Meta-strategy Archives - QUANTITATIVE RESEARCH AND TRADING

October 7, 2020

A Meta-Strategy in S&P 500 E-Mini Futures

In earlier posts I have described the idea of a meta-strategy as a strategies that trades strategies. It is an algorithm, or set of rules, that is used to decide when to trade an underlying strategy. In some cases a meta-strategy may influence the size in which the underlying strategy is traded, or may even amend the base code. In other word, a meta-strategy actively “trades” an underlying strategy, or group of strategies, much as in the same way a regular strategy may actively trade stocks, going long or short from time to time. One distinction is that a meta-strategy will rarely, if ever, actually “short” an underlying strategy – at most it will simply turn the strategy off (reduce the position size to zero) for a period.

For a more detailed description, see this post:

Improving Trading System Performance Using a Meta-Strategy

In this post I look at a meta-strategy that developed for a client’s strategy in S&P E-Mini futures. What is extraordinary is that the underlying strategy was so badly designed (not by me!) and performs so poorly that no rational systematic trader would likely give it a second look – instead he would toss it into the large heap of failed ideas that all quantitative researchers accumulate over the course of their careers. So this is a textbook example that illustrates the power of meta-strategies to improve, or in this case transform, the performance of an underlying strategy.

1. The Strategy

The Target Trader Strategy (“TTS”) is a futures strategy applied to S&P 500 E-Mini futures that produces a very high win rate, but which occasionally experiences very large losses. The purpose of the analysis if to find methods that will:

1) Decrease the max loss / drawdown
2) Increase the win rate / profitability

For longs the standard setting is entry 40 ticks below the target, stop loss 1000 ticks below the target, and then 2 re-entries 100 ticks below entry 1 and 100 ticks below entry 2

For shorts the standard is entry 80 ticks above the target. stop loss 1000 ticks above the target, and then 2 re-entries 100 ticks above entry 1 and 100 ticks above entry 2

For both directions its 80 ticks above/below for entry 1, 1000 tick stop, and then 1 re entry 100 ticks above/below, and then re-entry 2 100 ticks above/below entry 2

2. Strategy Performance

2.1 Overall Performance

The overall performance of the strategy over the period from 2018 to 2020 is summarized in the chart of the strategy equity curve and table of performance statistics below.
These confirm that, while the win rate if very high (over 84%) there strategy experiences many significant drawdowns, including a drawdown of -$61,412.50 (-43.58%). The total return is of the order of 5% per year, the strategy profit factor is fractionally above 1 and the Sharpe Ratio is negligibly small. Many traders would consider the performance to be highly unattractive.

2.2 Long Trades

We break the strategy performance down into long and short trades, and consider them separately. On the long side, the strategy has been profitable, producing a gain of over 36% during the period 2018-2020. It also suffered catastrophic drawdown of over -$97,000 during that period:

2.3 Short Trades

On the short side, the story is even worse, producing an overall loss of nearly -$59,000:

3. Improving Strategy Performance with a Meta-Strategy

We considered two possible methods to improve strategy performance. The first method attempts to apply technical indicators and other data series to improve trading performance. Here we evaluated price series such as the VIX index and a wide selection of technical indicators, including RSI, ADX, Moving Averages, MACD, ATR and others. However, any improvement in strategy performance proved to be temporary in nature and highly variable, in many cases amplifying the problems with the strategy performance rather than improving them.

The second approach proved much more effective, however. In this method we create a meta-strategy which effectively “trades the strategy”, turning it on and off depending on its recent performance. The meta-strategy consists of a set of rules that determines whether or not to continue trading the strategy after a series of wins or losses. In some cases the meta-strategy may increase the trade size for a sequence of trades, at times when it considers the conditions for the underlying strategy to be favorable.

The result of applying the meta-strategy are described in the following sections.

3.1 Long & Short Strategies with Meta-Strategy Overlay

The performance of the long/short strategies combined with the meta-strategy overlay are set out in the chart and table below.
The overall improvements can be summarized as follows:

Net profit increases from $15,387 to $176,287
Account return rises from 15% to 176%
Percentage win rate rises from 84% to 95%
Profit factor increases from 1.0 to 6.7
Average trade rises from $51 to $2,631
Max $ Drawdown falls from -$61,412 to -$30,750
Return/Max Drawdown ratio rises from 0.35 to 5.85
The modified Sharpe ratio increases from 0.07 to 0.5

Taken together, these are dramatic improvements to every important aspect of strategy performance.

There are two key rules in the meta-strategy, applicable to winning and losing trades:

Rule for winning trades:
After 3 wins in a row, skip the next trade.

Rule for losing trades:
After 3 losses in a row, add 1 contract until the first win. Subtract 1 contract after each win until the next loss, or back to 1 contract.

3.2 Long Trades with Meta-Strategy

The meta-strategy rules produce significant improvements in the performance of both the long and short components of the strategy. On the long side the percentage win rate is increased to 100% and the max % drawdown is reduced to 0%:

3.3 Short Trades with Meta-Strategy

Improvements to the strategy on the short side are even more significant, transforming a loss of -$59,000 into a profit of $91,600:

4. Conclusion

A meta-strategy is a simple, yet powerful technique that can transform the performance of an underlying strategy. The rules are often simple, although they can be challenging to implement. Meta strategies can be applied to almost any underlying strategy, whether in futures, equities, or forex. Worthwhile improvements in strategy performance are often achievable, although not often as spectacular as in this case.

If any reader is interested in designing a meta-strategy for their own use, please get in contact.

August 13, 2019

Outperforming Winton Capital

Winton Capital Management is a renowned quant fund and one of the world’s largest, most successful CTAs. The firm’s flagship investment strategy, the Winton Diversified Program, follows a systematic investment process that is based on statistical research to invest globally long and short, using leverage, in a diversified range of liquid instruments, including exchange traded futures, forwards, currency forwards traded over the counter, equity securities and derivatives linked to such securities.

The performance of the program over the last 19 years has been impressive, especially considering its size, which now tops around $13Bn in assets.

Source: CTA Performance

A Meta-Strategy to Beat Winton Capital

With that background, the idea of improving the exceptional results achieved by David Harding and his army of quants seems rather far fetched, but I will take a shot. In what follows, I am assuming that we are permitted to invest and redeem an investment in the program at no additional cost, other than the stipulated fees. This is, of course, something of a stretch, but we will make that assumption based on the further stipulation that we will make no more than two such trades per year.

The procedure we will follow has been described in various earlier posts – in particular see this post, in which I discuss the process of developing a Meta-Strategy: Improving A Hedge Fund Investment – Cantab Capital’s Quantitative Aristarchus Fund

Using the performance data of the WDP from 1997-2012, we develop a meta-strategy that seeks to time an investment in the program, taking profits after reaching a specified profit target, which is based on the TrueRange, or after holding for a maximum of 8 months. The key part of the strategy code is as follows:

If MarketPosition = 1 then begin
TargPrL = EntryPrice + TargFr * TrueRange;
Sell(“ExTarg-L”) next bar at TargPrL limit;

If Time >= TimeEx or BarsSinceEntry >= NBarEx1 or (BarsSinceEntry >= NBarEx3 and C > EntryPrice)
or (BarsSinceEntry >= NBarEx2 and C < EntryPrice) then
Sell(“ExMark-L”) next bar at market;
end;

It appears that by timing an investment in the program we can improve the CAGR by around 0.86% per year, and with annual volatility that is lower by around 4.4% annually. As a consequence, the Sharpe ratio of the meta-strategy is considerably higher: 1.14 vs 0.78 for the WDP.

Like most trend-following CTA strategies, Winton’s WDP has positive skewness, an attractive feature that means that the strategy has a preponderance of returns in the positive right tail of the distribution. Also in common with most CTA strategies, on the other hand, the WDP suffers from periodic large drawdowns, in this case amounting to -25.73%.

The meta-strategy improves on the baseline profile of the WDP, increasing the positive skew, while substantially reducing downside risk, leading to a much lower maximum drawdown of -16.94%.

Conclusion

Despite its stellar reputation in the CTA world, investors could theoretically improve on the performance of Winton Capital’s flagship program by using a simple meta-strategy that times entry to and exit from the program using simple technical indicators. The meta-strategy produces higher returns, lower volatility and with higher positive skewness and lower downside risk.

March 5, 2019

Improving A Hedge Fund Investment – Cantab Capital’s Quantitative Aristarchus Fund

In this post I am going to take a look at what an investor can do to improve a hedge fund investment through the use of dynamic capital allocation. For the purposes of illustration I am going to use Cantab Capital’s Aristarchus program – a quantitative fund which has grown to over $3.5Bn in assets under management since its opening with $30M in 2007 by co-founders Dr. Ewan Kirk and Erich Schlaikjer.

I chose this product because, firstly, it is one of the most successful quantitative funds in existence and, secondly, because as a CTA its performance record is publicly available.

Cantab’s Aristarchus Fund

Cantab’s stated investment philosophy is that algorithmic trading can help to overcome cognitive biases inherent in human-based trading decisions, by exploiting persistent statistical relationships between markets. Taking a multi-asset, multi-model approach, the majority of Cantab’s traded instruments are liquid futures and forwards, across currencies, fixed income, equity indices and commodities.

Let’s take a look at how that has worked out in practice:

Whatever the fund’s attractions may be, we can at least agree that alpha is not amongst them. A Sharpe ratio of < 0.5 (I calculate to be nearer 0.41) is hardly in Renaissance territory, so one imagines that the chief benefit of the product must lie in its liquidity and low market correlation. Uncorrelated it may be, but an investor in the fund must have extremely deep pockets – and a very strong stomach – to handle the 34% drawdown that the fund suffered in 2013.

Improving the Aristarchus Fund Performance

If we make the assumption that an investment in this product is warranted in the first place, what can be done to improve its performance characteristics? We’ll look at that question from two different perspectives – the investor’s and the manager’s.

Firstly, from the investor’s perspective, there are relatively few options available to enhance the fund’s contribution, other than through diversification. One other possibility available to the investor, however, is to develop a program for dynamic capital allocation. This requires the manager to be open to allowing significant changes in the amount of capital to be allocated from month to month, or quarter to quarter, but in a liquid product like Aristarchus some measure of flexibility ought to be feasible.

An analysis of the fund’s performance indicates the presence of a strong dependency in the returns process. This is not at all unusual. Often investment strategies have a tendency to mean-revert: a negative dependency in which periods of poor performance tend to be followed by positive performance, and vice versa. CTA strategies such as Aristarchus tend to be trend-following, and this can induce positive dependency in the strategy returns process, in which positive months tend to follow earlier positive months, while losing months tend to be followed by further losses. This is the pattern we find here.

Consequently, rather than maintaining a constant capital allocation, an investor would do better to allocate capital dynamically, increasing the amount of capital after a positive period, while decreasing the allocation after a period of losses. Let’s consider a variation of this allocation plan, in which the amount of allocated capital is increased by 70% when the last monthly equity value exceeds the quarterly moving average, while the allocation is reduced to zero when the last month’s equity falls below the average. A dynamic capital allocation plan as simple as this appears to produce a significant improvement in the overall performance of the investment:

The slight increase in annual volatility in the returns produced by the dynamic capital allocation model is more than offset by the 412bp improvement in the CAGR. Consequently, the Sharpe Ratio improves from o.41 to 0.60.

Nor is this by any means the entire story: the dynamic model produces lower average drawdowns (7.93% vs. 8.52%) and, more importantly, reduces the maximum drawdown over the life of the fund from a painful 34.87% to more palatable 23.92%.

The much-improved risk profile of the dynamic allocation scheme is reflected in the Return/Drawdown Ratio, which rises from 2.44 to 6.52.

Note, too, that the average level of capital allocated in the dynamic scheme is very slightly less than the original static allocation. In other words, the dynamic allocation technique results in a more efficient use of capital, while at the same time producing a higher rate of risk-adjusted return and enhancing the overall risk characteristics of the strategy.

Improving Fund Performance Using a Meta-Strategy

So much for the investor. What could the manager to do improve the strategy performance? Of course, there is nothing in principle to prevent the manager from also adopting a dynamic approach to capital allocation, although his investment mandate may require him to be fully invested at all times.

Assuming for the moment that this approach is not available to the manager, he can instead look into the possibilities for developing a meta-strategy. As I explained in my earlier post on the topic:

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.

It turns out to be quite straightforward to develop such a meta-strategy, using a combination of stop-loss limits and profit targets to decide when to turn the strategy on or off. In so doing, the manager is able to avoid some periods of negative performance, producing a significant uplift in the overall risk-adjusted return:

Conclusion

Meta-strategies and dynamic capital allocation schemes can enable the investor and the investment manager to improve the performance characteristics of their investment and investment strategy, by increasing returns, reducing volatility and the propensity of the strategy to produce substantial drawdowns.

We have demonstrated how these approaches can be applied successfully to Cantab’s Aristarchus quantitative fund, producing substantial gains in risk adjusted performance and reductions in the average and maximum drawdowns produced over the life of the fund.

February 19, 2019

A Meta-Strategy in Euro Futures

Several readers responded to my recent invitation to send me details of their trading strategies, to see if I could develop a meta-strategy with superior overall performance characteristics (see original post here).

One reader sent me the following strategy in EUR futures, with a promising-looking equity curve over the period from 2009-2014.

I have no information about the underlying architecture of the strategy, but a performance analysis shows that it trades approximately once per day, with a win rate of 49%, a PNL per trade of $4.79 and a IR estimated to be 2.6.

Designing the Meta-Strategy

My task was to see if I could design a meta-strategy that would “trade” the underlying strategy, i.e. produce signals to turn the underlying strategy on or off. Here we are designing a long-only strategy, where a “buy” trade represents the signal to turn the underlying strategy on, while an exit trade from the meta-strategy turns the underlying strategy off.

The meta-strategy is built in trade time rather than calendar time – we don’t want the meta-strategy trying to turn the underlying trading strategy on or off while it is in the middle of a trade. The data we use in the design exercise is the trade-by-trade equity curve, including the date and timestamp and the open, high, low and close values of the equity curve for each trade.

No allowance for trading costs is necessary since all of the transaction costs are baked into the PNL of the underlying strategy – there are no additional costs entailed in turning the strategy on or off, as long as we do that in a period when there is no open position.

In designing the meta-strategy I chose simply to try to improve the overall net PNL. This is a good starting point, but one would typically go on to consider a variety of other possible criteria, including, for example, Net Profit / Av. Max Drawdown, Net Profit / Flat Time, MAR Ratio, Sharpe Ratio, Kelly Criterion, or a combination of them.

I used 80% of the trade data to design and test the strategy and reserved 20% of the data to test the performance of the meta-strategy out-of-sample.

Results

The analysis summarized below shows a clear improvement in the overall performance of the meta-strategy, compared to the underlying strategy. Net PNL and Average Trade are increased by 40%, while the trade standard deviation is noticeably reduced, leading to a higher IR of 5.27 vs 3.10. The win rate increases from around 2/3 to over 90%.

Although not as marked, the overall improvement in strategy performance metrics during the out-of-sample test period is highly significant, both economically and statistically.

Note that the Meta-strategy is a long-only strategy in which each “trade” is a period in which the system trades the underlying EUR futures strategy. So in fact, in the Meta-strategy, each trade represents a number of successive underlying, real trades (which of course may be long or short).

Put another way, the Meta-Strategy turns the underlying trading strategy on and off 276 times in total.

Conclusion

It is feasible to design a meta-strategy that improves the overall performance characteristics of an underlying trading strategy, by identifying the higher-value trades and turning the strategy on or off based on forecasts of its future performance.

No knowledge is required of the mechanics of the underlying trading strategy in order to design a profitable Meta-strategy.

Meta-strategies have been successfully applied to problems of capital allocation, where decisions are made on a regular basis about how much capital to allocate to multiple trading strategies, or traders.

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