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Risk-Opportunity Analysis

November 25th, 2010 · 11 Comments · Money Management

leverage terrain

I have been travelling in the last three weeks. One of my destinations was Tampa, Florida, where I attended Ralph Vince‘s Risk-Opportunity Analysis course, over a weekend (check here for a presentation of the course).
My main objective for attending was to strengthen my knowledge of Money Management/Position Sizing and my understanding of the concepts presented in Vince’s books.
The secondary objective was to gain an understanding of how to practically apply these concepts to Trend Following systems, and check what improvements the Leverage Space Model framework could provide.

This is not a full review of the course but more of a “teaser” post giving you a “heads-up” that several posts covering this topic will be coming on the blog – as I explore and test the concepts on real-life trading systems.

The Course

The course was dense and covered a lot of material with all of the mathematical formulas behind the concepts explained in the Leverage Space paper that was discussed on this blog. In a way, there is a large overlap with the contents of his Leverage Space Trading Model book, which expands on the concepts in the paper, with the Mathematics behind the concepts. The main ideas and concepts are the same.

The pivotal concept in the framework that Vince introduces is the multi-dimensional leverage terrain, which draws the return of a portfolio based on the leverage (position size) applied to each instrument.

In this example the model builds the terrain for 2 simultaneous coin-toss with a payoff of 2:1

In this example the model builds the terrain for 2 simultaneous coin-toss with a payoff of 2:1. The x and y axis represent the respective f-values (leverage) for each of the bets/trades - while the z-axis (vertical) represents the expected return

The maximum portfolio growth is located at the peak of the terrain, resulting from the specific corresponding leverage (or f-values) combination. The terrain construction does not take into account correlation between the instruments – instead, the model uses the joint probability of two scenarios occurring simultaneously, dictated by the price data history.

During the course Vince showed us several ways to “navigate” the terrain and determining the corresponding leverage factors, based on different objectives: geometric return, risk of drawdown and probability of being profitable in the next “period”. Another concept developed was the idea of investment horizon.

The Software

The other aspect covered in the course was the software that implements the Leverage Space Model calculations, which you would typically use to evaluate the optimal combination of leverage for your portfolio based on your criteria/objective function.

We walked through several simple examples from the course using both software packages that implement the Leverage Space Model concepts

Vince used to make available on his homepage a java application that implemented the model. This is proprietary though and when I last quickly checked I could not see the link for it any more. You might have some luck obtaining a copy by emailing him.

However, Josh Ulrich, the author of the FOSS Trading blog and several R packages has implemented the Leverage Space Model in a dedicated R package. The implementation is actually faster than the Java software (so much faster that Vince’s java app now generates R commands to run the LSPM package functions instead of its own optimizer).

Josh was there in Tampa and it was great meeting him too. He definitely has a great handle on the Leverage Space Model and I strongly recommend following his blog if you are interested in this material. Take a look now if you are after more specific examples on how to get started with the package (which can be found on R-forge repository).

Next Steps

If I have a criticism about the course, it would be regarding the format. I would have liked to spend less time on the Maths behind the concepts (most of it is covered in the book anyway) and spend more time in a “workshop” format where we could have investigated the software with some of our specific cases.
I do not mind doing some homework on this after the course, and the fact that there is a google group where attendees can ask questions is useful, but being able to do this “in person” is probably better.

It has left me hungry for more (in a good way) and I am keen to explore some of the concepts more in detail. I anticipate several posts looking into this from a practical point of view in the next few weeks/months.

In the mean time, if you fancy getting started on this topic, you could take a quick look at Vince’s paper – in which he has managed to distill his ideas in a short, manageable 30 pages. – or a more in-depth look by getting his latest book on the Leverage Space Model. In any case you might want to get started on the software side of things by downloading the R package. It is very easy to get started with it.

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11 Comments so far ↓

  • Tal

    Shouds very interesting I will take a look on this paper. Do you know if anyone developed this tool woth Matlab as well?

  • Jez Liberty

    Tal – Vince did not mention any Matlab implementation so I do not think so.

  • Bill Chen

    Thanks for the introduction to this method.

    I had a quick look at the paper and it appears to me like a lot of hand waving. It starts with an attempt to apply concepts from Relativity Theory in physics (cones, space-time, etc.) to investments but what follows is more or less logically disconnected. I am looking forward to a few real and practical examples of how this applies to the real world of investing. One problem I can see right away is the fact that the real drawdown is a big unknown. The recent flash crash is an indication that even the best drawdown estimate is not a good risk measure for trading. Regardless, the use of drawdown values to calculate position size is a very old concept and I fail to see anything new here other than the introduction of fancy terminology and display of 3-D plots. As I said, a few real examples will show whether this is of any real use.

  • Jez Liberty

    I agree with the comment. The methods presented by Vince are based on historical data and there is always the uncertainty about what the future holds and these methods do not provide a magic bullet to this issue.
    Anyway – I hope you enjoy the future posts with practical applications.

  • Zack

    I just wanted to mention I’ve been following your blog for a long time now and have been very impressed. I’ve used Vince’s optimal-F and some of the runs tests from his Handbook of Portfolio Mathematics as a part of evaluating my systems for a while. In my experience, the largest drawdown tends to turn out about twice the optimal-F in $ (though that may be an artifact of my futures systems – it does seem to hold at the daily and minute level).
    I’ve moved on to longer timeframes recently and stocks, and have hit a wall in trying to formulate the “joint probabilities” of the LSM.
    What do you do when you have 10 stocks held simultaneously, but the trades are closed out on different days? I’ve considered mark-to-market, but that is not realistic in that it is not efficient to adjust daily with my trading. This induces an unrealistic upward bias on the results. But, I can’t use closed trades as they obviouly to do not align. Did he mention what to do in his seminar? It was disturbingly absent from his book on the LSM.
    Sorry to ramble – just trying to be detailed.

  • Jez Liberty

    Zack – I did have the same reaction during the course and this is indeed a problem of the methods presented by Vince – who briefly discussed this during the course. Basically the advice there was to use equity curves of systems or marketsystems (equity curves of each market x system combination)
    I have to admit that his model gave me the impression that it was more akin to a “portfolio optimizer” (ie a competitor to MVO portfolio construction for example) where instruments are held on a continuous basis than a position sizing method for trading systems.
    But my goal is to try and see how this can be adapted for these types of problems so stay tuned in the next few weeks..
    ps: thanks for the comments on the blog

  • Scott

    Totally off this topic, but how would I obtain historical spread data for euro dollars? For instance dec, red dec spread off of CSI?


  • Jez Liberty

    I don’t believe CSI offers spread historical data so you’d probably have to build it yourself – which you cannot really do with EOD data (unless you are only looking at the close spread).
    Spreads is an area, which I believe can offer additional diversification (with potentially lower correlation than other straight instruments). Adding them to a TF portfolio would probably be beneficial (something I want to test at some point…)

  • Fred


    I read the article and agree with some of Ralph’s observations regarding correlation. Correlations are not static and are therefore problematic when incorporating into a trading system design.

    I also agree that risk is not volatility but is more closely associated with maximum drawdown. As a system designer that has an ETF trend trading system on, I can assure you that even if you had a system that generated a 50% return/year for three years in a row but then had a 20% drawdown the criticism will be overwhelming.

  • Fred

    Jez: Did Ralph indicate how many money managers are using his techniques? You can talk about this stuff until you are blue in the face but your best learning experience will come from put trading theories into practice and, if you are brave enough, putting the trades out there for the public to see (e.g. Nothing forces you to focus on your trading system than having your own money on the line and allowing the public to view your performance!

  • Jez Liberty

    Vince did not mention any specifics on how many institutions were using his model – he simply referred to some of his clients for which ha had done some consulting work..
    Agree on putting your performance public: it’s the best test there is

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