Backtesting with Fixed Size vs Fixed Ratio

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...
 
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.

-Raystonn
 
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.
 
Position Sizing w/ Acrary:


Quote from acrary:

droth, I don't use % based stops. I use 1/2% of account for risk per-trade. Ex. If I had a 100k account, then the max. risk per-trade would be $500. If I wanted to trade 5 emini contracts I could only risk 2 pts on each contract for each trade (500/(5*50)).
I use it for my personal account because it's simple to calculate, test, and implement. My expectation is large enough that I don't worry about the drag caused by the % of account allocation.
I retired from a investment bank last year. There, the money management and risk management were decided by the company. It chose a method that doesn't have % of account in the formula to avoid the drag.

Here's something I posted elsewhere that gave a way to avoid the drag of the % of account method while being conservative to avoid the risk of ruin:

A unprofitable trading method can't be improved through any money management strategy, so you must first have a profitable method before going forward.

Once you have a profitable method, you need to know a couple of things about it's characteristics. You need to know the maximum drawdown and the % of losing trades before you can apply money management to your method. You should have a minimum of 100 trades (either real or hypothetical) to base the calculations. Why at least 100? Because we need a stable database. At 100 trades, the standard error is 10% (1/sqrt(# trades)). This is acceptable when getting started.

How often should you hit a new equity high? It can be calculated by using the % losing trades. Here's how, take the % of losing trades and multiply it by itself until the number is approx. .01 (meaning 99% chance of seeing a run of however many times you do the mutiplication). For example, if I have a method that loses 40% of the time, then the number will be (.4*.4*.4*.4*.4 = .0124). This means a method with 40% losers will have no more than 5 losers in a row 99% of the time. Next, take the number of consecutive losses and multiply by 3. In this case, the number will be 15. This is called the trading cycle. The cycle is the maximum number of trades that should happen before a new equity high is achieved. Draw a line every 15 trades on your statements and make sure a new equity high is hit within the 15 trade period.
If not, the % of losers is probably greater than the sample used to caluclate this and is a warning sign of a unstable trading method. Use a higher % of losers and re-calculate until each equity peak is within every cycle.
How many contracts should I initially trade? This is largely dependent on how much pain you can stand. If you don't mind a large % drawdown, then your number's will be higher than someone else. Take the amount of equity in your account and multiply by your maximum acceptable drawdown as a % of your equity. For ex. if you have 20k and you don't mind a 40% drawdown, then 20k * .4 = 8k. Next, divide the max. acceptable drawdown by the observed drawdown. For ex. if the method had a max. drawdown of 2k then 8k/2k = 4. This would be the initial number of contracts to trade in the market.
When do I change the size? First, if the max. drawdown as seen in the past is hit, STOP trading. Once the new drawdown has stopped and a new equity high has been achieved (paper trading), then re-calculate the money management numbers and start over.
As far as compounding goes, take the starting equity + (maximum drawdown * 3). Once the account equity goes above this number, you can safely add another contract. Ex. if I start with 20k and the max. drawdown is 2k then when the account goes above 26k, then I can add another contract. You should also do the initial calculation and make sure it's acceptable before adding to your size. In this case the 26k * .4 = 10.4k. The 10.4k / 2k = 5.1, so it's okay to increase from the 4 contracts to the 5 and stay within the acceptable drawdown.
This method does not have a negative edge (as does all % of equity methods), so it'll let your account grow as you apply your edge to the market without the drag.

http://www.elitetrader.com/vb/showthread.php?s=&postid=158479&highlight=drag#post158479
 
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.

RoughTrader
 
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?
 
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.
 
Quote from MustPlayOptions:

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

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.
 
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.
 
amen. and also look at fixed fractional position sizing.

Quote from 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.
 
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