Bonds Archives - QUANTITATIVE RESEARCH AND TRADING

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

Anyone active in the quantitative space will tell you that it has become a great deal more competitive in recent years. Many quantitative trades and strategies are a lot more crowded than they used to be and returns from existing strategies are on the decline.

THE CHALLENGE

Meanwhile, costs have been steadily rising, as the technology arms race has accelerated, with more money being spent on hardware, communications and software than ever before. As lead times to develop new strategies have risen, the cost of acquiring and maintaining expensive development resources have spiraled upwards. It is getting harder to find new, profitable strategies, due in part to the over-grazing of existing methodologies and data sets (like the E-Mini futures, for example). There has, too, been a change in the direction of quantitative research in recent years. Where once it was simply a matter of acquiring the fastest pipe to as many relevant locations as possible, the marginal benefit of each extra $ spent on infrastructure has since fallen rapidly. New strategy research and development is now more model-driven than technology driven.

THE OPPORTUNITY

What is needed at this point is a new approach: one that accelerates the process of identifying new alpha signals, prototyping and testing new strategies and bringing them into production, leveraging existing battle-tested technologies and trading platforms.

GENETIC PROGRAMMING

Genetic programming, which has been around since the 1990’s when its use was pioneered in proteomics, enjoys significant advantages over traditional research and development methodologies.

GP is an evolutionary-based algorithmic methodology in which a system is given a set of simple rules, some data, and a fitness function that produces desired outcomes from combining the rules and applying them to the data. The idea is that, by testing large numbers of possible combinations of rules, typically in the millions, and allowing the most successful rules to propagate, eventually we will arrive at a strategy solution that offers the required characteristics.

ADVANTAGES OF GENETIC PROGRAMMING

The potential benefits of the GP approach are considerable: not only are strategies developed much more quickly and cost effectively (the price of some software and a single CPU vs. a small army of developers), the process is much more flexible. The inflexibility of the traditional approach to R&D is one of its principle shortcomings. The researcher produces a piece of research that is subsequently passed on to the development team. Developers are usually extremely rigid in their approach: when asked to deliver X, they will deliver X, not some variation on X. Unfortunately research is not an exact science: what looks good in a back-test environment may not pass muster when implemented in live trading. So researchers need to “iterate around” the idea, trying different combinations of entry and exit logic, for example, until they find a variant that works. Developers are lousy at this; GP systems excel at it.

CHALLENGES FOR THE GENETIC PROGRAMMING APPROACH

So enticing are the potential benefits of GP that it begs the question as to why the approach hasn’t been adopted more widely. One reason is the strong preference amongst researchers for an understandable – and testable – investment thesis. Researchers – and, more importantly, investors – are much more comfortable if they can articulate the premise behind a strategy. Even if a trade turns out to be a loser, we are generally more comfortable buying a stock on the supposition of, say, a positive outcome of a pending drug trial, than we are if required to trust the judgment of a black box, whose criteria are inherently unobservable.

Added to this, the GP approach suffers from three key drawbacks: data sufficiency, data mining and over-fitting. These are so well known that they hardly require further rehearsal. There have been many adverse outcomes resulting from poorly designed mechanical systems curve fitted to the data. Anyone who was active in the space in the 1990s will recall the hype over neural networks and the over-exaggerated claims made for their efficacy in trading system design. Genetic Programming, a far more general and powerful concept, suffered unfairly from the ensuing adverse publicity, although it does face many of the same challenges.

A NEW APPROACH

I began working in the field of genetic programming in the 1990’s, with my former colleague Haftan Eckholdt, at that time head of neuroscience at Yeshiva University, and we founded a hedge fund, Proteom Capital, based on that approach (large due to Haftan’s research). I and my colleagues at Systematic Strategies have continued to work on GP related ideas over the last twenty years, and during that period we have developed a methodology that address the weaknesses that have held back genetic programming from widespread adoption.

Firstly, we have evolved methods for transforming original data series that enables us to avoid over-using the same old data-sets and, more importantly, allows new patterns to be revealed in the underlying market structure. This effectively eliminates the data mining bias that has plagued the GP approach. At the same time, because our process produces a stronger signal relative to the background noise, we consume far less data – typically no more than a couple of years worth.

Secondly, we have found we can enhance the robustness of prototype strategies by using double-blind testing: i.e. data sets on which the performance of the model remains unknown to the machine, or the researcher, prior to the final model selection.

Finally, we are able to test not only the alpha signal, but also multiple variations of the trade expression, including different types of entry and exit logic, as well as profit targets and stop loss constraints.

OUTCOMES: ROBUST, PROFITABLE STRATEGIES

Taken together, these measures enable our GP system to produce strategies that not only have very high performance characteristics, but are also extremely robust. So, for example, having constructed a model using data only from the continuing bull market in equities in 2012 and 2013, the system is nonetheless capable of producing strategies that perform extremely well when tested out of sample over the highly volatility bear market conditions of 2008/09.

So stable are the results produced by many of the strategies, and so well risk-controlled, that it is possible to deploy leveraged money-managed techniques, such as Vince’s fixed fractional approach. Money management schemes take advantage of the high level of consistency in performance to increase the capital allocation to the strategy in a way that boosts returns without incurring a high risk of catastrophic loss. You can judge the benefits of applying these kinds of techniques in some of the strategies we have developed in equity, fixed income, commodity and energy futures which are described below.

CONCLUSION

After 20-30 years of incubation, the Genetic Programming approach to strategy research and development has come of age. It is now entirely feasible to develop trading systems that far outperform the overwhelming majority of strategies produced by human researchers, in a fraction of the time and for a fraction of the cost.

SAMPLE GP SYSTEMS