Vol Targeting and Trend Following
- We are long.
- The price jumps up. Good.
- But this means the risk goes up
- So cut our position, just as we're finally making serious money.
How can this make feel?
This is a post about volatility targeting - dynamically adjusting your positions according to your estimate of market volatility - in the context of trend following systems. I blindly do this when building all my trading strategies without thinking about it - but is this a good thing to do?
It's also a publish approximately how you commonly have to stability different criteria whilst judging backtests - there aren't any loose lunches in finance.
What do we mean through volatility targeting?
It's not obvious whether "Volatility Targeting" is referring to the practice of scaling positions by volatility for a given level of convictionor targeting a constant portfolio or position level volatility regardless of conviction.
To be clean for the strange the way I run a CTA fashion strategy is:
1- Decide on a degree of conviction
2- From that infer the volatility target for a given position
3- Scale the location to a given volatility goal
There is then some other degree that some human beings do which I don't accept as true with:
4- Rescale the leverage in the entire portfolio to some fixed target.
Essentially doing the final issue will throw away absolutely the average stage of conviction which you have across your gadget. I do not think you ought to do this, even though it's very popular in eg equity neutral portfolios (in particular for historic reasons, take a bow Fama and French). To make matters difficult this is from time to time called "Vol focused on". But it is no longer what I'm discussing in this put up (perhaps another one).
Another element some humans do is run a binary gadget, wherein the extent of conviction is largely fixed. Doing this may throw away all the records you have about conviction, each absolute and relative. Again I suppose that is sub top of the line.
To be clear then what I am defending here is stage 2:the scaling of positions to a given volatility target, irrespective of whether conviction was involved. It's implicit here that the volatility target is dynamic, otherwise what you're doing is just some kind of long run risk budgeting exercise.
Why do people like fashion following
Trend following is considered a pleasant component, as it's go back profile is:
- a majority of time periods when we have small lossess
- a minority of time periods when we have big gains. Generally these come when other asset classes are suffering
This sort of return distribution will contain bothpositive skew (at least when measured at an appropriate time interval - at least monthly if not annually) and high kurtosis. Skew is an asymmetric measure of return 'non-Gausianness' (if that's a word), whereas kurtosis is a symmetric measure - it just means we have 'fat tails', without specifying which tail we're talking about.
Positive skew is generally agreed to be a good thing (to own a negatively skewed asset I'd want paying, in the form of higher expected Sharpe Ratio), but high kurtosis is generally agreed to be a bad thing, because it means we're going to get surprisingly large returns on both the up and down side. It makes no sense to talk about kurtosis that only existed on the right hand side of the distribution.
But a combination of positive skew and more kurtosis will give you more mass on the right hand side.
A possible case for now not vol focused on
Some humans don't like vol focused on because they think it degrades the exceptional belongings of fashion following: that extra mass at the right hand tail.
Essentially not vol concentrated on will make experience if there is an asymmetric effect in the markets: where we generally tend to cut our positions on vol spikes in triumphing positions more than we do on dropping positions. This certainly would decrease your skew, and this will certainly be a horrific issue. It would be higher to forestall vol concentrated on, and be rewarded with higher returns on triumphing positions, even after deliberating the higher losses on losers.
To be clear if you could get higher positive skew for free this would be a good thing. However if you have to pay for your higher positive skew with higher kurtosis then that wouldn't be so good. But intuitively removing vol targeting will mean worse kurtosis - vol targeting will tend to trim the tails of both sides of the distribution. This also ignores the first two moments of the distribution: if higher positive skew means a worse Sharpe Ratio would I be happy?
In standard phrases then it's unlikely that you can get positive skew totally free with out giving up something else: kurtosis or Sharpe Ratio. There are masses of conditions while this type of exchange off is gift - as an instance you may raise your Sharpe Ratio by using continually selling option vol, however that provide you with rather unsightly kurtosis and make your skew greater negative.
All this is a theoretical dialogue - let's have a look at what genuinely occurs to the moments of the return distribution whilst we get rid of vol focused on.
Empirical evidence
It's quite smooth to test this sort of issue with pysystemtrade. Here's an account curve for 37 futures markets the use of the machine in bankruptcy fifteen of my first ebook (with bring removed, for the reason that unique article turned into about fashion following), and additionally the month-to-month distribution of returns:
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| Account curve with vol targeting |
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| Distribution of monthly returns with vol targeting |
This is a machine which vol targets using the closing month or so of returns. Vol concentrated on also will increase charges, and all of the analysis on this publish are completed after prices.
Now for the counterfactual. It's without a doubt pretty hard to 'turn off' vol targeting as it's no longer apparent what you would replace it with: might you as an example provide all markets the equal cash function and forget about vol absolutely? That might cause some very distorted results certainly! I decided to preserve to use vol to scale positions, but a totally long time vol which didn't circulate around for every marketplace; so essentially move sectional vol budgeting, with out the time series adjustment to vol. I went with this set of config modifications:
gadget.Config.Volatility_calculation['days']=7500
system.Config.Volatility_calculation['min_periods']=a thousand
machine.Config.Volatility_calculation['backfill']=True
In simple english we are able to:
- Calculate the vol over the first 4 years of data (because I only have about 4 years of data for many instruments)
- Backfill and use that vol for the first 4 years (so forward looking, but <shrugs>)
- After that use a very slow moving average of vol (half life of 30 years)
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| Account curve without vol concentrated on |
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| Distribution of monthly returns with out vol targeting |
Well the account curve certainly is not as suitable. The distribution is harder to examine: it looks like there are some outliers that were not there earlier than on each the left and right tails.
Here are a few information that strengthen this end result (all primarily based on month-to-month returns):
With vol targeting Without
Skew +1.08 +2.46
Sharpe 0.92 0.569
Sortino 1.62 0.867
Min return -32.6% -55.6%
Max return +47.7% +100.6%
Kurtosis 5.28 33.0
1% point -16.5% -18.1%
99% point +31.8% +30.2%
To summarise then disposing of vol focused on ends in:
- Higher skew
- Worse Kurtosis
- Worse Sharpe Ratio
Now depending on your utility function you might argue this is a trade worth taking. If you cared about Skew above all else then maybe you'd accept this deal. Personally I wouldn't take this deal, but you might have a very strange utility function indeed.
But... And there's a huge but right here... I'm no longer sure how sizable these consequences are. Skew and Kurtosis are like something else statistical estimators, this means that they're situation to uncertainty, and they may be additionally issue to being stricken by more than one outliers.
(By the manner a formal T-check at the Sharpe Ratio difference inside the curves has a statistic of three.Fifty nine, so the difference is indeed extensive to something like ninety nine.Ninety seven%)
If we use a far better measure of left and right tail - the 1% and 99% points on the distribution of returns - we will see that removing vol concentrated on leads to slightly worse results at the left tail (1%), and greater enormously a slightly worse final results on the right tail as properly (99% factor). We had been sold no vol targeting as a product to improve our right tail, and we don't see it.
This strongly shows that the skew and kurtosis numbers are being closely driven by one or two outliers.
Formally if we bootstrap the distribution of skew for each curve we get this:
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| Distribution of monthly skew estimate with vol targeting |
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| Distribution of monthly skew estimate without vol targeting |
How do we get spherical this? Well both the largest effective and bad returns occur in 1979 - 1980; whilst there were not many units buying and selling within the information. Let's recheck the records, but this time ignoring the whole lot earlier than January 1981; this is nevertheless over 36 years of data:
With vol targeting Without
Skew +0.45 +0.64
Sharpe 0.78 0.52
Min return -26.5% -25.4%
Max return +33.4% +33.6%
Kurtosis 3.12 3.9
1% point -16.3% -14.2%
99% point +22.2% +22.0%
The development in Skew, and irritating Kurtosis, are both still there but nowhere close to as dramatic. The minima and maxima, and 1% / ninety nine% factors, are almost identical. It looks as if there is probably a moderate improvement inside the left tail with out vol targeting, and a mild worsening within the right tail - that is the other of what we would expected - however the values are not significantly one-of-a-kind. And, unluckily, the drop in Sharpe Ratio remains present (and it's miles nonetheless very extensive).
Summary
On the face of it vol focused on does certainly appear to remove some of the high-quality skew from fashion following. But there are some caveats:
- The improvement in Skew can be heavily influenced by one or two outliers in the data
- It looks like the improvement in Skew doesn't in fact lead to a better right tail
- The kurtosis is definitely worse, although again this could be influenced by outliers; taking these out the degradation in Kurtosis is still there but not as dramatic
- There is a substantial reduction in Sharpe Ratio, with or without outliers
So yes, maybe, there's some thing inside the idea that vol concentrated on involves giving up a number of the effective skew that fashion following gives you, at least with month-to-month statistics. But the price is terribly high: approximately a third of our Sharpe Ratio! This is the antique 'no loose lunch in finance' concept - we will enhance one moment of our go back distribution, but it usually involves giving some thing up. Another word for that is the 'waterbed' impact - whilst we push down at the skew a part of our waterbed to ensure a higher nights sleep, the water just moves elsewhere (the kurtosis and Sharpe Ratio parts of the mattress).
I cannot help thinking there are less expensive ways of getting effective skew; like perhaps shopping for a few out of the cash straddles as an overlay in your trading system.
Finally, it's also well worth reading this recent paper by my antique store, AHL, which goes into extra detail in this situation.
Acknowledgements - I'd like to thank Mark Serafini who by chance inspired this blog publish with a LinkedIn submit that became out to be on a wholly extraordinary topic, and Helder Palaro who observed that put up for me.
