Backwardation, from Jim Sogi

March 20, 2010 |

Can readers help me understand the meaning of backwardation vs contango in the past in the ES? Why is it negative now? Does it mean people think it's going to go down, or are the rates that low? I've studied, but don't really understood the formulas for computing the values of the future contracts or why there is a negative spread now when is was +4 points or higher spread in 2007 as the market topped on the rolls.

Nick White lends a hand:

Garden variety futures valuation is just a simple cost of carry model: the price of the underlying today adjusted for the cashflows you expect to pay/receive until expiry. The whole bundle is then appropriately adjusted via interest rates for time — effectively, the exact same as any other asset.

Intuitively, this is easy to understand if you think of how NPV — or a DCF model — works and then team it up with the laws of arbitrage. What is your asset worth today given what you will spend and receive for it over a given period, adjusted for interest rates? If your asset can be exactly replicated, is the price of that replication worth more or less than the original? If so — ceteris parabus — you can arb it.

The proviso to the above is that not everybody has the same interest rate in their model… your cost of funding may be very different to mine, which will be very different to GS's. I would argue that — care factor on Index Arb notwithstanding — one's ability and inclination to practice any form of index arb depends vitally on this cost of funding rather than some point spread in the rolls… and that in turn "depends" on whether the arb is long stock / short future or vice versa. Risk free rates are just a proxy.

So, if you cannot perform index arb… what is this info useful for? Knowing the fair value spread might give you a few ticks edge when placing an order because the future may already be a bit over/under extended vs the cash market. So, to provide an example, if you're buying, you may be better to place your order — per the Chair's admonition — a couple of ticks behind the BBO if the fut is over-extended vs the cash. Otherwise, you might want to lift the fut if the cash has moved and the future is lagging.

Very simplistic — but backwardation and contango are just natural progressions of these pricing models, adjusted for the vagaries of short-term supply and demand.

Steve Ellison comments:

 Philip L. Carret, in his 1931 book The Art of Speculation, considered it very bullish when stock dividend yields exceeded the margin interest rate. In such circumstances, he said, stocks "carried themselves", i.e., one could buy stocks on margin and pay the interest on the loan using dividends. Backwardation indicates that S&P 500 futures now carry themselves.

The S&P 500 futures began trading in 1982 and almost never traded in backwardation for the next 20 years. They went into backwardation in mid-2002 and stayed in backwardation for most of the next two years, advancing 53% during this time. They have been in backwardation continuously since October 17, 2008, advancing 25% during this time.

Russ Sears interjects:

 I have seen some option quotes on Enron, that had calls, same strike, different maturities (I believe it was Oct and Dec maturities) that apparently had some time arbitrage. Not sure they were actionable though. In 2000 I bought some deep deep out of the money long term custom interest rate options, that later became in the money, for my old company. The selling counterparty called in 2003 and begged us to sell them back, because they were very difficult to hedge. He told me they were so far out of the money that they sold them thinking they would never have to actually hedge them. I suspect in both cases the option seller, simply booked the premiums as 100% profit, so the theory really went out the door.

Quant Chicken writes in:

The personal impression I formed when I reviewed the empirical academic literature 4-5 years ago was that the forward is not an unbiased predictor (contrary to the theories of FX I had learned in school). The "forward premium puzzle" has been confirmed using so many different statistical tests (some quite esoteric) that I came to believe there is something to it.

I was getting interested in investing real money in this anomaly when I was dissuaded by wiser colleagues, who pointed out that this "carry trade" idea (borrow in low yielding currencies, invest in high yielding ones) was getting crowded, everyone was getting into it, DB started an ETF to allow public to participate (this was in 2006), etc. And statistically the evidence was not very strong. In retrospect I am glad my friends advised me to stay out of it.


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