Drixx Quant

February 16, 2021The inverse perpetual (or "inverse perp") is one of the most common instruments in crypto. However, it is also one of the most misunderstood. The instrument is a "perpetual" because unlike a traditional futures contract, it does not have an expiration. It is an "inverse" because the payout is in crypto (BTC, ETH, etc.) while sizes are quoted in fiat (USD,EUR, etc.). In this article, we will be looking at the detailed mechanics ofthe inverse perpetual, as well as the motivation behind some of its design choices. We will also look at some common use cases. To simplify the discussion, we will look only at the BTCUSD inverse perpetual. However, any explanation, formula, or charts will apply to any crypto inverse.

How exactly does the BTC inverse perpetual contract work? The perpetual is designed to give you a return based on the USD size of the contract**.** This means that if you purchase 10,000 units of the contract,and the price of BTCUSD goes up that 20%, you will make $2,000 (or exactly20%). Conversely, if the price of BTC drops 20%, you would lose $2,000. Effectively,your USD P&L is linear relative to the price of BTCUSD.

Let us look at some properties of the inverse perpetual.

- Contract units are quoted in USD. When you purchase 10,000 units of the contract, you are effectively purchasing $10,000 dollars of BTC. This design might be somewhat unintuitive to traders of non-inverse futures or actual BTC (where the quoted unit is BTC). However,thinking about contract units in dollars makes it much easier to know roughly how much USD you have invested (and have at risk).
- The payout is in BTC instead of USD. When you close or reduce a contract position, any P&L is settled in BTC.
- Every perpetual derivative contract references an underlying index. This index is supposed to reflect the price of the underlying BTC coin. For Drixx, this is the Drixx BTC Index.
- The BTC perpetual price is still quoted in USD per BTC (so the USD cost of 1 BTC). If you see a price of$20,000 BTCUSD, it means that it costs $20,000 to buy 1 BTC. Funding (which we will discuss in a later section) ties this BTCUSD perpetual price to the price of the index.

Because the payout of the inverse perp is in BTC, there isno need at all to deal with USD or a stable coin. This design benefits long-term BTC owners who have unrealized gains (and do not want to sell into a USD stable). In addition, it is beneficial to non-US customers who might not want USD exposure. All margining is also against BTC instead of USD. This is margin efficient because you can just offset your BTC perpetual shorts directly against your BTC underlying assets.

A position in an inverse perpetual is defined by the number of contract units and the average price (or your executed price). Using these two figures and the market price of BTCUSD, you can figure out your P&L:

- Long Position:

💠 BTC P&L = # contract units * (1 / avg price -- 1 / market price) - Short Position:

💠 BTC P&L = # contract units * (1 / market price -- 1 / avg price)

We can look at a quick example. Let us assume that the price of BTC is now $12,000, but you entered a long position at $10,000 for 10,000units. Then your BTC P&L is (1/10,000 -- 1/12000) x 10000 = 0.167 BTC. However,if we convert this 0.167 BTC to USD (at the $12,000 price), we see that it is exactly $2,000. We can interpret a "long" position in the inverse perpetual as follows. You have agreed to receive contract units / avg price BTC (your asset). However, in exchange, you will pay contract units / market price BTC (your liability) when you close. We can better illustrate this in the below chart. We use the same 10,000 size and $10,000 starting price.

Graph for Inverse Bitcoin Pepetual (BTC/USD)

- We see that relative to the number of contract units, the USD P&L is linear. This means that for a 1% increase in BTCUSD price, the USD P&L also increases by 1%.
- We see that BTC P&L is not linear.

o As the price of BTC increases, you receive less and less BTC. This is because the value of each BTC increases.

o As the price of BTC decreases, you will have to pay more and more BTC (because the target P&L is in USD).

Because your collateral for an inverse is also BTC, the non-linear BTC P&L has a much larger impact when the price drops (and you are long). By default, you are 100% long BTC already! Any additional long position becomes a levered position.

Before we talk about funding, let us quickly talk about the BTC Index. How do we get an accurate reflection of the price of BTC (the price that the perpetual should reflect)? Well, if the derivative exchange also has a spot exchange, we could potentially use the mid-price of the BTC spot order book as the "index". However, this might not be an accurate picture of the price everywhere. The liquidity on the spot exchange might be poor. A large market order could also drastically affect the bid or ask temporarily. To solve this, we use an aggregate index.

Effectively, an aggregated BTC index gather prices from several external exchanges and takes some average (or median). There are many ways you can design an aggregated index. The Drixx BTC Index uses a trimmed median from multiple different exchanges. Exchanges that appear down or lagging are removed from the price calculation. Great care is taken to make sure that the index price is the most accurate reflection of the actual BTC price. Refer to Drixx official Index documentation to see how it is calculated.

In a non-perpetual future, the future generally has a settlement / expiration date. On the expiration date, the contract would be closed out at the prevailing market price of the underlying BTC. As a result,the price of the standard future never deviates too much from the underlying price (with the future price converging to the underlying as expiration gets closer). Perpetuals, however, never expire, so there needs to be some mechanism to tether the price of the perpetual to that of the underlying. This mechanism is funding.

Effectively, funding "settles" the difference between the perpetual price and the price of the underlying index periodically. Generally, this period is one day. If the price of the perpetual is at $15,000 and the price of the underlying is $10,000, then longs should owe shorts $5,000 (or 50%) after24 hours. This is equivalent to a future that expires daily (against sometime-weighted average index).

How does funding apply to you as a trader? Positive funding means that the price of the perpetual has been trading above the underlying throughout the funding period. Longs will need to pay shorts. Conversely, negative funding means that the price of the perpetual has been trading below the underlying. Shorts will pay longs.

Funding has historically been positive. This is because borrowing dollars to open a leveraged position **should** theoretically not be interest free.

Given everything that we have learned earlier about the inverse perpetual, let us go over some common use cases.

🎚️ Probably the biggest use case of the inverse perpetual is leverage. You can use it to get multiples of your exposure to Bitcoin (or some other crypto). However, keep in mind that because your collateral is BTC, you start off 100% invested. Let us say the price of BTC is $10,000. If you buy an additional $10,000 units of the inverse contract, you are effectively long $20,000 BTC instead of just the $10,000. See our Leveraged Trading piece to learn more.

🔐 Instead of buying Bitcoin directly(and storing it on an exchange), you can open a leveraged perpetual position on an exchange instead. Because the margin requirements are small relative to the exposure, your losses will be much smaller if the exchange suffered security problems. Perpetuals are very liquid and let you enter or exit positions very quickly. Moving BTC between cold storage and a spot exchange could be very slow(and might result in missed opportunities).

🛡️ The most useful purpose of the inverse perpetual is hedging. If you sold the exact dollar worth of your BTC collateral as a contract, you would be perfectly hedged in USD terms. In addition, you will collect any positive funding (See our Yield article). Let us go through an example:

Let us assume that BTC underlying is trading at $10,000 and the perpetual is also trading at $10,000. You have 2 BTC so the value is $20,000. To hedge your BTC position, you could sell 20,000 units of the perpetual contract. What is your P&L then?

BTC Collateral P&L (USD) = 2 *(market price -- original BTC price) =

` 2* market price -- 20,000`

Short Perpetual P&L (USD) = 20,000* (1 / market price -- 1 / original price) * market price =

```
20,000/ market price * market price -- 20,000 * market price / 10,000
20,000-- 2 * market price
```

Therefore, Total P&L = BTC Collateral P&L + Short Perpetual P&L = 0. You are perfectly hedged!