2.2. The standard and poor's 500 stock index futures data

The basic features of the 5-minute S &P 500 are qualitatively similar to those of

the 5-minute DM-$ returns. Perhaps, the most notable difference is that the

standard deviation for the stock index futures return of 0.104% is more than

double the value for the foreign exchange market. However, since the overnight

returns for the S&P 500 are excluded, the average 5-minute standard deviation

corresponds to active trading on the CME only, whereas the foreign exchange

returns cover the entire 24-hour trading cycle and therefore include periods of

relatively slow activity. Even so, when judged by auxiliary statistics such as the

sample minimum and maximum of 2.22% and -2.76%, the equity market

exhibits the more volatile returns. Another distinguishing feature is the virtual

absence of autocorrelation in the futures returns. Although the first ten autocorrelation

coefficients are highly significant, the coefficients are economically small and

have unpredictable signs ~5. This lack of correlation contrasts sharply with results

reported by most studies on the intraday S&P 500 cash market, where non-synchronous

trading effects imply that stale prices may enter the calculation of the

index (see e.g. Chart et al., 1991) 16

The intraday periodic patterns over the eighty 5-minute intraday intervals are

depicted in Fig. lb and Fig. 2b. Apart from the positive returns over the initial

5-minute interval from 8.35 to 8.40 a.m. and towards the end of the trading day,

~3 We follow Dacorogna et al. (1993) in using GMT time scale throughout our analysis. Daylight

savings time is observed in Europe and North America, but not in East Asia. From the sub-sample

analysis in Andersen and Bollerslev (1994) this gives rise to a one hour difference in the peaks

associated with the regular release of U.S. macroeconomic announcements at 08.30 a.m. corresponding

to interval 162 for winter time and interval 150 for summer time. Ederington and Lee (1993) and

Harvey and Huang (1991) also suggest that macroeconomic announcement effects have a distinct

impact on the average volatility in early Friday morning trading in the U.S. segment of the market. We

do not pursue this or any other day-of-the-week effects any further here, however.

the violations of the 5% confidence bands for the average returns are dispersed

unpredictably over the trading day 17. Nonetheless, as was the case for the foreign

exchange market, the systematic return effects are dwarfed by the systematic

movements in the return volatility, here documented in Fig. 2b. The average

absolute returns attain the commonly observed intraday U-shape, starting out at

0.095% in the morning, followed by a smooth decline to a level of 0.055% around

noon and a steady rise to 0.105% towards the end of trading in the cash market.

The subsequent drop and rise over the last fifteen minutes corresponds to the post

cash market trading on the CME 18. The robustness of this intraday periodicity in

the S&P 500 returns is again underscored by the more detailed analysis in

Andersen and Bollerslev (1994) in which the full four year sample is divided into

calendar years as well as four daily volatility categories. The only discernible

difference across these sub-sample patterns is a tendency for the fight part of the

'U' to occasionally rise above the left part, creating more of a 'J' shape.

Interestingly, this tendency appears to be concentrated on high volatility days. The

model proposed in Section 5 below explicitly accounts for this phenomenon.

Several recent studies have attempted to rationalize the pronounced U-shape

pattern in intraday stock market volatility by strategic interaction of traders around

market openings and closures (see e.g. Admati and Pfleiderer, 1988, 1989; Foster

and Viswanathan, 1990; Son, 1991; Brock and Kleidon, 1992). Even though the

foreign exchange market operates on a continuous basis, the volatility pattern for

the DM-$ depicted in Fig. 2a may be viewed, tentatively, as a sum of two

overlapping U-shapes corresponding to the Far East and European trading hours,

along with an inverted U-shape for the U.S. segment of the market. Hence, in spite

of obvious differences in market microstructures, the foreign exchange returns are

calculated from quotes in a 24-hour over-the-counter market while the equity

returns are obtained from transaction prices on an organized futures market with

well defined daily closings, the pattern of intraday periodicity in the two markets

share important common characteristics.

The basic features of the 5-minute S &P 500 are qualitatively similar to those of

the 5-minute DM-$ returns. Perhaps, the most notable difference is that the

standard deviation for the stock index futures return of 0.104% is more than

double the value for the foreign exchange market. However, since the overnight

returns for the S&P 500 are excluded, the average 5-minute standard deviation

corresponds to active trading on the CME only, whereas the foreign exchange

returns cover the entire 24-hour trading cycle and therefore include periods of

relatively slow activity. Even so, when judged by auxiliary statistics such as the

sample minimum and maximum of 2.22% and -2.76%, the equity market

exhibits the more volatile returns. Another distinguishing feature is the virtual

absence of autocorrelation in the futures returns. Although the first ten autocorrelation

coefficients are highly significant, the coefficients are economically small and

have unpredictable signs ~5. This lack of correlation contrasts sharply with results

reported by most studies on the intraday S&P 500 cash market, where non-synchronous

trading effects imply that stale prices may enter the calculation of the

index (see e.g. Chart et al., 1991) 16

The intraday periodic patterns over the eighty 5-minute intraday intervals are

depicted in Fig. lb and Fig. 2b. Apart from the positive returns over the initial

5-minute interval from 8.35 to 8.40 a.m. and towards the end of the trading day,

~3 We follow Dacorogna et al. (1993) in using GMT time scale throughout our analysis. Daylight

savings time is observed in Europe and North America, but not in East Asia. From the sub-sample

analysis in Andersen and Bollerslev (1994) this gives rise to a one hour difference in the peaks

associated with the regular release of U.S. macroeconomic announcements at 08.30 a.m. corresponding

to interval 162 for winter time and interval 150 for summer time. Ederington and Lee (1993) and

Harvey and Huang (1991) also suggest that macroeconomic announcement effects have a distinct

impact on the average volatility in early Friday morning trading in the U.S. segment of the market. We

do not pursue this or any other day-of-the-week effects any further here, however.

the violations of the 5% confidence bands for the average returns are dispersed

unpredictably over the trading day 17. Nonetheless, as was the case for the foreign

exchange market, the systematic return effects are dwarfed by the systematic

movements in the return volatility, here documented in Fig. 2b. The average

absolute returns attain the commonly observed intraday U-shape, starting out at

0.095% in the morning, followed by a smooth decline to a level of 0.055% around

noon and a steady rise to 0.105% towards the end of trading in the cash market.

The subsequent drop and rise over the last fifteen minutes corresponds to the post

cash market trading on the CME 18. The robustness of this intraday periodicity in

the S&P 500 returns is again underscored by the more detailed analysis in

Andersen and Bollerslev (1994) in which the full four year sample is divided into

calendar years as well as four daily volatility categories. The only discernible

difference across these sub-sample patterns is a tendency for the fight part of the

'U' to occasionally rise above the left part, creating more of a 'J' shape.

Interestingly, this tendency appears to be concentrated on high volatility days. The

model proposed in Section 5 below explicitly accounts for this phenomenon.

Several recent studies have attempted to rationalize the pronounced U-shape

pattern in intraday stock market volatility by strategic interaction of traders around

market openings and closures (see e.g. Admati and Pfleiderer, 1988, 1989; Foster

and Viswanathan, 1990; Son, 1991; Brock and Kleidon, 1992). Even though the

foreign exchange market operates on a continuous basis, the volatility pattern for

the DM-$ depicted in Fig. 2a may be viewed, tentatively, as a sum of two

overlapping U-shapes corresponding to the Far East and European trading hours,

along with an inverted U-shape for the U.S. segment of the market. Hence, in spite

of obvious differences in market microstructures, the foreign exchange returns are

calculated from quotes in a 24-hour over-the-counter market while the equity

returns are obtained from transaction prices on an organized futures market with

well defined daily closings, the pattern of intraday periodicity in the two markets

share important common characteristics.