How do leveraged tokens rebalance?

Our leveraged tokens maintain notional 3x or -3x exposure to the daily returns of cryptoassets like Bitcoin or Ether through the use of perpetual swap contracts. These contracts allow us to get leveraged exposure to cryptoassets such as Bitcoin and Ether and we adjust this exposure on a daily basis based on our position’s Profit and Loss (PnL). Let’s consider a case of how BTC3S maintains its -3x leveraged exposure through rebalancing.

Our leveraged tokens maintain notional 3x or -3x exposure to the daily returns of cryptoassets like Bitcoin or Ether through the use of perpetual swap contracts. These contracts allow us to get leveraged exposure to cryptoassets such as Bitcoin and Ether and we adjust this exposure on a daily basis based on our position’s Profit and Loss (PnL). Let’s consider a case of how BTC3S maintains its -3x leveraged exposure through rebalancing. Essentially, the procedure for the rebalance process can be outlined as follows:

  1. Following a change in the mark price of Bitcoin perpetual swap contracts on exchange, we calculate the PnL of the outstanding tokens
  2. Calculating the PnL allows us to calculate three variables: (1) Required Exposure; (2) Current Exposure; (3) Rebalance Amount
  3. Required Exposure in BTC (RE): Target Leverage *Token Value (in USD) / Volume-weighted Average Mark Price (VWAP)
  4. Current Exposure in BTC (CE): Per Token Bitcoin Perpetual Swap Position
  5. Total Rebalance Amount in BTC (RA): (RE - CE)* Token Supply
  6. Total Rebalance Amount in USD: RA * Bitcoin Perpetual Swap VWAP

Suppose the mark price of a Bitcoin perpetual swap contract on two exchanges — Exchange A and Exchange B — is $10,000, that there are four outstanding BTC3S tokens, and that the initial price of the BTC3S token is $10,000. The inception price of at this stage for Bitcoin would be a volume-weighted average of the mark price of the Bitcoin perpetual contracts on the exchanges and therefore would also be $10,000. In total, Jasper’s proceeds from selling the tokens would be $39,960 which is the number of tokens multiplied by the current token price then multiplied by 1 - Creation/Redemption fee (i.e. $40,000 - $40).

To summarise:

Let’s say Bitcoin’s price increases by exactly 5.5% on exchange A and 4.5% on exchange B. Also, let’s assume 40% of perpetual swap exposure is sourced from exchange A and 60% from exchange B. To calculate the volume-weighted price and therefore the appropriate price change we must account for each exchange’s funding rate and the aforementioned volume breakdown.

Therefore, we can calculate the VWAP of the perpetual swap contract by taking a weighted average of the two exchange’s prices. We also take a VWAP of the funding rates, this allows us to calculate the aggregate synthetic PnL.

Despite this reduction in the PnL of the token’s positions, we still have BTC3S tokens outstanding which means that the PnL per token is -$1,461.82.

Therefore, the token value at the end of the period is $8,538.18 compared to $10,000 at the start of the period.

Token Value (End of Period): $10,000 - $1,461.82 = $8,538.18

However, the implied leverage is considerable higher than -3 at this point:

Implied Leverage (Per Token Notional Exposure/Token Value): -3.6858

Therefore, we need to undergo a rebalance to adjust the implied leverage back to the target of -3. Before the rebalance is initiated, the 0.03% daily fee is taken from the token’s holdings.

From the above numbers, we can work out the Per Token Notional value that we want to adjust to:

Notional $ Value to Execute (Target Leverage * Token Value Post Fee): -$25,606.83

Notional BTC Value to Execute: -2.441

Required rebalance amount Per Token (USD): $31,470 - $25,606.83 = $5,863.17

Required rebalance amount Per Token (BTC): 0.5589

Therefore, we would close 2.2166 BTC worth of our short positions in the BTC perpetual swap contracts in order to have a Total Post Rebalance Exposure of -9.7734026.

Therefore, the post-rebalance notional per token is -2.44 BTC, equivalent to -$25,606.83. This brings us back to our target leverage of -3.

When do leveraged tokens rebalance?

Our leverage tokens rebalance once a day at 5 PM CET in order to maintain the correct amount of daily exposure to Bitcoin or other cryptoassets, as we show in the “How do we maintain leverage exposure with leveraged tokens?” section.

While leverage tokens automatically rebalance at 5 PM CET every single day, they will also rebalance if the daily returns of their underlying cryptoasset changes by a specific amount. The threshold amount is the following for tokens with different levels of leverage:

  • 3X Leverage Tokens (i.e. BTC3L, BTC3S, ETH3L, ETH3S): 15%

For example, if Bitcoin were to go up by 15% on a single day at 11 AM CET then BTC3L would rebalance at that point and then also rebalance at 5 PM CET. This would only happen in cases where the market moves against the stated exposure — therefore as a stop loss.

Disclaimer

This document has been prepared and issued by Amun Limited (“Amun”). This document may contain market commentary. All information used in the publication of this document has been compiled from publicly available sources that are believed to be reliable, however we do not guarantee the accuracy or completeness of this document or the information contained/referenced herein.

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