In this article, I will describe patterns of price behavior on an intraday basis and their implications for trading. I believe that an adequate consideration of how price changes actually occur during the day will challenge traditional methods of trading and open the door to new ways of viewing and analyzing the markets.
The Challenge of Stationarity
I’d like to begin this article with a set of descriptive data on the ES market, the main market that I trade. For purposes of convenience, I looked at the market between October 9th, 2003 and January 16th, 2004, which gave me 68 full days of data. I broke down each trading morning (9:30 ET – 12:00 ET) into half-hour segments to see how each segment compares to the ones around it. Below is a table of the average range and standard deviation (in ES points) for each 30 minute period in the morning.
Now let’s look at the average number of trades placed per minute during each half-hour period from 10/9/03 to 1/16/04:
Here’s the average volume of trading in contracts per minute during each 30 minute morning period:
Finally, let’s look at the average one minute level of the NYSE Composite TICK over each half-hour period in the morning from 10/9/03 through 1/16/04:
9:30 – 10:00 ET
10:00 – 10:30 ET
10:30 – 11:00 ET
11:00 – 11:30 ET
11:30 – 12:00 ET
What do these numbers tell us? Most traders are aware that there is more volatility and volume in morning trading versus the early afternoon, and more volume and volatility late in the day than in the middle. These half-hour figures, however, drawn solely from early day trading, suggest that even the morning hours are not uniform. Volume and volatility is highest in the first half hour and tends to wane through the morning, with particularly notable drops from 10:30 ET on.
This suggests that even the very short-term trader is going to run into problems of stationarity. When analyzing a market from hour to hour, we are-to a large extent-comparing apples and oranges. The time series of price changes from one period may not be drawn from the same distribution as the time series of price changes from the next or the one before it. This seriously compromises any technical analysis strategy (moving averages, oscillators, chart pattern analysis) that involves blending one period’s trading with adjacent ones.
The lack of intraday stationarity also compromises quantitative efforts to model the markets, because we cannot use period one’s data to predict period two if we have reason to believe that the two periods were not drawn from the same distribution of price changes. To use the analogy from my previous article on stationarity, if we count cards in blackjack while the dealer is drawing from a two deck shoe, our count will be invalid once the dealer switches to a four deck shoe. The market, as dealer, is changing shoes every hour of the trading day. And this is a very big challenge to short-term trading.
Re-Visioning Market Analysis
Most traders, myself included, tend to view the market vertically. That is, if we build a spreadsheet, we array the recent data on top of the prior data and create all sorts of statistical manipulations that aggregate the data from bottom up. Vertical market analysis is problematic, however, in that it runs into the aforementioned challenge of stationarity.
When I created the tables above, I was looking at the market horizontally. Instead of putting each day’s data on top of the previous values, I placed it to the right. That means that the rows of the spreadsheets represent common time periods-in the case of the data above where we looked at ranges, these were thirty-minute periods. Viewing data horizontally tells us some interesting things, in part because there is greater likelihood of stationarity across sixty common time periods than across sixty adjacent, different periods.
Let me give a concrete example. Suppose during a given five minute period of the day we see 800 ES trades being placed. Is that a meaningful volume or not? If the 800 trades occur during the opening half hour of trading, the volume is not significant. On the other hand, 800 trades in a five minute period that occurs between 11:30 – 12:00 ET would be close to the top 5% of all values for that period. The average volume in early morning is actually a mini buying or selling climax around noon. And, as we shall see later, this is an important piece of information.
Here’s another example: Suppose we break out of a hour-long range and make a new high or new low on the ES. What are the odds of the move continuing in its breakout direction? If you aggregate all similar breakout moves through the day, you’ll get a very fuzzy reading. About half the breakout moves will continue; half will reverse. But if you analyze the market horizontally, you’ll find that breakouts behave differently early in the trading day than later on. There are many more false breakouts as you move on through the day. Why? On average, the reduced volume/volatility of those later hours makes it more difficult to power new market trends.
But wait! If the odds and extent of breakout moves is different from one hour to the next, then that means that chart patterns will vary from one period to the next. That also means that oscillator readings-what constitutes overbought and oversold-will similarly vary.
Here’s something to try: If you want to analyze the market by chart patterns or indicator readings, switch your analysis from vertical to horizontal. Look only at similar time segments from a stationary lookback period in the market and see what the market has done when the patterns or readings have been similar to those observed currently. If you see a breakout from a two-hour range that occurs at 9:45 ET, look at all similar breakouts that have occurred in the first half-hour of trading. The chances are good that your findings will be less fuzzy-and may even reveal a tradable edge. ?
Equivalent Bars: Another Approach to Slaying the Stationarity Beast
Richard Arms once came up with an intriguing idea: He drew charts where the bars were defined by volume rather than time. Tick charts accomplish something similar. Each bar represents X number of trades, not X units of time. The reason this is a promising concept is that volume and volatility are very highly correlated. If we draw our bars on a chart in such a way where they have equal volume, the odds are improved that we will have a stationary intraday distribution as we move from one bar to the next. This would improve our vertical analyses of the markets. For instance, if we wanted to use a 14 period RSI to define overbought and oversold levels, we would be on firmer ground if each of the fourteen periods were relatively uniform and drawn from the same distribution of values.
If we take the data from the tables above, we might think about making each bar equal approximately 2000 contracts of volume. That would, on average, give us one bar for each of the first two half-hours for the day; then one bar for each 45-minute period later in the morning; and one bar for each hour around midday. Making this segmentation of the day standard (where we always equate, say, the first half-hour of trading with the full noon hour) is a quicker and dirtier solution than Arms’, but it does have advantages as well. When you draw bars that are supposed to be equivalent in volume and volatility and then you see an unusually large or small bar, it is much easier to visually identify the significance of the breakout or consolidation.
Making the bars equivalent also affects the holding period of a trade. Instead of holding a trade for X hours-where morning hours will expose you to much more volatility than midday hours-you would hold the trade for X bars. Each trade would be more similar to others, which is helpful for risk control.
Most important of all, however, is that you could have greater confidence that the chart patterns and indicator readings that emerge on a uniform bar chart will be more reliable than those that show up on a standard chart. A breakout of certain size from bar 1 to bar 2 will be more likely to have the same meaning early in the day as later, since you are adjusting the time value of the bars.
My basic trading is intraday, but when I hold a position for swing periods, I use the equivalent bars to help me time the trade. A future article will detail this swing trading and how it addresses stationarity concerns.
Scalping: Still Another Response to Nonstationarity
In many ways, scalping is the opposite of creating equivalent bars. The scalper holds a trade for a very short period of time-so short that the next bars are likely to be drawn from the same distribution as the previous ones. Scalping reduces the average size of gains and losses per trade and runs the very significant risk of overtrading and allowing commissions and slippage to eat away at equity. If, however, the scalper can find reliable patterns for trading, this can be the tortoise’s response to the swing-trader’s hare.
Scalping can be anything as short as trading the next tick if you’re on the floor to holding a trade for multiple minutes. I define scalping pragmatically as exiting a position within a time frame after which you normally expect the distribution of price changes to shift. Thus, a scalp might be held for under 30 minutes early in the day, but could be held for over an hour around midday. To use the above idea of equivalent bars, a scalp is a position held within one of those bars.
Given this definition, most of my trading is scalping. Here’s an example: A market drops on high volume at 11:00 ET, with the NYSE Composite TICK hitting -750. Despite this drop, the market makes only a marginal new low for the day before rebounding smartly as the TICK moves to zero. As the market pulls back lazily on only modestly negative TICK, I might enter that trade on the long side to take advantage of the failed downside breakout. The recent low-and the -750 TICK level-serve as logical stops. On the first surge in upside volume and NYSE TICK, suggesting that the shorts are panicking to cover their positions, I might exit the position and take a few quick points of profit-particularly if it appears the larger time frame trend is down.
Note that a key to this trading is the horizontal analysis of the market. I know that the volume is high on the downside breakout attempt, because I know the exact distribution of volume for the 11:00 hour. I also know that the TICK reading is extreme for that hour based on an analysis of distribution. The horizontal analyses allow me to objectively define a buying or selling panic. I am buying a panic where the market shows underlying strength; selling a panic where there is weakness. Because the trade takes place within a half hour period, I need not be overly concerned about shifting distributions of price changes. I can use standard one-minute charts and indicators without the need for equivalence adjustment.
In a future article, I will elaborate both the scalping and swing trading strategies that I am developing. I will also be following the results of trading on my site’s weblog. My hope is that this article stimulates your thinking about markets and market analyses, making you question off-the-shelf modes of analysis and encouraging you to create your own. Designing the methods of trading that best fit your lifestyle and personality is half the trading psychology battle. I will have more on that topic in the next article in this series.
The first article in this series looked at intraday patterns of volume and implications for trading. A major conclusion was that the distribution of price changes through the day is nonstationary, making it hazardous to employ the same buying and selling parameters through the day. By analyzing markets horizontally as well as vertically-comparing action at one time of day to action at the same time during previous days-we can generally gauge whether or not a particular movement is significant.
How one employs this information will depend upon his or her time frame of trading, which in turn reflects one’s risk tolerance, which is closely related to personality traits. Longer holding periods yield more variable results-including drawdowns. Adjusting the mix of holding period and position size is essential in ensuring that one is taking a level of risk that will produce adequate rewards, but that will not court ruin during a losing streak. The management of risk is an oft-neglected facet of trading psychology.
Risk, Size, and Holding Period
Let us say, for instance, that we are going to risk 2% of our trading capital on a trade. If we are trading tick-by-tick, we could trade dozens of contracts and still remain risk-prudent. If, however, we are holding positions overnight, where the odds of a multipoint move are now greatly increased, the same 2% parameter would yield a position size of only a few contracts. Even on an intraday basis, a scalping trade placed early in morning has a greater risk of a multi-tick adverse move than the same trade placed nearer to midday. Keeping size constant during periods of nonstationarity-or worse yet, increasing size when you see volatility ramping up-courts the scenario in which a single losing trade undoes several previous winners.
A fixed-fractional trading strategy defines the number of contracts you can trade for a defined level of risk. Michael Bryant, in his article “Position Sizing With Monte Carlo Simulation” (Technical Analysis of Stocks and Commodities; Feb. 2001), shows how simulations of trading outcomes with particular strategies can help one define the fraction of trade capital to place in a trade while keeping the risk of severe drawdown under 5%. Simulations using his MiniMax swing trading system, for example, show that trading 2% of capital produces a maximum peak to valley drawdown of 24% on the ES futures with 95% confidence. If one wanted to reduce that drawdown to 12% of capital with the same level of confidence, one would risk only 1% of capital.
The fixed-fractional strategy described by Bryant is drawn from the following equation, where N = the number of contracts traded; ff = the percentage of trading capital allocated to the trade; E = total trading equity prior to placing the trade; and R = the risk of the next trade in dollars (which is your stop).
N = ff * E/R
Thus, if I am willing to risk 2% of my $100,000 trading account on a trade where my stop is set at 4 points ($200 per contract), I could trade 10 contracts and still remain risk-prudent. If I am a scalper and my stop is much smaller, I can trade a larger number of contracts with equivalent risk. If I am a swing trader willing to set a double-digit point stop, I will trade smaller size.
Adjusting Risk and Reward
This brings us back to the topic of stationarity. In the above example, I have set my stop at 4 points. The odds of a four-point setback, however, are not the same early in morning trading as in midday or late in the day. If I am an intraday trader and rely on a fixed-point stop, I no longer am managing risk consistently. I may be taking too much risk at one time of day and too little at others. I need Monte Carlo simulations on a horizontal basis to tell me the 95% probability of a defined market drawdown for morning trades, afternoon trades, etc. Just as I would not trade similar size on an intraday vs. swing basis, I would not trade identical size at various times of day.
It is difficult to square this position with the reality that very successful traders tend to increase their size in direct proportion to their confidence in a trade. A consistent theme among “Wizard” traders is that, once they identify a move, they exploit it for all its worth. The less-successful trader is apt to become risk-averse in the face of a profitable position and exit early. Since volatility is commonly increasing as a trade is working out, adding to positions is significantly adding to risk. A reversal at the end of a move, when size is greatest, could eliminate all profits, even if one has been correct in anticipating the direction of the move.
Scaling into positions over time can address this challenge. In a forthcoming book on Trend Following by Michael Covel, he quotes Ed Seyoka’s approach to pyramiding. The instructions for pyramiding, Seykota explains, are depicted on every dollar bill: add smaller and smaller units, while keeping your eye open at the top. The advantage of scaling into one’s maximum position is that it keeps risk lowest early in the trade, when its outcome is most in question. As the trade works out, adding to the position allows the trader to maximize profits. The successful trader is thus thinking like a Bayesian, watching the unfolding of a trade to see if the market is gaining or losing strength, and adjusting the position accordingly.
Short-term trading, like any trading, boils down to mathematics. If you have a roughly equal number of winning and losing trades, the average size of the winners will have to meaningfully exceed the average size of the losers in order to assure profitability. When traders do not properly adjust trading size and holding period, they can have a good trading methodology, but a red P&L. The average size of their losers will swamp the winners.
A good self-assessment is to measure the amount of time and energy that you spend defining market entries, gauging exits, determining trade size, and managing trades by scaling in and out. Most traders place great emphasis on entries, are too impulsive on exits, and give little thought to the definition and adjustment of trade size. Money management, and not simply “Buy when the RSI hits 30”, separates successful traders from less profitable ones. Very often, a trader’s emotionality during a trade stands in the way of good trade management. By Brett N. Steenbarger, Ph.D.