# Position sizing for quant analytics

(Last Updated On: March 6, 2012)

Position sizing for quant analytics

Say you did your homework and you have a strategy with relatively stable returns. What position sizing logic do you use? I am only interested in actual trading experience, not in a theoretical discussion. Is there any method that in your trading experience was better than the stereotypical 1 or 2% per trade fixed fractional position sizing?

In a way your question is the most fundamental of all as the evolving position size or how you manage your stock inventory over time is the most critical. I think you should accept theoretical points of view since if a position sizing algorithm is theoretically impractical or unfeasible; why should it be worth anything in real life trading? And a lot of real life position sizing algorithm are based on flawed theoretical premises. What follows is on the premise that one needs at least to beat the Buy & Hold, otherwise why do all the work.

Fixed fractional position sizing at the 1 or 2% level is theoretically almost impossible to implement at the discretionary level. Trading simultaneously 50 to 100 positions at a time requires more than fast fingers. Automation seems to be the only solution. I state this on the premise that a portfolio needs close to a 100% market exposure to benefit from long term price appreciation, or just appreciation for that matter. Under exposure to the market is the main reason for long term under-performance. If you put only 50% of your portfolio capital to work for 50% of the time, how can it outperform full market exposure?

And if you need to be automated, just to make it practical, then the whole process of finding profitable trading procedures becomes crucial. And if theoretically your discretionary procedures can not be automated for what ever reason then one should not be surprised that the resulting trading script does not produce the expected results.

http://www.seykota.com/tribe/risk/index.htm

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We apply a fixed position size for all components of the portfolio as a % of total AuM (AuM = assets allocated to portfolio * the leverage). So, if you have allocated \$ 1 mio to the portfolio and you have 10 components, each position is worth \$ 100k * leverage.

Variable position sizing, depending on the volatility of each currency pair (fx portfolio) did not significantly impact the overall return and just complicated matters. please note we are talking about a portfolio in one asset class. It goes without saying that FX and stock markets need to be weighted differently if they are part of the mandate given by your investor. (here we think 3 units fx versus 1 unit stocks is appropriate)

You wrote – “1 or 2% per trade fixed fractional position sizing” – this is far away from my methods. I trade equities and do not trade HFT trades but rather longer trades. To use 1-2% means I will need 50 instruments to invest in during most of the times. Managing a big equity this is not really possible. At list for my algorithms.

I will not post here a full solution but I am willing to give you the variables in use when I come to determine a position size –
The expected revenue from the trade
The expected loss from the trade
Fund current holding value
I also generate more than one buy or sell during an active trade, so position size is changing along the trade which is a must in real trading.

How do I decide on my variables – mainly simulations, optimizations and statistics. As I trade multiple algorithms, each has its own position sizing algorithm and a Meta system for positioning.

Jim provided an old link where the stock market game is compared to heads or tails making it a Gaussian distribution problem. Stress is put on Optimal-f and the Kelly number. Both of which if applied as is to the stock market game will clobber your account to oblivion.

The article uses a zero-sum game as the basis for a trading methodology and it wants to extract more than the zero expected outcome. The outcome of a zero-sum game is zero, no matter how you play, using what ever method or indicator you want. Nobody has ever won heads or tails except by pure luck. And there is no need to ask anyone who won at a heads or tails game how he/she did it!

This does not mean that randomness can not be put to use in trading. But it has to be within a trading plan, a structure where it could make some sense when applied. For instance, it could be used to time scale an entry position; this way catching by chance some good entry points.

Suppose I’m trading intraday ( and supposedly I have an edge of some sort using my signal ) and it’s the US equity market, say Russell 1000. I have a maximal notional amount that can be traded , say 10 mill on each side. Besides optimal f/kelly, does any know of literature out there that discusses position sizing in this context. I need to be flat at the end of the day and I don’t know what’s going to be opened and sold at any given moment, so it seems like a ridiculously difficult problem. Thanks for any references, comments. Oh, I’m familiar with optimal f and kelly criterion but I seriously doubt their applicability here because you don’t even control when you have an edge. That’s random.

I think Optimal-f and the Kelly Criterion are probably better for gambling strategies than for position sizing in trading: although you know mathematically that you can not go broke if you have positive expectation, the ride is simply too rough to be practical.

you may find some interesting ideas in Ralph Vince’s publications (Leverage Space Trading Model, …).

references that talk about Kelly or Optimal F as applied my situation. Because, in
my situation, I might be even able to estimate the mean and the var given a signal
but I don’t even know when the edges “occur” so this means that on any given day,
during the day. Thanks.

yes, but this is where optimal f comes in. see ralph vince’s book ( names
escapes me. has the words “portfolio mathematics” in it ) before his leverage space trading model book.

11 days ago• Like

the book is titled “handbook of portfilio mathematics. formulas for optimal allocation and leverage” I have a paper by Ralph Vince somewhere that I thought did a better job of explaining it than the book. I’m quite busy at the moment but I’ll look it for it on the

I hate to recommend books because everyone’s style for what they like is different
and I distinctly remember saying to myself: “neat paper”.

I was assuming that by Maarten’s reference to a “strategy with relatively stable returns” he is implying that he is able to construct a payoff distribution for any individual bet. Optimal F gives you the practical upper limit that you should bet at. Now that said, the drawdowns at that level can be hazardous to your emotional health. I find that I’m most comfortable with a number @ 25% of Optimal f, just so I can sleep at night.
Cheers,

you may want to read Vince’s LSPM book, as it is an updated version of his previous Handbook of Portfolio Mathematics. To me, the interesting part in his work is that it is a departure from Modern Portfolio Theory (mean/variance), and it avoids assumptions about the data, which can not be said about classic economic theory…

Interesting software for the position sizing issue is Market System Analyzer by Adaptrade. It lets you shuffle the trade order, use different techniques (like Optimal f, Kelly, % of equity, …) and it runs a Monte Carlo analysis of these trades. It is remarkable to see how certain position sizing techniques are clearly more risky for certain trading strategy returns.

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indeed, if you look at some of the MDD’s using Optimal f, it is practically impossible to trade the full number.

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I have the LSPM book and will check it out.

If you don’t mind and at your convenience, could you explain how position sizing would be done in the 2 stock case where

A) the means return and variances of two stocks, X and Y, are known
so u_x, u_y and sigma_x, sigma_y.

B) you have say 1 million to spend ( assume long only )

C) you have the historical wins and losses for each of the two stocks ( normalized to say per share ): call these x_stream and y_stream.

This still doesn’t deal with my case ( because I don’t know when trades are
getting triggered ) but I’m not absolutely certain that I understand optimal f even
for that simple case so I wanted to see what your thoughts were on it. thanks.

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I am continually testing money management plans to be applied on systems and I will tell you something: NEVER BASE YOUR MONEY MANAGEMENT ON THE BACKTESTING RESULTS. BASE IT ON THE ASSUMPTIONS THINGS WILL GO IN THE WRONG WAY. If your system is good it will make money on the long run but nobody knows what can happen before you make a lot of money with it. So, find a very conservative money management plan and trade it with a lot of money MORE than you think necessary. You can withdraw the excess later when you have a cushion of profits. For individual investors, unfortunately this leads to the following conclusion: either you trade VERY few markets with multiple contracts ( therefore applying a money management plan ) or you trade several different markets with 1 contract each. Just a curiosity from what I was testing yesterday morning: to trade 11 markets half a million would be barely sufficient and I am using a very good money management plan……
The point is: your system is good but what will happen with money management if you have a 40000 \$ drawdown ? It could easily become a 300,000 drawdown with a money management approach.
My suggestion: take 2-3 markets and trade them with a single contract.

The original work on Kelly seems to me to based on the assumption that each trading event (or horse race…) is independent of the others in the sequence. That may look to be statistically true most of the time, but when things turn bad (i.e. the market falls/rises by a lot) the short-term correlations move towards 1, and that makes the assumption of independence wrong, with potentially catastrophic results. Am I reading this wrong?

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below is a link to an article that I think does a decent job
of explaining optimal f and so one may not need the book. but both can be helpful in understanding the differences between optimal f and kelly.

NeI think you’re correct that his derivation assumes independence of bets. So, in a “turn bad” situation, unless you’re market neutral, it could be a problem ( I’m opened to being corrected here about the independence. )

But, in non “turn bad” periods, if you think that you’re possessing an edge on each bet ( i.e: something specific has happened that makes you bet ), then I don’t think independence of bets is such a terrible assumption. The problem is that the bets
are not-independent CAPITAL WISE. The paper below I think implies that you can just
scale up and down as you wish.

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