Adaptive Position Size

Position sizing is very important in any style of trading, being it discretionary, systematic or fully automated, and can easily be the determinant factor in whether your trading is profitable or not.
In regards to this, I found some interesting points in what David Varadi says in his excellent blog:
http://cssanalytics.wordpress.com/2012/03/07/adaptive-percentile-position-sizing/.
For the lazy ones, he is basically talking about investing a fixed percentage of your capital determined by the probability distribution of returns.

I want to take a little step back from this, and clearly highlight the presence of 3 different but mutually dependent layers on position sizes:

1) How much to invest given your current target and stop loss (or, if you don’t set target and stop levels beforehand, given the expected gain per unit traded) ;

The idea is that first you want to make your strategy risk a fixed dollar amount regardless of any adaptive parameter:

position_size = round(amount_to_risk_in_ticks/n_ticks_you_can_lose_today)

This could be seen as making your position sizing market neutral.

2) How much to invest given the current expected “edge” compared to the historic one (i.e. invest more if in current market environment your “edge” is increased);

You can now have a layer (multiplicative/additive variable) that modifies how much the strategy bets according to how the strategy is expected to perform. This kind of analysis is necessarily tricky – one way to do it is to regress your strategy returns against different variables, depending on the intrinsic characteristics of the strategy (examples could be volatility, market average returns, correlation of traded asset with assets, etc…).
If the strategy doesn’t have a “degree of confidence” indicator, it means you are implicitly assuming the strategy distribution of returns to be constant over time.

3) How much capital you allocate in each strategy as a percentage of your wealth;

The final layer is a multiplicative variable linked to your capital (initial and current) and the other strategies in your portfolio. This could be considered a classic asset allocation problem and cold be addressed using a fractional Kelly Criterion: http://en.wikipedia.org/wiki/Kelly_criterion

If done properly, each of the 3 points above should increase the profitability of your strategy (or at least reduce volatility of returns…).
What is more, keeping in mind the presence of these 3 different aspects (even if then you model them jointly, as CSS Analytics does) allows you to better understand what’s going on inside your grey box, something that can never be overvalued.

Andrea

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About mathtrading

My name is Andrea La Rosa and I am a quant trader based in the UK. In the past I worked as a quant in the prop desk of an investment bank, before deciding to fully dedicate myself to quantitative trading.
This entry was posted in On backtesting, Trading Strategies Design and tagged , . Bookmark the permalink.

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