QUANTITATIVE RESEARCH AND TRADING
The latest theories, models and investment strategies in quantitative research and trading
Our high frequency VIX scalping strategy is now the #1 top performing strategy on Collective2, with returns of over 2700% since April 2016 with a Sharpe Ratio above 10 and Profit Factor of 2.8.
For more background on HFT scalping strategies see the following post:
http://jonathankinlay.com/2014/05/the-mathematics-of-scalping/
HFT scalping strategies enjoy several highly desirable characteristics, compared to low frequency strategies. A case in point is our scalping strategy in VIX futures, currently running on the Collective2 web site:
The attractiveness of such strategies is undeniable. So how does one go about developing them?
It is important for the reader to familiarize himself with some of the background to high frequency trading in general and scalping strategies in particular. Specifically, I would recommend reading the following blog posts:
http://jonathankinlay.com/2015/05/high-frequency-trading-strategies/
http://jonathankinlay.com/2014/05/the-mathematics-of-scalping/
The key to understanding HFT strategies is that execution is everything. With low frequency strategies a great deal of work goes into researching sources of alpha, often using highly sophisticated mathematical and statistical techniques to identify and separate the alpha signal from the background noise. Strategy alpha accounts for perhaps as much as 80% of the total return in a low frequency strategy, with execution making up the remaining 20%. It is not that execution is unimportant, but there are only so many basis points one can earn (or save) in a strategy with monthly turnover. By contrast, a high frequency strategy is highly dependent on trade execution, which may account for 80% or more of the total return. The algorithms that generate the strategy alpha are often very simple and may provide only the smallest of edges. However, that very small edge, scaled up over thousands of trades, is sufficient to produce a significant return. And since the risk is spread over a large number of very small time increments, the rate of return can become eye-wateringly high on a risk-adjusted basis: Sharpe Ratios of 10, or more, are commonly achieved with HFT strategies.
In many cases an HFT algorithm seeks to estimate the conditional probability of an uptick or downtick in the underlying, leaning on the bid or offer price accordingly. Provided orders can be positioned towards the front of the queue to ensure an adequate fill rate, the laws of probability will do the rest. So, in the HFT context, much effort is expended on mitigating latency and on developing techniques for establishing and maintaining priority in the limit order book. Another major concern is to monitor order book dynamics for signs that book pressure may be moving against any open orders, so that they can be cancelled in good time, avoiding adverse selection by informed traders, or a buildup of unwanted inventory.
In a high frequency scalping strategy one is typically looking to capture an average of between 1/2 to 1 tick per trade. For example, the VIX scalping strategy illustrated here averages around $23 per contract per trade, i.e. just under 1/2 a tick in the futures contract. Trade entry and exit is effected using limit orders, since there is no room to accommodate slippage in a trading system that generates less than a single tick per trade, on average. As with most HFT strategies the alpha algorithms are only moderately sophisticated, and the strategy is highly dependent on achieving an acceptable fill rate (the proportion of limit orders that are executed). The importance of achieving a high enough fill rate is clearly illustrated in the first of the two posts referenced above. So what is an acceptable fill rate for a HFT strategy?
I’m going to address the issue of fill rates by focusing on a critical subset of the problem: fills that occur at the extreme of the bar, also known as “extreme hits”. These are limit orders whose prices coincide with the highest (in the case of a sell order) or lowest (in the case of a buy order) trade price in any bar of the price series. Limit orders at prices within the interior of the bar are necessarily filled and are therefore uncontroversial. But limit orders at the extremities of the bar may or may not be filled and it is therefore these orders that are the focus of attention.
By default, most retail platform backtest simulators assume that all limit orders, including extreme hits, are filled if the underlying trades there. In other words, these systems typically assume a 100% fill rate on extreme hits. This is highly unrealistic: in many cases the high or low of a bar forms a turning point that the price series visits only fleetingly before reversing its recent trend, and does not revisit for a considerable time. The first few orders at the front of the queue will be filled, but many, perhaps the majority of, orders further down the priority order will be disappointed. If the trader is using a retail trading system rather than a HFT platform to execute his trades, his limit orders are almost always guaranteed to rest towards the back of the queue, due to the relatively high latency of his system. As a result, a great many of his limit orders – in particular, the extreme hits – will not be filled.
The consequences of missing a large number of trades due to unfilled limit orders are likely to be catastrophic for any HFT strategy. A simple test that is readily available in most backtest systems is to change the underlying assumption with regard to the fill rate on extreme hits – instead of assuming that 100% of such orders are filled, the system is able to test the outcome if limit orders are filled only if the price series subsequently exceeds the limit price. The outcome produced under this alternative scenario is typically extremely adverse, as illustrated in first blog post referenced previously.
In reality, of course, neither assumption is reasonable: it is unlikely that either 100% or 0% of a strategy’s extreme hits will be filled – the actual fill rate will likely lie somewhere between these two outcomes. And this is the critical issue: at some level of fill rate the strategy will move from profitability into unprofitability. The key to implementing a HFT scalping strategy successfully is to ensure that the execution falls on the right side of that dividing line.
One solution to the fill rate problem is to spend millions of dollars building HFT infrastructure. But for the purposes of this post let’s assume that the trader is confined to using a retail trading platform like Tradestation or Interactive Brokers. Are HFT scalping systems still feasible in such an environment? The answer, surprisingly, is a qualified yes – by using a technique that took me many years to discover.
To illustrate the method I will use the following HFT scalping system in the E-Mini S&P500 futures contract. The system trades the E-Mini futures on 3 minute bars, with an average hold time of 15 minutes. The average trade is very low – around $6, net of commissions of $8 prt. But the strategy appears to be highly profitable ,due to the large number of trades – around 50 to 60 per day, on average.
So far so good. But the critical issue is the very large number of extreme hits produced by the strategy. Take the trading activity on 10/18 as an example (see below). Of 53 trades that day, 25 (47%) were extreme hits, occurring at the high or low price of the 3-minute bar in which the trade took place.
Overall, the strategy extreme hit rate runs at 34%, which is extremely high. In reality, perhaps only 1/4 or 1/3 of these orders will actually execute – meaning that remainder, amounting to around 20% of the total number of orders, will fail. A HFT scalping strategy cannot hope to survive such an outcome. Strategy profitability will be decimated by a combination of missed, profitable trades and losses on trades that escalate after an exit order fails to execute.
So what can be done in such a situation?
One approach that will not work is to assume naively that some kind of manual oversight will be sufficient to correct the problem. Let’s say the trader runs two versions of the system side by side, one in simulation and the other in production. When a limit order executes on the simulation system, but fails to execute in production, the trader might step in, manually override the system and execute the trade by crossing the spread. In so doing the trader might prevent losses that would have occurred had the trade not been executed, or force the entry into a trade that later turns out to be profitable. Equally, however, the trader might force the exit of a trade that later turns around and moves from loss into profit, or enter a trade that turns out to be a loser. There is no way for the trader to know, ex-ante, which of those scenarios might play out. And the trader will have to face the same decision perhaps as many as twenty times a day. If the trader is really that good at picking winners and cutting losers he should scrap his trading system and trade manually!
An alternative approach would be to have the trading system handle the problem, For example, one could program the system to convert limit orders to market orders if a trade occurs at the limit price (MIT), or after x seconds after the limit price is touched. Again, however, there is no way to know in advance whether such action will produce a positive outcome, or an even worse outcome compared to leaving the limit order in place.
In reality, intervention, whether manual or automated, is unlikely to improve the trading performance of the system. What is certain, however, is that by forcing the entry and exit of trades that occur around the extreme of a price bar, the trader will incur additional costs by crossing the spread. Incurring that cost for perhaps as many as 1/3 of all trades, in a system that is producing, on average less than half a tick per trade, is certain to destroy its profitability.
For many years I assumed that the only solution to the fill rate problem was to implement scalping strategies on HFT infrastructure. One day, I found myself asking the question: what would happen if we slowed the strategy down? Specifically, suppose we took the 3-minute E-Mini strategy and ran it on 5-minute bars?
My first realization was that the relative simplicity of alpha-generation algorithms in HFT strategies is an advantage here. In a low frequency context, the complexity of the alpha extraction process mitigates its ability to generalize to other assets or time-frames. But HFT algorithms are, by and large, simple and generic: what works on 3-minute bars for the E-Mini futures might work on 5-minute bars in E-Minis, or even in SPY. For instance, if the essence of the algorithm is something as simple as: “buy when the price falls by more than x% below its y-bar moving average”, that approach might work on 3-minute, 5-minute, 60-minute, or even daily bars.
So what happens if we run the E-mini scalping system on 5-minute bars instead of 3-minute bars?
Obviously the overall profitability of the strategy is reduced, in line with the lower number of trades on this slower time-scale. But note that average trade has increased and the strategy remains very profitable overall.
More importantly, the average extreme hit rate has fallen from 34% to 22%.
Hence, not only do we get fewer, slightly more profitable trades, but a much lower proportion of them occur at the extreme of the 5-minute bars. Consequently the fill-rate issue is less critical on this time frame.
Of course, one can continue this process. What about 10-minute bars, or 30-minute bars? What one tends to find from such experiments is that there is a time frame that optimizes the trade-off between strategy profitability and fill rate dependency.
However, there is another important factor we need to elucidate. If you examine the trading record from the system you will see substantial variation in the extreme hit rate from day to day (for example, it is as high as 46% on 10/18, compared to the overall average of 22%). In fact, there are significant variations in the extreme hit rate during the course of each trading day, with rates rising during slower market intervals such as from 12 to 2pm. The important realization that eventually occurred to me is that, of course, what matters is not clock time (or “wall time” in HFT parlance) but trade time: i.e. the rate at which trades occur.
What we need to do is reconfigure our chart to show bars comprising a specified number of trades, rather than a specific number of minutes. In this scheme, we do not care whether the elapsed time in a given bar is 3-minutes, 5-minutes or any other time interval: all we require is that the bar comprises the same amount of trading activity as any other bar. During high volume periods, such as around market open or close, trade time bars will be shorter, comprising perhaps just a few seconds. During slower periods in the middle of the day, it will take much longer for the same number of trades to execute. But each bar represents the same level of trading activity, regardless of how long a period it may encompass.
How do you decide how may trades per bar you want in the chart?
As a rule of thumb, a strategy will tolerate an extreme hit rate of between 15% and 25%, depending on the daily trade rate. Suppose that in its original implementation the strategy has an unacceptably high hit rate of 50%. And let’s say for illustrative purposes that each time-bar produces an average of 1, 000 contracts. Since volatility scales approximately with the square root of time, if we want to reduce the extreme hit rate by a factor of 2, i.e. from 50% to 25%, we need to increase the average number of trades per bar by a factor of 2^2, i.e. 4. So in this illustration we would need volume bars comprising 4,000 contracts per bar. Of course, this is just a rule of thumb – in practice one would want to implement the strategy of a variety of volume bar sizes in a range from perhaps 3,000 to 6,000 contracts per bar, and evaluate the trade-off between performance and fill rate in each case.
Using this approach, we arrive at a volume bar configuration for the E-Mini scalping strategy of 20,000 contracts per bar. On this “time”-frame, trading activity is reduced to around 20-25 trades per day, but with higher win rate and average trade size. More importantly, the extreme hit rate runs at a much lower average of 22%, which means that the trader has to worry about maybe only 4 or 5 trades per day that occur at the extreme of the volume bar. In this scenario manual intervention is likely to have a much less deleterious effect on trading performance and the strategy is probably viable, even on a retail trading platform.
(Note: the results below summarize the strategy performance only over the last six months, the time period for which volume bars are available).
We have seen that is it feasible in principle to implement a HFT scalping strategy on a retail platform by slowing it down, i.e. by implementing the strategy on bars of lower frequency. The simplicity of many HFT alpha generation algorithms often makes them robust to generalization across time frames (and sometimes even across assets). An even better approach is to use volume bars, or trade-time, to implement the strategy. You can estimate the appropriate bar size using the square root of time rule to adjust the bar volume to produce the requisite fill rate. An extreme hit rate if up to 25% may be acceptable, depending on the daily trade rate, although a hit rate in the range of 10% to 15% would typically be ideal.
Finally, a word about data. While necessary compromises can be made with regard to the trading platform and connectivity, the same is not true for market data, which must be of the highest quality, both in terms of timeliness and completeness. The reason is self evident, especially if one is attempting to implement a strategy in trade time, where the integrity and latency of market data is crucial. In this context, using the data feed from, say, Interactive Brokers, for example, simply will not do – data delivered in 500ms packets in entirely unsuited to the task. The trader must seek to use the highest available market data feed that he can reasonably afford.
That caveat aside, one can conclude that it is certainly feasible to implement high volume scalping strategies, even on a retail trading platform, providing sufficient care is taken with the modeling and implementation of the system.
A market-making strategy is one in which the system continually quotes on the bid and offer and looks to make money from the bid-offer spread (and also, in the case of equities, rebates). During a typical trading day, inventories will build up on the long or short side of the book as the market trades up and down. There is no intent to take a market view as such, but most sophisticated market making strategies will use microstructure models to help decide whether to “lean” on the bid or offer at any given moment. Market makers may also shade their quotes to reduce the buildup of inventory, or even pull quotes altogether if they suspect that informed traders are trading against them (a situation referred to as “toxic flow”). They can cover short positions through the repo desk and use derivatives to hedge out the risk of an accumulated inventory position.
A scalping strategy shares some of the characteristics of a market making strategy: it will typically be mean reverting, seeking to enter passively on the bid or offer and the average PL per trade is often in the region of a single tick. But where a scalping strategy differs from market making is that it does take a view as to when to get long or short the market, although that view may change many times over the course of a trading session. Consequently, a scalping strategy will only ever operate on one side of the market at a time, working the bid or offer; and it will typically never build inventory, since will it usually reverse and later try to sell for a profit the inventory it has previously purchased, hopefully at a lower price.
In terms of performance characteristics, a market making strategy will often have a double-digit Sharpe Ratio, which means that it may go for many days, weeks, or months, without taking a loss. Scalping is inherently riskier, since it is taking directional bets, albeit over short time horizons. With a Sharpe Ratio in the region of 3 to 5, a scalping strategy will often experience losing days and even losing months.
So why prefer scalping to market making? It’s really a question of capability. Competitive advantage in scalping derives from the successful exploitation of identified sources of alpha, whereas market making depends primarily on speed and execution capability. Market making requires HFT infrastructure with latency measured in microseconds, the ability to layer orders up and down the book and manage order priority. Scalping algos are generally much less demanding in terms of trading platform requirements: depending on the specifics of the system, they can be implemented successfully on many third party networks.
Some time ago my firm Systematic Strategies began research and development on a number of HFT strategies in futures markets. Our primary focus has always been HFT equity strategies, so this was something of a departure for us, one that has entailed a significant technological obstacles (more on this in due course). Amongst the strategies we developed were several very profitable scalping algorithms in fixed income futures. The majority trade at high frequency, with short holding periods measured in seconds or minutes, trading tens or even hundreds of times a day.
The next challenge we faced was what to do with our research product. As a proprietary trading firm our first instinct was to trade the strategies ourselves; but the original intent had been to develop strategies that could provide the basis of a hedge fund or CTA offering. Many HFT strategies are unsuitable for that purpose, since the technical requirements exceed the capabilities of the great majority of standard trading platforms typically used by managed account investors. Besides, HFT strategies typically offer too limited capacity to be interesting to larger, institutional investors.
In the end we arrived at a compromise solution, keeping the highest frequency strategies in-house, while offering the lower frequency strategies to outside investors. This enabled us to keep the limited capacity of the highest frequency strategies for our own trading, while offering investors significant capacity in strategies that trade at lower frequencies, but still with very high performance characteristics.
A typical example is the following scalping strategy in US Bond Futures. The strategy combines two of the lower frequency algorithms we developed for bond futures that scalp around 10 times per session. The strategy attempts to take around 8 ticks out of the market on each trade and averages around 1 tick per trade. With a Sharpe Ratio of over 3, the strategy has produced net profits of approximately $50,000 per contract per year, since 2008. A pleasing characteristic of this and other scalping strategies is their consistency: There have been only 10 losing months since January 2008, the last being a loss of $7,100 in Dec 2015 (the prior loss being $472 in July 2013!)
The next challenge for us to solve was how best to introduce the program to potential investors. Systematic Strategies is not a CTA and our investors are typically interested in equity strategies. It takes a great deal of hard work to persuade investors that we are able to transfer our expertise in equity markets to the very different world of futures trading. While those efforts are continuing with my colleagues in Chicago, I decided to conduct an experiment: what if we were to offer a scalping strategy through an online service like Collective2? For those who are unfamiliar, Collective2 is an automated trading-system platform that allowed the tracking, verification, and auto-trading of multiple systems. The platform keeps track of the system profit and loss, margin requirements, and performance statistics. It then allows investors to follow the system in live trading, entering the system’s trading signals either manually or automatically.
Offering a scalping strategy on a platform like this certainly creates visibility (and a credible track record) with investors; but it also poses new challenges. For example, the platform assumes trading cost of around $14 per round turn, which is at least 2x more expensive than most retail platforms and perhaps 3x-5x more expensive than the cost a HFT firm might pay. For most scalping strategies that are designed to take a tick out of the market such high fees would eviscerate the returns. This motivated our choice of US Bond Futures, since the tick size and average trade are sufficiently large to overcome even this level of trading friction. After a couple of false starts, during which we played around with the algorithms and boosted strategy profitability with a couple of low frequency trades, the system is now happily humming along and demonstrating the kind of performance it should (see below).
For those who are interested in following the strategy’s performance, the link on collective2 is here.
Past results are not necessarily indicative of future results.
These results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under-or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profits or losses similar to these being shown.
In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For example, the ability to withstand losses or to adhere to a particular trading program in spite of trading losses are material points which can also adversely affect actual trading results. There are numerous other factors related to the markets in general or to the implementation of any specific trading program, which cannot be fully accounted for in the preparation of hypothetical performance results and all of which can adversely affect actual trading results.
The following are material assumptions used when calculating any hypothetical monthly results that appear on our web site.
There is a substantial risk of loss in futures and forex trading. Online trading of stocks and options is extremely risky. Assume you will lose money. Don’t trade with money you cannot afford to lose.
This is a follow up post to my post on the Mathematics of Scalping. To illustrate the scalping methodology, I coded up a simple strategy based on the techniques described in the post.
The strategy trades a single @ES contract on 1-minute bars. The attached ELD file contains the Easylanguage code for ES scalping strategy, which can be run in Tradestation or Multicharts.
This strategy makes no attempt to forecast market direction and doesn’t consider market trends at all. It simply looks at the current levels of volatility and takes a long volatility position or a short volatility position depending on whether volatility is above or below some threshold parameters.
By long volatility I mean a position where we buy or sell the market and set a loose Profit Target and a tight Stop Loss. By short volatility I mean a position where we buy or sell the market and set a tight Profit Target and loose Stop Loss. This is exactly the methodology I described earlier in the post. The parameters I ended up using are as follows:
Long Volatility: Profit Target = 8 ticks, Stop Loss = 2 ticks
Short Volatility: Profit Target = 2 ticks, Stop Loss = 30 ticks
I have made no attempt to optimize these parameters settings, which can easily be done in Tradestation or Multicharts.
What do we mean by volatility being above our threshold level? I use a very simple metric: I take the TrueRange for the current bar and add 50% of the increase or decrease in TrueRange over the last two bars. That’s my crude volatility “forecast”.
The final point to explain is this: let’s suppose our volatility forecast is above our threshold level, so we know we want to be long volatility. Ok, but do we buy or sell the ES? One approach ia to try to gauge the direction of the market by estimating the trend. Not a bad idea, by any means, although I have argued that volatility drowns out any trend signal at short time frames (like 1 minute, for example). So I prefer an approach that makes no assumptions about market direction.
In this approach what we do is divide volatility into upsideVolatility and downsideVolatility. upsideVolatility uses the TrueRange for bars where Close > Close[1]. downsideVolatility is calculated only for bars where Close < Close[1]. This kind of methodology, where you calculate volatility based on the sign of the returns, is well known and is used in performance measures like the Sortino ratio. This is like the Sharpe ratio, except that you calculate the standard deviation of returns using only days in which the market was down. When it’s calculated this way, standard deviation is known as the (square root of the) semi-variance.
Anyway, back to our strategy. So we calculate the upside and downside volatilities and test them against our upper and lower volatility thresholds.
The decision tree looks like this:
LONG VOLATILITY
If upsideVolatilityForecast > upperVolThrehold, buy at the market with wide PT and tight ST (long market, long volatility)
If downsideVolatilityForecast > upperVolThrehold, sell at the market with wide PT and tight ST (short market, long volatility)
SHORT VOLATILITY
If upsideVolatilityForecast < lowerVolThrehold, sell at the Ask on a limit with tight PT and wide ST (short market, short volatility)
If downsideVolatilityForecast < lowerVolThrehold, buy at the Bid on a limit with tight PT and wide ST (long market, short volatility)
NOTE THE FOLLOWING CAVEATS. DO NOT TRY TO TRADE THIS STRATEGY LIVE (but use it as a basis for a tradable strategy)
1. The strategy makes the usual TS assumption about fill rates, which is unrealistic, especially at short intervals like 1-minute.
2. The strategy allows fees and commissions of $3 per contract, or $6 per round turn. Your trading costs may be higher than this.
3. Tradestation is unable to perform analysis at the tick level for a period as long at the one used here (2000 to 2014). A tick by tick analysis would likely show very different results (better or worse).
4. The strategy is extremely lop-sided: the great majority of the profits are made on the long side and the Win Rates and Profit Factors are very different for long trades vs short trades. I suspect this would change with a tick by tick analysis. But it also may be necessary to add more parameters so that long trades are treated differently from short trades.
5. No attempt has been made to optimize the parameters.
6 This is a daytading strategy that will exit the market on close.
So with all that said here are the results.
As you can see, the strategy produces a smooth, upward sloping equity curve, the slope of which increases markedly during the period of high market volatility in 2008.
Net profits after commissions for a single ES contract amount to $243,000 ($3.42 per contract) with a win rate of 76% and Profit Factor of 1.24.
This basic implementation would obviously require improvement in several areas, not least of which would be to address the imbalance in strategy profitability on the short vs long side, where most of the profits are generated.
NOTE: if you are unable to see the Mathematica models below, you can download the free Wolfram CDF player and you may also need this plug-in.
You can also download the complete Mathematica CDF file here.
In this post I want to explore aspects of scalping, a type of strategy widely utilized by high frequency trading firms.
I will define a scalping strategy as one in which we seek to take small profits by posting limit orders on alternate side of the book. Scalping, as I define it, is a strategy rather like market making, except that we “lean” on one side of the book. So, at any given time, we may have a long bias and so look to enter with a limit buy order. If this is filled, we will then look to exit with a subsequent limit sell order, taking a profit of a few ticks. Conversely, we may enter with a limit sell order and look to exit with a limit buy order.
The strategy relies on two critical factors:
(i) the alpha signal which tells us from moment to moment whether we should prefer to be long or short
(ii) the execution strategy, or “trade expression”
In this article I want to focus on the latter, making the assumption that we have some kind of alpha generation model already in place (more about this in later posts).
There are several means that a trader can use to enter a position. The simplest approach, the one we will be considering here, is simply to place a single limit order at or just outside the inside bid/ask prices – so in other words we will be looking to buy on the bid and sell on the ask (and hoping to earn the bid-ask spread, at least).
One of the problems with this approach is that it is highly latency sensitive. Limit orders join the limit order book at the back of the queue and slowly works their way towards the front, as earlier orders get filled. Buy the time the market gets around to your limit buy order, there may be no more sellers at that price. In that case the market trades away, a higher bid comes in and supersedes your order, and you don’t get filled. Conversely, yours may be one of the last orders to get filled, after which the market trades down to a lower bid and your position is immediately under water.
This simplistic model explains why latency is such a concern – you want to get as near to the front of the queue as you can, as quickly as possible. You do this by minimizing the time it takes to issue and order and get it into the limit order book. That entails both hardware (co-located servers, fiber-optic connections) and software optimization and typically also involves the use of Immediate or Cancel (IOC) orders. The use of IOC orders by HFT firms to gain order priority is highly controversial and is seen as gaming the system by traditional investors, who may end up paying higher prices as a result.
Another approach is to layer limit orders at price points up and down the order book, establishing priority long before the market trades there. Order layering is a highly complex execution strategy that brings addition complications.
Let’s confine ourselves to considering the single limit order, the type of order available to any trader using a standard retail platform.
As I have explained, we are assuming here that, at any point in time, you know whether you prefer to be long or short, and therefore whether you want to place a bid or an offer. The issue is, at what price do you place your order, and what do you do about limiting your risk? In other words, we are discussing profit targets and stop losses, which, of course, are all about risk and return.
Lets start by considering risk. The biggest risk to a scalper is that, once filled, the market goes against his position until he is obliged to trigger his stop loss. If he sets his stop loss too tight, he may be forced to exit positions that are initially unprofitable, but which would have recovered and shown a profit if he had not exited. Conversely, if he sets the stop loss too loose, the risk reward ratio is very low – a single loss-making trade could eradicate the profit from a large number of smaller, profitable trades.
Now lets think about reward. If the trader is too ambitious in setting his profit target he may never get to realize the gains his position is showing – the market could reverse, leaving him with a loss on a position that was, initially, profitable. Conversely, if he sets the target too tight, the trader may give up too much potential in a winning trade to overcome the effects of the occasional, large loss.
It’s clear that these are critical concerns for a scalper: indeed the trade exit rules are just as important, or even more important, than the entry rules. So how should he proceed?
Let’s make the rather heroic assumption that market returns are Normally distributed (in fact, we know from empirical research that they are not – but this is a starting point, at least). And let’s assume for the moment that our trader has been filled on a limit buy order and is looking to decide where to place his profit target and stop loss limit orders. Given a current price of the underlying security of X, the scalper is seeking to determine the profit target of p ticks and the stop loss level of q ticks that will determine the prices at which he should post his limit orders to exit the trade. We can translate these into returns, as follows:
to the upside: Ru = Ln[X+p] – Ln[X]
and to the downside: Rd = Ln[X-q] – Ln[X]
This situation is illustrated in the chart below.
The profitable area is the shaded region on the RHS of the distribution. If the market trades at this price or higher, we will make money: p ticks, less trading fees and commissions, to be precise. Conversely we lose q ticks (plus commissions) if the market trades in the region shaded on the LHS of the distribution.
Under our assumptions, the probability of ending up in the RHS shaded region is:
probWin = 1 – NormalCDF(Ru, mu, sigma),
where mu and sigma are the mean and standard deviation of the distribution.
The probability of losing money, i.e. the shaded area in the LHS of the distribution, is given by:
probLoss = NormalCDF(Rd, mu, sigma),
where NormalCDF is the cumulative distribution function of the Gaussian distribution.
The expected profit from the trade is therefore:
Expected profit = p * probWin – q * probLoss
And the expected win rate, the proportion of profitable trades, is given by:
WinRate = probWin / (probWin + probLoss)
If we set a stretch profit target, then p will be large, and probWin, the shaded region on the RHS of the distribution, will be small, so our winRate will be low. Under this scenario we would have a low probability of a large gain. Conversely, if we set p to, say, 1 tick, and our stop loss q to, say, 20 ticks, the shaded region on the RHS will represent close to half of the probability density, while the shaded LHS will encompass only around 5%. Our win rate in that case would be of the order of 91%:
WinRate = 50% / (50% + 5%) = 91%
Under this scenario, we make frequent, small profits and suffer the occasional large loss.
So the critical question is: how do we pick p and q, our profit target and stop loss? Does it matter? What should the decision depend on?
We can begin to address these questions by noticing, as we have already seen, that there is a trade-off between the size of profit we are hoping to make, and the size of loss we are willing to tolerate, and the probability of that gain or loss arising. Those probabilities in turn depend on the underlying probability distribution, assumed here to be Gaussian.
Now, the Normal or Gaussian distribution which determines the probabilities of winning or losing at different price levels has two parameters – the mean, mu, or drift of the returns process and sigma, its volatility.
Over short time intervals the effect of volatility outweigh any impact from drift by orders of magnitude. The reason for this is simple: volatility scales with the square root of time, while the drift scales linearly. Over small time intervals, the drift becomes un-noticeably small, compared to the process volatility. Hence we can assume that mu, the process mean is zero, without concern, and focus exclusively on sigma, the volatility.
What other factors do we need to consider? Well there is a minimum price move, which might be 1 tick, and the dollar value of that tick, from which we can derive our upside and downside returns, Ru and Rd. And, finally, we need to factor in commissions and exchange fees into our net trade P&L.
Here’s a simple formulation of the model, in which I am using the E-mini futures contract as an exemplar.
WinRate[currentPrice_,annualVolatility_,BarSizeMins_, nTicksPT_, nTicksSL_,minMove_, tickValue_, costContract_]:=Module[{ nMinsPerDay, periodVolatility, tgtReturn, slReturn,tgtDollar, slDollar, probWin, probLoss, winRate, expWinDollar, expLossDollar, expProfit},
nMinsPerDay = 250*6.5*60;
periodVolatility = annualVolatility / Sqrt[nMinsPerDay/BarSizeMins];
tgtReturn=nTicksPT*minMove/currentPrice;tgtDollar = nTicksPT * tickValue;
slReturn = nTicksSL*minMove/currentPrice;
slDollar=nTicksSL*tickValue;
probWin=1-CDF[NormalDistribution[0, periodVolatility],tgtReturn];
probLoss=CDF[NormalDistribution[0, periodVolatility],slReturn];
winRate=probWin/(probWin+probLoss);
expWinDollar=tgtDollar*probWin;
expLossDollar=slDollar*probLoss;
expProfit=expWinDollar+expLossDollar-costContract;
{expProfit, winRate}]
For the ES contract we have a min price move of 0.25 and the tick value is $12.50. Notice that we scale annual volatility to the size of the period we are trading (15 minute bars, in the following example).
Let’s take a look at how the expected profit and win rate vary with the profit target and stop loss limits we set. In the following interactive graphics, we can assess the impact of different levels of volatility on the outcome.
Notice to begin with that the win rate (and expected profit) are very far from being Normally distributed – not least because they change radically with volatility, which is itself time-varying.
For very low levels of volatility, around 5%, we appear to do best in terms of maximizing our expected P&L by setting a tight profit target of a couple of ticks, and a stop loss of around 10 ticks. Our win rate is very high at these levels – around 90% or more. In other words, at low levels of volatility, our aim should be to try to make a large number of small gains.
But as volatility increases to around 15%, it becomes evident that we need to increase our profit target, to around 10 or 11 ticks. The distribution of the expected P&L suggests we have a couple of different strategy options: either we can set a larger stop loss, of around 30 ticks, or we can head in the other direction, and set a very low stop loss of perhaps just 1-2 ticks. This later strategy is, in fact, the mirror image of our low-volatility strategy: at higher levels of volatility, we are aiming to make occasional, large gains and we are willing to pay the price of sustaining repeated small stop-losses. Our win rate, although still well above 50%, naturally declines.
As volatility rises still further, to 20% or 30%, or more, it becomes apparent that we really have no alternative but to aim for occasional large gains, by increasing our profit target and tightening stop loss limits. Our win rate under this strategy scenario will be much lower – around 30% or less.
Now let’s address the concern that asset returns are not typically distributed Normally. In particular, the empirical distribution of returns tends to have “fat tails”, i.e. the probability of an extreme event is much higher than in an equivalent Normal distribution.
A widely used model for fat-tailed distributions in the Extreme Value Distribution. This has pdf:
PDF[ExtremeValueDistribution[,],x]
Plot[Evaluate@Table[PDF[ExtremeValueDistribution[,2],x],{,{-3,0,4}}],{x,-8,12},FillingAxis]
Mean[ExtremeValueDistribution[,]]
+EulerGamma
Variance[ExtremeValueDistribution[,]]
In order to set the parameters of the EVD, we need to arrange them so that the mean and variance match those of the equivalent Gaussian distribution with mean = 0 and standard deviation . hence:
The code for a version of the model using the GED is given as follows
WinRateExtreme[currentPrice_,annualVolatility_,BarSizeMins_, nTicksPT_, nTicksSL_,minMove_, tickValue_, costContract_]:=Module[{ nMinsPerDay, periodVolatility, alpha, beta,tgtReturn, slReturn,tgtDollar, slDollar, probWin, probLoss, winRate, expWinDollar, expLossDollar, expProfit},
nMinsPerDay = 250*6.5*60;
periodVolatility = annualVolatility / Sqrt[nMinsPerDay/BarSizeMins];
beta = Sqrt[6]*periodVolatility / Pi;
alpha=-EulerGamma*beta;
tgtReturn=nTicksPT*minMove/currentPrice;tgtDollar = nTicksPT * tickValue;
slReturn = nTicksSL*minMove/currentPrice;
slDollar=nTicksSL*tickValue;
probWin=1-CDF[ExtremeValueDistribution[alpha, beta],tgtReturn];
probLoss=CDF[ExtremeValueDistribution[alpha, beta],slReturn];
winRate=probWin/(probWin+probLoss);
expWinDollar=tgtDollar*probWin;
expLossDollar=slDollar*probLoss;
expProfit=expWinDollar+expLossDollar-costContract;
{expProfit, winRate}]
WinRateExtreme[1900,0.05,15,2,30,0.25,12.50,3][[2]]
0.21759
We can now produce the same plots for the EVD version of the model that we plotted for the Gaussian versions :
Next we compare the Gaussian and EVD versions of the model, to gain an understanding of how the differing assumptions impact the expected Win Rate.
As you can see, for moderate levels of volatility, up to around 18 % annually, the expected Win Rate is actually higher if we assume an Extreme Value distribution of returns, rather than a Normal distribution.If we use a Normal distribution we will actually underestimate the Win Rate, if the actual return distribution is closer to Extreme Value.In other words, the assumption of a Gaussian distribution for returns is actually conservative.
Now, on the other hand, it is also the case that at higher levels of volatility the assumption of Normality will tend to over – estimate the expected Win Rate, if returns actually follow an extreme value distribution. But, as indicated before, for high levels of volatility we need to consider amending the scalping strategy very substantially. Either we need to reverse it, setting larger Profit Targets and tighter Stops, or we need to stop trading altogether, until volatility declines to normal levels.Many scalpers would prefer the second option, as the first alternative doesn’t strike them as being close enough to scalping to justify the name.If you take that approach, i.e.stop trying to scalp in periods when volatility is elevated, then the differences in estimated Win Rate resulting from alternative assumptions of return distribution are irrelevant.
If you only try to scalp when volatility is under, say, 20 % and you use a Gaussian distribution in your scalping model, you will only ever typically under – estimate your actual expected Win Rate.In other words, the assumption of Normality helps, not hurts, your strategy, by being conservative in its estimate of the expected Win Rate.
If, in the alternative, you want to trade the strategy regardless of the level of volatility, then by all means use something like an Extreme Value distribution in your model, as I have done here.That changes the estimates of expected Win Rate that the model produces, but it in no way changes the structure of the model, or invalidates it.It’ s just a different, arguably more realistic set of assumptions pertaining to situations of elevated volatility.
Let’ s move on to do some simulation analysis so we can get an understanding of the distribution of the expected Win Rate and Avg Trade PL for our two alternative models. We begin by coding a generator that produces a sample of 1,000 trades and calculates the Avg Trade PL and Win Rate.
GenWinRate[currentPrice_,annualVolatility_,BarSizeMins_, nTicksPT_, nTicksSL_,minMove_, tickValue_, costContract_]:=Module[{ nMinsPerDay, periodVolatility, randObs, tgtReturn, slReturn,tgtDollar, slDollar, nWins,nLosses, perTradePL, probWin, probLoss, winRate, expWinDollar, expLossDollar, expProfit},
nMinsPerDay = 250*6.5*60;
periodVolatility = annualVolatility / Sqrt[nMinsPerDay/BarSizeMins];
tgtReturn=nTicksPT*minMove/currentPrice;tgtDollar = nTicksPT * tickValue;
slReturn = nTicksSL*minMove/currentPrice;
slDollar=nTicksSL*tickValue;
randObs=RandomVariate[NormalDistribution[0,periodVolatility],10^3];
nWins=Count[randObs,x_/;x>=tgtReturn];
nLosses=Count[randObs,x_/;xslReturn];
winRate=nWins/(nWins+nLosses)//N;
perTradePL=(nWins*tgtDollar+nLosses*slDollar)/(nWins+nLosses);{perTradePL,winRate}]
GenWinRate[1900,0.1,15,1,-24,0.25,12.50,3]
{7.69231,0.984615}
Now we can generate a random sample of 10, 000 simulation runs and plot a histogram of the Win Rates, using, for example, ES on 5-min bars, with a PT of 2 ticks and SL of – 20 ticks, assuming annual volatility of 15 %.
Histogram[Table[GenWinRate[1900,0.15,5,2,-20,0.25,12.50,3][[2]],{i,10000}],10,AxesLabel{“Exp. Win Rate (%)”}]
Histogram[Table[GenWinRate[1900,0.15,5,2,-20,0.25,12.50,3][[1]],{i,10000}],10,AxesLabel{“Exp. PL/Trade ($)”}]
Next we can do the same for the Extreme Value Distribution version of the model.
GenWinRateExtreme[currentPrice_,annualVolatility_,BarSizeMins_, nTicksPT_, nTicksSL_,minMove_, tickValue_, costContract_]:=Module[{ nMinsPerDay, periodVolatility, randObs, tgtReturn, slReturn,tgtDollar, slDollar, alpha, beta,nWins,nLosses, perTradePL, probWin, probLoss, winRate, expWinDollar, expLossDollar, expProfit},
nMinsPerDay = 250*6.5*60;
periodVolatility = annualVolatility / Sqrt[nMinsPerDay/BarSizeMins];
beta = Sqrt[6]*periodVolatility / Pi;
alpha=-EulerGamma*beta;
tgtReturn=nTicksPT*minMove/currentPrice;tgtDollar = nTicksPT * tickValue;
slReturn = nTicksSL*minMove/currentPrice;
slDollar=nTicksSL*tickValue;
randObs=RandomVariate[ExtremeValueDistribution[alpha, beta],10^3];
nWins=Count[randObs,x_/;x>=tgtReturn];
nLosses=Count[randObs,x_/;xslReturn];
winRate=nWins/(nWins+nLosses)//N;
perTradePL=(nWins*tgtDollar+nLosses*slDollar)/(nWins+nLosses);{perTradePL,winRate}]
Histogram[Table[GenWinRateExtreme[1900,0.15,5,2,-10,0.25,12.50,3][[2]],{i,10000}],10,AxesLabel{“Exp. Win Rate (%)”}]
Histogram[Table[GenWinRateExtreme[1900,0.15,5,2,-10,0.25,12.50,3][[1]],{i,10000}],10,AxesLabel{“Exp. PL/Trade ($)”}]
The key conclusions from this analysis are:
