There is a long-standing literature on seasonal patterns, say at the monthly, quarterly, or annual frequency, in stock returns (see Keim (1983), Ariel (1987), Lakonishok and Smidt (1988)). Some of this periodicity is consistent with patterns of trading by investors. For example, Keim (1989) finds the turn-of the-year trading patterns induce patterns in equity trades that occur at the ask price versus the bid price and that this trading pattern explains the size-related turn-of-the-year effect in stock prices. Intraday patterns in returns and volatility are found by Wood, McInish, and Ord (1985). Returns and volatility are higher, on average, at the beginning and end of the trading day. Harris (1986) and Andersen and Bollerslev (1997) find similar results.
While intraday patterns of volume and volatility found in Wood, McInish, and Ord (1985), Harris (1986), and Pagano, Peng, and Schwartz (2008) can be justified with models of discretionary liquidity trading (e.g., Admati and Pfleiderer (1998) and Hora (2006)), predictable patterns in returns are harder to explain. We study the nature of this intraday periodicity of returns. We divide the trading day into 13 half-hour trading intervals. A stock’s return over a trading interval is negatively related to its returns over recent intervals, which is consistent with the negative autocorrelation induced by "microstructure effects" such as bid-ask bounce. However, there is a statistically significant positive relation between a stock’s return over an interval and its past returns at daily frequencies (i.e., 13, 26, 39, ... interval lags). This relation is stronger over the first and last half-hour of the trading day, as one might expect, given the results of Wood, McInish, and Ord (1985) and Harris (1986), but remains statistically significant over the other periods of the day. Thus, the intraday return pattern is not merely due to uniformly high returns at the beginning and end of the trading day.
What can explain these patterns in intraday returns? There are several possible explanations, though some are quite difficult to test due to data limitations. One explanation is that traders consistently trade at the same time of the day and at the same direction. For example, if the output of an active trader’s investment model is relatively stable from day to day, then executing similar trades for several accounts on different days could generate intraday periodicity in order flow. This is particularly true if the trader uses a trading algorithm that specifies a specific pattern of trades, such as Almgren and Chriss (2000), Grinold and Kahn (2000), Huberman and Stanzl (2005), Hora (2006), and Engle and Ferstenberg (2007). Another example is trading by index funds at the close to reduce tracking error. However, this index fund behavior would not explain the existence of periodicity during the rest of the trading day. Campbell, Ramadorai, and Schwartz (2007) present evidence that there is strong persistence, at a daily frequency, in the direction of trades by institutional investors, in the aggregate. Our results might indicate that there is persistence in the intraday timing of institutional order flow as well. They are also consistent with the model of sequential information acquisition of Holden and Subrahmanyam (2002) if agents tend to become informed at intervals that correspond to our observed periodicity.
Explanations based on autocorrelation in trading activity would theoretically imply a similar periodicity in trading volume or order flow/imbalance. Indeed, an examination of trading volume shows that it has similar patterns to those of returns, i.e. firms that experience a relatively high change in their trading volume over a particular half-hour interval of a day typically experience a high change in their volume during the same half-hour interval during each of the next few days. Although related, the periodicity in trading volume does not completely explain the periodicity of returns. We also split volume into that due to large versus small trade size. Both measures of volume show daily periodicity, but neither explains the daily return periodicity. Oddly, the level of order imbalance (OI) does not exhibit obvious periodicity, even when partitioned into small versus large trades, e.g. Hvidkjaer (2008). However, percentage changes in order imbalance exhibit periodicity similar to returns, but that pattern in order imbalances does not explain the pattern in returns. Possibly the Lee and Ready (1991) algorithm used to classify buyer- versus seller-initiated trades, used to calculate OI, results in error-prone estimates for our experimental design (i.e., individual stocks over short, half-hour, intervals).
Several other tests indicate that the intraday periodicity at the daily frequency is not merely an artifact of previously shown patterns. For example, it is not concentrated in any particular weekday and, therefore, is not a manifestation of the day-of-the-week effect (see French (1980) and Smirlock and Starks (1986)). It is not concentrated in any particular month (for monthly seasonality see Heston and Sadka (2008a, b)). The effect is also not particularly related to the turn-of-the-month effect (Ariel (1987)) or the turn-of-the-quarter effect (Carhart, Kaniel, Musto, and Reed (2002)). The pattern of intraday returns is highly persistent as it seems to last for over a month (20 trading days). It is not due to a particular market capitalization group, inclusion in the S&P500 index, nor a manifestation of intraday movements in systematic risk. There is substantial evidence of intraday periodicity of return volatility (Andersen and Bollerslev (1997)), which we also find in our sample. However, patterns in volatility do not explain our return periodicity.
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