Ralph Vince‘s book Handbook of Portfolio Mathematics has been shamefully lying untouched on my desk for a few months… I started reading it but never finished it.
I recently found a 30-page paper introducing the ideas and principles of his Leverage Space Model. I thought reading it might be a good way to get back into Vince’s material.
Follows a summary of the paper (PDF download link), which is maths-less (only concepts and principles are discussed). It is a good introduction to Ralph Vince theories.
Vince’s Optimal f
This is what Vince is famous for. It is basically a way to determine trading quantity (aka leverage) using the probability distributions of the trade outcomes.
If f represents the fraction of capital to wager (risk) on each bet (trade), the optimal value is the one which optimises the geometric growth of the bankroll (account balance).
In his previous books, Vince has defined the formula to determine the optimal f. The first part of the paper discusses the optimal f concept and is a good introduction for the non-initiated (showing how over-betting on a game with positive expectancy can and will result in a loss).
Leverage Space Model promises
The optimal f section discusses a single-component approach whereas the Leverage Space Model deals with multiple components portfolio.
It is presented as an improvement on the Modern Portfolio Theory, briefly discussed. This is based on the following advantages:
- Risk is defined as drawdown (instead of variance in the MPT)
- The fallacy and danger of correlation is eliminated
- Valid for any distributional form – Fat-tails are addressed
- The model is all about Leverage, which is not addressed in the MPT model.
The model starts by building a multi-dimensional terrain, drawing the overall expected return, based on multiple combinations of components in the portfolio and their respective f-values.
The maximum portfolio growth is located at the peak of the terrain, resulting from the specific corresponding 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.
The Risk Aspect
So far, the model has only looked at returns. To introduce the risk component, you must determine your maximum allowed drawdown. This is a hard and fast rule: no combination should breach that limit.
Using a derivation of the risk of ruin, the model computes the risk of maximum drawdown for each set of f-values (for a specific timeline – as, in the long run, the risk of drawdown tends to 100%). If the risk of drawdown is too high, the specific f-values combination is ignored.
In practice, the initial terrain is truncated: by removing all points breaching the maximum drawdown threshold.
Vince implements a genetic algorithm to calculate the terrain, by initially calculating the expected return for each set of f-values, and secondly by running the maximum drawdown test on this same set. Once the whole set combination has been run through, the terrain is built (including truncations). The the aim is then to find the optimal set (highest return with lowest f-values).
Comments and Extra Info
The paper is rather short and does not deal with any of the maths behind the models. For this you’d have to get yourself a copy of the Handbook of Portfolio Mathematics which introduces the model in more detail or Vince’s latest book, dedicated to the Leverage Space Model, which has had a not-so-positive review by Max Dama.
The ideas in the paper are an interesting take on position sizing. Vince uses a simple objective/bliss function (CAGR with a binary risk/drawdown filter) to evaluate all possible scenarios of portfolio allocation/leverage. It might be interesting to use the concepts of the model with your own bliss function recipe.
One of Vince’s claim that the MPT does not address leverage sounds a bit simplistic – surely the percentage of Cash as an asset in the portfolio is an implicit measure of leverage. On the other hand, the approach on correlation/joint probability of scenarios sounds interesting and seems to go in the right direction. As Vince says:
Counting on correlation fails you when you need it the most.
Another point that seems missed out is how the model handles non-stationarity of the market. Vince mentions the chronomorphism of market prices distributions (i.e. they change with time) and even draws a betting comparison with blackjack – in which the optimal f curve changes for each card dealt. However there is no mention of how the model takes an adaptive approach to these chronomorphic distributions.
Vince’s homepage contains a link to the java software that implements his model (needs to register/leave email to download) and another one with a spreadsheet example. I have not had time to take a serious look at all those. Please let me know your feedback if you do.
Joshua Ulrich – blogger and reader of this blog (hello there: finally got round to adding you to the blogroll!) – is collaborating with Ralph Vince to port the Leverage Space Model to the R platform. His FOSS Trading blog is definitely worth a read too.