Systematic Strategies Archives - Page 2 of 3 - QUANTITATIVE RESEARCH AND TRADING

February 25, 2020

Volatility ETF Trader – June 2017: +15.3%

The Volatility ETF Trader product is an algorithmic strategy that trades several VIX ETFs using statistical and machine learning algorithms.

We offer a version of the strategy on the Collective 2 site (see here for details) that the user can subscribe to for a very modest fee of only $149 per month.

The risk-adjusted performance of the Collective 2 version of the strategy is unlikely to prove as good as the product we offer in our Systematic Strategies Fund, which trades a much wider range of algorithmic strategies. There are other important differences too: the Fund’s Systematic Volatility Strategy makes no use of leverage and only trades intra-day, exiting all positions by market close. So it has a more conservative risk profile, suitable for longer term investment.

The Volatility ETF Trader on Collective 2, on the other hand, is a highly leveraged, tactical strategy that trades positions overnight and holds them for periods of several days . As a consequence, the Collective 2 strategy is far more risky and is likely to experience significant drawdowns. Those caveats aside, the strategy returns have been outstanding: +48.9% for 2017 YTD and a total of +107.8% from inception in July 2016.

You can find full details of the strategy, including a listing of all of the trades, on the Collective 2 site.

Subscribers can sign up for a free, seven day trial and thereafter they can choose to trade the strategy automatically in their own brokerage account.

January 7, 2020January 7, 2020

Algorithmic Trading on Collective 2

Regular readers will recall my mentioning out VIX Futures scalping strategy which we ran on the Collective2 site for a while:

The strategy, while performing very well, proved difficult for subscribers to implement, given the latencies involved in routing orders via the Collective 2 web site. So we began thinking about slower strategies that investors could follow more easily, placing less reliance on the fill rate for limit orders.

Our VIX ETF Trader strategy has been running on Collective 2 for several months now and is being traded successfully by several subscribers. The performance so far has been quite good, with net returns of 58.9% from July 2016 and a Sharpe ratio over 2, which is not at all bad for a low frequency strategy. The strategy enters and exits using a mix of limit and stop orders, so although some slippage is incurred the trade entries and exits work much more smoothly overall.

Having let the strategy settle for several months trading only the ProShares Short VIX Short-Term Futures ETF (SVXY)we are now ready to ramp things up. From today the strategy will also trade several other VIX ETF products including the VelocityShares Daily Inverse VIX ST ETN (XIV), ProShares Ultra VIX Short-Term Futures (UVXY) and VelocityShares Daily 2x VIX ST ETN (TVIX). All of the trades in these products are entered and exited using market or stop orders, and so will be easy for subscribers to follow. For now we are keeping the required account size pegged at $25,000 although we will review that going forward. My guess is that a capital allocation should be more than sufficient to trade the product in the kind of size we use on the Collective 2 versions of the strategies, especially if the account uses portfolio margin rather than standard Reg-T.

With the addition of the new products to the portfolio mix, we anticipate the strategy Sharpe ratio with rise to over 3 in the year ahead.

The advantage of using a site like Collective 2 from the investor’s viewpoint is that, firstly, you get to see a lot of different trading styles and investment strategies. You can select the strategies in a wide range of asset classes that fit your own investment preferences and trade several of them live in your own brokerage account. (Setting up your account for live trading is straightforward, as described on the C2 site). A major advantage of investing this way is that it doesn’t entail the commitment of capital that is typically required for a hedge fund or managed account investment: you can trade the strategies in much smaller size, to fit your budget.

From our perspective, we find it a useful way to showcase some of the strategies we trade in our hedge fund, so that if investors want to they can move up to more advanced, but similar investment products. We plan to launch new strategies on Collective 2 in the near futures , including an equity portfolio strategy and a CTA futures strategy.

If you would like more information, contact us for further details.

December 24, 2019December 24, 2019

The New Long/Short Equity

High Frequency Trading Strategies

One of the benefits of high frequency trading strategies lies in their ability to produce risk-adjusted rates of return that are unmatched by anything that the hedge fund or CTA community is capable of producing. With such performance comes another attractive feature of HFT firms – their ability to make money (almost) every day. Of course, HFT firms are typically not required to manage billions of dollars, which is just as well given the limited capacity of most HFT strategies. But, then again, with a Sharpe ratio of 10, who needs outside capital? This explains why most investors have a difficult time believing the level of performance achievable in the high frequency world – they never come across such performance, because HFT firms generally have little incentive to show their results to external investors.

By and large, HFT strategies remain the province of proprietary trading firms that can afford to make an investment in low-latency trading infrastructure that far exceeds what is typically required for a regular trading or investment management firm. However, while the highest levels of investment performance lie beyond the reach of most investors and money managers, it is still possible to replicate some of the desirable characteristics of high frequency strategies.

Quantitative Equity Strategy

I am going to use an example our Quantitative Equity strategy, which forms part of the Systematic Strategies hedge fund. The tables and charts below give a broad impression of the performance characteristics of the strategy, which include a CAGR of 14.85% (net of fees) since live trading began in 2013.

This is a strategy that is designed to produce returns on a par with the S&P 500 index, but with considerably lower risk: at just over 4%, the annual volatility of the strategy is only around 1/3 that of the index, while the maximum drawdown has been a little over 2% since inception. This level of portfolio risk is much lower than can typically be achieved in an equity long/short strategy (equity market neutral is another story, of course). Furthermore, the realized information ratio of 3.4 is in the upper 1%-tile of risk-adjusted performance amongst equity long/short strategies. So something rather more interesting must be going on that is very different from the typical approach to long/short equity.

One plausible explanation is that the strategy is exploiting some minor market anomaly that works fine for small amounts of capital, but which cannot be scaled. But this is not the case here: the investment universe comprises more than a hundred of the most liquid stocks in US markets, across a broad spectrum of sectors. And while single-name investment is capped at 10% of average daily volume, this nonetheless provides investment capacity of several hundreds of millions of dollars.

Nor does the reason for the exceptional performance lie in some new portfolio construction technique: rather, we rely on a straightforward 1/n allocation. Again, neither is factor exposure the driver of strategy alpha: as the factor loading table illustrates, strategy performance is largely uncorrelated with most market indices. It loads significantly on only large cap value, chiefly because the investment universe is defined as comprising the stocks with greatest liquidity (which tend to be large cap value), and on the CBOE VIX index. The positive correlation with market volatility is a common feature of many types of trading strategy that tend to do better in volatile markets, when short-term investment opportunities are plentiful.

While the detail of the strategy must necessarily remain proprietary, I can at least offer some insight that will, I hope, provide food for thought.

We can begin by comparing the returns for two of the stocks in the portfolio, Home Depot and Pfizer. The charts demonstrate one of important strategy characteristic: not every stock is traded at the same frequency. Some stocks might be traded once or twice a month; others possibly ten times a day, or more. In other words, the overall strategy is diversified significantly, not only across assets, but also across investment horizons. This has a considerable impact on volatility and downside risk in the portfolio.

Home Depot vs. Pfizer Inc.

Overall, the strategy trades an average of 40-60 times a day, or more. This is, admittedly, towards the low end of the frequency spectrum of HFT strategies – we might describe it as mid-frequency rather than high frequency trading. Nonetheless, compared to traditional long/short equity strategies this constitutes a high level of trading activity which, in aggregate, replicates some of the time-diversification benefits of HFT strategies, producing lower strategy volatility.

There is another way in which the strategy mimics, at least partially, the characteristics of a HFT strategy. The profitability of many (although by no means all) HFT strategies lies in their ability to capture (or, at least, not pay) the bid-offer spread. That is why latency is so crucial to most HFT strategies – if your aim is to to earn rebates, and/or capture the spread, you must enter and exit, passively, often using microstructure models to determine when to lean on the bid or offer price. That in turn depends on achieving a high priority for your orders in the limit order book, which is a function of latency – you need to be near the top of the queue at all times in order the achieve the required fill rate.

How does that apply here? While we are not looking to capture the spread, the strategy does seek to avoid taking liquidity and paying the spread. Where it can do so, it will offset the bid-offer spread by earning rebates. In many cases we are able to mitigate the spread cost altogether. So, while it cannot accomplish what a HFT market-making system can achieve, it can mimic enough of its characteristics – even at low frequency – to produce substantial gains in terms of cost-reduction and return enhancement. This is important since the transaction volume and portfolio turnover in this approach are significantly greater than for a typical equity long/short strategy.

Portfolio of Strategies vs. Portfolio of Equities

But this feature, while important, is not really the heart of the matter. Rather, the central point is this: that the overall strategy is an assembly of individual, independent strategies for each component stock. And it turns out that the diversification benefit of a portfolio of strategies is generally far greater than for an equal number of stocks, because the equity processes themselves will typically be correlated to a far greater degree than will corresponding trading strategies. To take the example of the pair of stocks discussed earlier, we find that the correlation between HD and PFE over the period from 2013 to 2017 is around 0.39, based on daily returns. By comparison, the correlation between the strategies for the two stocks over the same period is only 0.01.

This is generally the case, so that a portfolio of, say, 30 equity strategies, might reasonably be expected to enjoy a level of risk that is perhaps as much as one half that of a portfolio of the underlying stocks, no matter how constructed. This may be due to diversification in the time dimension, coupled with differences in the alpha generation mechanisms of the underlying strategies – mean reversion vs. momentum, for example

Strategy Robustness Testing

There are, of course, many different aspects to our approach to strategy risk management. Some of these are generally applicable to strategies of all varieties, but there are others that are specific to this particular type of strategy.

A good example of the latter is how we address the issue of strategy robustness. One of the principal concerns that investors have about quantitive strategies is that they may under-perform during adverse market conditions, or even simply stop working altogether. Our approach is to stress test each of the sub-strategy models using Monte Carlo simulation and examine their performance under a wide range of different scenarios, many of which have never been seen in the historical data used to construct the models.

For instance, we typically allow prices to fluctuate randomly by +/- 30% from historical values. But we also randomize the start date of each strategy by up to a year, which reduces the likelihood of a strategy being selected simply on the strength of a lucky start. Finally, we are interested in ensuring that the performance of each sub-strategy is not overly sensitive to the specific parameter values chosen for each model. Again, we test this using Monte Carlo, assessing the performance of each sub-strategy if the parameter values of the model are varied randomly by up to 30%.

The output of all these simulation tests is compiled into a histogram of performance results, from which we select the worst 5%-tile. Only if the worst outcomes – the 1-in-20 results in the left tail of the performance distribution – meet our performance criteria will the sub-strategy advance to the next stage of evaluation, simulated trading. This gives us – and investors – a level of confidence in the ability of the strategy to continue to perform well regardless of how market conditions evolve over time.

An obvious question to ask at this point is: if this is such a great idea, why don’t more firms use this approach? The answer is simple: it involves too much research. In a typical portfolio strategy there is a single investment idea that is applied cross-sectionally to a universe of stocks (factor models, momentum models, etc). In the strategy portfolio approach, separate strategies must be developed for each stock individually, which takes far more time and effort. Consequently such strategies must necessarily scale more slowly.

Another downside to the strategy portfolio approach is that it is less able to control the portfolio characteristics. For instance, the overall portfolio may, on average, have a beta close to zero; but there are likely to be times when a majority of the individual stock strategies align, producing a significantly higher, or lower, beta. The key here is to ask the question: what matters more – the semblance of risk control, or the actual risk characteristics of the strategy? In reality, the risk controls of traditional long/short equity strategies often turn out to be more theoretical than real. Time and again investors have seen strategies that turn out to be downside-correlated with the market, regardless of the purported “market-neutral” characteristics of the portfolio. I would argue that what matters far more is how the strategy actually performs under conditions of market stress, regardless of how “market neutral” or “sector neutral” it may purport to be. And while I agree that this is hardly a widely-held view, my argument would be that one cannot expect to achieve above-average performance simply by employing standard approaches at every turn.

Parallels with Fund of Funds Investment

So, is this really a “new approach” to equity long/short? Actually, no. It is certainly unusual. But it follows quite closely the model of a proprietary trading firm, or a Fund of Funds. There, as here, the task is to create a combined portfolio of strategies (or managers), rather than by investing directly in the underlying assets. A Fund of Funds will seek to create a portfolio of strategies that have low correlations to one another, and may operate a meta-strategy for allocating capital to the component strategies, or managers. But the overall investment portfolio cannot be as easily constrained as an individual equity portfolio can be – greater leeway must be allowed for the beta, or the dollar imbalance in the longs and shorts, to vary from time to time, even if over the long term the fluctuations average out. With human managers one always has to be concerned about the risk of “style drift” – i.e. when managers move away from their stated investment mandate, methodologies or objectives, resulting in a different investment outcomes. This can result in changes in the correlation between a strategy and its peers, or with the overall market. Quantitative strategies are necessarily more consistent in their investment approach – machines generally don’t alter their own source code – making a drift in style less likely. So an argument can be made that the risk inherent in this form of equity long/short strategy is on a par with – certainly not greater than – that of a typical fund of funds.

Conclusions

An investment approach that seeks to create a portfolio of strategies, rather than of underlying assets, offers a significant advantage in terms of risk reduction and diversification, due to the relatively low levels of correlation between the component strategies. The trading costs associated with higher frequency trading can be mitigated using passive entry/exit rules designed to avoid taking liquidity and generating exchange rebates. The downside is that it is much harder to manage the risk attributes of the portfolio, such as the portfolio beta, sector risk, or even the overall net long/short exposure. But these are indicators of strategy risk, rather than actual risk itself and they often fail to predict the actual risk characteristics of the strategy, especially during conditions of market stress. Investors may be better served by an approach to long/short equity that seeks to maximize diversification on the temporal axis as well as in terms of the factors driving strategy alpha.

Disclaimer: past performance does not guarantee future results. You should not rely on any past performance as a guarantee of future investment performance. Investment returns will fluctuate. Investment monies are at risk and you may suffer losses on any investment.

August 27, 2019

Machine Learning Trading Systems

The SPDR S&P 500 ETF (SPY) is one of the widely traded ETF products on the market, with around $200Bn in assets and average turnover of just under 200M shares daily. So the likelihood of being able to develop a money-making trading system using publicly available information might appear to be slim-to-none. So, to give ourselves a fighting chance, we will focus on an attempt to predict the overnight movement in SPY, using data from the prior day’s session.

In addition to the open/high/low and close prices of the preceding day session, we have selected a number of other plausible variables to build out the feature vector we are going to use in our machine learning model:

The daily volume
The previous day’s closing price
The 200-day, 50-day and 10-day moving averages of the closing price
The 252-day high and low prices of the SPY series

We will attempt to build a model that forecasts the overnight return in the ETF, i.e. [O(t+1)-C(t)] / C(t)

In this exercise we use daily data from the beginning of the SPY series up until the end of 2014 to build the model, which we will then test on out-of-sample data running from Jan 2015-Aug 2016. In a high frequency context a considerable amount of time would be spent evaluating, cleaning and normalizing the data. Here we face far fewer problems of that kind. Typically one would standardized the input data to equalize the influence of variables that may be measured on scales of very different orders of magnitude. But in this example all of the input variables, with the exception of volume, are measured on the same scale and so standardization is arguably unnecessary.

First, the in-sample data is loaded and used to create a training set of rules that map the feature vector to the variable of interest, the overnight return:

In Mathematica 10 Wolfram introduced a suite of machine learning algorithms that include regression, nearest neighbor, neural networks and random forests, together with functionality to evaluate and select the best performing machine learning technique. These facilities make it very straightfoward to create a classifier or prediction model using machine learning algorithms, such as this handwriting recognition example:

We create a predictive model on the SPY trainingset, allowing Mathematica to pick the best machine learning algorithm:

There are a number of options for the Predict function that can be used to control the feature selection, algorithm type, performance type and goal, rather than simply accepting the defaults, as we have done here:

Having built our machine learning model, we load the out-of-sample data from Jan 2015 to Aug 2016, and create a test set:

We next create a PredictionMeasurement object, using the Nearest Neighbor model , that can be used for further analysis:

There isn’t much dispersion in the model forecasts, which all have positive value. A common technique in such cases is to subtract the mean from each of the forecasts (and we may also standardize them by dividing by the standard deviation).

The scatterplot of actual vs. forecast overnight returns in SPY now looks like this:

There’s still an obvious lack of dispersion in the forecast values, compared to the actual overnight returns, which we could rectify by standardization. In any event, there appears to be a small, nonlinear relationship between forecast and actual values, which holds out some hope that the model may yet prove useful.

From Forecasting to Trading

There are various methods of deploying a forecasting model in the context of creating a trading system. The simplest route, which we will take here, is to apply a threshold gate and convert the filtered forecasts directly into a trading signal. But other approaches are possible, for example:

Combining the forecasts from multiple models to create a prediction ensemble
Using the forecasts as inputs to a genetic programming model
Feeding the forecasts into the input layer of a neural network model designed specifically to generate trading signals, rather than forecasts

In this example we will create a trading model by applying a simple filter to the forecasts, picking out only those values that exceed a specified threshold. This is a standard trick used to isolate the signal in the model from the background noise. We will accept only the positive signals that exceed the threshold level, creating a long-only trading system. i.e. we ignore forecasts that fall below the threshold level. We buy SPY at the close when the forecast exceeds the threshold and exit any long position at the next day’s open. This strategy produces the following pro-forma results:

Conclusion

The system has some quite attractive features, including a win rate of over 66% and a CAGR of over 10% for the out-of-sample period.

Obviously, this is a very basic illustration: we would want to factor in trading commissions, and the slippage incurred entering and exiting positions in the post- and pre-market periods, which will negatively impact performance, of course. On the other hand, we have barely begun to scratch the surface in terms of the variables that could be considered for inclusion in the feature vector, and which may increase the explanatory power of the model.

In other words, in reality, this is only the beginning of a lengthy and arduous research process. Nonetheless, this simple example should be enough to give the reader a taste of what’s involved in building a predictive trading model using machine learning algorithms.

April 30, 2019

Reflections on Careers in Quantitative Finance

CMU’s MSCF Program

Carnegie Mellon’s Steve Shreve is out with an interesting post on careers in quantitative finance, with his commentary on the changing landscape in quantitative research and the implications for financial education.

I taught at Carnegie Mellon in the late 1990’s, including its excellent Master’s program in quantitative finance that Steve co-founded, with Sanjay Srivastava. The program was revolutionary in many ways and was immediately successful and rapidly copied by rival graduate schools (I help to spread the word a little, at Cambridge).

The core of the program remains largely unchanged over the last 20 years, featuring Steve’s excellent foundation course in stochastic calculus; but I am happy to see that the school has added many, new and highly relevant topics to the second year syllabus, including market microstructure, machine learning, algorithmic trading and statistical arbitrage. This has moved the program in terms of its primary focus, which was originally financial engineering, to include coverage of subjects that are highly relevant to quantitative investment research and trading.

It was this combination of sound theoretical grounding with practitioner-oriented training that made the program so successful. As I recall, every single graduate was successful in finding a job on Wall Street, often at salaries in excess of $200,000, a considerable sum in those days. One of the key features of the program was that it combined theoretical concepts with practical training, using a simulated trading floor gifted by Thomson Reuters (a model later adopted by the ICMA centre at the University of Reading in the UK). This enabled us to test students’ understanding of what they had been taught, using market simulation models that relied upon key theoretical ideas covered in the program. The constant reinforcement of the theoretical with the practical made for a much deeper learning experience for most students and greatly facilitated their transition to Wall Street.

Masters in High Frequency Finance

While CMU’s program has certainly evolved and remains highly relevant to the recruitment needs of Wall Street firms, I still believe there is an opportunity for a program focused exclusively on high frequency finance, as previously described in this post. The MHFF program would be more computer science oriented, with less emphasis placed on financial engineering topics. So, for instance, students would learn about trading hardware and infrastructure, the principles of efficient algorithm design, as well as HFT trading techniques such as order layering and priority management. The program would also cover HFT strategies such as latency arbitrage, market making, and statistical arbitrage. Students would learn both lower level (C++, Java) and higher level (Matlab, R) programming languages and there is a good case for a mandatory machine code programming course also. Other core courses might include stochastic calculus and market microstructure.

Who would run such a program? The ideal school would have a reputation for excellent in both finance and computer science. CMU is an obvious candidate, as is MIT, but there are many other excellent possibilities.

Careers

I’ve been involved in quantitative finance since the beginning: I recall programming one of the first 68000 Assembler microcomputers in the 1980s, which was ultimately used for an F/X system at a major UK bank. The ensuing rapid proliferation of quantitative techniques in finance has been fueled by the ubiquity of cheap computing power, facilitating the deployment of quantitate techniques that would previously been impractical to implement due to their complexity. A good example is the machine learning techniques that now pervade large swathes of the finance arena, from credit scoring to HFT trading. When I first began working in that field in the early 2000’s it was necessary to assemble a fairly sizable cluster of cpus to handle the computation load. These days you can access comparable levels of computational power on a single server and, if you need more, you can easily scale up via Azure or EC2.

It is this explosive growth in computing power that has driven the development of quantitative finance in both the financial engineering and quantitative investment disciplines. As the same time, the huge reduction in the cost of computing power has leveled the playing field and lowered barriers to entry. What was once the exclusive preserve of the sell-side has now become readily available to many buy-side firms. As a consequence, much of the growth in employment opportunities in quantitative finance over the last 20 years has been on the buy-side, with the arrival of quantitative hedge funds and proprietary trading firms, including my own, Systematic Strategies. This trend has a long way to play out so that, when also taking into consideration the increasing restrictions that sell-side firms face in terms of their proprietary trading activity, I am inclined to believe that the buy-side will offer the best employment opportunities for quantitative financiers over the next decade.

It was often said that hedge fund managers are typically in their 30’s or 40’s when they make the move to the buy-side. That has changed in the last 15 years, again driven by the developments in technology. These days you are more likely to find the critically important technical skills in younger candidates, in their late 20’s or early 30’s. My advice to those looking for a career in quantitative finance, who are unable to find the right job opportunity, would be: do what every other young person in Silicon Valley is doing: join a startup, or start one yourself.

April 2, 2019

Alpha Extraction and Trading Under Different Market Regimes

Market Noise and Alpha Signals

One of the perennial problems in designing trading systems is noise in the data, which can often drown out an alpha signal. This is turn creates difficulties for a trading system that relies on reading the signal, resulting in greater uncertainty about the trading outcome (i.e. greater volatility in system performance). According to academic research, a great deal of market noise is caused by trading itself. There is apparently not much that can be done about that problem: sure, you can trade after hours or overnight, but the benefit of lower signal contamination from noise traders is offset by the disadvantage of poor liquidity. Hence the thrust of most of the analysis in this area lies in the direction of trying to amplify the signal, often using techniques borrowed from signal processing and related engineering disciplines.

There is, however, one trick that I wanted to share with readers that is worth considering. It allows you to trade during normal market hours, when liquidity is greatest, but at the same time limits the impact of market noise.

Quantifying Market Noise

How do you measure market noise? One simple approach is to start by measuring market volatility, making the not-unreasonable assumption that higher levels of volatility are associated with greater amounts of random movement (i.e noise). Conversely, when markets are relatively calm, a greater proportion of the variation is caused by alpha factors. During the latter periods, there is a greater information content in market data – the signal:noise ratio is larger and hence the alpha signal can be quantified and captured more accurately.

For a market like the E-Mini futures, the variation in daily volatility is considerable, as illustrated in the chart below. The median daily volatility is 1.2%, while the maximum value (in 2008) was 14.7%!

The extremely long tail of the distribution stands out clearly in the following histogram plot.

Obviously there are times when the noise in the process is going to drown out almost any alpha signal. What if we could avoid such periods?

Noise Reduction and Model Fitting

Let’s divide our data into two subsets of equal size, comprising days on which volatility was lower, or higher, than the median value. Then let’s go ahead and use our alpha signal(s) to fit a trading model, using only data drawn from the lower volatility segment.

This is actually a little tricky to achieve in practice: most software packages for time series analysis or charting are geared towards data occurring at equally spaced points in time. One useful trick here is to replace the actual date and time values of the observations with sequential date and time values, in order to fool the software into accepting the data, since there are no longer any gaps in the timestamps. Of course, the dates on our time series plot or chart will be incorrect. But that doesn’t matter: as long as we know what the correct timestamps are.

An example of such a system is illustrated below. The model was fitted to 3-Min bar data in EMini futures, but only on days with market volatility below the median value, in the period from 2004 to 2015. The strategy equity curve is exceptionally smooth, as might be expected, and the performance characteristics of the strategy are highly attractive, with a 27% annual rate of return, profit factor of 1.58 and Sharpe Ratio approaching double-digits.

Dealing with the Noisy Trading Days

Let’s say you have developed a trading system that works well on quiet days. What next? There are a couple of ways to go:

(i) Deploy the model only on quiet trading days; stay out of the market on volatile days; or

(ii) Develop a separate trading system to handle volatile market conditions.

Which approach is better? It is likely that the system you develop for trading quiet days will outperform any system you manage to develop for volatile market conditions. So, arguably, you should simply trade your best model when volatility is muted and avoid trading at other times. Any other solution may reduce the overall risk-adjusted return. But that isn’t guaranteed to be the case – and, in fact, I will give an example of systems that, when combined, will in practice yield a higher information ratio than any of the component systems.

Deploying the Trading Systems

The astute reader is likely to have noticed that I have “cheated” by using forward information in the model development process. In building a trading system based only on data drawn from low-volatility days, I have assumed that I can somehow know in advance whether the market is going to be volatile or not, on any given day. Of course, I don’t know for sure whether the upcoming session is going to be volatile and hence whether to deploy my trading system, or stand aside. So is this just a purely theoretical exercise? No, it’s not, for the following reasons.

The first reason is that, unlike the underlying asset market, the market volatility process is, by comparison, highly predictable. This is due to a phenomenon known as “long memory”, i.e. very slow decay in the serial autocorrelations of the volatility process. What that means is that the history of the volatility process contains useful information about its likely future behavior. [There are several posts on this topic in this blog – just search for “long memory”]. So, in principle, one can develop an effective system to forecast market volatility in advance and hence make an informed decision about whether or not to deploy a specific model.

But let’s say you are unpersuaded by this argument and take the view that market volatility is intrinsically unpredictable. Does that make this approach impractical? Not at all. You have a couple of options:

You can test the model built for quiet days on all the market data, including volatile days. It may perform acceptably well across both market regimes.

For example, here are the results of a backtest of the model described above on all the market data, including volatile and quiet periods, from 2004-2015. While the performance characteristics are not quite as good, overall the strategy remains very attractive.

Another approach is to develop a second model for volatile days and deploy both low- and high-volatility regime models simultaneously. The trading systems will interact (if you allow them to) in a highly nonlinear and unpredictable way. It might turn out badly – but on the other hand, it might not! Here, for instance, is the result of combining low- and high-volatility models simultaneously for the Emini futures and running them in parallel. The result is an improvement (relative to the low volatility model alone), not only in the annual rate of return (21% vs 17.8%), but also in the risk-adjusted performance, profit factor and average trade.

CONCLUSION

Separating the data into multiple subsets representing different market regimes allows the system developer to amplify the signal:noise ratio, increasing the effectiveness of his alpha factors. Potentially, this allows important features of the underlying market dynamics to be captured in the model more easily, which can lead to improved trading performance.

Models developed for different market regimes can be tested across all market conditions and deployed on an everyday basis if shown to be sufficiently robust. Alternatively, a meta-strategy can be developed to forecast the market regime and select the appropriate trading system accordingly.

Finally, it is possible to achieve acceptable, or even very good results, by deploying several different models simultaneously and allowing them to interact, as the market moves from regime to regime.

March 14, 2019

Protected: Systematic Fund

January 29, 2019

Improving Trading System Performance Using a Meta-Strategy

What is a Meta-Strategy?

In my previous post on identifying drivers of strategy performance I mentioned the possibility of developing a meta-strategy.

A meta-strategy is a trading system that trades trading systems. The idea is to develop a strategy that will make sensible decisions about when to trade a specific system, in a way that yields superior performance compared to simply following the underlying trading system. Put another way, the simplest kind of meta-strategy is a long-only strategy that takes positions in some underlying trading system. At times, it will follow the underlying system exactly; at other times it is out of the market and ignore the trading system’s recommendations.

More generally, a meta-strategy can determine the size in which one, or several, systems should be traded at any point in time, including periods where the size can be zero (i.e. the system is not currently traded). Typically, a meta-strategy is long-only: in theory there is nothing to stop you developing a meta-strategy that shorts your underlying strategy from time to time, but that is a little counter-intuitive to say the least!

A meta-strategy is something that could be very useful for a fund-of-funds, as a way of deciding how to allocate capital amongst managers.

Caissa Capital operated a meta-strategy in its option arbitrage hedge fund back in the early 2000’s. The meta-strategy (we called it a “model management system”) selected from a half dozen different volatility models to be used for option pricing, depending their performance, as measured by around 30 different criteria. The criteria included both statistical metrics, such as the mean absolute percentage error in the forward volatility forecasts, as well as trading performance criteria such as the moving average of the trade PNL. The model management system probably added 100 – 200 basis points per annum to the performance the underlying strategy, so it was a valuable add-on.

Illustration of a Meta-Strategy in US Bond Futures

To illustrate the concept we will use an underlying system that trades US Bond futures at 15-minute bar intervals. The performance of the system is summarized in the chart and table below.

Strategy performance has been very consistent over the last seven years, in terms of the annual returns, number of trades and % win rate. Can it be improved further?

To assess this possibility we create a new data series comprising the points of the equity curve illustrated above. More specifically, we form a series comprising the open, high, low and close values of the strategy equity, for each trade. We will proceed to treat this as a new data series and apply a range of different modeling techniques to see if we can develop a trading strategy, in exactly the same way as we would if the underlying was a price series for a stock.

It is important to note here that, for the meta-strategy at least, we are working in trade-time, not calendar time. The x-axis will measure the trade number of the underlying strategy, rather than the date of entry (or exit) of the underlying trade. Thus equally spaced points on the x-axis represent different lengths of calendar time, depending on the duration of each trade.

It is necessary to work in trade time rather than calendar time because, unlike a stock, it isn’t possible to trade the underlying strategy whenever we want to – we can only enter or exit the strategy at points in time when it is about to take a trade, by accepting that trade or passing on it (we ignore the other possibility which is sizing the underlying trade, for now).

Another question is what kinds of trading ideas do we want to consider for the meta-strategy? In principle one could incorporate almost any trading concept, including the usual range of technical indictors such as RSI, or Bollinger bands. One can go further an use machine learning techniques, including Neural Networks, Random Forest, or SVM.

In practice, one tends to gravitate towards the simpler kinds of trading algorithm, such as moving averages (or MA crossover techniques), although there is nothing to say that more complex trading rules should not be considered. The development process follows a familiar path: you create a hypothesis, for example, that the equity curve of the underlying bond futures strategy tends to be mean-reverting, and then proceed to test it using various signals – perhaps a moving average, in this case. If the signal results in a potential improvement in the performance of the default meta-strategy (which is to take every trade in the underlying system system), one includes it in the library of signals that may ultimately be combined to create the finished meta-strategy.

As with any strategy development you should follows the usual procedure of separating the trade data to create a set used for in-sample modeling and out-of-sample performance testing.

Following this general procedure I arrived at the following meta-strategy for the bond futures trading system.

The modeling procedure for the meta-strategy has succeeded in eliminating all of the losing trades in the underlying bond futures system, during both in-sample and out-of-sample periods (comprising the most recent 20% of trades).

In general, it is unlikely that one can hope to improve the performance of the underlying strategy quite as much as this, of course. But it may well be possible to eliminate a sufficient proportion of losing trades to reduce the equity curve drawdown and/or increase the overall Sharpe ratio by a significant amount.

A Challenge / Opportunity

If you like the meta-strategy concept, but are unsure how to proceed, I may be able to help.

Send me the data for your existing strategy (see details below) and I will attempt to model a meta-strategy and send you the results. We can together evaluate to what extent I have been successful in improving the performance of the underlying strategy.

Here are the details of what you need to do:

1. You must have an existing, profitable strategy, with sufficient performance history (either real, simulated, or a mixture of the two). I don’t need to know the details of the underlying strategy, or even what it is trading, although it would be helpful to have that information.

2. You must send the complete history of the equity curve of the underlying strategy, in Excel format, with column headings Date, Open, High, Low, Close. Each row represents consecutive trades of the underlying system and the O/H/L/C refers to the value of the equity curve for each trade.

3. The history must comprise at least 500 trades as an absolute minimum and preferably 1000 trades, or more.

4. At this stage I can only consider a single underlying strategy (i.e. a single equity curve)

5. You should not include any software or algorithms of any kind. Nothing proprietary, in other words.

6. I will give preference to strategies that have a (partial) live track record.

As my time is very limited these days I will not be able to deal with any submissions that fail to meet these specifications, or to enter into general discussions about the trading strategy with you.

You can reach me at jkinlay@systematic-strategies.com

January 22, 2019

Identifying Drivers of Trading Strategy Performance

Building a winning strategy, like the one in the e-Mini S&P500 futures described here is only half the challenge: it remains for the strategy architect to gain an understanding of the sources of strategy alpha, and risk. This means identifying the factors that drive strategy performance and, ideally, building a model so that their relative importance can be evaluated. A more advanced step is the construction of a meta-model that will predict strategy performance and provided recommendations as to whether the strategy should be traded over the upcoming period.

Strategy Performance – Case Study

Let’s take a look at how this works in practice. Our case study makes use of the following daytrading strategy in e-Mini futures.

The overall performance of the strategy is quite good. Average monthly PNL over the period from April to Oct 2015 is almost $8,000 per contract, after fees, with a standard deviation of only $5,500. That equates to an annual Sharpe Ratio in the region of 5.0. On a decent execution platform the strategy should scale to around 10-15 contracts, with an annual PNL of around $1.0 to $1.5 million.

Looking into the performance more closely we find that the win rate (56%) and profit factor (1.43) are typical for a profitable strategy of medium frequency, trading around 20 times per session (in this case from 9:30AM to 4PM EST).

Another attractive feature of the strategy risk profile is the Max Adverse Execution, the drawdown experienced in individual trades (rather than the realized drawdown). In the chart below we see that the MAE increases steadily, without major outliers, to a maximum of only around $1,000 per contract.

One concern is that the average trade PL is rather small – $20, just over 1.5 ticks. Strategies that enter and exit with limit orders and have small average trade are generally highly dependent on the fill rate – i.e. the proportion of limit orders that are filled. If the fill rate is too low, the strategy will be left with too many missed trades on entry or exit, or both. This is likely to damage strategy performance, perhaps to a significant degree – see, for example my post on High Frequency Trading Strategies.

The fill rate is dependent on the number of limit orders posted at the extreme high or low of the bar, known as the extreme hit rate. In this case the strategy has been designed specifically to operate at an extreme hit rate of only around 10%, which means that, on average, only around one trade in ten occurs at the high or low of the bar. Consequently, the strategy is not highly fill-rate dependent and should execute satisfactorily even on a retail platform like Tradestation or Interactive Brokers.

Drivers of Strategy Performance

So far so good. But before we put the strategy into production, let’s try to understand some of the key factors that determine its performance. Hopefully that way we will be better placed to judge how profitable the strategy is likely to be as market conditions evolve.

In fact, we have already identified one potential key performance driver: the extreme hit rate (required fill rate) and determined that it is not a major concern in this case. However, in cases where the extreme hit rate rises to perhaps 20%, or more, the fill ratio is likely to become a major factor in determining the success of the strategy. It would be highly inadvisable to attempt implementation of such a strategy on a retail platform.

What other factors might affect strategy performance? The correct approach here is to apply the scientific method: develop some theories about the drivers of performance and see if we can find evidence to support them.

For this case study we might conjecture that, since the strategy enters and exits using limit orders, it should exhibit characteristics of a mean reversion strategy, which will tend to do better when the market moves sideways and rather worse in a strongly trending market.

Another hypothesis is that, in common with most day-trading and high frequency strategies, this strategy will produce better results during periods of higher market volatility. Empirically, HFT firms have always produced higher profits during volatile market conditions – 2008 was a banner year for many of them, for example. In broad terms, times when the market is whipsawing around create additional opportunities for strategies that seek to exploit temporary mis-pricings. We shall attempt to qualify this general understanding shortly. For now let’s try to gather some evidence that might support the hypotheses we have formulated.

I am going to take a very simple approach to this, using linear regression analysis. It’s possible to do much more sophisticated analysis using nonlinear methods, including machine learning techniques. In our regression model the dependent variable will be the daily strategy returns. In the first iteration, let’s use measures of market returns, trading volume and market volatility as the independent variables.

The first surprise is the size of the (adjusted) R Square – at 28%, this far exceeds the typical 5% to 10% level achieved in most such regression models, when applied to trading systems. In other words, this model does a very good job of account for a large proportion of the variation in strategy returns.

Note that the returns in the underlying S&P50o index play no part (the coefficient is not statistically significant). We might expect this: ours is is a trading strategy that is not specifically designed to be directional and has approximately equivalent performance characteristics on both the long and short side, as you can see from the performance report.

Now for the next surprise: the sign of the volatility coefficient. Our ex-ante hypothesis is that the strategy would benefit from higher levels of market volatility. In fact, the reverse appears to be true (due to the negative coefficient). How can this be? On further reflection, the reason why most HFT strategies tend to benefit from higher market volatility is that they are momentum strategies. A momentum strategy typically enters and exits using market orders and hence requires a major market move to overcome the drag of the bid-offer spread (assuming it calls the market direction correctly!). This strategy, by contrast, is a mean-reversion strategy, since entry/exits are effected using limit orders. The strategy wants the S&P500 index to revert to the mean – a large move that continues in the same direction is going to hurt, not help, this strategy.

Note, by contrast, that the coefficient for the volume factor is positive and statistically significant. Again this makes sense: as anyone who has traded the e-mini futures overnight can tell you, the market tends to make major moves when volume is light – simply because it is easier to push around. Conversely, during a heavy trading day there is likely to be significant opposition to a move in any direction. In other words, the market is more likely to trade sideways on days when trading volume is high, and this is beneficial for our strategy.

The final surprise and perhaps the greatest of all, is that the strategy alpha appears to be negative (and statistically significant)! How can this be? What the regression analysis appears to be telling us is that the strategy’s performance is largely determined by two underlying factors, volume and volatility.

Let’s dig into this a little more deeply with another regression, this time relating the current day’s strategy return to the prior day’s volume, volatility and market return.

In this regression model the strategy alpha is effectively zero and statistically insignificant, as is the case for lagged volume. The strategy returns relate inversely to the prior day’s market return, which again appears to make sense for a mean reversion strategy: our model anticipates that, in the mean, the market will reverse the prior day’s gain or loss. The coefficient for the lagged volatility factor is once again negative and statistically significant. This, too, makes sense: volatility tends to be highly autocorrelated, so if the strategy performance is dependent on market volatility during the current session, it is likely to show dependency on volatility in the prior day’s session also.

So, in summary, we can provisionally conclude that:

This strategy has no market directional predictive power: rather it is a pure, mean-reversal strategy that looks to make money by betting on a reversal in the prior session’s market direction. It will do better during periods when trading volume is high, and when market volatility is low.

Conclusion

Now that we have some understanding of where the strategy performance comes from, where do we go from here? The next steps might include some, or all, of the following:

(i) A more sophisticated econometric model bringing in additional lags of the explanatory variables and allowing for interaction effects between them.

(ii) Introducing additional exogenous variables that may have predictive power. Depending on the nature of the strategy, likely candidates might include related equity indices and futures contracts.

(iii) Constructing a predictive model and meta-strategy that would enable us assess the likely future performance of the strategy, and which could then be used to determine position size. Machine learning techniques can often be helpful in this content.

I will give an example of the latter approach in my next post.

January 8, 2019

Trading Strategy Design

In this post I want to share some thoughts on how to design great automated trading strategies – what to look for, and what to avoid.

For illustrative purposes I am going to use a strategy I designed for the ever-popular S&P500 e-mini futures contract.

The overall equity curve for the strategy is show below.

This is often the best place to start. What you want to see, of course, is a smooth, upward-sloping curve, without too many sizable drawdowns, and one in which the strategy continues to make new highs. This is especially important in the out-of-sample test period (Jan 2014- Jul 2015 in this case). You will notice a flat period around 2013, which we will need to explore later. Overall, however, this equity curve appears to fit the stereotypical pattern we hope to see when developing a new strategy.

Let’s move on look at the overall strategy performance numbers.

STRATEGY PERFORMANCE CHARACTERISTICS

(click to enlarge)

1. Net Profit
Clearly, the most important consideration. Over the 17 year test period the strategy has produced a net profit averaging around $23,000 per annum, per contract. As a rough guide, you would want to see a net profit per contract around 10x the maintenance margin, or higher.

2. Profit Factor
The gross profit divided by the gross loss. You want this to be as high as possible. Too low, as the strategy will be difficult to trade, because you will see sustained periods of substantial losses. I would suggest a minimum acceptable PF in the region of 1.25. Many strategy developers aim for a PF of 1.5, or higher.

3. Number of Trades
Generally, the more trades the better, at least from the point of view of building confidence in the robustness of strategy performance. A strategy may show a great P&L, but if it only trades once a month it is going to take many many years of performance data to ensure statistical significance. This strategy, on the other hand, is designed to trade 2-3 times a day. Given that, and the length of the test period, there is little doubt that the results are statistically significant.

Profit Factor and number of trades are opposing design criteria – increasing the # trades tends to reduce the PF. That consideration sets an upper bound on the # trades that can be accommodated, before the profit factor deteriorates to unacceptably low levels. Typically, 4-5 trades a day is about the maximum trading frequency one can expect to achieve.

4. Win Rate
Novice system designers tend to assume that you want this to be as high as possible, but that isn’t typically the case. It is perfectly feasible to design systems that have a 90% win rate, or higher, but which produce highly undesirable performance characteristics, such as frequent, large drawdowns. For a typical trading system the optimal range for the win rate is in the region of 40% to 66%. Below this range, it becomes difficult to tolerate the long sequences of losses that will result, without losing faith in the system.

5. Average Trade
This is the average net profit per trade. A typical range would be $10 to $100. Many designers will only consider strategies that have a higher average trade than this one, perhaps $50-$75, or more. The issue with systems that have a very small average trade is that the profits can quickly be eaten up by commissions. Even though, in this case, the results are net of commissions, one can see a significant deterioration in profits if the average trade is low and trade frequency is high, because of the risk of low fill rates (i.e. the % of limit orders that get filled). To assess this risk one looks at the number of fills assumed to take place at the high or low of the bar. If this exceeds 10% of the total # trades, one can expect to see some slippage in the P&L when the strategy is put into production.

6. Average Bars
The number of bars required to complete a trade, on average. There is no hard limit one can suggest here – it depends entirely on the size of the bars. Here we are working in 60 minute bars, so a typical trade is held for around 4.5 hours, on average. That’s a time-frame that I am comfortable with. Others may be prepared to hold positions for much longer – days, or even weeks.

Perhaps more important is the average length of losing trades. What you don’t want to see is the strategy taking far longer to exit losing trades than winning trades. Again, this is a matter of trader psychology – it is hard to sit there hour after hour, or day after day, in a losing position – the temptation to cut the position becomes hard to ignore. But, in doing that you are changing the strategy characteristics in a fundamental way, one that rarely produces a performance improvement.

What the strategy designer needs to do is to figure out in advance what the limits are of the investor’s tolerance for pain, in terms of maximum drawdown, average losing trade, etc, and design the strategy to meet those specifications, rather than trying to fix the strategy afterwards.

7. Required Account Size
It’s good to know exactly how large an account you need per contract, so you can figure out how to scale the strategy. In this case one could hope to scale the strategy up to a 10-lot in a $100,000 account. That may or may not fit the trader’s requirements and again, this needs to be considered at the outset. For example, for a trader looking to utilize, say, $1,000,000 of capital, it is doubtful whether this strategy would fit his requirements without considerable work on the implementations issues that arise when trying to trade in anything approaching a 100 contract clip rate.

8. Commission
Always check to ensure that the strategy designer has made reasonable assumptions about slippage and commission. Here we are assuming $5 per round turn. There is no slippage, because the strategy executes using limit orders.

9. Drawdown
Drawdowns are, of course, every investor’s bugbear. No-one likes drawdowns that are either large, or lengthy in relation to the annual profitability of the strategy, or the average trade duration. A $10,000 max drawdown on a strategy producing over $23,000 a year is actually quite decent – I have seen many e-mini strategies with drawdowns at 2x – 3x that level, or larger. Again, this is one of the key criteria that needs to be baked into the strategy design at the outset, rather than trying to fix later.

ANNUAL PROFITABILITY

Let’s now take a look at how the strategy performs year-by-year, and some of the considerations and concerns that often arise.

1. Performance During Downturns
One aspect I always pay attention to is how well the strategy performs during periods of high market stress, because I expect similar conditions to arise in the fairly near future, e.g. as the Fed begins to raise rates.

Here, as you can see, the strategy performed admirably during both the dot com bust of 1999/2000 and the financial crisis of 2008/09.

2. Consistency in the # Trades and % Win Rate
It is not uncommon with low frequency strategies to see periods of substantial variation in the # trades or win rate. Regardless how good the overall performance statistics are, this makes me uncomfortable. It could be, for instance, that the overall results are influenced by one or two exceptional years that are unlikely to be repeated. Significant variation in the trading or win rate raise questions about the robustness of the strategy, going forward. On the other hand, as here, it is a comfort to see the strategy maintaining a very steady trading rate and % win rate, year after year.

3. Down Years
Every strategy shows variation in year to year performance and one expects to see years in which the strategy performs less well, or even loses money. For me, it rather depends on when such losses arise, as much as the size of the loss. If a loss occurs in the out-of-sample period it raises serious questions about strategy robustness and, as a result, I am very unlikely to want to put such a strategy into production. If, as here, the period of poor performance occurs during the in-sample period I am less concerned – the strategy has other, favorable characteristics that make it attractive and I am willing to tolerate the risk of one modestly down-year in over 17 years of testing.

INTRA-TRADE DRAWDOWNS

Many trades that end up being profitable go through a period of being under-water. What matters here is how high those intra-trade losses may climb, before the trade is closed. To take an extreme example, would you be willing to risk $10,000 to make an average profit of only $10 per trade? How about $20,000? $50,000? Your entire equity?

The Maximum Average Excursion chart below shows the drawdowns on a trade by trade basis. Here we can see that, over the 17 year test period, no trade has suffered a drawdown of much more than $5,000. I am comfortable with that level. Others may prefer a lower limit, or be tolerant of a higher MAE.

Again, the point is that the problem of a too-high MAE is not something one can fix after the event. Sure, a stop loss will prevent any losses above a specified size. But a stop loss also has the unwanted effect of terminating trades that would have turned into money-makers. While psychologically comfortable, the effect of a stop loss is almost always negative in terms of strategy profitability and other performance characteristics, including drawdown, the very thing that investors are looking to control.

CONCLUSION
I have tried to give some general guidelines for factors that are of critical importance in strategy design. There are, of course, no absolutes: the “right” characteristics depend entirely on the risk preferences of the investor.

One point that strategy designers do need to take on board is the need to factor in all of the important design criteria at the outset, rather than trying (and usually failing) to repair the strategy shortcomings after the event.