Thus, the coefficient on open interest or dollar volume (i.e.,, and ) is expected to be signed positive in the pre-crisis period. On the other hand, if an increase of open interest or dollar volume in options and futures is primarily anticipated during a market crash, the coefficient on open interest or dollar volume (i.e.,, and ) will be signed negative in the pre-crisis period. Demand for a long call or put will pressure the corresponding contract upward. In general, there is a reduction in the demand for long calls (and short puts) and an increase in demand for short calls (and long puts) during a financial crisis period. Hence, a call (put) option price tends to decline (rise) during a market downturn, which decreases (increases) the likelihood of having an equity market crisis. The coefficient on the option price,, is expected to be signed negative (positive) for a call (put) option in the pre-crisis period. Uncertainty increases and equity market liquidity decreases during times of a financial crisis. A theoretical paper by Routledge and Zin (2009) examines the relationship between model 15

16 uncertainty and liquidity from a market maker s perspective. Routledge and Zin (2009) show that liquidity crises are associated with uncertainty aversion, which limits a market maker s ability to hedge a position in derivatives. The effect of uncertainty aversion thus makes market markers raise the bid and ask prices to reduce the desirability of a derivative trade, and market liquidity declines. The theoretical argument by Routledge and Zin (2009) implies that the coefficient on the effective spread,, should be signed positive in the pre-crisis period. In order to evaluate the performance of the models presented above, a probability threshold must be selected. This is due to the fact that the predicted probability of a financial crisis is a continuous variable while the occurrence of a financial crisis is presented by a discrete value in the dependent variable. The current research follows existing literature and sets 20% as the value of the probability threshold. 13 The model predicts a crisis if the estimated probability is above the threshold value in each month. We compute the following conditional probabilities to evaluate predictive power of models: the percentage of observations correctly called, the percentage of pre-crisis periods correctly called, the percentage of false alarms of total alarms, the percentage of probabilities of crisis given an alarm, and the percentage of probabilities of crisis given no alarm. 14 Table 6 presents conditional probabilities for each model. The present study also conducts in-sample tests to evaluate the performance of models. The out-of-sample simulations are not conducted because: 1) there are no crises at the end of our 13 The 20% probability threshold is used in Bussiere and Fratzscher (2006), and Coudert and Gex (2008). 14 Following Bussiere and Fratzscher (2006) we define these conditional probabilities as follows: the percentage of observations correctly called is equal to the number of observations in the normal and precrisis periods correctly predicted divided by the total number of observations in normal and pre-crisis periods; the percentage of pre-crisis periods correctly called is equal to the number of observations in precrisis period correctly predicted divided by the number of observations in the pre-crisis period; the percentage of false alarms of total alarms is equal to the number of observations in the normal period incorrectly predicted as a pre-crisis period divided by the number of observations in normal and pre-crisis periods predicted as a pre-crisis period; the percentage of probabilities of crisis given an alarm is equal to the number of observations in the pre-crisis period correctly predicted divided by the number of observation in the normal and pre-crisis periods predicted as a pre-crisis period; the percentage of probabilities of crisis given no alarm is equal to the number of observations in the pre-crisis period wrongly predicted as the normal period divided by the number of observations in normal and pre-crisis periods predicted as a normal period. 16

17 sample, and 2) the sample is not large, and if we split it, this would weaken the reliability of the estimates. 15 Furthermore, Inoue and Kilian (2005) show that in-sample tests are often more powerful than out-of-sample tests when small samples are used. We compute three statistics to analyze the accuracy of predicted probabilities with the actual occurrence of the crises: the quadratic probability score (QPS), the log probability score (LPS), and Efron s (1978) fit measure. 16 The results of in-sample performance for S&P 500 futures and options are presented in Table 6. Quadratic probability score is calculated as follows: QPS = (Eq. 5) where is the estimated probability of pre-crisis periods, is set to 1 for pre-crisis periods, and set to zero otherwise. Quadratic probability score (QPS) ranges from 0 to 2, with a zero for a perfect forecast. Log probability score is calculated as follows: LPS = (Eq. 6) Log probability score (LPS) ranges from 0 to infinity, with a zero for a perfect forecast. Efron s (1978) fit measure is defined as: (Eq. 7) where is the dependent variable with values of 0, 1, and 2 for normal, pre-crisis, and post-crisis periods, respectively; is the average value of the dependent variable; is the estimated probability of pre-crisis periods. Efron s (1978) fit measure,, is designed to evaluate the 15 Courdert and Gex (2008) encountered theses two identical problems in their attempt to predict currency crises. They also present resutls from in-sample simulations. 16 Diebold and Rudebusch (1989) provide a few methods to evaluate leading indicator forecasts. The quadratic probability score (QPS) is commonly seen in a few studies [e.g., Kaminsky (2000); Kumar et al. (2003); Chen (2009)]. 17

18 relationship between the fitted probabilities and the actual values. Its value ranges from 0 to 1, with a 1 for a perfect forecast. 4. EMPIRICAL RESULTS 4.1 Summary statistics Table 2 reports the mean values and standard deviations of key variables used in this study. Statistics are presented separately for three segmented periods (i.e. normal, pre-crisis, and post-crisis periods) from 1997 to The sample period comprises a total of 156 months. 109, 26, and 21 months out of the 156 months are for a normal, a pre-crisis, and a post-crisis periods, respectively. An examination of whether variables in index futures and options markets behave differently in these segmented allows for identification of candidate leading indicators of financial crises. [Table 1 here] As the world has witnessed over the past two decades, equity markets are characterized by increased levels of volatility in periods surrounding financial crises. Our data confirms the statistically significant difference in means between normal and pre/post-crisis periods in Table 2. The mean VIX for normal months is 19.57%, whereas the VIX spikes to 29.76% and 29.49% for pre and post-crisis periods, respectively. The difference of the mean VIX between normal and pre/post-crisis months is statistically significant at a 1% significance level. This finding argues for the potential of the VIX as an important variable in the development of an early warning system (EWS) of equity crises. Examination of variables related to the S&P 500 index futures and options reveals significant differences in behavior surrounding financial crises. At a 1% significance level, we document that the mean of futures open interest is higher during the pre-crisis period than that in the normal period, while the mean open interest of options is higher in the post-crisis period than that in the normal periods. As to dollar volume, it is noted that at a 1% significance level, the 18

19 mean value of futures dollar volume is lower in the post-crisis period than that in the normal period. Different from the reported futures dollar volume, the mean value of options dollar volume is statistically higher during the pre/post-crisis period than that in the normal period at a 1% significance level. 17 The different patterns of dollar volume in futures and options markets indicate that on average there is less (more) trading of futures (options) contracts in the pre/post-crisis period than that in the normal period. A possible explanation for higher dollar value of options trading volume surrounding times of market turmoil is associated higher equity price volatility. The higher equity price volatility makes options more valuable, consequently inducing more options trading. Futures traders may switch to trade options during times of a financial crisis. Table 2 also reports the mean values of the average daily closing price and the effective spread for S&P 500 options in normal, pre-crisis, and post-crisis periods, respectively. It is noted that at a 1% significance level, the average daily option price of $50.42 and $45.04 in the pre and post-crisis periods, respectively, is higher than that of $37.37 in the normal period. Since the option price is positively associated with volatility, we find that the option prices increase in periods characterized by spikes in volatility according to standard option pricing theories. In addition, we document at a 1% significance level that the mean effective spread on options widens from $3.08 in the normal period to $5.07 in the pre-crisis period. However, the difference in mean effective spreads between the post-crisis and normal periods is not statistically significant. The summary statistics demonstrate that variables relating to the information content of index futures and options are often dissimilar surrounding times of market turmoil when compared to relatively normal periods. It is one of the objectives of this paper to use these differences to develop an EWS of impending market downturns. 17 The total volume of futures/options is examined, and its results are similar to those of total dollar volume. To conserve space, this paper does not report the statistics of total volume and its estimates in the multinomial models. These statistics and estimates are available upon request. 19

20 Table 3 presents the correlations of key variables. When looking at the correlations between the discrete dependent variable ( ) and selected explanatory variables, we find a positive significant correlation with the VIX. This indicates that higher volatilities are associated with periods outside of normal. One interesting result is the contrast in the correlations between dollar volume and the discrete dependent variable ( ) in futures and options markets. The correlation between dollar value of volume and the discrete dependent variable ( ) is negative in the futures market, but is positive in the options market, both statistically significant at a 10% level or better. We also note a statistically negative correlation of dollar volume between options and futures markets at a 5% significance level. These findings may indicate that investors, when anticipating a period outside of normal, increase (decrease) their trading in options (futures) markets. [Table 3 here] It is further noted that open interest and dollar value of volume in the options market are highly correlated. Due to the strong positive correlation between open interest and dollar volume in the options market, option open interest and dollar volume are not simultaneously included in a given model specification. We also note a statistically positive correlation between an option price and the associated effective spread as an effective spread is derived from an option price. The VIX and the option price are positively correlated, as expected. Holding other factors constant, if the implied volatility of an option rises (declines), the associated option price will increase (decrease). In addition, we report a strong positive correlation between the VIX and the effective spread. Routledge and Zin (2009) argue that because of the uncertainty aversion effect during a financial crisis, market makers raise spreads to reduce derivative trading. The theory of Routledge and Zin (2009) explains the strong and positive correlation between the VIX and the effective spread. The estimation results of multinomial logit models for S&P 500 futures and options, reported in Tables 4 and 5, show the marginal contributions of each variable on the prediction of 20

21 a pre or post-crisis period. The empirical findings are presented in the following manner: Section 4.2 presents the results of futures models 1-3, Section 4.3 reports the results of option models 1-6, and Section 4.4 evaluates the performance of models. 4.2 Empirical results: S&P 500 futures Table 4 summarizes the estimation results from three multinomial logit models for S&P 500 futures. One of the attractive features of a multinomial logit model is that the model not only provides an EWS of a potential financial crisis, but also provides clues as to when a market maybe returning to normal. For example, an exceptionally high VIX may signal the potential for a financial crisis, but in the post-crisis period a declining VIX may signal the return to a normal market period. [Table 4 here] Futures model 1 includes the VIX and the log of open interest as independent variables. Giot (2005) shows that the VIX has superior predictive power on future market returns. In addition, Bessembinder et al. (1996) document that open interest of futures contracts is positively related to increase in information flow between markets. We find that both variables positively forecast the likelihood of entering a pre-crisis and a post-crisis periods. Estimates for model 1 show a strong positive marginal impact of log open interest in the pre-crisis period. This indicates that spikes in the number of futures contracts outstanding are indicative of increased probabilities of entering into a pre-crisis period. The marginal impact of open interest is much more muted in the post-crisis period, but remains significant, where a 1% increase in open interest signals a 6% increase in the probability of the market entering into a post-crisis period. The marginal impact of the VIX is relatively stable in all segmented periods. A 1% increase in the VIX will increase the probability of entering a pre-crisis (post-crisis) period by 1.7% (1.5%). The finding that the implied volatility of S&P 500 futures raises during times of financial turmoil is consistent with the empirical findings in Schwert (1990), Bates (1991), and Rappoport and 21

22 White (1994). It is noted that the marginal impact of the VIX is stable across futures models 1-3, with estimated probabilities from 1.3% to 2.1%. Our results show that the VIX not only has predictive power on future realized returns, but also is an excellent leading indicator of market periods outside of normal. Existing literature shows that volume increases are generally related to greater information flows. Futures model 2 investigates whether an increase in dollar volume of futures contracts improves information dissemination and therefore functions as a leading indicator of financial turmoil beyond the information contained in the VIX. We find that a 1% increase in contract dollar volume marginally impacts the probability of a pre-crisis period by -9.4%. For the post-crisis period, the impact of the dollar volume of futures contracts remains statistically significant and is even greater than that in the pre-crisis period. A 1% increase in the dollar trading volume leads to a reduction in the probability of being in a post-crisis period by 19.7%. The results provide key insights about the nature of trading in futures surrounding financial crises. If we consider the futures market made up of two sets of players, hedgers and speculators. In times of financial uncertainty, hedgers will take the short position and increase the number of contracts initiated. Therefore we should see an increase in open interest. Speculators, on the other hand, will time the market, wait for the market to rebound, and thus reduce the volume of trades in times of financial uncertainty. So while the number of contracts outstanding increases during times of financial crises, the trading of futures contracts is reduced. When markets are returning to normal, speculators return to the market and trading volume increases. Futures model 3 includes the VIX, log of open interest, and log of dollar volume as explanatory variables. The estimates show that log of open interest has significantly positive forecastability in the pre-crisis period, similar to the result in futures model 1. However, in the post-crisis period open interest does not marginally contribute to the forecastability of the future state of the economy. It is noted that similar to futures model 2, dollar volume remains statistically significantly negative in both the pre and post-crisis periods. A 1% increase in dollar 22

23 volume of futures contracts reduces the likelihood of entering the pre and post-crisis periods by 3.5% and 17.5%, respectively. In general, our results to this point are consistent with prior work, which document that returns on S&P 500 index futures lead the cash index returns [e.g., Kawaller et al. (1987); Stoll and Whaley (1990); Chan (1992); Fleming et al. (1996)]. In particular, we show that variables relating to information flow between index futures and equity markets contribute to the predictability of market periods outside of normal. 4.3 Empirical results: S&P 500 options Figure 2 graphs the put-call ratios of open interest and dollar volume for S&P 500 options from 1997 to As the figure shows, there are significant spikes in the put-call ratio of dollar volume in the beginning of and during the pre-crisis periods. This indicates that increased dollar trading volume in put options maybe indicative of a pre-crisis period. A similar pattern is found in the put-call ratio of open interest although the spikes prior or during the second pre-crisis period are not as pronounced as those in the first pre-crisis period. Figure 2 confirms much of existing literature that option markets tend to lead equity markets. [Figure 2 here] Table 5 reports the estimation results for option models 1-6. Panels A-D contain the estimation results of 6 option models for four moneyness groups namely: all options, call options, put options, and out-of-the-money (OTM) put options. Option models 1 and 2 are comparable to futures models 1 and 2. It is observed consistent with our estimates for the futures market that the coefficients on the VIX are positive and significant in all models over four option classes. The robust positive impact of the VIX in both the futures and options models demonstrates that a higher VIX is indicative of a greater probability of entering into a pre or post-crisis period. In option models 1-2, we find that a 1% increase in the VIX increases the probability of entering the 23

24 pre-crisis and post-crisis periods by 0.8%-1.8% and 1.1%-1.3%, respectively. These findings provide clear evidence of the importance of the VIX as a leading indicator of financial crises. [Table 5 here] In option model 1, the log of open interest is included along with the VIX. As expected, we find a consistently positive impact of open interest. In both the pre and post-crisis periods, higher levels of open interest, irrelevant of which moneyness class, increase the probability of entering into a pre or post-crisis period. The most significant result is for OTM put options, where a 1% increase in the open interest leads to a 6.2% (8.2%) higher probability of entering into a pre-crisis (post-crisis) period. Based on the argument of Bessembinder and Seguin (1992), this finding would argue that in the S&P 500 option market, the majority of open interest in the pre and post-crisis periods is unexpected and likely due to increased hedging activities. Option model 2 combines the VIX with log of dollar volume as explanatory variables. It does not include open interest because dollar volume and open interest are highly correlated (.851). We find that the marginal impact of increases in dollar volume is significant across both pre and post-crisis periods and in all moneyness groups. With the exception of post-crisis estimate for OTM puts, dollar volume positively impacts the probability of entering into a pre or post-crisis period. For example, a 1% increase in the dollar volume is associated with a 7.7% (4.5%) increase in the probability of entering into a pre-crisis (post-crisis) period. For the OTM put options, the results are even stronger with a 1% increase in dollar volume leading to a 15.6% increase in the likelihood of a pre-crisis period. These findings show that information flow increases in the option markets prior to markets entering into a pre or post-crisis period. In option model 3, the average daily closing price of options is included along with the log of open interest. It is noted due to the high correlation between the VIX and average daily option price (0.809), that the VIX is excluded from models containing average daily option prices to avoid problems of multicollinearity. For all options, it is found that a $1 increase in an option price increases the probability of entering a pre-crisis period by 1.2%. When options are broken 24