Every day at 00:02:00 UTC the leveraged tokens 'rebalance'. That means that each leveraged token trades on FTX in order to once again reach its target leverage.

For instance, say that the current holdings of ETHBULL are -$20,000 and + 150 ETH per token, and ETH is trading at $210. ETHBULL has a net asset value of (-$20,000 + 150*$210) = $11,500 per token, and an ETH exposure of 150*$210 = $31,500 per token. Thus its leverage is 2.74x, and so it needs to buy more ETH in order to return to 3x leverage, and will do so at 00:02:00 UTC.

Thus, every day each leverage token reinvests profits if it made money. If it lost money, it sells off some of its position, reducing its leverage back to 3x in order to avoid liquidation risk.

In addition, any token will rebalance if an intraday move causes its leverage to be 33% higher than its target. So if markets move down enough that BULL token is 4x leveraged it will rebalance. This corresponds to market moves of roughly 11.15% for BULL tokens, 6.7% for BEAR tokens, and 30% for HEDGE tokens.

This means that leveraged tokens can give up to 3x leverage without much risk of liquidation. It would require a 33% market move to liquidate a 3x leveraged token, but the token will generally rebalance within a 6-12% market move, reducing its risk and returning to 3x leveraged.

Specifically, the way rebalances happen is:

- FTX periodically monitors for LT leverages. If any LT leverage goes above 4x in magnitude, it triggers a rebalance for that LT.
- When a rebalance is triggered, FTX calculates the number of units of the underlying the LT needs to buy/sell to return to 3x leverage, marked to prices at that time.

This is the Formula:

A. Desired position (DP): [Target Leverage] * NAV / [underlying mark price]

B. Current Position (CP): current holdings per token of the underlying

C. Rebalance size: (DP - CP) * [LT tokens outstanding] - FTX then sends orders in the associated FTX perpetual futures orderbook to rebalance (e.g. ETH-PERP for ETHBULL/ETHBEAR). It sends a maximum of $4m of orders per 10 seconds until it has sent the desired total size. These are all normal, public IOCs that trade against the prevailing bids/offers in the order-book at the time.
- Note that this ignores difference between the underlying price when a rebalance is triggered and when it happens; ignores fees; and may have rounding errors.

This means that leveraged tokens can give up to 3x leverage without much risk of liquidation. It would require a 33% market move to liquidate a 3x leveraged token, but the token will rebalance on a 10% market move, reducing its risk and returning to 3x leveraged.

What Are Leveraged Tokens' Performance?

Daily Move

Each *day*, leveraged tokens will have their target performance; so for example, each day (from 00:02:00 UTC to 00:02:00 UTC the next day) ETHBULL will move 3x as much as ETH.

Multiple Days

However, over longer time periods leveraged tokens will perform differently than a static 3x position.

For instance, say that ETH starts at $200, then goes to $210 during day 1, and then to $220 during day 2. ETH increased 10% (220/200 - 1), so a 3x leveraged ETH position would have increased 30%. But ETHBULL instead increased 15% and then 14.3%. On day 1 ETHBULL increased the same 15%. Then it rebalanced, buying more ETH; and on day 2 it increased 14.3% of its *new, higher* price, whereas a 3x long position would have just increased another 15% of the original $200 ETH price. So during this 2-day stretch, the 3x position is up 15% + 15% = 30%, but ETHBULL is up 15% from the original price, plus 14.3% of the new price--so it's actually up 31.4%.

This difference comes because the compounded increase on a new price is different from moving up 30% from the original price. If you move up twice, the second 14.3% move is on a new, higher price--and so it's actually a 16.4% increase on the original, lower price. In order words, your gains *compound* with leveraged tokens.

#### Rebalance Times

Leveraged tokens' performance will be 3x the underlying performance if you're measuring since the *last rebalance time*. In general leveraged tokens rebalance every day at 00:02:00 UTC. This means that the *trailing 24h moves* might not be exactly 3x the underlying performance, rather the *moves since midnight UTC* will be. In addition, leveraged tokens that are over leveraged rebalance whenever their leverage reaches 33% higher than its target. This happens, roughly, when the underlying asset moves 10% for BULL/BEAR tokens and 30% for HEDGE tokens. So in fact the leverage token performance will be 3x the underlying asset since the asset last moved 10% that day if there was a large move and the token lost to it, and since midnight UTC if there wasn't.

#### The Formula

If the movement of the underlying asset on days 1, 2, and 3 is M1, M2, and M3, then the formula for the price increase of the 3x leveraged token is:

New Price = Old Price * (1 + 3*M1) * (1 + 3*M2) * (1 + 3*M3)

Price movement in % = New Price / Old Price - 1 = (1 + 3*M1) * (1 + 3*M2) * (1 + 3*M3) - 1

*Disclaimers*

*None of this is investment advice.**Much of the below analysis ignores any difference between futures and spot prices, and ignores the effects of fees.**Leveraged tokens greatly reduce the risk of liquidation but cannot make it fully impossible; if markets instantaneously gap down 50%, there is nothing that can stop a +3x leveraged position from getting liquidated.*

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