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Mapping Intraday Price Movement in the S&P 500 Index (IRSA) – Part II

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    Equities Indexes

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In IRSA – Part II, our testing will examine the dominant price patterns that drive the intraday session of the S&P 500 Index. The ability to identify these patterns may allow traders to benefit by tailoring their trading strategies to exploit intraday price action. In this paper, we use two common approaches, momentum and mean reversion, to objectively describe and test for the existence of such patterns. We investigate the possible significance of these patterns, their effects on a trading strategy and how one might incorporate them in an intraday trading strategy or plan.


Equity Curve Detailed

Within the world of strategy trading, most strategies fall under the broad headings of momentum or mean reversion. In "Mapping Intraday Price Movement in the S&P 500 Index" (Analysis Concepts Issue 19 – March 8, 2011), we wrote of the return structure of the index as analyzed by segmenting the intraday session into three equal periods of 130 minutes. That paper touched on the idea of character differences in the price structure within each third of the intraday session. But we did not discuss an objective testing process or how to model the price action patterns in each third. This paper will use technical analysis rules based on momentum and mean reversion to objectively describe the nature of intraday price movement in the S&P 500 Index. Momentum and mean reversion methods tend to behave oppositely, allowing for useful and differing perspectives in our testing. We would expect the results to show either that the price movements in the index are nothing more than a random sequence of moves or that there are indeed momentum or mean-reversion tendencies in the intraday return structure of the index.

Understanding the Process

Fundamental to understanding this process is having some familiarity with the idea of Intraday Return Structure Analysis (IRSA). If you are not familiar with IRSA, you may want to read "Mapping Intraday Price Movement in the S&P 500 Index" before reading this paper, as some of the ideas discussed here were first introduced in that paper.

IRSA required that we segment the intraday session of the S&P 500 Index into three equal time periods, or three 130-minute bars (9:30 to 11:40 a.m., 11:40 a.m. to 1:50 p.m., and 1:50 to 4:00 p.m., U.S. Eastern time), that make up the intraday session. We then simulate the performance of each third of the trading session by showing how a $100,000 investment would have performed over time if continuously invested in one of the three periods. (See Figure 1 below.)

Figure 1 – $100,000 Invested (1/01/2005–1/01/2006) in Each Third of the Trading Day (Red = 9:30–11:40, Green = 11:40–1:50, Blue = 1:50–4:00). (The black line represents day-to-day returns.)

Figure 1 – $100,000 Invested

In "Mapping Intraday Price Movement in the S&P 500 Index," we did not disclose how frequently we reset the simulated value of each third of the trading session back to $100,000. Due to scaling issues, this can be an important consideration when using some technical indicators and testing techniques, as each simulated one-third period can separate too far away from the others over time, making it impossible to compare them. We made it a standard practice to reset these values on a quarterly basis, even if the reset had no effect on the indicator that we were using to measure the return structure of the security (see Figure 2). A quarterly reset is not the only alternative. One could use weekly, monthly, or even annual resets, but be aware that the reset frequency could have an effect on the underlying patterns in the data.

Figure 2 – Scaling Each Simulated Third of the Trading Session Back to $100,000 Investment

Figure 2 – Scaling Each Simulated Third

The next step of the process is to apply traditional momentum and mean reversion trading strategies to each of the three periods that make up the intraday trading session. Our trading signals will be generated in this manner and positions can be held on a day-to-day basis after a signal is given. Our focus will be to determine in which of the three periods of the intraday session are momentum or mean reversion signals most profitable. Below we explain the technical indicators we are using to describe momentum and mean reversion, as well as the strategy rules for these indicators. You will notice that our attention is not on any indicator's single input value, optimal or otherwise. We are more interested in evaluating the results of the patterns over all the input values we tested for each momentum and mean reversion strategy (1–30 inputs for each strategy).

Indicators Used in This Study

  • Momentum – This is the difference between the current price and the price n bars ago. We evaluate the input values of 1–30 bars (you will notice 1–30 input values in the momentum bar graphs below).
  • Bollinger Bands® – We are using the Lower Bollinger Band or -2 standard deviations, along with input values of 1-30 bars for evaluation. The -2 standard deviation value is static; it is the same for all tests.
  • Simple Moving Average – The simple moving average uses n bars as its length input. We evaluate the results from 1–30 bars for this input value.

Note: Both the Lower Bollinger Band and simple moving average length inputs were matched to have the same values throughout our testing; that is, if the Lower Bollinger Band's length was 10 when we ran the optimization, the simple moving average's length input was also 10 for that particular test in the optimization.

Study Testing Rules

Momentum Rules

  • Long Entries (this study was restricted to Long Entries and Exits only):
    • Buy the S&P 500 Index ($INX) if the momentum is greater than 0.
  • Exits:
    • Sell the S&P 500 Index if the momentum is less than 0.

Mean Reversion Rules

  • Long Entries (this study was restricted to Long Entries and Exits only):
    • Buy the S&P 500 Index ($INX) if the close crosses above the Lower Bollinger Band.
  • Exits:
    • Sell the S&P 500 Index if the close crosses above the moving average.

Analysis – Key Findings

Our study surveyed historical intraday data (130-minute bars) in the S&P 500 Index going back to 9/16/1983. We invested $100,000 per trade and applied $.02 commission and slippage per share. As noted earlier, in evaluating our results, the conclusions we drew were not exclusive to any single input from the indicators used. We focused on their overall significance. We divided the results below into momentum and mean reversion and used TradeStation's optimization reports to display a bar graph showing the historical performance of trades for all inputs in each study. For each strategy, the bar graphs display the net profit and maximum intraday drawdown for each input value. Once again, we apply input values 1–30 for the momentum calculation and 1–30 for the mean reversion calculations, both the Lower Bollinger Band length and the simple moving average length. Recognize as we make our way through these graphs that there are two very obvious themes that exist within the intraday session of the S&P 500 index.

Momentum Results

Figure 3 – Momentum (9:30–11:40) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 3 – Momentum

In Figure 3, we see that momentum signals given between 9:30 and 11:40 have very consistent net profitability for 1–30 input values. Notice the very low max intraday drawdown for each input.

Figure 4 – Momentum (11:40–1:50) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 4 – Momentum

Figure 5 – Momentum (1:50–4:00) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 5 – Momentum

From 11:40 to 1:50 (Figure 4) and especially from 1:50 to 4:00 (Figure 5), momentum wanes and does not work as well. As we examined the trades from these periods in detail, we noticed that more trades had false breakouts. And if you examine the momentum trades during the 9:30 to 11:40 period, you'll see that the price action has more of a tendency to follow through, which is why momentum worked better in the earlier part of the intraday session.

Mean Reversion Results

Figure 6 – Mean Reversion (9:30–11:40) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 6 – Mean Reversion

In evaluating the mean reversion results, we can see that mean reversion signals improve in the exact opposite fashion of momentum signals. The mean reversion performs the worst from 9:30 to 11:40, improving as the day progresses.

Figure 7 – Mean Reversion (11:40–1:50) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 7 – Mean Reversion

In the 11:40 to 1:50 period, the mean reversion signal is consistently profitable for almost every input value tested (1–30).

Figure 8 – Mean Reversion (1:50–4:00) – (1–30 bars). Blue Bars = Net Profit, Green Bars = Max Intraday Drawdown.

Figure 8 – Mean Reversion

By the 1:50 to 4:00 period, the mean reversion signal is even more consistently profitable for each input value, while the max intraday drawdowns are half of what they were in the 9:30 to 11:40 period.


The main goal of this paper is to reveal the dominant price patterns inherent in the S&P 500 Index's intraday session. We were not interested in the extent of the profitability of these patterns as much as we were concerned about their sustainability. Although the profitability of a pattern is the benchmark of its success, we found that these patterns were profitable enough over time to render them worthy of acknowledgement.

Momentum and mean reversion are common characteristics of stock price movement. These characteristics have opposite behavioral natures. Their behavior offers a convenient mode for our testing. At the risk of oversimplification, if mean reversion strategies do not produce profitable results, then momentum strategies must be profitable; or, if momentum strategies do not produce profitable results, then mean reversion strategies must be profitable. As you have probably already recognized, this relationship held true throughout our testing (Figure 9).

Figure 9 - Momentum and Mean Reversion (Average Net Profit for 1–30 input values, since 1983). (Red = 9:30–11:40, Green = 11:40–1:50, Blue = 1:50–4:00)

Figure 9 - Momentum and Mean Reversion 1Figure 9 - Momentum and Mean Reversion 2

Figure 9 summarizes the information from Figures 3 through 8, showing the average net profit for each intraday period (9:30 to 11:40, 11:40 to 1:50, and 1:50 to 4:00) for both momentum and mean reversion trading signals. We calculate this average net profit by adding up all the net profit values for each input value, from 1 to 30, and dividing by 30. As our preceding charts demonstrated, momentum signals behave in an opposite fashion to the mean reversion signals; that is, as the apparent utility of mean reversion trading signals improves, momentum trading signals become less useful.

Consideration should be given to testing how these biases can be incorporated in your intraday strategies for trading stock indexes and related securities.


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