Dynamic risk allocation

The purpose of this thread is to propose a dynamic risk allocation technique. Your input is greatly appreciated.

After gathering risk management techniques from Aparsai and Fijitrader, I have experienced first hand the value of VAR and R%.

I want to push the topic a bit further. My latest experiments show that although my system is profitable, it experiences inevitable drawdowns from time to time.

How do I deal with that?

Most traders are content to trade a fixed percent of their capital at any point in time. IE) Risk 2% of their capital for each trade. Suppose the capital drops down to 60% during a very slow period.... the rollercoaster effect is gut wrenching.

In dynamic risk allocation, we do the following:

We always know the highest capital we have achieved in trading. IE) I started my account with 10K, and eventually reached 20K, so my new highest capital achieved is 20K.

Dependent my account's current capital vs. highest capital achieved, my risk is as follows:

90% - 100% of highest capital achieved, I risk 2% per trade
80% - 89% of highest capital achieved, I risk 1.5% per trade (I will increase risk to 2% once the account recovers to 90%)
Below 80% of highest capital achieved, I risk .5% per trade (I will increase risk to 1.5% once the account recovers to 80%)

The idea here is that during drawdowns, I do not jeoprodize my capital by risking large when I am already in the hole. Eventually my system will pull out of the slump, and I will bet large again. This technique allows for large gains, but limits the dips in my equity curve.

Hi tdion,

I believe you are on the right track to build a powerful position sizing system. Actually there are some standard methods to do so. Please read the following article and you'll have a better idea of optimization process:

http://www.adaptrade.com/Articles/article-op.htm

The most important step to make sure you are doing it right is to know your system. This needs some statistical information about the behaviour of your system and then correction of VAR per trade accordingly.

Good Luck,
Al

thanks for this great article, aparsai

You have to remember that 2% of 80% is 1.6% of the original 100%, so in a sense you are already there, betting less with the drawdown.

Very true. This is actually one big advantage of a fixed fractional approach to position sizing. As your equity drops during a Draw Down the amount of dollars that you risk gets smaller even if you use the same percentage of your equity.
There are approaches to position sizing out there that atepmt to adjust the position size depending on what the equity (or the last n trades) is doing however i believe that such techniques are not easily implemented. It is true that every system experiences DD from time to time. The difficulty lies in determining when the DD starts and ends. Just like in trading that is easy to do in hindsight. Not as easy though without the benefit of the former. The only way to determine whether or not you should use a variation of the classical Fixed Fractional position sizing is to backtest your position sizing approach on a large enough sample of trades. I have done this with every system i have backtested and have found that nothing beats the fixed fractional. Just like trading, something might look good and make sence in theory but when you start backtesting things can take a very unexpected turn.
Good Luck!

Interesting replies.

For me, the dynamic allocation is attractive for several reasons.

1.5% of 90% is 1.35%.... so you begin reducing your risk substantially at 90%.... opposed to 2% of 90% which is 1.8%....

The reason I thought this was worth starting a thread is that you heavily reduce your risk at a much earlier stage than with fixed fraction.

The goal is not to find the "end" of your drawdown period, but rather to break even during phases where you are not profiting heavily.

As for backtesting: I find that backtesting help determine how profitable you will probably be during trending vs. sideways markets. You will experience both, but it is uncertain for how long. Therefore, as Aparsai's article states, your optimization of backtests will never be on the money.

I conclude by conceding that fixed fraction will often bring the highest returns. I can not support fixed fractions though, because huge drawdowns are currently unacceptable to my way of trading.

exelent thread! i defenedly going to look into this Monte Carlo analysis from the link what aparsai supplied.

keep it rocking! gonna keep eyes in here!

xPip you will find that if you are wrong, the interest collected will not make up for the negative pips. Depending on leverage and magnitude of the move, you can have a margin call.

In one such system, HawkFX attempted to ride out bad trades and wait for them to come back. Results can be found here:

http://www.collective2.com/cgi-perl/...temid=14538640

Before you gawk over the profitable equity curve, read the reviews of the system's subscribers. These folks that ride out bad trades are begging for Doomsday scenarios, if you ask me. Just my two cents.

It's fine and dandy to reduce size once you start losing. However, what will make you money is increasing size when you win. As you gain profits, risk more and more. Once you hit a predetermined amount of losers, you scale back.

Another thing to consider is how you're going to count your equity and profit. The approach I take is simple. I consider my equity separate from my profit up to a point. As I win, I risk a larger percentage of my profits. At a predetermined level, I sweep it all into the equity pool and start over again.

tdion, while i understand your approach, i don't really agree with it. if you are emotionally sound and can trade each and every trade by your rules without becoming emotional, then (assuming you have 50% win expectancy) your next trade could go either way. losses are to be expected, but shouldn't get you down, if you followed your rules properly then losses are still good trades, and should not influence your next trade. If you consistently lose (and you follow your rules) then there is something wrong with your system, which you need to re-evaluate. I am just saying that IMO if you consistently risk a fixed percentage of your real time account balance you will get more consistent results. if your drawdown went to 75% (.5%), you would have to make more than 4 times the amount of winning trades than as if you were still at 100% (risking 2% per trade), which i think is giving yourself a big handicap. when your account gets smaller due to drawdown, the fixed 2% risk also gets smaller, helping to preserve your capital without hindering your ability to make some money at a decent rate

Thanks Scott....

Just to clarify my technique, I do not keep my risk at 0.5% until I recover to 100%. Once my balance is back up to 80% of my highest capital achieved, I increase my risk back to 1.5%.... Once up to 90%, I go back to 2% risk. I will post equity curve graphs later today that compare fixed fraction vs. dynamic risk.

Tom, by decreasing position size percentage-wise when your account balance falls, you are also slowing your recovery rate. While I fully endorse the fact that position size must be kept small enough to ensure that worst-case-drawdown-during-testing-plus-an-arbitrary-safety-margin can’t ever reduce your account balance irretrievably, I think it’s also possible to become too intimidated, and eventually emotionally incapacitated, by loss (remembering that “scared money never wins”). Provided we have statistical justification to have faith in the soundness of our method, and a proven belief in ourselves to trade it consistently, then “attack can be the best form of defense” (in much the same way that letting profits run in winners can offset several smaller losses), and can become a source of optimism. Anyway, the “correct” approach to sizing should ultimately be determined by an individual’s emotional tolerance to risk.

Mathematically (IMHO) position size should in some way be proportional to the probability of profit with the current trade, and not prior history (the end result of which is the account balance). That assumes that each trade is probabilistically independent. However, if (wins and) losses tend to cluster together (perhaps because the market is encountering conditions unfavorable to one’s system, e.g. prices are ranging sideways, and the system is trend-following), then I believe there is valid reason for reducing position size, or indeed not trading altogether. But if, realistically, there is no real way of determining in advance which trades are more likely to be profitable, and which are not, then I can’t see a valid reason for varying the percent risk on any trade.

In other words, unless our account balance somehow reflects that the current candidate trade is less likely to profit than "normal", there is no mathematical justification for reducing position size from the "normal" percentage. Would a casino be justified in lowering the max bet size just because some punter is on a winning streak? No, because the game rules and probabilities, and the way in which they're implemented, remain exactly the same. Given its positive edge, the casino will recover.

The market doesn’t care about our account balance (prices will invariably move however they please), and neither should our entry/exit method. Two percent (or whatever percentage we use) risk is always two percent, whether our account balance is $1,000 or $10,000,000; and regardless of where it started, or what heights or depths it might have reached previously. We can't undo the past; we can only move forward from the current point, by continuing to consistently implement our existing strategy.

Irusoh and Sergiu both make the valid point that FFS is self-adjusting, offering inherent protection in that “diminishing balance” will decelerate the slide as the account balance falls.

Position sizing can never atone for a negative expectancy method; all it does is accelerate or decelerate our equity curve. A trader with a positive edge (method + implementation) will eventually reach financial freedom; one with no edge will eventually become defeated by costs, and experience ruin (or be forced to retire). Position size determines the rate at which this occurs, and its only function should be that it must be modest enough to:

1) preserve capital by ensuring that the probability of any losing sequence, that would cause irretrievable drawdown, is negligible; AND

2) allow us to trade with as much emotional detachment as is humanly possible.

Just my 2 pips worth.

David

This are all valid points but....
by reducing you risk substantially you also substantially reduce the rate at which you will recover from the DD. So by the time you have come from under water chances are the amount of positive trades provided by your edge is up and you will enter a new DD period.

One further point: given that the goal is capital preservation, even more so if one is a beginner and/or is still in the process of forward testing the system, then a declining account balance may reflect that the system needs refining, in which case lowering position size is justified. My previous post assumes that one has already attained a proven edge.

David

PS Sergiu, looks like our posts crossed, and we both make the same point about recovery rate.

My rebutal to this is very simple: what is the risk/reward ratio of the system's trades?

Case and point: If my risk has been reduced to 1.5% per trade (because I am below 90% of my highest capital achieved), but my reward is a 6% gain, I will climb out of the hole quickly. Two wins in a row will put me back to breakeven in this scenario.

I am getting very comfortable with the following risk/trade allocation:

8% if the current balance is > 80% of the highest balance achieved, 4% otherwise.

Have you considered Binary equation? It seems to be all the rave lately in forex.

Using Kelley Betting Criterion is probably the best place to start. For those with access to Wikipedia, you can find it here:

http://en.wikipedia.org/wiki/Kelly_criterion

For those without access, here's a link to the original paper:
http://www.bjmath.com/bjmath/kelly/kelly.pdf

It's from this site:
http://www.bjmath.com/bjmath/kelly/kelly.htm, which appears to be somewhat abandoned, but still has good information on it. It's from a blackjack perspective, but math doesn't really care who she hangs out with

Disadvantages
Using the Kelly system in practice does have drawbacks. While it guarantees that you will never lose all your bankroll, it does not guarantee that you will not lose money. When a series of serial bets are made the chance of dropping to 1/n of your bankroll is 1/n. Thus you have a 50% chance of at some point losing 50% of your bankroll, a 10% chance of dropping to 10%, and so on.
The optimum bet for the greatest growth of bankroll is making the full bet suggested by the Kelly criterion, but this produces a volatile result. There is a 1/3 chance of halving the bankroll before it is doubled. A popular alternative is to bet only half the amount suggested which gives three-quarters of the investment return with much less volatility. Where money would accumulate at 10% compound interest with full bets, it still accumulates at 7.5% for half-bets.
Over-betting beyond that suggested by Kelly is counter-productive as the long run return will fall, dropping to zero (with the loss of all the bankroll) when the Kelly bet is doubled. Using half-Kelly bets also safeguards against being ruined by unknowingly overbetting, as it can be easy to over-estimate the true odds by a factor of two.
The above applies to a sequence of serial bets. It is better to diversify, as the gambler who for example bets on every horse at a race using the Kelly criterion makes on average a better long-run return than the gambler who only bets on one horse per race, and similarly for the diversified stock market investor.

Yes, we can all cut and paste from Wikipedia. That's why I pointed out the KC is a good place to start; if you follow the links at the bottom of the page you c&p'd from, you'll find some more extensions as well...