Futures Arbitrage Guide

Futures arbitrage strategy is possible when the market is in the Contango or Backwardation. It consists of the long (respectively short) position in an asset (in this case USD) and long (resp. short) position in the futures contract. Choosing between long and short position depends on whether the market is in Contango or Backwardation. Let us consider the following example.

Unless stated otherwise, we will assume that Settlement Price is the same as spot price at maturity in the whole article.

Example

Assume that current spot price of 1 BTC and expected future spot price both equal to $11,000 and one-month futures contract is priced at $10,000 (so market is in Contango). In this particular situation it is possible to perform Cash & Carry Arbitrage strategy. The arbitrageur:

  • buys $11,000 for 1 BTC,
  • has 5 BTC deposit,
  • takes long position in 11,000 inverse futures contracts at the price of $10,000,
  • holds this portfolio until contract expires.

At Quedex margin percent for initial margin is 4% and for maintenance margin is 3%. Recall the margin (initial and maintenance) formula

Margin = margin percent * 1/Entry Price * Notional Amount * Quantity,

where, in our example:

Notional Amount = 1 ($1), Quantity = 11,000, Entry Price = $10,000.

So, initial margin = 0.044 BTC and maintenance margin = 0.033 BTC. In our example, at the beginning

Free Balance = Deposit - Initial Margin + Unsettled P/L = 4.956 BTC.

We assume that investor will not receive margin call, so Free Balance always has to be greater than 0. This implies that Unsettled P/L must be higher than - 4.956 BTC, so futures price has to be at least $1,816.39, because

Unsettled P/L > - 4.956 BTC 1 * (1/10,000 - 1/Mark Price) * 11,000 > - 4.956 Mark Price > $1,816.39

Recall settlement P/L formula.

Settlement P/L = Side * (1/Entry Price - 1/Settlement Price) * Notional Amount * Quantity,

in our example investor takes long position (Side = 1).

Now, we show investors profit in two different scenarios of Settlement Prices. Assume that

  1. Settlement Price = $12,000,
  2. Settlement Price = $1,816.39 - smallest possible value not to receive margin call.

On the expiration date investor has

  1. P/L + $11,000 * (1/12,000) = (1/10,000 - 1/12,000) * 11,000 + $11,000 * (1/12,000) = 1.1 BTC,
  2. P/L + $11,000 * (1/1,816.39) = (1/10,000 - 1/1,816.39) * 11,000 + $11,000 * (1/1,816.39) = 1.1 BTC.

Hence, for each scenario for 1 BTC invested, investor receives one month later 0.1 BTC, so more than doubles his initial margin (which equals to 0.044 BTC). However, the success of this strategy depends on the behaviour of the prices until expiration (Mark Price cannot drop below $1,816.39, at which the position will be liquidated).