# Why are stock index futures not used to forecast how much the stock market will rise, given that interest rates futures are used for this purpose?

In news articles, the reader often read interest rates forecasts calculated based on interest rate futures.

I have never come across anyone forecasting how much the S&P500 will rise for the year based on S&P500 futures. Why not, given that interest rates futures can be used to forecast how much interest rates can rise?

What is the difference between interest rates futures and stock index futures that one can be used to make forecast while the other cannot?

Interest rate futures enable you to build an interest rate projection curve which you can think of as representing the risk neutral expectation of rates in the future, therefore providing you with a "forecast" of rates in the future.

Likewise, stock index futures enable you to build a dividend yield and repo cost projection curve which you can think of as representing the risk neutral expectation of dividend yield and repo cost in the future. To build such as curve you first compute the stock index forward curve and then divide by the current stock index value. That curve provides you with a "forecast" of dividend yield and repo cost in the future.

In essence when you work in the interest rate world the natural numeraire is the currency, whereas when you work in the stock world the natural numeraire is the stock itself, and dividend yield & repo cost for stocks become the equivalent of interest rates for currencies.

• Please check if I understand you correctly. Index futures curve contains the market expectation of the future dividend yield and interest expense of holding the underlying stocks. Interest rate futures curve contains the market expectation of what the future interest rates look like. Is this correct? Feb 15, 2018 at 10:59
• Yes exactly. To put it differently interest rate futures contain the expected rate of return of investing in the interest rate market, when you compute the rate of return using the currency as numeraire, whereas stock futures contain the expected rate of return of investing in the stock market, when you compute the rate of return using the stock itself as numeraire. If there is zero dividend and zero repo cost then the rate of return is zero: one share of stock in the future is worth exactly one share of stock today. Feb 15, 2018 at 11:10

The main reason is that with interest rate futures interest rates are entering the pricing formula because they are not hedged while with stock index futures the indices are being hedged (while interest rates also enter the pricing formula here!)

So with index futures you price the index in a risk-neutral way while with interest rate futures (and index futures!) you don't price the interest rates in a risk-neutral way.

More on the rationale behind risk-neutral pricing see here: https://quant.stackexchange.com/a/107/12

This might be helpful too: https://quant.stackexchange.com/a/8252/12

• Not sure if I understand you correctly. Index futures are mainly used for hedging while interest rate futures are mainly used for speculation. Is this the right interpretation? Feb 15, 2018 at 9:25
• @user3848207: No, you can use all instruments for either hedging or speculation. It always depends on what you want to hedge or what you want to speculate on! Mathematically you would ask what your degrees of freedom are. Feb 15, 2018 at 9:26
• @user3848207: In this context this might be interesting for you: quant.stackexchange.com/a/6990/12 Feb 15, 2018 at 9:47

I would put it slightly differently. For Stock index futures , the 2019 contract has the same underlying stocks as the spot index. Therefore the futures price can be simply calculated as spot price increased by interest rates and decreased by dividends. The futures price does not contain any interesting new information about stocks that you cannot see in the spot index.

For interest rate futures , the Fed Funds futures for March 2019 (say) is a completely different underlying than the Fed Funds futures for Feb 2018. One cannot be calculated from the other. Hence there is interesting new information by looking at the interest rate futures.

People are all kinda dancing around the straighforward answer, which is that you can trade the underlying for a stock index future but not for an interest rate future. When you can trade the underlying, arbitrageurs will push the future and its underlyer prices as close together as possible. The difference is roughly the cost or gain from the arbitrage strategy.

Thus the price of the future for a stock index is determined by arbitrage and has no forecasting value (in theory, or at least the theory I'm referencing -- the real world may beg to differ).

Since the same consideration is not true for an interest rate future (at least not in such a straightforward way), its price is set by market expectations. Whether or not that has forecasting value is its own question, but hopefully this answers the question of why one future seems to be a reflection of expectations while the other basically just moves with spot.