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Hedging Dynamics of BTC and ETH Using Quanto Perpetual Swap

Despite the crypto market downturn which began after the news of the US Securities and Exchange Commission’s (SEC) delayed decision on an ETF product approval, BitMEX has also announced the launch of two derivatives products, namely, ETHUSD perpetual swaps and UPs & DOWNs to meet market demand.

Hedging a quanto perpetual swap is not straightforward. The added component of correlation risk between two crypto assets complicates things. I will take things from first principles, then provide a more general formula.

Let’s visualize ETHUSD
ETHUSD Price: $500

Multiplier: 0.000001 XBT
.BETH (ETHUSD Spot Index): $500
.BXBT (XBTUSD Spot Index): $10,000

Short ETHUSD and Hedge:

100,000 contracts of ETHUSD.

Let’s compute the currency exposures:

XBT Value = $500 * 0.000001 XBT * -100,000 = -50 XBT
ETH Value = XBT Value / (.BETH / .BXBT) = -1,000 ETH

Next you hedge your ETHUSD exposure by purchasing 1,000 ETH at the spot price. Assume you can match the current .BETH index price on your purchase.

You have hedged your underlying currency exposure. At this point your exposure is perfectly hedged. However, as the price of ETHUSD changes, your PNL on ETHUSD will be in XBT, while the PNL on your ETH hedge will be in USD.

Let’s now glance at two extreme scenarios.

Scenario 1: .BETH Rises and .BXBT Falls

.BETH and ETHUSD rises to $750
.BXBT falls to $5,000

ETHUSD PNL = (ETHUSD Exit Price - ETHUSD Entry Price) * Multiplier * Contracts = -25 XBT, USD Value -$125,000.

ETH Spot USD PNL = (.BETH Exit Price - .BETH Entry Price) * # ETH = $250,000.

Net USD PNL = ETHUSD XBT PNL in USD + ETH Spot USD PNL = +$125,000.

In this instance, the correlation between the USD value of XBT and ETH is -1. They moved in a perfectly negatively correlated fashion, and you made money.

Scenario 2: .BETH Rises and .BXBT Rises

.BETH and ETHUSD rises to $750
.BXBT rises to $15,000

ETHUSD PNL = -25 XBT, USD Value -$375,000
ETH Spot USD PNL = $250,000
Net USD PNL = -$125,000

In this instance, the correlation between the USD value of XBT and ETH is +1. They moved in a perfectly positively correlated fashion, and you lost money.

The short ETHUSD position + Hedge profited when correlation fell, and lost when the correlation rose. Due to the flat ETHUSD vs .BETH basis, the entry price assumed a correlation of zero between the two cryptos. Courtesy: BitMEX

Currency Strength Index: FxWirePro's hourly BTC spot index has shown 50 (which is bullish), while hourly USD spot index was at 56 (bullish) while articulating at 12:45 GMT. 

For more details on the index, please refer below weblink: 

http://www.fxwirepro.com/currencyindex

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