The definition of arbitrage is simple, ensuring profitability without assuming any risk, which is also known as a Free Lunch. We will address this issue from a theoretical concept, because in reality, to arbitration is not as simple as explained below and only is available to very few, because to arbitrate is necessary to have a large capital and speed of execution of operations, because here who hesitates is lost.
The future dow jones is nowadays one of the financial centers of the world future market. There are several types of arbitration (with options, with ETF’s, with cross rates, etc …) but today we are going to focus on the future arbitration. To do this we need to know how the theoretical price of a future is calculated, it is clear that this formula will vary minimally if the underlying future are stocks, currencies, commodities, etc. For example, the formula of the theoretical price of a future dow jones index is as follows:
- “F0” is the futures price at 0, ie the price that would have to be today.
- “S0” is the price of the underlying to 0.
- “r” is interest free continuous risk, expressed in continuous terms.
- “q” is the dividend yield of all shares index percentage, expressed in continuous terms. Clarify that represents the average annual dividend rate over the life of the contract. Dividends used to estimate “q” should be those for which the dividend date postpaid occur during the life of the contract.
- “T” is the period to maturity of the future on an annual basis, for example, if the future dow jones expires in three months T = (3/12) = 0.25.
How you can arbitrate with index future Dow Jones?
For when putting equality above is not met, that is, when not match the theoretical price with the market price of the future. That is, when the theoretical futures price is higher or lower than the contract price of the future, so we have two possible cases:
Case 1: the price of the futures contract is greater than the theoretical price, ie:
To arbitrate when this situation to have to position ourselves short in the future on the index and buy all the shares of the index by weighting.
Case 2: the price of the futures contract is lower than the theoretical price, ie:
As this is not the case, we have to position ourselves to arbitrate future long and short index in the stock index by weighting.
An example of index futures arbitrage
Imagine that the current value of the Dow Jones index is $ 10,000, which provide stock index dividend yield of 2% per year and that the type of risk-free continuous interest is 6% per annum. On the other hand we have a future contract on the Dow Jones index due within three months trading at $ 10,005. So we’ll get the following formula:
It turns out that this equality is not satisfied, because if we solve the formula would give us the following: 10,105> 10100.50167. So we have to position ourselves to arbitrate short in the future on the Dow Jones and long on all shares comprising the index and would obtain a total of $ 4.4983 per $ 10,000.