Trading the equity curve doesn't seem to work

[globalarbtrader]

Everyone hates draw downs (those periods when you're losing money whilst trading). If only there was a way to reduce their severity and length....

Quite a few people seem to think that "trading the equity curve" is the answer. The basic idea is that when you are doing badly, you reduce your exposure (or remove it completely) whilst still tracking your 'virtual' p&l (what you would have made without any interference). Once your virtual p&l has recovered you pile back into your system. The idea is that you'll make fewer losses whilst your system is turned off. It sounds too good to be true... so is it? The aim of this post is to try and answer that question.

This is something that I have looked at in the past, as have others, with mixed results. However all the analysis I've seen or done myself has involved looking at backtests of systems based on actual financial data. I believe that to properly evaluate this technique we need to use large amounts of random data, which won't be influenced by the fluke of how a few back tests come out. This will also allow us to find which conditions will help equity curve trading work, or not.

Here is an excerpt from my results. It turns out the key characteristic of any system is the autocorrelation of returns.

X-axis: Length in days of moving average used for equity curve filter. "1000" (far right point) means no filter is used.
Y-axis: Average annual return / maximum drawdown (averaged over 200 random draws of 20 years of daily data)
Cost level: Expensive futures market / spread bet / cheap underlying equity
Rho: Autocorrelation parameter

Conclusion

The idea that you can easily improve a profitable equity curve by adding a simple moving average filter is, probably, wrong. This result is robust across different positive sharpe ratios and levels of skew. Using a shorter moving average for the filter is worse than using a slower one, even if we ignore costs.

There is one exception. If your trading strategy returns show positive autocorrelation then applying a filter with a relatively short moving average will probably improve your returns, but only if your trading costs are sufficiently low.

However if your strategy is a trend following strategy, then it probably has negative autocorrelation, and applying the filter will be an unmitigated disaster.


This is just an excerpt. Full results and explanation in the usual place
http://qoppac.blogspot.co.uk/2015/11/random-data-evaluating-trading-equity.html

 

[R1234]

thanks for that post! exactly what I've found empirically.
the trick is to come up with strategies that have autocorrelated daily returns ie. when they do well they should continue to do well and when they do badly they should continue do do badly, and the transitions between good to bad to good should be gradual and without too much noise.

 

[Scataphagos]

Everyone hates draw downs (those periods when you're losing money whilst trading). If only there was a way to reduce their severity and length....

Quite a few people seem to think that "trading the equity curve" is the answer. The basic idea is that when you are doing badly, you reduce your exposure (or remove it completely) whilst still tracking your 'virtual' p&l (what you would have made without any interference). Once your virtual p&l has recovered you pile back into your system. The idea is that you'll make fewer losses whilst your system is turned off. It sounds too good to be true... so is it? The aim of this post is to try and answer that question.

This is something that I have looked at in the past, as have others, with mixed results. However all the analysis I've seen or done myself has involved looking at backtests of systems based on actual financial data. I believe that to properly evaluate this technique we need to use large amounts of random data, which won't be influenced by the fluke of how a few back tests come out. This will also allow us to find which conditions will help equity curve trading work, or not.

Here is an excerpt from my results. It turns out the key characteristic of any system is the autocorrelation of returns.

X-axis: Length in days of moving average used for equity curve filter. "1000" (far right point) means no filter is used.
Y-axis: Average annual return / maximum drawdown (averaged over 200 random draws of 20 years of daily data)
Cost level: Expensive futures market / spread bet / cheap underlying equity
Rho: Autocorrelation parameter

Conclusion

The idea that you can easily improve a profitable equity curve by adding a simple moving average filter is, probably, wrong. This result is robust across different positive sharpe ratios and levels of skew. Using a shorter moving average for the filter is worse than using a slower one, even if we ignore costs.

There is one exception. If your trading strategy returns show positive autocorrelation then applying a filter with a relatively short moving average will probably improve your returns, but only if your trading costs are sufficiently low.

However if your strategy is a trend following strategy, then it probably has negative autocorrelation, and applying the filter will be an unmitigated disaster.


This is just an excerpt. Full results and explanation in the usual place
http://qoppac.blogspot.co.uk/2015/11/random-data-evaluating-trading-equity.html

If you're "stringing together" losses with few winners, the "bias" you are trading around is wrong.

I once had 9 consecutive losers. My buddy once had 14. One guy on ET admitted he'd had 23. That kind of thing is almost always from "wrong bias".

 

[Visaria]

George Soros on drawdowns/equity curve:

 

[johnbennett103]

I have tried trading equity curves, and the only sound way is to cut leverage as you fall. This is mathematically correct (see Ralph Vince's work).

 

[rvince99]

I think it depends on what your criterion is (to the notion of trading your equity curve "working"). Let's suppose my criterion is expected growth maximization -- then I'd want to trade at the peak (a percent) of the curve f{0..1}. If it is maximizing expected gain to expected drawdown, then it is at the tangent point of a line from 0,1 to the curve, which comes out less aggressive than the peak. If it is to put a floor value on the account, then you want to trade more (as a percent) as equity increases, trade less (down to 0%) as the equity drops to that floor.

I've detailed these and other "patterns" that one can use to satisfy various criterion in the Risk Opportunity book (and I'm not trying to huckster it here, it's cheap, like fourteen dollars on amazon or something). My point is that I think that we can trade our equity curve (and de facto, we are, whether we want to acknowledge that or not) but we first need to articulate what the criterion is that we are trying to solve for -- which is no easy task.

I have tried trading equity curves, and the only sound way is to cut leverage as you fall. This is mathematically correct (see Ralph Vince's work).

 

[globalarbtrader]

I think it depends on what your criterion is (to the notion of trading your equity curve "working"). Let's suppose my criterion is expected growth maximization -- then I'd want to trade at the peak (a percent) of the curve f{0..1}. If it is maximizing expected gain to expected drawdown, then it is at the tangent point of a line from 0,1 to the curve, which comes out less aggressive than the peak. If it is to put a floor value on the account, then yr ou want to trade more (as a percent) as equity increases, trade less (down to 0%) as the equity drops to that floor.

I've detailed these and other "patterns" that one can use to satisfy various criterion in the Risk Opportunity book (and I'm not trying to huckster it here, it's cheap, like fourteen dollars on amazon or something). My point is that I think that we can trade our equity curve (and de facto, we are, whether we want to acknowledge that or not) but we first need to articulate what the criterion is that we are trying to solve for -- which is no easy task.

Hi Ralph

I will check out your book (when reviewing my book someone said "If you subscribe to the notion that money management is the most important part of any trading system ... this one is for you.". I don't believe there are enough books on this subject and I can't believe I've missed yours).

The experiments I did suggested that it doesn't matter whether you're maximising expected return or expected return to expected drawdown; in neithier case does the equity overlay improve things.

To put a floor value on the account of course the easiest way is to mentally half your account size and only risk the 'top' 50%. Of course that means you might never get back from a 50% loss once you've hit it (although if you're reducing capital pro-rata with losses, you should never get exactly to 50% unless you are leveraging too much and get a shock before you can adjust positions accordingly).

However this isn't always appropriate, even if it is optimal. In the fund I worked for we had a lot of guaranteed products. There you'd be given say $1 million, but guarantee to return the capital to the investor after 10 years. Obviously what you'd do is buy a zero coupon bond for say $600K (interest rates were higher when these things worked best ), and then use the $400K to trade with (of which incidentally you'd only about $100K for margin), but you'd trade as if you had $1 million in the account (so a $40K loss would mean reducing your risk by 4%).

Once the loss started to approach 40%, at say 30%, you'd start to gradually derisk.

The alternative was to trade the $400K with higher leverage, but that would have meant making large adjusting trades for each loss even when positions were relatively modest (a $40K loss, 4% on the original capital, would mean reducing positions by 10%). Wheras with the derisking method you'd only start to make large adjustments once you'd already lost quite a bit.

GAT

 

[tonysoprano]

I think it depends on what your criterion is (to the notion of trading your equity curve "working"). Let's suppose my criterion is expected growth maximization -- then I'd want to trade at the peak (a percent) of the curve f{0..1}. If it is maximizing expected gain to expected drawdown, then it is at the tangent point of a line from 0,1 to the curve, which comes out less aggressive than the peak. If it is to put a floor value on the account, then you want to trade more (as a percent) as equity increases, trade less (down to 0%) as the equity drops to that floor.

I've detailed these and other "patterns" that one can use to satisfy various criterion in the Risk Opportunity book (and I'm not trying to huckster it here, it's cheap, like fourteen dollars on amazon or something). My point is that I think that we can trade our equity curve (and de facto, we are, whether we want to acknowledge that or not) but we first need to articulate what the criterion is that we are trying to solve for -- which is no easy task.

I think it depends on what your criterion is (to the notion of trading your equity curve "working"). Let's suppose my criterion is expected growth maximization -- then I'd want to trade at the peak (a percent) of the curve f{0..1}. If it is maximizing expected gain to expected drawdown, then it is at the tangent point of a line from 0,1 to the curve, which comes out less aggressive than the peak. If it is to put a floor value on the account, then you want to trade more (as a percent) as equity increases, trade less (down to 0%) as the equity drops to that floor.

I've detailed these and other "patterns" that one can use to satisfy various criterion in the Risk Opportunity book (and I'm not trying to huckster it here, it's cheap, like fourteen dollars on amazon or something). My point is that I think that we can trade our equity curve (and de facto, we are, whether we want to acknowledge that or not) but we first need to articulate what the criterion is that we are trying to solve for -- which is no easy task.

Hi Ralph,
Your writings on position sizing (optimal F, etc) naturally assume a, I believe, 100% mechanical trading system.

You may have written about this before but if not - what are your thoughts on, and how does one apply the various position sizing algorithms if you're a discretionary trader. By discretionary I mean anything not 100% mechanical.

Thanks

 

[johnbennett103]

Ralph,

I am thrilled that you are on this forum. I have been trading for over 20 years, and your influence has been extremely important. While it has been a while since I read your text book, what I learned is that I should cut back during drawdown, and define my worst loss (set a stop, and stick to it). In practice, this has kept me alive, and ready to trade for another day. I will take a look at the book that you mention. Thanks for your many contributions.

John

 

[rvince99]

Yes, to trade the equity curve itself you need some sort of discernible auto-correlation of returns (and a belief that it is not a spurious happenstance, that there is causality involved).

But I believe that if one defines a criterion (I want to increase my probability of being profitable by such-and-such a date, or I want to maximize my MAR ratio, or the portfolio insurance style strategy discussed earlier) it is possible though the means to doing this are not the same as trading the equity curve, per se as we are referring to it here.