I recently spent more time doing “reading research” rather than “testing research”. As result, this post resembles a collection of links on ideas seen on the web of how to trade futures with a small account – one of the topics I have been interested in.

The Issue: Diversification with Small Account

A small account size – or starting equity – can make it difficult to achieve diversification (a “free lunch” with a high “cover charge” as described in this post – you can read more on diversification and correlation from this blog here and here).

Diversification can be achieved by trading a large number of components in a portfolio, whether “components” represent:

• Instruments
• Systems
• Timeframes

Instruments Diversification

“Instruments” is usually the first aspect that comes to mind when thinking about diversification.
Including more assets/markets/instruments in a portfolio is often described as the “free lunch” – and this is one of the main reasons why large CTAs often include upwards of 100 markets in their portfolio selection.

A small account most likely cannot trade a portfolio of 100+ instrument. This is an issue that Dean Hoffman tries to address in this article: The Conundrum of Small Managed Futures Accounts.

Noting that most diversified trend follower CTAs have a minimum account size of at least $1M, Hoffman describes the advantages of trading larger accounts (able to trade many instruments including those with high margin requirements, more granular position sizing with contract scaling).

Hoffman then describes Dynamic Portfolio Selection as a potential solution for small accounts to achieve increased results from a “virtual high diversification”. The system monitors a large set of instruments but instead of taking all signals (as a diversified trend follower would most likely do), it evaluates and ranks each instrument relatively (based on each market’s potential on a risk-adjusted basis), resulting in about 90% of trading signals being filtered out. This naturally cuts down the number of positions held at the same time, and consequently the required account size.

As this is mostly a “marketing” article for Hoffman’s CTA offering (implementing this concept), there is not much more information on what sort of filtering is applied to select the “best” signals but the general idea is worth investigating (and you can check for yourself whether their performance seems to hold up against the theory).

The subject of dynamic portfolio selection has also been covered in the inevitable Trading Blox forums in this “Dynamic Portfolio Selection” post started by Dean Hoffman himself.

A couple of posts on this blog also describe potential filtering ideas based on relative market volatility and higher-level trend direction.

This idea of filtering trades is not new: the Turtles used to use the concept decades ago, as mentioned by TB forum user sluggo in this post (which contains a link to Trading Blox code implementing similar “heat limitation” mechanism).

Systems (and Timeframes) Diversification: Swarm Behaviour

Combining several systems is also a possibility to achieve diversification. With the extra advantage that it is possible – to some extent – to design systems and control their correlations to the rest of the suite of systems (as opposed to markets, which can have a furious tendency to correlate to +1 or -1 during crisis times).

And as we all know, correlation is a key element of the “diversification benefits” equation (check this thread from user sluggo on TB forums for a good presentation/discussion on the topic).

Adding a profitable mean reversion/counter-trend system to a trend following system will, in all likelihood, reduce the volatility of the combined portfolio, thanks to the negative correlation that it brings. Adding many uncorrelated systems is likely to increase this positive effect.

However, trading a diversified suite of systems has a similar constraint to trading a large portfolio: it increases the required account equity.

A comment from Pumpernickel on a recent post from Quantum Financier (who is starting a series of posts on “signal aggregation: how we form and use an ensemble of signals isolating different pieces of information to build a profitable strategy” ) pointed to a couple of documents from Fall River Capital.

The (pdf) document (part 1 and part 2 of their white paper) describe how they tackle this issue on a large scale, by trading hundreds to thousands systems simultaneously, using the concept of swarm behaviour (which can be seen throughout the natural world, such as in the mesmerising starling flights in the English Somerset Winter, pictured above).

From the white paper (other Fall River white papers and general website are also interesting to read):

An […] approach is to assign each trading system a vote. Each model is polled for its position (long, short, or out) daily, and the total is aggregated into a tally that may be thought of as a “Vox Populi,” or crowd opinion poll. Research showed that aggregating the systems by this simple tally method was a quite workable approach, allowing us to “cheat” by holding a single position per market rather than hundreds or thousands. Regardless of the number of component models, the master strategy holds a position in accordance with the majority of the crowd.

How they choose the models/systems to be included in the portfolio is mostly driven by each system’s correlation to other systems:

The portfolio of individual candidate systems consists of between several hundred and a few thou‐ sand members that share both low correlations to one another and robust returns over many years of market history. The result is a “swarm” of trading models, each attacking the market from a different direction. This process of system development, evaluation, and selection does not prioritize superior standalone system performance, but rather seeks to uncover profitable trading rules that complement one another when implemented together.

Their testing results seem to show that this approach tracks fairly well an “equal allocation” approach with hundreds/thousands of systems, which itself benefits greatly from low correlated system diversification (reduced volatility, or increased vol-adjusted returns).

This “systems voting” strategy has also been discussed on the TB forums there (again started by user sluggo…).

Other Alternatives

These are ideas to stimulate research on how to alleviate the “futures trading diversification with a small account” issue. Other ideas can also be found on other threads from the TB forum (examples 1, 2 and 3 – search the forum for more discussions), showing that the topic is a “popular” one.

Another alternative would be to move away from trading actual futures but instead focus on “proxy” instruments such as ETFs (see this post for a quantification of how ETFs can track futures) or spread betting (they usually offer lower minimum trading lots, allowing for lower required trading equity, but can have other disadvantages, such as counterparty risk, less instruments available or cost of funding/leverage). Another trade-off to make in system/strategy design..
 

I recently came across the story of how ancient Peruvian farmers used the concept of diversification in order to reduce their risks. I liked the comparison to trading diversification and I thought it would be a good subject for a quick “Friday post”.

I was pointed to this story by a new interesting systematic trading blog: STROM Macro, set up by Ström, a reader of this blog – thanks for the pointer.

The story is part of the foreword by Jared Diamond to the book The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money.
The book “focuses on the mistakes made and lessons learned in the financial crisis of 2008″ and contains interviews with managers who “survived and prospered through the financial crisis” discussing “new paradigm of risk management and profit making opportunities in the post-crisis world”.

Investment Managers and Peruvian Farmers: Similar Goals

In the foreword, Diamond draws a parallel between investment managers and Peruvian farmers in the way they have to manage their risks.

The farming story explains how ancient Peruvian peasants adopted a seemingly puzzling cultivation strategy: instead of growing crops on a large plot of land, they used to cultivate several smaller strips scattered around where they lived. This was of course less convenient to manage, and also reduced overall crop yield (compared to a single large plot), but this “diversification strategy” ensured the peasants a lower risk of starvation, if one of their plot failed (due to rats, thiefs, climate). Since potatoes cannot be saved from one year to the next, planting one large plot only would be the equivalent of “betting the ranch” on that one big trade: one failure, and you’re out of the game.

What is interesting is the unaware sophistication of the Peruvian farmers “diversification strategy”, as studied by an anthropologist. Obviously, an increasing number of strips cultivated had a negative impact on the average potato harvest, but also had a positive impact on the potato harvest variance, by lowering it (i.e. more diversification means lower return potential but with less variability). After-the-facts calculation by anthropologists showed that peasants used to plant just 2 or 3 strips over the theoretical target required to achieve a zero-frequency of starvation years (when total harvest was not high enough to sustain the farmers).

As Diamond concludes:

Peasants do not aim at maximizing long-term averaged yield, instead they only maximize long-term yield insofar as that is consistent with their overriding goal of eliminating their risk of starving in any given year, and throwing in a small safety margin for that calculation.

In the same way, trading is, before all else, a survival game.

The above is a quick summary but you can read most of the foreword in the “Look inside” view on the book Amazon page). I have not read the book itself but it seems to have been reviewed positively.

I have read a few books from Jared Diamond and really enjoyed them and found them interesting. A good one to start with is the most famous Guns, Germs and Steel, which has also been turned into a great National Geographic documentary.

Enjoy your weekend!
~Jez
 

Many combinations...

Following the last study on diversification using a “portfolio randomizer”, I wanted to further explore further the concept of hindsight bias in portfolio selection and how it can impact performance. This short post is an illustration of that concept.

51 Instruments, 40 Picks, How Many Combinations?

The answer is… a lot: there are 47,626,016,970 ways of picking a portfolio of 40 instruments from a total set of 51 (formula is: 51! / [40! x 11!]). Running so many simulations was not practical (!) so I decided to run a fraction of the possible combination (5,000 random iterations). We get a similar set of results as the last study:

This is still for a run of the 20/50 Moving Average cross-over system running from 1990.
Note that the results are slightly different from the run with 40 instruments from the last post, as the position size was greater here (and therefore the “cloud” of CAGR/MaxDD results has moved towards the top-right).

The average performance figures for the systems are as follows:

Isolating portfolios

The next step was to isolate the worst and best cases (circled on the scatter plot) and identify the difference in portfolio composition between the two. Since this is a combination of 40 elements from a set of 51, there can only be 11 differences at a maximum between each portfolio.

Indeed, the “worst” and “best”portfolios share 32 of their 40 components but still exhibit a wide difference in their performance figures (the MAR ratio for example is 3.5 times better for the best case: 1.02 v. 0.29). For reference, the “good part” of the best portfolio (ie its instruments that do not overlap with the other portfolio) are:

• Cattle-Feeder-CME(Floor+Electronic Combined)
• CopperHG-COMEX(Floor Trading Only)
• Euro(Floor+Electronic Combined)-CME
• Gas Oil(Combined)-ICE(IPE)
• IBEX 35 Index-MEFF
• Natural Gas-Henry Hub-NYMEX(Floor+Electronic Combined)
• OMX Helsinki 25-EUREX
• Palm Oil-Crude-MDEX

On the other hand, the “bad part” of the portfolio is:

• Azuki Beans-Red-TGE
• Cocoa-CSCE
• DJ Euro STOXX 50 Index-EUREX
• EURIBOR-3 Mth-EURONEXT(LIFFE)
• Gold-COMEX(Floor Trading Only)
• MSCI Taiwan Index-SGX(SIMEX)
• Silver-COMEX(Floor Trading Only)
• Soybeans-CBT(Floor Trading Only)

To take the comparison to a further extreme, I ran the exact same system over both bad and good portfolios by themselves.

The difference in results is fairly striking:

Good portfolio

Bad portfolio

Robustness Testing

If anything, I believe this illustrates that testing over several portfolio sets might be a good way to identify robustness in system results. If the system only shows good results on specific portfolios, it might simply be a “lucky” outlier.

On Diversification

Finally, there were a few comments on the last post with regards to how to implement diversification. I had only focused on diversification from a portfolio point of view. However I believe that ideally one would diversify with a large set of instruments to trade, different systems covering different timeframes.

One problem is that diversification on all these levels bring on an increase in required starting capital (one likely reason why most Trend Following Wizards have a minimum managed account size in the millions).

So you might have to make a choice in how to apply diversification.

As diversification is really beneficial thanks to the non-correlation it brings, diversifying across different systems could also be a good idea, as systems can be more or less “engineered” to be un-correlated to each other (ie a Trend Following system with a Mean Reversion system).
It is also possible to “trade” a large portfolio without taking all the signals (by using filters or an overall risk/size limiter).
After all, this is something that the Turtles used to do (when they were at full position size they had to skip signals)
Some ideas to think about…
 
 
Credits: Thanks to Trading Blox forum member sluggo for the reminder of how the Turtles used to skip trades, and how filtering trades could enable small accounts to trade a large portfolio – on this thread.

As the cliche goes:

Diversification is the only free lunch on Wall Street.

This is a concept equally shared by Modern Portfolio Theorists and Trend Following Wizards, who usually emphasise the concept – and are often quoted as trading around 100 different types of instrument, if not more.

The State of Trend Following report contains a decent level of diversification with around 50 instruments and I wanted to use this as a base to check the impact of diversification on performance.

The idea is to run the same strategy using a subset of the portfolio (ie less instruments = less diversification) and see how it performs.

The problem, though, in selecting a subset of instruments out of the 51 in the original portfolio is that it could affect performance in the same way as any portfolio selection can (ie you could obtain vastly different results in trading the same system with two different sets of instruments, just by virtue of a “lucky” pick of strong performers).

Historical Performance

First, let’s get a reference point and look at the historical performance of the system chosen for this test: the 20-50 Moving Average system. Below is the performance back-test of that system over the last 20 years with the original portfolio:

Tests with Less Diversification

As mentioned below, the idea is to work on a subset of instruments and compare the results with the initial portfolio. To avoid any sort of data mining/hindsight bias in the portfolio selection, I decided to run a Monte-Carlo-like approach to test the system with multiple instrument subset combinations: instead of picking a single portfolio subset of 25 instruments, I’ll run the system over 1,000 different sub-portfolios, chosen randomly.

In order to get an idea of how gradually diversification affects the performance, I ran the test in three steps:

• sub-portfolio of 15 instruments
• sub-portfolio of 25 instruments
• sub-portfolio of 40 instruments

All instruments are picked at random from the list of 51 instruments in the original portfolio.

Each of the 3,000 runs generated a full system performance record. Below are plotted the CAGR and Max Drawdown for each instance:

Click to zoom in

The original system is also represented as the yellow dot.

Note that the “portfolio randomizer” did not account for any logic in terms of sector allocation. The original portfolio is balanced over several sectors (currencies, energies, rates, agriculturals, etc.) and there is no account for correlation between the different instruments (obviously correlation plays a big role in diversification: there is not much point in having dozens of instruments if they are all strongly correlated). However, over the large number of simulations, the main ideas of the test still come through.

Another point is that the only difference between the different runs were regarding the position sizing of each trade (fixed fractional), which were adjusted to obtain results of similar magnitude in each test (a portfolio with less instruments will require a slightly higher position size to match the return/drawdown rate of a portfolio with more instruments).

Looking at the plot chart, there are two main observations:

• We can see the gradual effect of diversification improving the system results by “moving” the cloud of performance points towards the left (less drawdown) and up (more return).
• The other observation is that the more diversification there is, the lower the deviation in the system results – therefore providing more robustness and less chance of data mining impact from portfolio selection on your back-tests.

Diversification or Why the Coffee Cup Never Jumps

That last point makes me think of an example discussed by Nassim Taleb in his Black Swan explaining the averaging of randomness:

Yet physical reality makes it possible for my coffee cup to jump – very unlikely, but possible. Particles jump around all the time. How come the coffee cup, itself composed of jumping particles, does not? The reason is, simply, that for the cup to jump would require all of the several trillion particles to jump in the same direction, and do so in lockstep several times in a row. This is not going to happen in the lifetime of this universe

Every trade/instrument can be seen as a particle composed of a (large) random element and a smaller edge that we try to extract via a mechanical system.

A portfolio composed of too few instruments would be like drinking your coffee or tea from a cup made up of only a few particles: cups would be jumping around everywhere, making coffee drinking a perilous venture. Same concept applies to trading.

This is the way I see diversification: by adding a large number of mostly random elements, you can ensure that random moves have some cancelling effect on each other so that your “trading cup” never jumps. All that is left is to collect the small edge from all the instruments via your preferred trading strategy(ies).

In effect, this is how casinos operate – and with diversification you somehow get to be the house!
 
 
Credits: The use of a portfolio randomizer and the display of results in a CAGR/MaxDD scatterplot was directly inspired from user sluggo on this Trading Blox forum thread.
 
 

Mount Everest Sunrise - picture from phobus@flickr (CC)

Being a small trader and “taking on” the big funds such as Winton Capital or Renaissance Technologies can seem as arduous as climbing the Everest. You might think: “What chance do I have to even come close to these guys and their army of PhDs? I might just send them a cheque to manage my money”.

Well, maybe it does not require rocket science to experience some success, as some simple mechanical strategies illustrate. Let’s examine the opportunities for the “small fish” trader.

The free lunch

If we consider traditional Trend Following, it pays to have deep pockets. Diversification is often referred to as “the only free lunch in finance”. The problem is that you need to have significant capital to be able to trade a wide array of futures, with possibly several different systems. This makes it hard to the small system trader to benefit from diversification.

The lunch is free only if you can spend big bucks on dinner!

New instruments on the block

However, a few new, and more accessible instruments have appeared in recent years.

Many ETFs and ETCs now exist for most markets now have their dedicated Exchange Traded Instrument. I have recently picked up a good book on the subject (A Practical Guide to ETF Trading Systems) and it does provide good ideas, especially on money management and how to increase returns without the leverage that can be found in the futures world (WARNING: I would not use leveraged ETFs for anything else than day-trading as they exhibit volatility decay).

The advent of spread betting (mostly in the UK) also allows retail traders to “bet” on financial markets with smaller starting positions than in futures trading but with similar leverage.

Finally, Forex trading has been made easier to access for retail traders, with new firms literally invading the scene in the last 10 years (OANDA even offers trading in any size starting at one dollar!).

Although not ideal, these new instruments help lower the barriers to entry and allow small traders to join the free lunch diversification party.

No footprints

Large funds have to deal with the extra complexity that their size entails. Their large orders and positions can weigh on the markets, impacting them negatively and forcing them to have dedicated efforts to execution algorithms development.

As a small trader, you are free from most of these constraints and can just get in and out of the market more easily. More importantly, this also gives you access to more markets.

Let’s check the monthly futures performance (with the new exciting tool from FinViz):

FinViz new futures tool showing some strong trends

Lumber had a particularly good month but given the size of this market, I doubt that any Trend Following Wizard significantly profited from that trend. Whereas, as a smaller trader, you could have.

Additionally I believe that these smaller, more exotic markets, exhibit less efficiency and therefore more opportunities to exploit them.

A big headstart: no fees

Even if you cannot match the performance of the large funds, the fact that you do not have to incur management/incentive fees when trading your own account is a big advantage. The difference can add up to a lot with compounding (deemed as “the most powerful force in the universe” by Albert Einstein some urban myth inventors).

No pressure

Another aspect that impedes fund managers “freedom” is the aversion of investors to drawdowns. However, reward is indissociable from risk and/or volatility. This means that managers will often tune down their strategy to offer a “less risky” but more appealing profile, at the expense of better returns. As an independent trader, you are free to decide your own tolerance level for risk and associated performance targets. You can be as aggressive as you want to be (for as long as the market keeps you alive ^_^).

a matter of personality

Finally, I believe it boils down to your personality. If you are an enterprising character, you will more likely be attracted to building and trading your own system. It might even be an irrational proposition, but I am sure some traders would prefer to invest a lot of time developing and then trading a system even if it achieved a slightly lower performance than the top Trend Following Wizards’ funds. But who said that trading in the markets was rational?…