ES futures and SPX

Those of you with good eyes have noticed that ES futures trade sometimes at a discount to SPX and other times they seem to trade at a premium. Right now they look discounted (cheaper than SPX) but last week they were a tad higher, why is that ?

The explanation resides in the fact that ES futures trade closely the SPX forward value expected at settlement day. And if you remember a Forward is computed like this:

Forward = SPX * exp((r-q)*t)

Where r is the risk free rate, and q is the dividend yield and t is the time to settlement in years. Also exp() is the usual exponential function. Even if you are not familiar with these kind of math the important thing to keep an eye is on the (r-q) substraction. Some properties can be seen from there:

1. If r = q, in other words if risk free rate is equal to the dividend yield of the basket, then r-q =0 and in that case Forward = SPX. That means that in that case ES futures will trade at the exact same level than SPX.

2. If r > q, if the risk free rate is bigger than the dividend yield, then r-q > 0 and in that case the Forward > SPX. That means the ES trades higher than SPX.

3. And finally if q > r, if the dividend yield is higher than the risk free rate, then Forward < SPX, which means that ES will trade lower than SPX.

What we have seen in the last couple of sessions is that ES went from trading higher than SPX to now trading a bit lower, however nothing has changed much, interest rates haven't changed and dividends remain the same, so why ? The explanation is that the dividend yield has changed !

Even though dividends are the same remember that they are always expressed in absolute dollars and the yield is computed as a fraction:

q = total dividends/ total cost of the basket.

So during a big market fall, the cost of the basket comes down a lot and the dividend yield goes up a lot which causes the q > r condition. That is why ES will trade at a discount at these levels (and below these levels too).

Leo Valencia hosts the Gamma Optimizer options service at