So You Want To Understand S&P Futures Basis Trades (aka, Index Arb)?

I swear - there's nothing I'd rather do less than spend my time being the re-educator for all the incorrect crap that ZeroHedge spews into the Interwebs, but when a blog as widely read as they are publishes such utter and complete nonsense, threatening to miseducate masses of readers, well, I can't help myself.  So let's turn it into another educational lesson, right in my wheelhouse: today's topic is the "backwardation" in the S&P 500 futures.

Backwardation, although a term I've never heard applied to S&P futures before (that's a commodities futures markets term), means that the longer dated futures contracts are trading at a discount to the near contracts.  In other words, the price to buy the June 2011 S&P 500 future (herein referred to as the ESM1)  is lower than the price to buy the December 2010 S&P 500 future (herein referred to as the ESZ0).  This is a function of two things:  interest rates, and dividends, but not at all an indication of future supply and demand for stocks.

In the index arbitrage world, we want to know how the futures are trading versus their "fair value." The fair value of the futures vs. the cash index (underlying stock basket) is the difference in cash flows between holding one or the other.  The inputs are the "carry effect," derived from interest rates, the index level,  and time to maturity, and the "dividend effect," derived from the dividends that the companies in the index will pay between now and the expiration date on the futures.

When you buy the ESM1 - the June 2011 S&P 500 future, you don't actually have to pay for the full notional value of the future. You post margin.   Since you don't actually own the underlying stocks, you don't receive the dividends on them.  On the other hand, you earn "carry," because you can invest the money that you would have otherwise spent buying all the underlying stocks.  We can write a very simple equation to tell us what the equality would be if everything were trading at "fair value" and there was no arbitrage opportunity:

(ESM1) + carry = (SPX) + dividends

In other words, buying futures (that's why it's in parenthesis - it's a negative cash flow - we're spending money) and receiving interest on the money you don't have to spend buying the index itself is equal to buying the index itself and receiving dividends. Let's do some 6th grade algebra, rearrange those terms, and come up with the value of the basis: the difference between the futures and the cash index:

Carry - Dividends = ESM1 - SPX          aka, Futures Price - Cash Price, or "Fair Value"

Now, for my entire career, the "fair value" of S&P futures was always positive. The further out the curve you went (ie, if you looked at September instead of June futures,) the larger the fair value number got.  Why is this?  Simple:  the yield on the S&P was lower than the interest rate.  In other words, you'd rather own the futures than the entire basket of underlying stocks, because you can earn more money on the money that you don't have to spend buying the cash index than you can receive in dividends.  It's basically a simple interest rate equivalency.

Now, however, interest rates are zero, or near to it, so the fair value basis has turned negative - the futures are "less desirable" than the cash index because you'll earn dividends by holding the underlying stocks, but you don't have any opportunity cost that you're saving by buying the futures - because the alternative reinvestment rate on that cash is zero.  Thus, if you go out further on the futures curve, the basis becomes even more negative - because even more dividends are paid (yet the return on cash is still piddly).  

Which brings us to ZeroHedge, who writes:

"The ES futures curve is now at inverted term levels that have been unseen for months. For all who claim that by next summer the economy will be coasting well on its way to 3.5% growth or whatever imaginary number the crowd of lemming sell-side analysts pulls out of their pocket in their imitation of Goldman's upgrade, there sure is no actual conviction in this call. The differential between the Dec and the June ES contracts is a notable 10 points: December is at 1,246 while June is at 1,236. This is reminiscent of the curve last December, when those who bet that the market would be substantially lower half a year forward ended up being right on the money. For those who still believe in logic, a compression trade where one sells the Dec and buys the Jun contract may make sense, although with the only variable these days being what side of the bed Brian Sack wakes up on, we would be very cautious. As a reminder, the last time the VIX curve had a normal contango curve structure, was back in 2008, when the Bernanke Put was still being digested."

Of course, anyone with a rudimentary understanding of equity index arbitrage, even on the level I have just explained it above, will understand the reason that the June 2011 contract is trading at a 10  point "discount" to the December 2010 contract:  lotsa dividends will be paid between now and June, yet the interest rate curve out until June still provides for meager returns on riskless cash.   In other words, the 10 point discount isn't a discount at all - it's the difference between the June fair value and the Dec fair value. Of course, back in 2008, interest rates had not yet tanked, which is why the futures curve was upward sloping: the interest rate carry side of the equation was dominating the dividend side of the equation.  The equation has nothing to do with supply and demand for stocks. 

Class dismissed.  Ask questions in the comments if I've been unclear about anything here.

-KD

postscript: 

Now, in the interest of completeness, I should note a few slightly more advanced caveats.  First, the interest rate component is really based on the rate at which one can "fund" themselves.  In other words, for a bank, it's their cost of funds.  If I have a lower funding rate than you do, I can afford to perform the index arbitrage of selling futures and buying stocks before you can, because I require less of a futures premium to do the trade, since I have a lower funding hurdle.  Second, futures do of course sometimes trade rich or cheap to fair value.  In fact, most of my career, they constantly traded slightly rich, and many people on the street made a good living by selling futures at a slight premium to the calculated fair value, buying stocks, and holding those positions.  How do you do that?  You need a big balance sheet and cheap funding.  In other words, the futures richness is an indication of demand for FUNDS, not demand for stocks.  But I need another caveat here - the ZeroHedge post is talking about the roll trade - the difference between not futures and cash, but different futures months. I don't have the dividend and interest numbers handy, so I don't know if the -10 basis between June and December that they refer to is "rich" or "cheap" to fair value - but in either case, it's no indication of implied demand for stocks - rather, implied demand for balance sheet - for cash.   I would guess that it's trading pretty close to fair value.

Quick example:  suppose we calculate that the June S&P 500 future is trading 2 points higher than its "Fair value" (that would be a huge premium, by the way) - what do we do?  We sell the June S&P 500 future, we buy the basket of S&P 500 stocks, and we lock in our funding rate until June (so that if the Fed comes in and raises rates on us, we don't get crushed).  There's still a risk - that our dividend estimates were incorrect:  if we estimated that we'd get $12 in dividends, but only get $10, well then, there goes the $2 premium that we thought we had.  During my career, which was basically a bull market, this "risk" was actually more of a freeroll to the upside - because more companies increased dividend payouts on a surprise basis.  During 2008 and 2009, it must have been a risk, as companies slashed dividends - this would have been murder for index arb desks, who are generally long stock, short futures in the S&P 500.    However, a colleague tells me that as banks ran into trouble with their mortgage positions, they reduced balance sheet exposure elsewhere, and frequently lucked out of this risk by reducing large index arb positions.

Finally, I should mention the effect changes in various inputs have on the fair value basis, although readers can calculate this on their own easily from the equation.  If we hold all other inputs equal, higher index levels --> higher fair values, higher interest rates --> higher fair values, and higher dividends --> lower fair values.   We can easily understand why, because higher fair values mean holding futures is more desirable than holding the cash basket.   Higher index levels or higher interest rates each mean higher carry costs, which means futures are more desirable.  Of course, higher dividends means the cash basket is more desirable.