# Why is the future quote lower than the underlying?

I guess this is a simple one for experts: Looking now (12noon CET Nov 7, 2014) at the DAX ^GDAXI on yahoo finance, it says S = 9.361. The Future FDAXM5.EX quotes F = 9.388.

• What is the exact contract specification - does the buyer promise to buy the index in half a year? For which price - the current S = 9.361?
• If so, why is F not more than S?
• What is the theoretical formula? I thought the price F of the future on the underlying S should be F = S exp(r Delta_t). Given the interest rate r is today about 0.5% p.a. and Delta_t is about 0.5, I should expect about F = 9.361*exp(0.25%), but at least more than S.

## 3 Answers

9388 is the last price but it is not where the future is trading right now. If you look at the bid/ask it tells a different story.

For example a few minutes you would have seen:

• spot (index) price = 9329
• June Future: price = 9388, bid = 9363, ask = 9365

So had you wanted to buy the June future you would have paid 9365, not 9388, which is just a stale price. The reason is that for financial futures, unless you are running a very specific arbitrage, it makes little sense to go for longer dated future and the first contract is the most liquid. The June contract has only traded 18 contracts today vs. more than 50,000 for the Dec 14 contract.

Your formula is wrong.

Let's say that A and B sign a future contract. In half a year, A buys a share from B at a fixed price. During that time, A earns interest on his money, so you need to take this into account (which you did). Also, B may earn dividend from the company, so you need to take this into account too (which you didn't do). Thus, when you calculate the theoretical price for the future contract, you need to consider whether some of the DAX index companies will pay any dividend during the following six months, and if so, how much dividend they will pay.

• Thanks a lot you guys. Ok I guess I the order of the prices is correct - 9388 > 9361, and about exp(0.5% * 0.5) * 9361, assuming current rates at 0.5%, and Delta_t being about 0.5. I guess I had turned it upside down... Taking into account an expected dividend payment of D per share just before the exercise date in June, is the correct formula then F = S exp((r) Delta_t) - D? One more question: Is there a future which can be seen to follow pretty well this formula (or the correct one, if the above is not so)? Eg. for commodities, is the underlying commodity spot price also quoted? Best, F – Futurist Nov 8 '14 at 13:11

Expected dividends for the life of the future will push your price down, as futures don't pay dividends, so they must be cheaper than the underlying.

Risk free interest rate (i.e. the interest of the fix income product of the country you will invest with the same maturity of the future) will push your price up, as the future allows the investor to put part of the notional in a (theoretical) risk free product, such as a bank account.

Note also that the expected dividend can change during the life of the future, and also the interest rate. This can impact the value of the future, apart of the change on theprice of the underlying.