Historical Var for commodity books

[bramj]

I'm looking for some advice regarding historical VaR on commodity books. Any pointers on how to implement historical VaR on a book where the underlyings are different futures for a commodity?



If one takes the historic returns of what is now the first future, it is well possible that this history has too little volatility. If one always takes the history of returns of the first nearby future there might be issues with seasonality.



Any thoughts would be appreciated!

[aaron]

The key is to remember you're doing historical simulation on market factors, not market prices. For equities there's no differnce, which is why people can forget that. But for bonds, you don't use the historical prices of the bond you hold, you use historical interest rates for a bond with the credit and maturity of your bond, and compute the bond price from the interest rates.



For commodities the usual model is:



Futures_Price = Theoretical_Spot_Price x Seasonality_Factor x exp[r x Time_to_Delivery]



The seasonality factors are a fixed mapping from day of the year which you can estimate historically, the theoretical spot price and r are set from the first two futures contracts. You use historical values of spot price and r to price your current position.



If you trade farther out on the curve than two contracts, or run highly offset positions, this might not be enough. But the principle is the same. Model the prices and simulate the model parameters, not the prices.

[Tradenator]

Weather (and politics?) drives deviations from Gaussian to be too large to give me any faith in VaR.  Sure, you can calculate it for a portfolio of futures, but I would be very wary of it for a directional commodity program.  (Hedging and spreading, I'm not the person for those, there are others here...)



I would ignore aaron's advice and not try to back out spot prices from the arb-free model.  You are trading futures, not spot, so just use the contract months held in the book at any time.  In general, volatility declines as you go out along the forward curve in line with the Samuelson Effect.  You can try to smooth out periodicity over an integer number of cycles.



In 2008-9 you should expect to see VaR go through the roof as both volatility and correlations ramped up and then declined.  Note that inter-commodity correlations have increased with the influx of index investors over the past decade or so, and this will influence your results on either side of the 2008-9 event.

[bramj]

Thanks for your comments. Let me start out by saying that I don't have faith in VaR either, but   my risk management will be looking in the near future to implement historical VaR for our commodity book (which is  a multi-commodity derivatives book with both plain vanilla and exotic options in it with maturities up to say 5y) and I want to be prepared



The VaR calculated will be based upon a history of 1y daily returns (or factor changes).



Tradenator, you are saying (if I understand correctly) that I should base myself for the n-th future on the historic movements of the n-th future. Problem with that seems to be that this n-th future rolling over time has returns driven by seasonality. This will probalby be an issue, and I don't understand what you mean by solving that by soothing out the periodicity over an integer number of cycles.



Aaron, what worries me a bit about your approach is that it probably is that for a single commodity I probably have to have roughly let's say three different r's for different maturities (actually I've never tried explaining the forward curve via pca with different numbers of factors), but I'm assuming 3 will do the trick for now. Now even though a lot of commodities in our book are highly correlated, we're still talking about various precious metals, base metals, energies & softs, so that is 12 factors already if I assume that I can take just one factor for each asset class. I think I actually read a post by you on W****tt once about the problems associated with a large number of factors when considering historical VaR. Another way of sort of saying the same: doesn't a VaR number htus computed underestimate the VaR coming from stochastic convenience yield?



Thanks again!

[sfca]

I think you need to first figure out a model and then the details.  There are different ways to do VAR, such as the historical simulation approach or various parametric approaches or results from a remapping algorithm and such.  You ask about historical, but then Aaron answers you giving a remapping example that is not historical simulation.  A mapping like that might be fine for various applications, but that is not an historical simulation.  If you do want historical simulation and you are bothered by the seasonality of returns, my initial thought is to just deal with that directly.  There are all sorts of free and easily available seasonality algorithms such as X-11 and X-12 from the Census Bureau website and other software (eg. eViews).  You could initially create deseasonalized returns, calculate the history, and then reseasonalize them for a conditional VAR result.

[aaron]

Historical simulation VaR is not VaR. It's just a number, handy to know. A real VaR will backtest, that is you should be willing to take either side of bets at 19 to 1 that there will be a break of a 95%, 1-day VaR tomorrow. Doing that with historical simulation VaR will be very expensive.



Historical simulation VaR does not depend on a Guassian assumption, you just take the 5th percentile of the historical P&L moves.



You are correct that my answer is impractical for complicated books. If you trade more than two dates in each commodity and have highly offset positions, I know of no way to compute a meaningful historical simulation VaR. If you use enough factors to get a decent mark on the portfolio, you'll have too many factors to fit. If you use the number of factors you can fit, your P&L computation will be too inaccurate.



But this isn't a criticism of the method, it's a criticism of the question. There is no meaningful answer to, "How would a fixed complicated portfolio of commodity futures have performed over the last year?" Contracts clearly change their nature as they approach and pass delivery. The best you can do is a crude adjustment for that.



For complicated positions, you just have to say you can't compute the HSIM VaR and do a Monte Carlo instead.

[Tradenator]

Historical simulation...what I was trying to suggest was that you model whatever contract you are holding on any day and look back N*12 months in your calcs for that time.  Leave out the roll for a first approximation.  I admit this is a gross simplification and there may be contract liquidity constraints if you have to go back too far, though.  But it makes good engineering sense to have fewer moving parts if you can.  The N*12 month roll-less scheme can help for very seasonal contracts like natural gas, but less so with markets that can swing between backwardation and contango for longer periods of time.

[bramj]

Thanks for the insights