Position sizing that isn't complete nonsense

Discussion in 'Risk Management' started by Ghost of Cutten, Jun 23, 2013.

  1. Here's I'll discuss position sizing in a novel way - I will use truthful and accurate assumptions. Every position sizing method I have ever seen fails to do this: optimal F, Kelly, seat of the pants etc.

    I will start with a few indisputable truths:

    1. You never know the trade odds on any trade. All estimates of trade odds are subject to gargantuan margin of error.
    2. The worst case loss is usually very bad
    3. Backtesting is almost useless for estimating trade odds or losing streaks. The reason is that the worst losing streaks occur during conditions different to, and worse than, backtested conditions e.g. the strategy degrades or becomes obsolete/unprofitable; the trader becomes ill-disciplined; market conditions become unusually hostile for the strategy etc.

    Obvious logical conclusions we can draw from this are:

    1. Any method reliant on relatively precise estimates of trade odds is flawed.
    2. Any method that is not paranoid about the worst case is likely over-optimistic in sizing.
    3. Any method based on backtested results is likely overly risky in size recommendations.

    Thus, we can completely forget about Kelly sizing, Optimal F, or anything that uses backtesting.

    How then should we decide trade size? We can't know profit in advance. We can't know win rate in advance. We can't know the black/grey swan risk in advance. What can we know? We can know how much we will lose if each trade loses the maximum amount we will tolerate before exiting, assuming we get to stop out in orderly fashion; and we could lose beyond that in a grey swan event, unless we have a clearly defined limited risk (e.g. long position; truly hedged position). So we know 2 things - theoretical worst case loss, and 'real world' likely worst case loss.

    Do we know anything else? Yes, our risk tolerance, and the amount of capital we can lose before continuing to trade for a living ceases to become viable.

    So, given that all we can really know is our maximum, and realistic maximum loss, and our trading uncle point, then it is obvious that this is all we can base our position sizing on. If we base it on anything else, then (because that 'else' is totally unverifiable) we are basing it on pure guesswork, and our size estimates are likely to be completely inaccurate.

    Position sizing therefore becomes relatively simple. Look at the worst case theoretical loss, look at the realistic worst case loss (on each losing trade, and on a sequence), and make sure your chances of suffering loss greater than your trading uncle point is sufficiently low.

    What is your worst case losing streak? What trading size would keep the depth of that losing streak within your maximum drawdown uncle point? That is your maximum position size.

    Example: you use trading system X. It backtests as a 40% win rate with 4:1 payout ratio. It has a profit target roughly 3 times its stop loss. In a purely random market it would be expected to win about 33% of the time. What win rate would it have in very hostile market conditions for the strategy? Maybe something like 15%. So, your worst case is an 85% loss rate. How big would 99% of losing streaks be? 27 losing trades or less (.85^29<1%). What's your drawdown uncle point? Let's say 20%. Thus, 29 losers in a row must lose <20%. So your maximum bet size is about 0.75% per trade (.9925^28>0.8).

    Now look at the grey swan risk. If the market gaps down 50% overnight, how much would you lose. Is it >20%, when you bet 0.75% per trade using your normal stop? If not, you are fine. If so, you must reduce your size further, so that the grey swan event doesn't take you beyond a 20% loss.

    That's it. Everything else is bullshit based on false or unverifiable assumptions.
  2. Pipflow


    Position sizing is very much important and constitutes the important part of the trading plan.
  3. I think this is all fine, and a sensible reference.
    If I understand what you're doing above, you're effectively taking the backtest result as a starting point, but then using various valid arguments to apply progressively more realistic adjustment factors to this result. That's fair enough, too. After all, if you based your strategy design on backtests in the first place, IMO it wouldn't make sense to completely ignore those results when you position size. Use them as a reference and then apply reality adjustment factors; seems sensible to me ...
  4. Daal


    The problem with sizing to the worst case losing streak without taking into account the profit factor (as it is the case when you only consider the loss chance probability) is that, I believe, it will underperform a position sizing strategy that takes into account that factor. As a result, you will spend a lot more time closer to the uncle point than with other strategies (you are certainly likely to spend more time with a worse equity curve, that is, in most distributions over your lifetime)

    The grey swan risk is a good point, but an aggressive assumption there is already embedded as a variable in the Optimal F formula. So the same assumption there would bring down size considerably

    A potential superior solution would be the following
    Last edited: Apr 7, 2016
  5. Daal


    I'm not saying one should plug in a backtested reward to risk figure into a kelly/optimal F type formula. They should probably use stressed figures just in case. And if the trader is wrong about the stressed figures (to the downside), then he is probably a losing trader anyway and no position sizing can save him. Your method would only postpone his certain blowup
    Last edited: Apr 7, 2016