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Pre event trends in implied and intraday volatilities
Pat Obi
ABSTRACT
This study explores the nature of pre-event investor sentiments based on anomalies in implied options and intraday volatilities. Implied volatility is known to convey investor sentiments by its tendency to rise in advance of a market downturn. Because the airline industry was particularly distressed by the 2001 terror attacks in the United States, the magnitude of its pre-event volatility patterns is measured against that of the rest of the market. Empirical results show that pre-event abnormal returns for airlines is negative and is, in general, larger than that of the market as a whole. There was also a remarkable increase in pre-event implied volatility, which provided short position holders with profitable trading opportunities. In the price-risk relationship, Granger causality results are mixed, showing in particular that a bi-directional causality exists between implied volatility and equity market valuation.
Keywords: Implied Options Volatility, Intraday Volatility, Pre-event Abnormal Returns, Granger Causality.
1. INTRODUCTION
This study examines the ability of implied options volatility to predict near-term market anomalies using the 9-11 incident as a backdrop. Intraday volatility is also examined as a means to capture prevailing market sentiments. By evaluating market behavior with both implied and intraday volatilities, a composite picture of investor anxiety is captured especially in pre-event time. Empirical results show that the magnitude of pre-event cumulative abnormal return for the airline stocks is statistically significantly larger than that of the market as a whole. Also, there was a remarkable rise in implied volatility just before the incident, as evidenced by a significant positive abnormal trend.
Implied options volatility conveys the expectation of the rate and magnitude of future price changes of the underlying asset, not the derivative contract. Every so often, there is a discrepancy between the theoretical price of an option and its market value. Summa (2002) explains that this deviation is due to the amount of expected or implied volatility (IV) which the market prices into the option. Thus, a high IV suggests that the option's market price is greater than its theoretical price. A rising IV reflects the growing uncertainty that the market imputes in the price of the derivative. In the circumstance, a high volatility indicates that the sale of options, rather than their purchase, is a more attractive strategy.
Volatilities, in general, convey the essence of risk in the market. Three notable volatility metrics are the historical close-to-close variance, intra-day volatility, and implied volatility. Implied volatility, derived from option prices, is used to gauge investor sentiments about future market disturbances. In 1993, the Chicago Board Options and Exchange (CBOE) began the construction of an implied volatility index, called the VIX. Since then, this index has remained a popular indicator of near-term market anomaly. Corrado and Miller (2005) investigate the ability of the VIX to predict market events, whereas Whaley (2000) show how traders use up-to-the-minute estimates of expected volatility to gauge investor fear. In addition, Corrado and Miller (2006) show that a positive relation exists between expected and realized excess returns when risk is measured using implied option volatility, rather than historical volatility.
2. LITERATURE
The use of volatility metrics to evaluate market performance and investor risk is not new in the literature. Earlier studies were based on range-based estimators of investment risk. Parkinson (1980) first considered this problem under the assumption that securities follow a continuous Brownian motion. Using a distribution first derived by Feller (1951), he finds a variance estimator for a security whose natural log follows a zero-mean diffusion. His estimator is about five times as efficient as the conventional close-to-close variance estimator.
Garman and Klass (1980) extend Parkinson's work by incorporating open and close prices as well as intraday price data. Subsequently, Spurgin and Schneeweis (1998) show that the binomial model may better explain intraday volatility when price changes are not continuous. Although Duque and Paxson (2005) argue that volatility estimates calculated in this way might still be biased since prices are only observable in discrete time, many other studies have shown that range volatility estimators are, in general, robust and typically provide more superior estimates than daily close-to-close variance metrics (Daigler and Wiley, 1999; Yang and Zhang, 2000; Shu and Zhang, 2005; and Daigler, 2005).
In a post 9-11 survey of active investors, Glaser and Weber (2003) find that volatility forecasts by active investors were higher in post 9-11 than before. They also discover that returns forecasts were significantly higher than realized returns as investors believed that markets had overreacted to the attacks. This view is partly supported by Graham and Harvey (2002) who find that investor estimate of the one-year risk premium fell sharply after 9-11. But Graham and Harvey also find that volatility forecasts increased as respondents grew more wary of the likelihood of further attacks.
Two notable studies that examine the notion of illegal insider trading in the days leading up to 9-11 are Carter and Simkins (2004) and Poteshman (2006). Carter and Simkins present evidence of post 9-11 short-term negative excess returns in the airlines industry. Their study also shows that while being concerned about the increased likelihood of financial distress, investors were able to separate strong from weak airlines based on the financial strength of the airlines. In a study of option market activity leading up to 9-11, Poteshman finds that while put volume ratios were at their typical levels, the long put volume indicator was unusually high. He then concludes that such behavior is consistent with a condition where informed investors trade in advance of a negative event.
3. DATA DESCRIPTION
Daily intraday prices and implied volatility data are obtained for the following stocks and indexes: American Airlines, United Airlines, Airlines equity index, S&P 500 equity index, and Chicago Board of Options Exchange volatility index (VIX). Sample period for all data is from January 1996 to December 2002. The VIX series are obtained from the CBOE data base, while the rest of the data are generated from the S&P data base.
By its construct, the VIX is designed to capture market expectations of near-term volatility. When the VIX was first introduced in 1993, the index was computed based on volatilities implied in options on the S&P 100 index (symbol OEX) and was based on the Black-Scholes option pricing model. Later, in September 2003, it was recalculated based on options on S&P 500 index (symbol SPX). Since the S&P 500 is considered the core index for U.S. equities, the VIX serves as the benchmark for the overall equity market volatility.
The natural relationship between the VIX and the direction of the market is negative. Implied volatility rises as the market declines and falls as the market rises. A rise in implied volatility is considered a sign of investor nervousness. Conversely, a drop suggests investor bullishness or complacency. The greater the perceived risk in the equity market, the higher the VIX. When the VIX rises, options, especially puts, become more expensive because puts rise if the market is expected to fall. Rising put demand means higher put prices and therefore, higher implied volatilities. Consequently, VIX is widely regarded as the investor fear gauge (Whaley, 2000) since volatility often indicates financial instability.
4. EMPIRICAL METHODOLOGY
Pre-event examination of price anomaly is over the five-day period prior to September 11, 2001. The estimation period is the 500 trading days from t = -510 to -10. To test whether a difference exists between pre-event cumulative abnormal returns for the airline index and that of the overall market, the following test statistic is applied (Hawawini and Swary, 1990):
t = ([CAR.sub.1] - [CAR.sub.2])/1/[[square root of t - 2] [[square root of [t.summation over (t = 1)] [([D.sub.t] - D).sup.2] (1)
where
[CAR.sub.1] = Cumulative average abnormal return for stocks in group 1 (airlines index)
[CAR.sub.2] = Cumulative average abnormal return for stocks in group 2 (market index)
T = Number of days in the estimation period (500)
[D.sub.t] = Difference in returns between [CAR.sub.1] and [CAR.sub.2] at time t
D = Average difference in returns between [CAR.sub.1] and [CAR.sub.2] over the estimation period
Additionally, Granger causality tests are performed on the VIX in relation to the underlying equity indices. The bivariate vector autoregressive model in the sense of Granger (1969) is defined as follows:
[DELTA][Y.sub.t] = [alpha] + [p.summation over (i = 1)] [[phi].sub.i] [DELTA][Y.sub.t-1] + [q.summation over (i = 1)] [[theta].sub.i] [DELTA][X.sub.t-1] + [[epsilon].sub.t] (2)
where [DELTA] is the first difference operator and X and Y represent the defined market variables. If the [theta] coefficients are significant, then X Granger-causes Y. To test for reverse causality, the X's and Y's are reversed. The optimal lags of the model are determined using the Akaike Information Criterion (AIC).
5. EMPIRICAL RESULTS
Empirical results are summarized in Tables 1 to 4 and Figure 1. Panel A of Table 1 shows that the pre-event cumulative abnormal return (CAR) for airline stocks is -8.44 percent, which is statistically significant but only at the 0.10 level. For the whole market, pre-event CAR shown in Panel B is -3.57 percent. Although equally negative, it is not statistically significant at any conventional level. The result in Panel C of Table 1 shows that the difference in pre-event CAR between airline stocks and the rest of the market is statistically significant at the 0.05 level. These comparative results appear to support the view that the airline industry was more adversely predisposed to 9-11 than the rest of the market (Obi, 2007).
Impending market anomaly can also be gauged by the level of implied option volatility. Table 2, Panel A contains results of abnormal patterns in the CBOE's volatility index, the VIX. The pre-event CAR of about 24 percent is statistically significant at the 0.10 level. Since the VIX typically rises in advance of a market downtrend, this increase in both pre-event and event day cumulative abnormal returns shows support, albeit weak, of an impending market anomaly. It is noteworthy that post-event cumulative abnormal returns decreased to a negative return, an indication that the markets may have overestimated the degree of investor risk perception.
Panel B of Table 2 shows implied volatility anomalies for the two target airlines: American Airlines and United Airlines. Pre-event CAR for these two airlines is 18.4 percent, which is significant at the 0.10 level. Much of the abnormal trend occurred one day before the attacks, with a level of 11.8 percent. This value is significant at the 0.05 level. Also, as Figure 1 shows, there was a marked increase in abnormal returns just before September 11, 2001.
[FIGURE 1 OMITTED]
Intraday volatility levels are presented in Table 3. Intraday volatility is measured using a variant of the Garman and Klass (1980) volatility estimator. When volatility levels are compared between the target airlines and the composite airlines index, the pre-event volatility difference is statistically significant at the 0.05 level. Also, the difference between the target airlines and the rest of the market is statistically significant at the 0.05 level. These comparative results are based on a simple F test of significance. It is worth pointing out though that the observed higher intraday volatility levels between the target airlines and other indexes are not exclusive to the pre-9-11 period. In fact, these differences are seemingly more significant in the non-event comparison period, as the results show. This latter outcome convolutes the essence of the earlier comparison around 9-11.
Finally, Granger causality results are presented in Table 4. Most notable in the empirical results is the two-way causality between the implied volatility index, VIX, and the market index itself (SPX-Price). There is however a one-way causality from the VIX to the intraday volatility metric for the market index (GK-SPX) as well as the implied volatility on the airline index (XAL-IV). There is no evidence that implied volatility on the airline index Granger-causes the airlines equity index (XAL-Price). It is also noteworthy that while the all-powerful VIX does not appear to Granger-cause the airline equity index (XAL-Price), the airline equity index actually Granger-causes the VIX. This apparent contradiction is not easily explainable.
6. CONCLUSIONS
Pre-event abnormal returns show that on average, there is a marginal rise in negative excess returns for airline stocks prior to September 11, 2001. The same is not the case for the market as a whole. More importantly, cumulative negative excess returns for airline stocks are statistically significantly larger than that of the rest of the market. Abnormal trends in implied option volatility for American Airlines and United Airlines were at a statistically significant level at least a day before the incident. These results support the contention that investor uncertainty for airline stocks before the disaster was markedly greater, especially for the two stocks directly involved in the attacks. It is thus arguable that if insiders knew that a catastrophe was in the offing, they entered their trade positions gradually making sure that the market was not alarmed of their trepidation.
Implied option volatility captures changes in investor uncertainty prior to an event. There is some evidence of an abnormal rise in implied options volatility for the entire market just before 9-11. The metric for implied volatility is the CBOE's volatility index, the VIX. The usefulness of the VIX is its ability to often foretell an event prior to its occurrence. To this end, Granger causality studies were carried out to confirm the VIX's ability to lead the market. Results of this latter analysis are mixed. For example, there is a two-way causality between the VIX and the underlying market index. However, there is a direct causality from the VIX to the intraday day volatility metric for the entire market. The same is also true with regard to the implied volatility for the airline stock index. On the other hand, there is a one-way causality from the airline stock index to the VIX. There is no immediate explanation for this apparent anomaly in the direction of causality.
In general, while these results show some evidence of pre-knowledge of 9-11 especially in the trading of airline stocks, there is really no compelling empirical evidence to support illegal insider information and trading prior to the event (Appendix 1 contains a chronology of trading events prior to the incident). This is because abnormal return in pre-event time is weakly significant for both equity returns and the implied volatility index. There is evidence however that implied volatility precedes market performance. But there is no evidence that the relationship between volatility levels for the airline index and the rest of the market changed from their natural levels before and after 9-11. For both of these sectors, implied volatility levels rose and remained markedly higher in the days and months following the attacks.
APPENDIX 1. CHRONOLOGY OF TRADING ANOMALIES BEFORE 9-11
Between September 6 and 7, there were purchases of 4,744 put options on UAL at the CBOE, but only 396 call options. United Airlines stock fell 42 percent, from $30.82 per share to $17.50, when the market reopened after the attacks.
On September 10, there were purchases of 4,516 put options on AMR at the CBOE, compared to only 748 calls. American Airlines stock fell 39 percent, from $29.70 to $18.00 per share, when the market reopened after the attacks.
No similar trading in other airlines occurred at the CBOE in the days immediately preceding 9-11.
Between September 6 and 9, there were purchases of 2,157 put options on Morgan Stanley Dean Witter & Co. at the CBOE. The trades were on the October $45 put options. This compares to an average of 27 contracts per day before September 6, 2001. It is noteworthy that Morgan Stanley was located in the World Trade Center. This company's stock price fell from $48.90 to $42.50 after attacks.
Between September 5 and 7, there were purchases of 12,215 October $45 put option contracts on Merrill Lynch & Co. at the CBOE. The company's headquarters were in the Twin Towers vicinity. This compares to an average volume in these options of 252 contracts per day prior to 9-11. After the attacks, Merrill's stock price fell from $46.88 to $41.50.
In Europe, government regulators scrutinized trades in Munich Re (Germany), Swiss Re (Switzerland), and AXA (France). These are multinational reinsurers with significant exposure to 9-11. Although these stocks fell drastically in value after 9-11, it is arguable that negative earnings reports on these firms, shortly before the attacks, may have also been responsible for the unusual selling of these stocks.
Primary news source: Bloomberg News, September 19, 2001, "Chicago Options Exchange Probing Pre-attack Trading"
REFERENCES:
Carter, David, and Betty J. Simkins, "The Market's Reaction to Unexpected Catastrophic Events: The Case of Airline Stock Returns and the September 11th Attacks," Quarterly Review of Economics and Finance, Vol. 44, 2004, 539-558.
Corrado, C.J. and T.W. Miller, Jr., "The Forecast Quality of CBOE Implied Volatility Indexes," Journal of Futures Markets, Vol. 25, 2005, 339-373.
--, "Estimating Expected Excess Returns Using Historical and Option-Implied Volatility," The Journal of Financial Research, Vol. XXIX, No. 1, 2006, 95-112
Daigler, Robert T., "Changes in the Structure of the Currency Futures Markets: Who Trades and Where They Trade," Working Paper, Florida International University, February, 2005, daiglerr@fiu.edu.
Daigler, Robert T. and M. Wiley, "The Impact of Trader Type on the Futures Volatility-Volume Relation," Journal of Finance, December, 2002, 2297-2316.
Duque, Joao and Dean A. Paxson, "Empirical Evidence on Volatility Estimators," Working Paper, ISEG--Instituto Superior de Economia e Gestao, Universidade Tecnica de Lisboa, 2005, jduque@iseg.utl.pt.
Feller, William, "The Asymptotic Distribution of the range of Sums of Independent Random Variables," Annals of Mathematical Statistics, Vol. 22, 1951, 427-432.
Garman, Mark and Michael Klass, "On the Estimation of Security Price Volatilities from Historical Data," Journal of Business, Vol. 53, 1980, 67-78.
Glaser, Markus and Martin Weber, "September 11 and Stock Return Expectations of Individual Investors," Working Paper, University of Mannheim, September 2003, 2003.
Graham, John R. and Campbell R. Harvey, "Expectations of Equity Risk Premia, Volatility, and Asymmetry," Working Paper, Duke University, 2002.
Granger, C.W.J., "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Volume 37, 1969, 424-438
Hawawini, Gabriel A. and Itzhak Swary, Mergers and Acquisitions in the U.S. Banking Industry: Evidence from the Capital Markets, Elsevier Science Publishers, Amsterdam, 1980.
Obi, Pat, "Market Sector Reactions to 9-11: An Event Study," The International Journal of Business and Finance Research Vol. 1 (1), 2007, 48-58.
Parkinson, Michael, The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, Vol. 53, 1980, 61-66.
Poteshman, Allen M., "Unusual Option Market Activity and the Terrorist Attacks of September 11, 2001," Journal of Business, July, Vol. 79 (4), 2006, 105-110.
Shu, Jinghong and Jin E. Zhang, "Testing Range Estimators of Historical Volatilities," Journal of Economic Literature, 2005, 101-107.
Spurgin, Richard B. and Thomas Schneeweis, "Efficient Estimation of Intraday Volatility: A Method-of-Moments Approach Incorporating the Trading Range," Financial Markets Tick by Tick, September 1998.
Summa, John, "The ABCs of Option Volatility," March 11, htttp://www.investopedia.com/articles.
Whaley, R. E., "The Investor Fear Gauge," Journal of Portfolio Management, Vol. 26, 2000, 12-17.
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Pat Obi, Purdue University Calumet, Hammond, Indiana, USA
Dr. Pat Obi is a Professor of Finance at Purdue University Calumet. He earned his Ph.D. in Finance with a minor in Econometrics from The University of Mississippi in 1989. He teaches MBA-level courses in Corporate Finance and Statistics. Dr. Obi's research is primarily in derivatives trading and international finance. He consults extensively for business and industry and is widely published in various business and finance journals. He is the author of Basics of Business Finance, a Lithuanian Language text.
TABLE 1. EVENT STUDY RESULTS ON EQUITY INDEXES
Panel A. Airlines Index (XAL) Abnormal Returns
Cumulative
Event Time (+) Abnormal Return t Statistic
t = +1 -0.4028 *** -19.9461 t = -1 -0.0168 -0.8295 t = -5 to t = -1 -0.0844 * -1.8684 t = 2 to t = 50 0.3132 ** 2.2157
Panel B. Market Index SPX Abnormal Returns
Cumulative
Event Time (+) Abnormal Return t Statistic
t = +1 -0.0491 *** -3.6617 t = -1 0.0064 0.4760 t = -5 to t = -1 -0.0357 -1.1903 t = 2 to t = 50 0.1011 1.0779
Panel C. Com Darison of Pre-Event Cumulative Abnormal Returns (++)
[CAR.sub.1] Airlines -0.0844 [CAR.sub.2] Market -0.0357 t Statistic -2.6200 **
- Significant at a = 0.01 level
- Significant at a = 0.05 level
- Significant at a = 0.10 level
(+) Day 0 (September 11, 2001): markets yet to open when the attacks occurred at 8:46 AM local time
(++) Test statistic based on Hawawini and Swary (1990) fort = -5 to t = -1
TABLE 2. IMPLIED VOLATILITY TEST RESULTS
Panel A. Abnormal Returns for the CBOE Volatility Index (+)
Cumulative
Event Time Abnormal Index t Statistic
T = +1 0.3103 *** 5.6035 T = -1 0.0262 0.4732 T = -5 to t = -1 0.2469 * 1.9940 T = 2 to t = 50 -0.5592 -1.4424
Panel B. Abnormal Performance of Implied Volatility on Target Stocks ++
Cumulative
Event Time Abnormal Index t Statistic
T = +1 1.1471 *** 24.1426 T = -1 0.1181 *** 2.4852 T = -5 to t = -1 0.1841 * 1.7332 T = 2 to t = 50 -0.3168 -0.9524
- Significant at [alpha] = 0.01 level
- Significant at [alpha] = 0.05 level
- Significant at [alpha] = 0.10 level
+ Abnormal returns are calculated from CBOE's trading data on the VIX
TABLE 3. PRE EVENT INTRADAY VOLATILITY COMPARISON OF TARGET STOCKS +
Volatility Metric
Sample Target Airlines Market Period Stocks Index Index
Observation Time 0.00033 0.00013 0.00009
Non Event Time 0.00072 0.00023 0.00011
F Statistics *
Sample Target Target Airline Period Stocks to Stocks to Index to
Airline Market Market
Index Index Index
Observation Time 2.61 3.52 1.35
Non Event Time 3.13 6.37 2.04
(+) Target stocks are American Airlines (AMR) and United Airlines (UAL)
- For df [greater than or equal to] 19 in the numerator and
denominator, F statistic [greater than or equal to] 2.50 is significant at [alpha] = 0.05 level
Observation time: 8/13/2005-9/10/2005 (n = 20)
Non event time: 1/4/1999-12/29/2000 (n = 504)
TABLE 4. GRANGER CAUSALITY WALD STATISTICS
Causality to:
VIX SPX-price GK-SPX
Causality from: VIX 3.2999 ** 86.7749 ** SPX-price 4.6863 *** 45.4686 ** GK-SPX 0.3861 2.3953 XAL-IV 0.8622 0.9226 10.7659 ** XAL-price 4.6863 ** 1.4984 20.3735 **
Causality to:
XAL-IV XAL-price
Causality from: VIX 9.2001 *** 1.4645 SPX-price 2.3916 * 3.3037 ** GK-SPX 3.9804 ** 1.1062 XAL-IV 0.2654 XAL-price 0.5269
- Significant at [alpha] = 0.01 level
- Significant at [alpha] = 0.05 level
- Significant at [alpha] = 0.10 level
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