Do less liquid assets trend better or is that they are just more diversified?

 As most of you know, one of the many projects / things I am involved with is the TTU Systematic Investor podcast series where I'm one of the rotating cast of co-hosts.

On a recent episode (at 24:05) we discussed the reasons why 'alt' CTAs tend to do better than traditional CTAs. Examples of alt-CTAs mentioned in that segment are the Man-AHL Evolution fund which I was heavily involved with when I was at AHL, and the Florin Court product  which is run by some ex-AHL colleagues. 

(Other funds are available and this is not endorsement or financial advice which I am not regulated to provide. It may be utterly illegal of you to even be aware of these products in your jurisdiction never mind invest in them them, and that is your problem not mine)

An 'alt-CTA' is one that trades non traditional markets, but in a traditional way (eg mostly by trend following). These could be less liquid futures markets, but is more likely to be non futures markets like options, OTC derivatives or cash equities. In this article I'm going to focus on the 'less liquid futures' definition of alt-, because that is the data I happen to have. This means that the analysis is also analogous to one of the classical issues in financial economics - the small cap effect in equities. 

In that episode I mentioned some research I had once done on that very topic; albeit many, many years ago, and that document certainly isn't available on my blog. So I thought it worth redoing this exercise.

Reasons why alt CTAs might do better

There are a number of reasons why one CTA might outperform another, but we're going to focus on just three here:

• more diversification (the products they trade have lower correlations with each other, and/or nice co-skewness properties)
• better pre-cost performance from the products they are trading
• lower costs

Now of course we would expect higher costs from less liquid futures; the key question is whether we get enough extra pre-cost performance to compensate.... or no extra performance at all. In which case is the extra alt-CTA juice coming from the diversification properties of the alt-markets (eithier linear correlation or something funkier in the higher moments)? Or will my simple analysis fail to uncover any extra alt-performance, eithier because the alt-CTA's have some extra magic or because their special black magic power can only be found in non futures markets. Or because they've just been lucky.

In any case we'll see if the equivalent of the 'small cap' effect in stocks is present in futures, or if it's something that was around in the past but has gone.

Note: There is some debate about whether the small cap effect, eithier outright, or in combination with the value effect, is still a thing. 

What we are measuring

We need a way of measuring:

•  the liquidity of futures
• the trend following performance

To keep things simple, for trend following performance I'm going to use the Sharpe Ratio of an EWMAC16,64 trend following continous forecast with my usual vol based position sizing. To calculate the Sharpe Ratio for a given period (eg a year), I'll use the annualised average daily percentage return divided by the expected annual percentage standard deviation. So this is a Sharpe Ratio based on the vol targeted, not the realised vol. This is because for short periods we might have a weak signal producing a high SR on a contract we didn't actually make any significant money out of. 

For futures liquidity, I'm going to use the 30 day rolling average of daily volume in $ million of annualised risk units for the contract that currently has the highest volume. That is the same measure I track daily here. And then I'm going to log(x) this volume, as these figures vary by many orders of magnitude.

Note: I currently set this measure at a minimum of $1.5 million to trade a given future. 

Note: The definition of $ annualised risk units is the number of contracts of volume, multiplied by the annual standard deviation in price units, mutiplied by the $ value of each price unit.

There could be other ways of measuring liquidity; for example open interest, or the cost of trading. I'm wary of using open interest since there are contracts with large open interest and small volume, and the reverse is also true. Personally I think unless you are a massive trader the size of the volume is more important than the open interest. I don't want to use cost of trading as a measure of liquidity, since I will be analysing that seperately.

Normally when I do this kind of analysis, I exclude instruments for all kinds of reasons including because they are too expensive or illiquid to trade. In this case I don't want to do that. I will however exclude instruments in my data set that are:

• Duplicates. For example, I don't analyse both the micro and mini S&P 500. The instrument in my dataset are those which meet my minimum requirements for liquidity but have the smallest contract size. Note that the definition of which is the duplicate contract to trade could have been different in the past. For example, immediately after the micro future came in to being it wouldn't have met my requirements for liquidity, so I would have in practice used the mini future. This will affect the results in a small number of edge cases, but mostly for high volume instruments.
• Ignored. These instruments eithier have garbage data, or they are spread instruments.

I won't exclude instruments that have:

• Trading Restrictions - mostly ICE markets for which I don't have access to live data so don't currently trade, and certain US derivatives I'm banned from trading
• 'Bad markets' - these are those that are too expensive or illiquid for me to trade - I want to see if there are size effects so I want to keep these. 

This gives me 205 instruments to analyse. Finally, I have around 12 years of data since I don't have volume data prior to 2013 in my dataset. 

Results across all years

Let's start by just plotting the average volume across all the available data, versus the pre-cost trend following p&l, by instrument.

That isn't especially suggestive of a strong relationship; although our eyes are drawn to the outlier in the top left (US housing equity sector if you care). If I do this as a 'bin cross' plot, which shows statistical significance (explained in more detail in chapter 12 of AFTS), then we can see there is really nothing there - in fact there is a slight tendency for very liquid markets to have a higher trend following SR:

What about costs?

Perhaps a slightly better relationship here - lower volume means higher costs - but not super consistent. There are instruments with very volume but not bad costs, such as the CLP and CZK FX markets at the extreme left. However these costs are based on sampled bid-ask spreads so are unlikely to be indicative of what you could actually achieve trading any size.

The cross plot shows that very illiquid markets do indeed cost more, but beyond that the relationship is relatively non linear. There is a 'zone of increasing costs' up to around $20m of volume in annual risk units, but beyond that risk adjusted costs are relatively flat. Again, this applies to bid-ask spreads only (and commisions) and for institutional size traders the 'zone of increasing costs' would apply to more instruments. 

Trend following p&l: Year by year results

This kind of market analysis has a fatal flaw; it doesn't account for the fact that some instruments will have been trading across the entire 12 year dataset whilst others will only have a few years of data. It also doesn't account for time series effects such as a given instrument seeing an increase or decrease in volume over the relevant period. To get around this, instead I'm going to break the results down into year by year results. So each point on the following scatter plot is the SR and volume for a given instrument and a given year. 

There is little point doing this for costs, since the costs in my backtest aren't actual costs, but here are the results for pre-cost returns. I haven't bothered with a scatter plot as it will be insanely noisy; here is the cross plot:

As with costs it does look like there is something there for very illiquid instruments; roughly those with less than $1m of volume units per day. But it's not statistically significant. The results incidentally survive the application of costs:

The median SR for log(volume) less than 0 (volume units < $1m per day) is 0.04 SR units higher even after costs, and the less robust mean SR is 0.12 units higher.

Measuring diversification via IDM

OK so it looks like very illiquid markets might have a slight edge in performance. But this isn't enough to explain the outperformance of alt-CTAs (with all the caveats from before); I'd also like to look at diversification.

Expected linear diversification can be measured easily by using what I call the 'IDM'. Intuitively, it's the multiplication factor required to leverage up a portfolio of assets with some weightings and correlations. See any of books on trading for details. A portfolio of assets with all correlations=1 will have an IDM of 1. A portfolio of N assets with all correlations zero will have an IDM of sqrt(N).

Note: We can also measure the actual diversification (which will confound both linear and non linear effects) by looking at the ratio between the portfolio SR and the SR of individual instruments - the Sharpe Ratio Ratio (SRR). This tends to be higher than we'd expect from looking at the IDM, as I note in AFTS and here; there is also another take from an ex colleague here. It's tricky to do here however as there are a lot of instruments jumping in and out of the portfolio.

So what I need to do is create portfolios of different liquidity instrument trend following sub-strategies and measure their diversifications (not the correlation of the underlying returns!). An open question is how these portfolios are weighted. I will do this two ways; firstly with equal weights. Secondly, using my handcrafting method (H/C) but in it's simplest form with just correlations (but naturally, using out of sample optimisation). 

This will be a crude in sample test where I look at the average volume over the entire trading period when we have volume figures and then use that to split the portfolio into different buckets. Because I'm trying to work out the why not the how of how this result could be exploited. I will use the final IDM (likely an overestimate given the IDM should increase as more instruments are added).

First by cutting off the portfolio at the median log(volume) of 2.8 (about $16m of daily volume units):

                          IDM EW                        IDM H/C 

Low volume                 2.30                           2.10

High volume                2.28                           2.14

That's... not very much difference. Here are the results as a time series, just to check it isn't a weird end of days effect:

Notice that IDM's fall over time, probably because correlations generally are rising. Earlier in the period when more diversification is available, the less liquid markets do better. But the differences aren't especially substantial.

But above it did seem that the better performance effect only kicked in once we were at very low volumes - below log(volume) of 0 (less than $1m in volume units). Let's go a bit more granular and cut our list of instruments into four groups of ~50 instruments, and for simplicity just look at handcrafted results:

Note the key is in log(volume) units. Note also that there isn't much going on here.

A very silly comparison

The one thing we haven't yet done is plot an account curve, so let's see what the portfolio p&l is like for each of the four buckets of liquidity (which essentially will confound both any improvement in per instrument trend following, plus the realised diversification both linear and non linear). To make this really silly, I'm going to do this for the whole of history despite only using volumes from 2013 to the present to decided which instrument goes in which bucket. This is a shocking idea for a huge number of reasons, almost too many to elucidate here.

With all that in mind, this is the strongest effect yet with less liquid markets underperforming. However this is very likely to be luck; and it's confined mostly to the period prior to 1985 when the less liquid market sets probably only contained only a few instruments which happened to do badly. After that there really isn't much in it.

Summary

On an individual market basis there is indeed a faint 'small cap' effect in futures, at least at this single speed. But it doesn't look like there is much of a difference in measurable diversification benefits. 

As I warned none of this goes very far to explaining the puzzle of the alt-CTA's outperformance, mainly because I don't really have the data to do this properly (so perhaps Man AHL or Florin coud do so?) - the benefit's of being an alt- aren't so much having a higher exposure to illiquid futures, than to trading things that aren't futures at all.

Although perhaps it really was luck, since the outperformance has started to fade recently and the five year track records for say Evo and AHL Alpha are now very similar. That could be because the diversification benefit has fallen off in alts more than in liquid futures, or because the alt- markets have 'matured' and become less 'trendy'.

What we haven't done here is look at the effect of including less liquid instruments in an existing portfolio of liquid instruments; ceritus paribus that should be a good thing since my starting assumption is that more diversification is better, especially as many of the less liquid instruments are commodities rather than another flipping US bond future.

Perhaps I should rethink my very strict policy on what I trade (minimum liquidity of $1.5m volume units per day); after all one of the advantages of being a smaller trader is being able to trade less liquid markets, and not all of the instruments with that sort of volume are super expensive as one of the earlier plots showed.