This article describes futures and its payoffs. In order to see how to apply basic arbitrage and hedging strategies, visit our Futures Arbitrage and Hedging Guide.

Quedex offers inverse futures contracts on BTCUSD exchange rate. Futures are financially settled in bitcoins and inverse notation is used. Realized P/L is calculated as follows:

`Realized P/L = Side * (1/Entry Price - 1/Exit Price) * Quantity`

where:

`Side`

- 1 (long position) or -1 (short position),`Quantity`

- number of contracts, we assume that notional amount equals to $1,`Entry Price`

- price, at which position was opened,`Exit Price`

- price, at which position is closed.

To calculate `Unsettled P/L`

of open position one has to put `Mark Price`

(the price for valuing the contract) in the above mentioned formula instead of `Exit Price`

.

Assume that there are two investors (A and B) who have entered into the following inverse futures contract:

`Quantity = 10000, Entry Price = $10000.`

What is more, assume that investor A took long position (she bought the contract) and investor B took short position (he sold the contract). Below we present P/L in BTC for the sequence of possible Exit Prices.

As we can observe, the payoff functions are nonlinear with respect to the `Exit Price`

. It is consequence of the P/L formula for inverse futures contract. What is more, the payoff function of the investor A (B) is increasing (decreasing). It is explicable, as long (short) position should be profitable, if price of the contract increases (decreases). In fact, inverse relation in exchange rates implies that long (short) position in inverse futures contract is short (long) the theoretical contract on USD.

Another important feature of the futures contract is that if Free Balance is big enough compared to possible `Unsettled P/L`

than short futures cannot ever get margin called when trading with leverage lower than 1.

Investor sells 20000 futures contract for $10000. On Quedex margin percent for initial margin equals to 4%. Therefore

`Initial Margin = margin percent * 1/Mark Price * Quantity = 0.04 * 1/10000 * 20000 = 0.08 BTC.`

What is more investor has 3 BTC deposit. Hence, in our example at the beginning `Free Balance = 2.92 BTC`

. Investor receives margin call, if `Free Balance`

falls below 0. It would be possible, if `Unsettled P/L < - 2.92`

, so

`(1 / Mark Price - 1 / 10000) * 20000 < -2.92 1 / Mark Price < -0.92`

It is impossible, because `Mark Price`

is always positive, so in this particular example investor cannot receive margin call. On the other side, if the investor had had less than 2 BTC deposit, then she might have received margin call.

Log returns describes the relation between current spot price and entry price. We will define log returns as logarithm of quotient of current spot price and entry price

`Log returns = log( Spot Price / Entry Price ).`

We are going to display the relation between payoff values and log returns. Assume that there is an investor A (investor B), who takes long (short) position in futures contract with:

`Quantity = 10,000, Entry Price = $10,000.`

The relation between payoff values and log returns in this specific situation is presented at the following chart.

The results are quite clear. In case of Investor A (Investor B), the higher (lower) the Spot Price is, the higher (lower) P/L is. Since logarithm is an increasing function than above mentioned implication is also true, if we consider log returns instead of `Spot Price`

. We can observe that P/L in BTC of futures contract is “almost linear” with respect to log returns.

Now, we consider the situation in which investors observe P/L in USD. It is quite easy to notice, that in this case P/L will be constantly equal 0. In our contract we perceive USD as underlying `($1 * Quantity)`

, so the value of the contract denominated in underlying is constant (determined at the beginning - `$1 * Quantity)`

.

Investor, who has long (resp. short) position, wants Backwardation (Contango), due to the fact that futures price has to converge to spot price. Below we present exemplary behaviour of the futures prices at Contango and Backwardation market.

Contango and Backwardation indicate pricing inefficiencies and enable futures arbitragestrategies.