## Careful when you long Inverse Contracts or Careful When You Long Bitmex

This is an extract from June Monthly Digest

*This section is written by Clarens Caraccio - Quant Trader at Nibbio*

Nowadays in the crypto derivatives market, the perpetual contract is clearly king. While early exchanges like Bitmex offered “inverse” perpetual contracts, a more recent trend embraced by FTX, Binance Futures, and others is about trading “linear” contracts. So what are the differences?

In traditional markets, most of the instruments are actually “linear” contracts, that means that the exposure, i.e. the delta, is a constant. If one gets long 1 “linear” contract on BTC/USD, he will have a delta of 1, regardless of the BTC/USD price. The PNL for such a position is realized in USD: 1 x (Exit Price – Entry Price). It is the basic formula that everyone is familiar with.

However, early crypto derivatives exchanges did not want to deal with USD (probably for regulatory reasons – who wants to get in trouble with the SEC, right?) - but in BTC. It would be great if the collateral could be posted in BTC and the PnL realized in BTC.

Here the “inverse” contract enters the fray. It is still quoted with a BTC/USD price, but the contract quantity is now in USD instead of BTC. The trader gets a constant Dollar delta, but a variable Bitcoin delta, equals to $$\frac{SizeInUSD}{Spot}$$.

His position delta is now a function of the spot. The “inverse” contract PNL formula is:

$$SizeInUsd * (\frac{1}{EntryPrice} – \frac{1}{ExitPrice})$$.

It is a PNL realized in BTC, thus avoiding any interaction with USD.

To get into more details, the “inverse” delta is $\frac{1}{Spot}$, its gamma is $\frac{-1}{Spot^2}$

Being long “inverse” gives negative gamma, that means that hedging the delta will cost money (buy delta at a higher price, sell delta at a lower price), and reciprocally, being short “inverse” will give you a positive gamma (buying delta at a lower price and selling delta at a higher price).

So being long “Inverse” is riskier than being “short”. As the price goes down, the position accumulates more and more delta and puts the trader at a greater risk of liquidation.

Another way of understanding this is, the USD value of the position stays constant, but the value of the BTC collateral posted goes down as BTC/USD goes down, therefore increasing the liquidation risk.

A recent development in the crypto derivatives market has been the linear contracts collateralized with stablecoins, such as USDC, TUSD, etc. and the controversial USDT. FTX falls in this category, accepting stablecoin collateral and trading linear contracts (FTX also accepts non-USD collateral but that will not be discussed in this article). Binance Futures chose to accept only USDT collateral, and offers a contract quoted on the BTC/USDT pair, which can be quite different from the BTC/USD price.

A big advantage of linear contracts collateralized with stablecoins is that with a single collateral currency, a trader can gain exposure to a multitude of currency pairs. Be it BTC/USD or ETH/USD or whatever altcoin/USD, the collateral is still a stablecoin and the PnL realized in stablecoin.

Therefore, a trader does not need to own shitcoins to be able to go long/short on this particular shitcoins perpetual contracts.

Bitmex tries to have the same advantages by trading quanto contracts.

They are still collateralized and settled in BTC, but the underlying pair does not involve BTC. If we take the example of ETH/USD quanto contract on Bitmex, the contract value in ETH would be 0.000001 x BTC/USD

Therefore the Delta would be a function of the BTC/USD Price and the constant multiplier 0.000001. The PnL is realized in BTC with this formula: 0.000001 x (ExitPrice – EntryPrice). So the PnL is linear with the ETH/USD variation but it is settled not in USD but in BTC. This adds complexity for the trader. What if ETH/USD goes up but BTC/USD goes down? The trader will realize a BTC gain, but the BTC/USD dropped and in the end his USD gain is much lower.

Hence, if you are a USD-based trader, trading quanto contracts can be tricky and you might consider trading linear contracts with stablecoin collateral as it seems a much more straightforward solution.

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