Backtesting with Fixed Size vs Fixed Ratio

Discussion in 'Strategy Development' started by MustPlayOptions, Jan 14, 2007.

  1. To me it makes more sense to use a Fixed Size trade for backtesting since it makes all trades "equal". When you use a fixed ratio (e.g. 1% of equity), it seems like all drawdowns will be exaggerated since the trades are bigger after gains and gains are smaller after losses.

    I've noticed strategies almost always look worse with fixed ratios. The problem is that's how one would probably trade - so do you backtest how you actually trade to see if a strategy works - knowing it may miss out on strategies that work by chance, or do you use a fixed size for equal comparison?

    I've read about acrary's edge test but I'm looking at this as a first step...
  2. Part of the strategy is position sizing. So you must back-test exactly as you would have sized your positions had you been trading it in real time. Many people leave position sizing up to their own discretion. This usually leads to blow outs as size is increased in a series of revenge trades, even with a strategy that would otherwise have had an edge.

    Don't let your position sizing destroy your account before your edge has enough time to kick in. There is a reason every table in Vegas has a limit.

  3. You are correct to say that the increasing trade size implied by fixed ratio will create bigger drawdowns as profits increase, though they will also narrow drawdowns when losing because of decreased trade size. Fixed ratios produces higher returns in good times than fixed lots, but is also slower to make back losses coming out of bad times. Fixed lots tend to smooth things out a bit.

    The issue with fixed lots is that of diminishing returns over time. As your porfolio increases in value, the impact of the fixed lot trade profits will becoming increasingly less. The more your profits accumulate, the lower the return each trade will be.

    The best of both worlds would seem to be some kind of step situation whereby instead of having a fixed lot or a preset ratio, you increase the trade size incrementally every time you increase you portfolio by some amount.
  4. sulli


    Position Sizing w/ Acrary:
  5. The idea behind fixed-ratio position sizing is that every contract should perform an equal amount of work (profit return) before position size is increased. It is equivalent to starting with, let's say, 1 contract in 1 account, then at a later time opening a new account with the profits and trading the same strategy with an additional contract, and so on and so on. All that is happening is that your added contracts are starting trade of the same strategy at a different point in time.

    HOWEVER, in a backtest you are evaluating over a fixed time window. Your first contract will see the full length of data , while each subsequent contract will see less and less of the data. Because of this, the expectancy per contract will not be calculated on an even time basis, and the returns will be skewed from a fixed-contract evaluation.

    The backtest window is there to evaluate the integrity of your trading logic. If the logic is sound, you should be able to trade the strategy indefinitely, which means that as time tends to infinity, the expectancy achieved by each contract added will converge to the same number.

    I personally believe that the usefulness of adding compounding money management to the strategy evaluation lies in determining how much compounding is too aggressive vs. too conservative. Using tools like monte carlo analysis will yield insightful results about how to scale the compounding money management. It could be fixed-ratio, fixed-fractional, whatever.

  6. Thank you all for your replies so far...

    So I'm not sure there's a consensus yet.

    I guess my issue was that while it makes sense to use a fixed ratio for money management in an account, I was concerned that any later drawdowns could skew the results to be more negative than they truly are and thus lead to abandonment of the strategy.

    I know that the later results are also the most important though since they are closest to present time, but still, without using a Monte Carlo analysis, I think it might give too much weight to the drawdown.

    On the flip side, a strategy that gets lucky later on might have too much of a rise in equity if the later trades are overweighted. I thought using a fixed trade size in dollars would make sense for backtesting only as it would equalize the playing field throughout the backtest period.

    Raystonn: If I was using Monte Carlo then I don't think there would be any question to use the actual strategy since the sizing is part of it, but since I'm not it made me wonder.

    Rhody Trader: Agreed for the actual implementation, but what about just backtesting?

    sulli: Thanks for the link. I've actually summarized several of acrary's posts into strategy determination and multi-strategy management documents. If there is any interest I can post the summaries in separate threads. In this post it seems like he's talking more about implementation than backtesting. He uses Monte Carlo I believe for the backtesting so he uses the actual position sizing as well.

    RoughTrader: I may have misunderstood but it seems like you might agree that for backtesting purposes a fixed size makes sense because of the limited time period of the backtest - did I understand that correctly?
  7. sulli


    Sorry, I didn't realize you were talking about backtesting. I kinda skimmed over your post.

    I think to determine whether a system is statistically significant, the designer should use a fixed number of contracts in their backtest. Thereafter, position sizing methods may be modelled.

    That's how I operate.
  8. Not sure what you mean by "just backtesting". You should be making every effort in your system evaluation to have it replicate what actual trading implementation will be like.
  9. minmike


    Why not do both. Any reason to limit yourself to just one?

    The fixed size helps you determine if you have an edge or not.

    Fixed ratio will help you see how "stable" the system is. ie how aggressivly you can add size.
  10. Prevail

    Prevail Guest

    amen. and also look at fixed fractional position sizing.

    #10     Jan 16, 2007