picture credits: WilWheaton@flickr

Several CTAs or fund managers offer a standard version of their fund, along with a leveraged version (called enhanced risk, 2x or 3x fund, etc.). However a simple performance comparison of the leveraged option against the standard option usually makes it obvious that the former does not offer a simple performance multiplier of latter.

I was looking at Conquest Capital Group and their MFS fund (based on the Trend Following benchmark used in their paper discussed here), which offers two such options: their standard fund and a 3x option.

The main fund, since inception (2004), returns 56% (net of fees) with a max drawdown of 14%. Their 3x leveraged option, over the same period, returns 85% with a max drawdown of 47%. The risk is indeed tripled, but the reward falls fairly short of it. When removing the fees on both funds (1% for the standard fund and 3% on the leveraged fund), the performances are 66% vs. 120%. This is just an example. Most CTAs are similar in that respect and it highlights some effects of leverage.

Leverage is not a magic bullet

A similar concept has become more mainstream with the recent apparition of leveraged ETFs and the realisation by some investors of the large volatility decay that they incur (when they are held on a long term-basis, i.e. anything longer than intra-day). Check the long-term charts of FAS and FAZ (3x leveraged bullish and bearish financial ETFs): the only long-term profitable trade would be to short both, to cash in on the volatility decay while being hedged (since Nov 08 they are down respectively 58% and 98%).

This is simply due to the design of these instruments, which aim to replicate and triple the daily returns of the tracked benchmark. This highlights a fact about leverage: multiplying the arithmetic returns will not result in the same multiplication of the geometric returns.

Leverage with Position Sizing

A typical way of leveraging a trading strategy is to increase the position size, and the resulting risk and return for each trade.

Assuming a fractional betting strategy for position sizing, the leverage dictated by the value of the fraction of capital risked on each trade will impact the overall average geometric return. Theories describing this phenomenon are the Kelly criterion and Ralph Vince’s Optimal f.

One of the main implications of this type of Money Management is that, for every strategy, there is an optimal fractional position size to maximize the (past) geometric return (and future if you assume that the past is a good representation of the future). Any fractional position size higher than this optimal value would result in a lower return.

Any strategy (with its resulting stream of returns) has an embedded maximum leverage, which can be defined with the optimal f.

Notional funding: another type of Leverage

Notional funding can be compared to trading with imaginary money. Typically, CTAs also offer notional funding: they trade your account based on an agreed notional amount, which is different from the actual funds in the account. For example, you could send 100k to your CTA and instruct them to trade it as if it were a 300k account. Or you could do the same thing with your own trading system.

One could intuitively think that this is exactly the same thing as tripling the position size but there is a difference.

Let’s consider this simple example with a strategy producing two consecutive trades of +10% and -5%:

The notional-funded account would close at 300 x 1.10 x 0.95 = 313.50. This would result in a gain of 13.50 on actual funds of 100: +13.50%, which is exactly triple the return one would get on a fully-funded, unleveraged account (100 x 1.10 x 0.95 = 104.50 for a 4.5% return)

Leveraging by tripling the position size on an account of 100 would result in two consecutive trades of +30% and -15%. Final balance would be: 100 x 1.30 x 0.85 = 110.50 – or a +10.50% return.

Initially, notional funding appears a better solution to the leverage issue as it does not suffer from the volatility decay or erosion of returns introduced by increasing position size.

Issues with Notional Funding: Cost

But funding always comes at a cost, pretty much in the same way as an overdraft gets charged by your bank. Another way to look at notional funding is to compare it to borrowing trading capital. The higher ratio of your notional account you borrow (higher leverage), the more the cost of borrowing will impede your trading returns.

In practice, you do not really borrow any funds (only by the power of imagination) but this practice still ends up impacting your return when you start taking into consideration the return on margin.

Impact of Margin Interest on Trend Following Returns

This paper from EDHEC Risk (PDF) looks at Trend Following/Managed Futures performance and presents an interesting breakdown of the overall return of such strategy. Assuming interest being paid at T-bill rates on the margin used for trading, it represents the bulk of the returns compared to actual Trend Following gains and rebalancing gains.

This is one of the reasons for the hidden cost of notional funding: a notional-funded account would enjoy the same Trend Following and rebalancing gains as a fully-funded account of the same size, but only a fraction of the return on margin (which is based on the actual account size).

To illustrate that point, below is a chart showing the impact of fees and margin interest on an arbitrary performance curve:

Notice the fairly sizable difference between taking return on margin into account or not (red v. blue curves). The green curve adds fees at 1% annually. The return on margin was assumed to be the T-bill rate for that month.

Risk and Margin Requirements

Another issue of Notional funding used as leverage are the constraints imposed by the underlying strategy.

Any strategy requires a minimum margin commitment to support the positions. Effectively the Margin-to-Equity ratio will dictate the maximum leverage one can use to trade a strategy.

The Drawdown is also a leverage-limiting factor: the more risk the strategy generates (higher drawdowns), the less leverage can be applied. If a strategy regularly exhibits drawdowns at the 40% level, there is a always the possibility that such drawdown appears at the beginning of trading the strategy. Based on the level of leverage, a notional-funded account might not have the time to build enough equity cushion to withstand the drawdown, which would result in the actual account funds going to 0 or a margin call.

Note that in this case, the sequence of trade returns has an impact on the outcome: if the strategy produces gains of 100% followed by a drawdown of 40% a 3x leverage via notional funding would still result in a gain of 60% (300 x 2 x 0.6 = 360, or a profit of 60 with actual funds of 100). If the 40% drawdown appears first, the notional account would shrink to 180, which would result in a negative actual account balance (trading would have to be stopped before then).

Leverage Comparisons

With these considerations and the benefit of hindsight, here is a comparison between the same arbitrary strategy as above (fees and interest included) traded with:

• no leverage
• 6x leverage using notional funding
• 6x leverage using position sizing

The notional funding appears to be the better option. However the position sizing leverage is independent of the order in the sequence of returns – as opposed to the notional funding leverage. If that nasty current drawdown (which is the largest one historically) had appeared at the beginning of trading and carried on further to reach 17%, the notional-funded account would have been wiped out.

The next chart highlights the impact of leverage on the difference between the two types of leverage for that specific strategy:

The target curve represents a simple multiplier (equal to the leverage factor) of the unleveraged performance (which, as we have shown is not attainable). The position sizing leverage clearly exhibits the behaviour discussed in Optimal f theories with the return breaking down past the optimal value.

Hopefully, this gives you a few ideas about how to work leverage in your trading strategies or when sending funds to CTAs. Taking the time to look into it has cleared up a few points for me.

Regular readers might think that I suffer from backtesting-software-indecision-itis. Having first settled for TradersStudio, I then evaluated (and purchased) AmiBroker and found that it was 25 times faster than TradersStudio (at least for the calculation of the e-ratio). However, AmiBroker is not really geared towards true portfolio allocation testing with Futures and could not just replace TradersStudio – so I purchased it as a (cheap: $199) complement to it.

Why TradersStudio in the first place?

During my first round of evaluation, I did hesitate between TradersStudio and Trading Blox. At the time, it appeared that there was not a huge difference in functionality but a substantial price difference ($499 for TradersStudio, $3,000 for the full version of Trading Blox Builder). And this is how the choice was made.

However, I never really got past my TraderStudio’s first (not so good) impressions. Ultimately, I find the platform awkward to work with, documentation rather poor and the user community is very small.

So I decided to give Trading Blox another go and test their latest trial version (v3.3), and give you a teaser review of it.

Trading Blox: friendly, efficient, fast, professional

Trading Blox is vastly superior in terms of user interface “friendliness” and efficiency (love that script management/edit screen!). This makes the documentation lookup less necessary (and in any case, it is rather better).

The simulation runs are also very fast (300 stepped parameter tests under 7 minutes) and the software comes pre-packed with about a dozen ready-coded systems including the famous Turtle Trading system.

Finally, the numerous backtest options (slippage, commission, rollover slippage, volume, interest, etc.) should simulate trading reality much more closely.

Overall, it feels that the difference between Trading Blox and TradersStudio can be summed up by Pro vs. Amateur: both good at what they do, but playing in different leagues.

User community

Trading Blox forum is very good, with top-notch contributors. I joined it a few months ago and the discussion there is top-level, be it on all aspects of trading in general, backtesting, Data problems, Trading Blox questions, etc. It also has a marketplace where users can exchange code/systems, etc. This forum played a big part in my decision to re-consider Trading Blox (TradersStudio’s own forum and yahoo user group are barely ticking…).

In closing: screenshots

I feel I am about to give in and “cut my losses short” with TradersStudio and redeploy my resources towards Trading Blox. In the end, it is a “time vs dollar trade” and I feel that the initial outlay will give a great payback (in time savings and progress made). After all, automated trading is a business and one should not shy away from the essential investments.

Tomorrow, I should post a detailed system test using Trading Blox; but for now please find below some screenshots of the software (click to zoom in):

Result Reports

rich choice in general options

System Editor

Blox Editor

Heat map for stepped parameter

Robustness in trading is a tough beast to tame and understand. The more “robust” the research and development process, the better (read: robust) the results ought to be, right? With this in mind, I decided to test robust “tools” within the actual mechanical trading strategy itself.

The moving average indicator is so ubiquitous in trading that most folks (me included) use it without second thoughts. Its legacy probably dates from the era of expensive and complicated computing (it is relatively inexpensive to compute), so I wanted to revisit its hegemony – and give it a run for its money: by pitching it against a moving median indicator (on the basis of better statistical robustness for the latter).

Could it be that a moving median is actually a better indicator than the moving average?…

The experiment

To find out I used a basic and simple mechanical trading strategy: the Moving Average Crossover. This trading systems is always in the market, buys when the fast moving average crosses over the slow moving average and sells short when the fast average crosses under the slow average.

The second system would be a Moving Median Crossover. You guessed it: the same system, but replacing the average by the median.

The markets tested were a random collection of 17 Futures daily prices (proportionally back-adjusted contracts) – all going back as far as CSI history goes (1920′s for Wheat!):

 
The money management for both systems is to trade each instrument in a separate independent sub-account, fully funded (i.e. no leverage used) with profit re-invested. All commissions or slippage are ignored.

The main interest of the experiment is the robustness of each indicator. To quantify this, each system is run over 9 combinations of parameters for the Golden Cross (fast indicator values: 45, 50 and 55 days; slow indicator values: 180, 200 and 220 days). A measure of the robustness of the indicator is the uniformity of the results over the 9 combinations.

The results

Below are the total returns for both systems over each parameter set:

 
At first glance, it appears that the Moving Median indicator significantly under-performs the standard Moving Average indicator for these crossover systems.

Let’s look a bit deeper at the results with some basic statistical analysis:

 
The calculation confirms the under-performance of the Moving Median Crossover system. What about robustness you ask? Well, the Moving Median still scores worse than the Moving Average on both measures of uniformity/dispersion: the standard Coefficient of Variation (0.64 v 0.68) and its alternative cousin based on Median and Median Absolute Deviation (0.36 v 0.45): The Moving Average System produces more uniform (robust?) results!

Below is also a histogram of all 288 individual returns (per market per parameter combination, i.e. Wheat 180/45, Wheat 200/50, Silver 200/50, etc.):

There is clearly more blue presence on the left side of the chart and more red one on the right side…

A potential explanation

Using some inductive logic (warning: this might be dangerous when dealing with data from Extremistan^*), I started eye-balling the charts in search for some clues as to why the Median under-performs the Average. Below is an example of what I found:

Crossovers for Cocoa 2004-2010

The chart above only shows Moving Averages and Moving Medians (the prices have been removed to make the picture clearer). Average and Median seem to closely follow each other both on slow and fast sides. Indeed the bulk of the trades take place at roughly the same time (i.e. they both detect large trends fairly similarly).

However, if we zoom in over that red-circled congested area:

Zoomed-in portion of Cocoa chart

We can see that the Median Crossover system generates more signals than the Moving Average one (9 v 5). Trend following systems notoriously make big bucks in large moves but lose money in trend-less, range-bound markets – like the one being zoomed into. If the Moving Median Crossover system is more active in these sort of markets it will generate more losing trades while capturing similar big winners to the Moving Average Crossover system.

Intuitively, it could be hypothesized that the Moving Average evolves in a smoother manner and will generate smoother curves with less erratic moves and consequently less losing trades during trend-less markets – while the Moving Median does not generate a significant edge in detecting large trends.

One test is hardly enough to provide siginificant evidence, however this should give us some insights in the nature of the Moving Median indicator. The first insights being no increase in robustness and a drop in performance (when comparing total returns).

 
 
^*Extremistan: concept popularised by Nassim Taleb to describe the “province” where the total can be conceivably impacted by a single observation (e.g. financial data, wealth distribution). The opposite is Mediocristan: the province dominated by the mediocre, with few extreme successes or failures. No single observation can meaningfully affect the aggregate (e.g. human height and weight distribution). The bell curve is grounded in Mediocristan. There is a qualitative difference between Gaussians and scalable laws, much like gas and water.

For more info on Taleb’s terms, check his Fooled by Randomness glossary (PDF).

• Broker Account – The starting point to trade in the markets
• Live Market Data – To feed to your trading robot so that it can generate trading signals. Most brokers provide market data with proprietary or third-party technology- although market data can also be obtained from an independent vendor (e.g. eSignal).
• Order Routing – To transmit your orders to the exchange. These can be proprietary to the executing broker or third-party based (e.g. Zen Fire).
• Broker Trading Platform – To access your account information, place orders, etc.
• Charting Platform – Sometimes the broker platform charting capabilities are mediocre and an independent charting platform is required (e.g. eSignal)
• Signal Generation Platform – The actual trading robot: it analyses market data, account and positions information and implements the automated trading strategies to generate trade management signals (i.e. Buy / Sell / Exit, etc.).
• Excecution Platform – Receives trade signals and forwards them to the order routing.
• Platform Hosting – You can host the trading robot on your local machine, host it in a dedicated rented server or entrust a specialised broker to host and run your trading robot.
• Historical Market Data – Used as source for back-testing trading strategies
• Strategy Development Application – Allows for coding, optimisation, back-test and result analysis of trading strategies.
• Statistical Analysis package – for in-depth statistical analysis of back-testing results.

Some of these distinctions are physical, some are logical. For example, TradeStation packs many of the points above into one system: a broker account and a trading platform that allows you to:
Access live market data + Visualise price charts + Automate trading strategies that generate signals + Route the trading signals as orders on the exchange + Access account information + Store historical data + Back-test strategies

Sounds like it fits the bill perfectly, doesn’t it?
Well let’s look at the areas you need to consider when deciding on your automated platform.

Type of broker

Different issues to consider: is the broker a clearing broker, a non-clearing FCM or an introducing broker? If the latter is it an independent introducing broker or a guaranteed introducing broker (backed by a clearer)? It would seem that the closer to the exchange you broker is (in terms of relationship), the better/safer it is. See Anatomy of a Futures transaction for more detail on the different types of brokers.

Markets supported

Every broker offers access to different products and different markets. For example Interactive Brokers offers one of most complete coverage (worldwide Futures, Options, Equites and Forex) all “housed” under the same Universal Account. Other brokers only offer access to specific products/markets.

Latency/Speed

For some type of trading strategy, this can have a large impact and various platforms/feeds offer different levels of performance. This has led to specialist companies such as Zen Fire or Trading Technologies – which locate their servers very close to the exchange – achieving speed and reliability for data feed and order routing. They offer their services to brokers who can in turn offer it to their clients.

Development Language

This is mostly a matter of personal preference, experience and expertise. TradeStation has been around for longer and a big collection of Easy Language scripts are available for re-use while NinjaTrader, for example, uses C# and CQG Trader their own language.

Strategy Complexity vs. Platform Functionality

Most of the automated trading platforms that offer back-testing functionality lack sophistication of dedicated applications such as Mechanica, TraderStudio or Trading Blox. For example portfolio testing is usually not available in the live trading platforms. This might work for some simple strategies but not for more complex Money Management ones.

Hosting

You can run the trading robot on your machine, which makes you subject to power and connection failures or you can choose to rent a server to host your robot. Some brokers also offer trading strategy hosting and execution on their own servers.

Charting

Some specialised platforms offer better charting capabilities than the standard trading platforms and can be used as a standalone charting application. Some, such as eSignal, also offer a data feed.

Costs

An obvious one but between platform costs, execution costs, hardware, etc. there exists a wide range between bottom-end and top-end offerings.

What/how to choose?

While researching for this article I have come across many different packages offering different solutions. One of the best ways to help you decide on a solution that makes sense to you is to list your goals and cross-check each platform against them in this fashion (PDF doc).

There are endless possibilities for combining all the differenty packages. Just for fun I tried to “virtually build” the opposite of an all-in-one package such as TradeStation (which will probably not address most automated trader goals) – here is one “wacky” implementation.

A trader decides to use TradeStation as a signal generating platform. However she does not want to use TradeStation data feed and instead decides to go for the eSignal package integrating the broker Dorman Trading and the Zen-Fire connection for market data and a charting platform. In order to route the market data to TradeStation, she needs a bridge application - OwnData from TS Support for example. The backup feed solution would be TradeStation data feed. For the execution side of things, our trader decides to send the trading signals generated by TradeStation to NinjaTrader, which can route the orders to the exchange through a broker. The primary route is through Velocity Futures broker using Trading Technologies order routing, while the secondary route is through Interactive Brokers via their TWS trading platform and API! Additionally, the strategy research and testing is performed with Mechanica using CQG tick data while the results are analysed using R.

Conclusion

Sorry to end up on a cliche but there are no silver bullet to making the choice. If you take away one point is that you need to list your own requirements clearly and make the choice for yourself based on them.

Check that 60-page thread at EliteTrader if you want an endless discussion as to which is the best platform/architecture…

Software and manuals

You can download a fully-functioning Amibroker demo (you cannot with TraderStudio and even when you buy it you have to wait for CDs by post!) which contains some limitations (i.e no more than 5 markets back-tested at a time, etc.).
The manuals are all online and very thorough, complemented with additional articles, presentations and other materials. This makes it very handy (again compared to TradersStudio printed 300 page manual – yet incomplete) as you can search them electronically to look for exactly what you need.

Large Community

The Amibroker community seems much wider and as a result there is loads of available scripts for re-use. There is actually a whole library hosted on amibroker website.
There is also much, much more information available on the internet. As a sample test I googled “Amibroker Donchian” vs. “TradersStudio Donchian”: 23,200 results vs. 17 (including this blog!).
Finally the yahoo group is much more active. There are about 10 times more daily messages (although the TradersStudio one can go days without getting a single message). As an example I posted a question related to the custom backtester and got a useful answer the next day.

The platform

It takes a bit of time to get used to the concept and principles of Amibroker. It is quite different from TradersStudio. For example, all afl files are self-contained and might implement indicator, system, back-test procedure, scan and exploration code all at once (although only one part really runs at once – alightly confusing at first). In TradersStudio you can also define functions to be called in other code files; this does not appear possible in Amibroker (you would have to copy/paste the code over and over again). Both platforms allow you to build COM dlls to code up your functions.

The GUI is different but I would not say better or worse than TradersStudio.The charting forms a more central part of the Amibroker platform and just firing up a chart with several indicators is pretty quick. At first glance the money management/portfolio allocation does not appear very rich in Amibroker (in terms of functionality) but I would have to do more testing to confirm this.

AmiBroker screenshot

The language to create your own indicators, systems, etc. (AFL: Amibroker Formula Language) is based on C and not very hard to pick up especially with the very useful in-line help – it does help to read the tutorials first (!) to get a grasp of the main keywords/built-in functions.

Data loading

Loading the data extracted from CSI Unfair Advantage was fairly straight-forward and there seems to be a bunch of ready-made interfaces with other data vendors in addition to the Amiquote utility – which allows you import quotes in Amibroker. It seems that there is more flexibility in the type of data fields that can be loaded.

Conclusion

Overall I was pretty pleased at what I was able to achieve in a short amount of time. For some reason I found it very hard to get into TradersStudio whereas Amibroker was easier to tackle (once you understand its working concept).
Obviously I have not explored all the functionalities of either software and this is definitely not an exhaustive review. As a result of all this I will be buying a copy of Amibroker to complement (or replace?) TradersStudio. I am sure both platforms each have their pros and cons so having both is probably a good idea (and not a very costly one since Amibroker costs only $200!).