# Stock index futures options and the predictability of intraday index price changes.

INTRODUCTIONThe Chicago Board Options Exchange began offering standardized call options on equities in 1973. These options were standardized in terms of expiration dates and exercise prices. The popularity of these options, in terms of trading volume, grew quickly. The introduction of these options and the fast growth in their popularity raised the empirical question of how the underlying markets were being affected by option trading. Many studies have examined the impact of equity option introduction on the return variability and trading volume of the underlying equities. Such studies include Bansal, Pruitt and Wei (1989), Whiteside, Dukes and Dunne (1983), and Hayes and Tennenbaum (1979).

More recently, beginning in 1982, standardized option trading was initiated on futures contracts. Currently futures options are traded on many agricultural, financial, currency and stock index futures. Options on futures contracts allow investors and risk managers to define and limit their risk in the form of a premium paid for the right to buy or sell a futures contract at a specified price known as the exercise price.

The impact of futures option introduction on their underlying instruments is not well understood. The case of options on futures is particularly interesting because, for many contracts, the underlying futures contract plays a price discovery role. There are many types of futures contracts and the magnitude of the price discovery role appears to vary by contract type and in some cases even within contract type. Studies such as Figlewski (1987), Kawaller, Koch and Koch (1987), Finnerty and Park (1987), Swinnerton, Curcio and Bennett (1989), Swinnerton (1988), and Kawaller, Koch and Koch (1993) examine the temporal price relationship between stock index futures and the underlying index and find a significant positive relationship. Theoretical futures mispricings and lagged index price changes have also been utilized by Swinnerton, Curcio and Bennett (1989) to try to predict subsequent intraday index price changes. Irwin (1990) suggests it would be a "particularly interesting question whether the introduction of option trading has a perceptible impact on the efficiency of cash and futures price movements."

This paper utilized a regression framework to examine the impact of stock index futures option initiation on the predictability of intraday index price changes based on 1) theoretical futures mispricings, 2) lagged index changes and 3) lagged futures price changes.

DATA

The data used in this study consists of tick-by-tick MMI stock index futures price quotes as well as MMI stock index price quotes. In calculating the theoretical futures price, the treasury bill rate was used as a proxy for the risk-free rate of interest and actual dividend payments by firms represented in the MMI were used as a proxy for the expected dividends. The MMI divisors which must be multiplied by the reported index value to convert the index point value to the index dollar value used in computing a theoretical futures price were obtained from the Chicago Board of Trade.

METHODOLOGY

The impact of futures option introduction on the predictability of intraday price changes was examined with respect to three predictor variables using the ordinary least squares regression approach developed by Curcio, Swinnerton and Bennett (1988). The three predictor or independent variables examined are 1) theoretical futures mispricings, 2) lagged spot index price changes and 3) lagged futures price changes. The dependent variable in the regression is the change in the spot price from the [j.sup.th] minute of day t to the j+[n.sup.th] minute of day t where n ranges from 5 to 30 minutes. The regression model is as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where,

[S.sub.tj] = the spot price of the index on the [j.sup.th] minute of day t,

[S.sub.tj+n] = the spot price of the index at the [(j+n).sup.th] minute of day t where n is the forecast period in minutes,

[S.sub.tj-5] = the spot price of the index on the [(j-5).sup.th] minute of day t,

[F*.sub.tj,T] = the theoretical futures price on the [j.sup.th] minute on day t for a stock index having a cash settlement at T,

[F.sub.tj,T] = the actual futures price on the [j.sup.th] minute of day t for a stock index which will have cash settlement at T,

[F.sub.tj-5,T] = the actual futures price on the [(j-5).sup.th] minute of day t for a stock index with cash settlement at T.

In the above regression [[beta].sub.1] represents the coefficient on the theoretical futures mispricing on the [j.sup.th] minute of day t, [[beta].sub.2] represents the coefficient on the lagged stock index cash price change and [[beta].sub.3] represents the coefficient on the lagged futures price change. [alpha] and represent the intercept and random disturbance coefficient, respectively.

The theoretical futures mispricing is calculated as the difference between the actual and the theoretical futures price at time t. The theoretical futures price is determined using the following cost of carry model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where,

[F.sub.tT] = the current price (at time t) of a stock index futures contract for delivery at time T,

[S.sub.t] = the market value of the stock at time t,

[D.sub.j] = the dividend expected to be paid by firm j at time t,

r = the riskless rate of interest assumed to be constant over (T-t).

With respect to [[beta].sub.1] the coefficient on the theoretical futures mispricing variable, relatively fewer significant positive coefficients are expected in the post-futures option period. This would be indicated by a reduction in the ratio of significant positive to significant negative coefficients on the theoretical futures mispricing variable following futures option initiation.

A positive mispricing would indicate that the current futures price is above its theoretical value and the market reaction would be to sell futures and buy the spot index which would tend to drive up the price of the spot index. A negative mispricing would indicate that the current futures price is below its theoretical value and the market reaction would be to buy the futures contract and sell the spot index which would tend to reduce the index price.

The second predictor variable in the regression, lagged index price changes, is expected to be largely unaffected by the introduction of index futures options. The basis of this hypothesis is that, although option introduction may increase the efficiency of the underlying assets, in the case of futures options the asset directly underlying the futures option contract is a futures contract on the stock index and not the index itself. Separate options are traded on the index itself. Therefore, the ratio of significant positive to significant negative [[beta].sub.2] coefficients on the lagged cash index variable is expected to remain relatively constant following stock index futures option initiation.

With respect to [[beta].sub.3], the coefficient on the lagged futures price change variable, evidence 3 is provided by Kawaller, Koch and Koch (1987), Stoll and Whaley (1990) and Swinnerton, Curcio and Bennett (1989) that the lagged futures price changes are able to predict, to some degree, subsequent stock index price changes. This is known as the price discovery role of futures. The introduction of a futures option should reduce the ability of lagged index futures price changes to predict subsequent intraday index price changes. According to weak form market efficiency past price changes should be of no value in predicting subsequent price changes, therefore to the extent that futures options introduction improves efficiency in the futures market we would expect lagged futures price changes to be a less valuable predictor of intraday index price changes. This would be indicated by a reduction in the number of significant positive to significant negative coefficients on the lagged futures price change variable.

RESULTS

Table 1 shows the change in the ratio of significant positive to significant negative coefficients from the pre-to the post-futures option periods. These ratios are grouped by lag time (ranging from 5 to 30 minutes) and by variable (lagged cash index, lagged futures or futures mispricing). This table shows the value of the ratio with options and without options by lag time.

A graphical representation comparing the ratio of significant positive to significant negative coefficients in the pre- and post-futures option periods appears in illustrations 1 through 3. Again, the results are grouped by lag time and variable. It can be seen that the ratio of significant positive to significant negative coefficients for the lagged cash index variable (all lag times) and the lagged futures price change variable (all lag times) are much less than the same ratio for the theoretical futures mispricing variable.

The ratio of significant positive to significant negative coefficients on the lagged index value variable in the regression model was less than one for all lag times in both the pre- and post-futures option periods. This ratio, overall showed no change from the pre- to the post-futures option period.

The number of significant positive coefficients on the lagged index value variable was greater for all lag times except 20 minutes. The number of significant negative coefficients on the lagged index value variable was greater for all lag times in the optioned period. Overall, the ratio of significant positive coefficients (for all lag times) to significant negative coefficients (for all lag times) did not change from the pre- to the post-futures option period.

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The ratio of significant positive to significant negative coefficients on the lagged futures price variable was 42 percent lower for the 5 minute lag time and 40 percent lower for the 10 minute lag time when options were trading. The ratio remained greater than one for both the 5 and 10 minute lag times. For the longer lag times, the ratio was less than one and remained relatively constant from the pre- to the post-futures option period.

Overall, the ratio of ratio of significant positive to significant negative coefficients on the lagged futures price change variable declined following futures option initiation. While this was especially true for the shorter lag times, the overall results indicate that the price discovery role of the index futures contract is diminished following futures option initiation.

The ratio of significant positive to significant negative coefficients on the theoretical futures mispricing variable was lower in the post-futures option period for all lag times. The reduction in this ratio ranged from a 34 percent reduction for the 15 minute lag time to a 73 percent reduction for the 10 minute lag time. This ratio (over all lag times) fell by 56 percent in the optioned period.

Overall, the reduction in the ratio of significant positive to significant negative coefficients indicates that the value of the index futures mispricings as a predictor variable is reduced following futures option initiation. This could be indicative of more accurate pricing of the index futures contract and would be consistent with greater efficiency in the MMI futures market with the trading of options contracts on MMI futures.

SUMMARY AND CONCLUSIONS

This study examined the impact of index futures options on the predictability of intraday index price changes by examining the MMI futures contract. The predictor variables examined were 1) lagged cash index values, 2) lagged futures price changes and 3) theoretical futures mispricings.

With regard to the lagged cash index as a predictor variable, the ratio of significant positive to significant negative coefficients in the regression equation remained unchanged following futures option initiation on the MMI. Although the changes in the ratios were not consistent across all lag times, the value of lagged index price changes as a predictor variable appears to be unaffected by MMI futures option initiation.

The impact of futures option initiation on the price discovery role of the futures contract was evaluated through the lagged futures price change variable. The ratio of significant positive to significant negative coefficients on the lagged futures price change variable dropped slightly following futures option initiation. These results indicate that the value of the lagged futures price change variable or the price discovery role of the futures contract appears to have diminished somewhat following initiation of the futures option contract.

With respect to the theoretical futures mispricing variable there was a reduction in the ratio of significant positive to significant negative coefficients in the post-futures option period. This relative decrease in the number of significant positive coefficients indicates that the value of the theoretical futures mispricing variable as a predictor of subsequent intraday index price changes is diminished following futures option initiation.

REFERENCES

Abhyankar, Abhay H., "Return and Volatility Dynamics in the FT-SE 100 Stock Index and Stock Index Futures Markets", Journal of Futures Markets, June 1995, pp. 457-488.

Bansal, V., Pruitt, S., and Wei, K., "An Empirical Reexamination of the Impact of CBOE Option Initiation on the Volatility and Trading Volume of the Underlying Equities: 1973-1986", Financial Review. February, 1989, pp. 19-29.

Callahan, C., The Impact of Listed Call Options on the Return Variability of the Underlying Common Stock, Doctoral Dissertation, Graduate School of Business Administration, Kent State University, June 1979.

Figlewski, S., "The Interaction Between Derivative Securities and the Underlying Cash Markets: An Overview", Journal of Accounting, Auditing and Finance, Summer, 1987, pp. 299-318.

Finnerty, J., and Park, Y., "Stock Index Futures: Does the Tail Wag the Dog?", Financial Analysts Journal, March/April 1987, pp. 57-61.

Hayes, S., and Tennenbaum, M., "The Impact of Listed Options on the Underlying Shares", Financial Management, Winter 1979, pp. 72-76.

Herbst, A., McCormack, J., and West, E., "Investigation of a Lead-Lag Relationship Between Spot Stock Indices and Their Futures Contracts", Journal of Futures Markets, August 1987, pp. 373-381.

Kawaller, I., Koch, P., and Koch, T., "The Temporal Price Relationship Between S&P 500 Futures and the S&P 500 Index", Journal of Finance, Dec. 1987, pp. 1309-1329.

Kawaller, I., Koch, P., and Koch, T., "Intraday Market Behavior and the Extent of Feedback Between S&P 500 Futures Prices and the S&P Index", The Journal of Financial Research, Summer 1993, p. 107.

Martikainen, T., and Puttonen, V., "International Price Discovery in Finnish Stock Index Futures and Cash Markets", Journal of Banking and Finance, October 1994, pp. 809-822.

Shyy, G., Vijayraghavan, V., and Scott-Quinn, B., "A Further Investigation of the Lead-Lag Relationship Between the Cash Market and Stock Index Futures Market with the use of Bid/Ask Quotes: The Case of France", Journal of Futures Markets, June 1996, pp. 405-420.

Stoll, H., and Whaley, R., "Expiration Day Effects: What Has Changed?", Financial Analysts Journal, January/February 1990, pp. 58-72.

Swinnerton, E., Predictive Aspects of Stock Index Futures: A Study of the Major Market Index, Doctoral Dissertation, Graduate School of Management, Kent State University, 1988.

Swinnerton, E., Curcio, R., and Bennett, R., "Index Arbitrage Program Trading and the Prediction of Intraday Stock Price Changes", Review of Futures Markets, 7(2), 1989, pp. 300-323.

Whiteside, M., Dukes, W., and Dunne, P., "Short-Term Impact of Option Trading on Underlying Securities", Journal of Financial Research, Winter 1983, pp. 313-320.

James Stotler, North Carolina Central University

Richard Curcio, Kent State University

Eugene Swinnerton, University of Detroit, Mercy

Table 1: Ratio of Significant Positive to Significant Negative Coefficients Variable Option Lag=5 Lag=10 [S.sub.tj]-[S.sub.tj-5] no .76 .68 [S.sub.tj]-[S.sub.tj-5] yes .94 .71 [F.sub.tj,T]-[F.sub.tj-5,T] no 2.23 1.72 [F.sub.tj,T]-[F.sub.tj-5,T] yes 1.30 1.03 [F.sub.tj,T]-[F *.sub.tj-5,T] no 9.13 8.14 [F.sub.tj,T]-[F *.sub.tj-5,T] yes 5.78 2.21 Variable Lag=15 Lag=20 [S.sub.tj]-[S.sub.tj-5] .58 .58 [S.sub.tj]-[S.sub.tj-5] .65 .32 [F.sub.tj,T]-[F.sub.tj-5,T] .67 .92 [F.sub.tj,T]-[F.sub.tj-5,T] .70 .69 [F.sub.tj,T]-[F *.sub.tj-5,T] 5.20 4.17 [F.sub.tj,T]-[F *.sub.tj-5,T] 3.45 2.22 Variable Lag=25 Lag=30 [S.sub.tj]-[S.sub.tj-5] .46 .50 [S.sub.tj]-[S.sub.tj-5] .57 .52 [F.sub.tj,T]-[F.sub.tj-5,T] .63 .65 [F.sub.tj,T]-[F.sub.tj-5,T] .68 .81 [F.sub.tj,T]-[F *.sub.tj-5,T] 4.50 4.00 [F.sub.tj,T]-[F *.sub.tj-5,T] 1.75 1.39

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Author: | Stotler, James; Curcio, Richard; Swinnerton, Eugene |
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Publication: | Academy of Accounting and Financial Studies Journal |

Date: | Jul 1, 1997 |

Words: | 2737 |

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