The Skewness of Commodity Futures Returns

KCOJ

KCOJ

I came across the above named paper (a quick google will get you a pdf copy) a few months ago now and have been meaning to take a closer look at the topic of skewness and it’s applicability in predicting returns on commodity futures. I don’t normally get a lot of value from “academic” papers, as I find they’re largely written by non-practitioners looking to impress other non-practitioners. That said, I’ve read some of this particular paper’s authors’ works before and have found their past analysis of term structure and hedging pressure worthwhile reading.

Anyway over the next few days/weeks I plan to put some time aside to see if I can use historical skew in any way to improve my trading profitability. By posting here, this may or may not benefit others, but I’m hopeful that I’ll also learn from any constructive feedback. Who knows, there may be some among you that have already examined this precise issue, but regardless I look forward to any thoughts along the way.

For those who may be unfamiliar with skew, it’s a pretty standard statistical measure that when applied to returns of financial markets basically says that if a market has in recent times had a lot of big up days then it can be described as having a positive skew and vv. if a market has had a lot of big down days then it has a negative skew over that time period. Note that it pays no attention to the overall direction of a market, but simply the relationship between the size/frequency of up and down days. OK so that’s not a textbook definition but its good enough for our purposes.

So the authors are simply looking to examine if there is a relationship between past skewness and subsequent commodity returns … much in the same way that many papers have looked at the relationship between say, past momentum and subsequent returns. And surprise, surprise they do indeed find that there is a relationship such that …

“Systematically buying commodities with low total skewness and shorting commodities with high total skewness generates a significant excess return”

… of course this is really no surprise as the paper would not have been published if no relationship was found :sneaky:

The methodology they use is to implement a simple rotational strategy that each month, from a portfolio of 27 commodities buys the commodities with the 20% lowest skew and sells the commodities with the 20% highest skew using a range of different lookbacks to measure each market’s skew.

So that should be pretty easy to replicate in an attempt to verify the results, but more importantly also intend to consider a number of practical issues that real world traders may face.

I will post results of my back-testing along with other pre-test considerations shortly, however any early feedback or advice is welcome and feel free to pm me if you would prefer.
 
Sergio77 said:
It is entirely possible that the result is due to data-mining.
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Indeed Sergio, you may well be correct … in fact the sample period used is limited to 26 years and covers a fairly concentrated portfolio of some quite similar markets. I intend to conduct testing over a longer time frame and use a much more diverse range of commodities.

That said I do like the fact that this is a very simple strategy with little potential for over-fitting given that apart from the percentage threshold used to include/exclude markets, the only other optimizable parameter is the lookback used to measure the skew. In this case the authors do make some attempt to analyze robustness by including results for a wide range of lookbacks as well as assessing performance for different trading sub-periods. So we shall see …
 
JackRab said:
Isn't this like mean-reversion?
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Same … but different. Same, in the sense that we may be buying into a market that has had lots of big down days vs few big up days … so maybe in that case you are looking for a type of mean reversion.

However consider a market that has a negative skew over the last 200 days … it is entirely possible that the skew results from frequent big down days that occurred in the beginning of that 200 day period whereas for the last 100 days the market may be in a steady uptrend. In this case our buy signal would not in any way look like what we would normally consider an entry into a mean reversion trade.

You could also continually be holding a long position in a market that maintains a negative skew yet is long term profitable, so there is neither price nor skew reversion.

That said I don’t think that the way we define this style of trading is overly important. Of more relevance is an understanding of the type of investor behavior that we are trying to take advantage of. As the authors put it, investors …

“have a strong preference to hold assets with extreme outcomes in the gains domain (i.e. lotteries), and have an aversion to holding assets with extreme outcomes in the loss domain (disasters). This leads to positively skewed assets being relatively overpriced, and negatively skewed assets being relatively underpriced”

… well that’s the theory anyway. However the potential attraction for me is that while a lot of quantitative trading strategies base their entry decision on recent price direction, in this case we are solely basing our entry signals on the historical asymmetry of daily returns. So for anyone currently trading a suite of momentum and counter-trend strategies … even if employment of this skewness trading system doesn’t produce stellar Sharpes on its own … it will certainly add a diversification in trading styles.

But of course it must prove robust and that’s why I want to conduct a broader analysis that addresses what I think are some of the paper’s oversights.
 
So prior to carrying out any testing I wanted to take a look at a few issues (some important, some not so important) that concern me regarding the authors’ methodology.

Firstly their selection of commodities to include within the testing portfolio. Here’s what they say …

“We use 12 agricultural commodities (cocoa, coffee C, corn, cotton n°2, frozen concentrated orange juice, oats, rough rice, soybean meal, soybean oil, soybeans, sugar n° 11, wheat), 5 energy commodities (electricity, gasoline, heating oil n° 2, light sweet crude oil, natural gas), 4 livestock commodities (feeder cattle, frozen pork bellies, lean hogs, live cattle), 5 metal commodities (copper, gold, palladium, platinum, silver), and random length lumber.”

To start, there are three markets … Light Crude, Heating Oil and Gasoline, which are effectively duplicates of each other when it comes to the skew of daily returns. I can pretty much guarantee that if one of these markets is included within the top/bottom 20% skewed, then all three will be, which will clearly distort results as well as taking on unnecessarily higher risk exposure. It’s a little like someone thinking that they are investing in a diversified commodity portfolio by buying the Goldman Sachs Commodity Index which is effectively just a proxy for the price of Oil.

To a lesser extent the same can be said with the following groups …

Soybeans/Soybean Meal/Soybean Oil (and maybe Corn)

Live Cattle/Feeder Cattle

Gold/Silver/Platinum

To be clear, I’m not saying that only one member of each group should be traded in real-time, I’m simply stating that if you are trying to test the effectiveness of skew as a predictor of future returns then you need to sample this across a diverse a group of commodities as possible. Anyone that has traded the market groupings that I have listed above will tell you that they demonstrate almost identical measures of skew based on recent big up/down days.

Regards Electricity, that’s one market I’ve never traded. Even though it appears available via the European Energy Exchange, as far as I can see on most days there is zero volume, so for an academic paper this may be interesting but in the real world we can’t trade it, so even if skew does predict its future returns I’m not interested. The same applies to Pork Bellies … I used to trade it, but from memory this contract was delisted by CME some 6-7 years ago.

OK that’s my thoughts on the study’s portfolio. I am working on what I think is a far more applicable portfolio for testing purposes and will post shortly, meantime any comments are welcome.
 
So following on, here is what I feel is a far more diverse and therefore appropriate portfolio to analyze the effect of past skewness on future returns ….

Grains: Soybeans, Wheat, Rice, European Rapeseed, Milling Wheat and White Maize

Energies: Crude Oil, NY Natural Gas, UK Natural Gas and Ethanol

Meats: Live Cattle and Lean Hogs

Metals: Copper, Gold and Palladium

Others: Rubber, Cocoa, Cotton, Lumber, Orange Juice, Sugar #11, Coffee and Palm Oil

Here’s what I like about this portfolio …

- None of these markets have a high correlation to any of the others and so all should display quite different skewness properties

- I can and have traded all of these markets so can accurately measure commission and slippage costs

- While the size of the portfolio has reduced from 27 to 23 we have a much more diversified portfolio thereby making our back-testing process more robust

- A few of these markets such as Ethanol, Rice and Lumber are not by any means highly liquid and therefore may not be suitable for an institutional sized book however they’re all fine at a retail level

- With the exception of Ethanol most of these markets have been actively traded for 20 or more years and some considerably longer so plenty of data to test.

- In case anyone is wondering Natural Gas contracts traded in NY and the UK are subject to quite distinct supply and demand factors and as such are not highly correlated.​

As per usual any feedback is welcome
 
The next potential issue I have concerns the construction of the return series used in calculating the skewness of each market.

The authors appear to have a lot of experience working with futures data so I am surprised to see no mention of the methodology used to construct a continuous price series, i.e. how are they accounting for the price gaps when rolling from one contract to another? This may seem obvious but I’ve read papers before where the author has totally ignored this aspect of historical futures data. In this case the non-removal of price gaps would significantly increase the level of skewness for those markets that traditionally present in a strong state of contango or backwardation.

The method employed to calculate the daily returns used in the skew calculation is as follows …

“The futures returns are constructed as logarithmic price differences assuming that we hold the nearest-to-maturity contract up to one month before maturity and then roll to the second nearest contract”

If price gaps at rolling have been removed then that seems fine, but it’s a big if. For my purposes I will be constructing a continuous price series by back-adjusting all closing prices (rolling with a combination of Volume and Open Interest) and calculating daily returns as follows …

Daily return = (today’s close – yesterday’s close)/yesterday’s unadjusted close
 
Another important point that I think needs to be addressed correctly is the allocation of capital made to each commodity. The paper says …

“The constituents in the long-short portfolios are equally-weighted”

But equally-weighted according to what? Keeping in mind that we are trading futures here, are the authors really saying that they will buy/sell the same nominal dollar value for each commodity, i.e. $100,000 of Oil, $100,000 of Cotton etc. If so, then knowing that all markets within the Energy sector have historically, consistently and significantly higher levels of volatility than all other commodities, this will result in Energies having an overweight impact on the strategy’s performance.

This is a significant concern as the paper may be in fact be unwittingly concluding that skew is a predictor of future returns in Energy markets rather than all Commodity markets.

From my perspective for robustness purposes I would like all commodities to have an equal impact on the strategy’s profitability or otherwise and so, will be weighting allocations based on each market’s recent volatility.
 
If it's realized volatility you will be using, what is your in-sample period? Or will you be using implied vol?

This is a good project, BTW. Best of luck!
 
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