A parimutuel pool of leveraged tokens
This post describes an approach to designing leveraged tokens. Looking for feedback on potential problems with this design or ways to improve it.
Tracking price^3
Let’s say BTC goes up by 5% in a day. Normally 3x leverage tokens are designed to go up by 3 x 5 = 15%. However, we do something a bit different — we design the LT to go up by a multiple of 1.05³, or a gain of around 15.76%.
So the LT tracks price^3. Similarly, the inverse LT tracks 1 / price ^ 3
Tracking price^3 is actually equivalent to rebalancing 3x return continuously, and doesn’t suffer from volatility drag (traditionally LTs tends to lose value over time).
Example
Alice thinks BTC will go up so spends $1000 on a 3x BTC LT. Bob thinks ETH will go down so spends $2000 on a 3x inverse ETH LT. So in total, there’s $3000 in the pool and the sum of the values of Alice and Bob’s LTs has to always equal $3000.
Let’s say BTC goes up by 5% and ETH goes up by 10%. Theoretically Alice’s LT increases in value from $1000 → $1158 (= 1000 x 1.05³) and Bob’s LT loses value from $2000 → $1502 (= 2000 / 1.1³).
The problem is the pool would now be worth 1158 + 1502 = $2660, which is different from the actual balance of the pool of $3000. So a crude way to fix this is to normalize all values so that they sum up to the balance. So Alice’s LT is actually worth $1158 x 3000 / 2660 = $1306 and Bob’s LT is worth $1502 x 3000 / 2660 = $1694
Caveats
1. In the example above, Alice’s LT gained value and Bob’s LT lost value as expected, but because of the normalization it doesn’t exactly track price^3. So these LTs aren’t useful for getting a precise exposure or hedge (unlike our options AMM). They’re useful as a simple way to get leverage without caring about the precise level of leverage.
2. LTs performances are relative to each other. For example, if you have a BTC LT and BTC goes up by 1%, your LT might still lose value if other assets went up by more. This can be mitigated by offering LTs for many different assets, so their performance is diversified. A cool thing about this approach is there isn’t much extra cost to adding more assets, so the pool could offer LTs for several different tokens at launch.
3. If too many people buy the same LT, that LT might no longer be worth holding. The upside is capped by the amount held by the rest of the pool, but the downside is the same as before. The easiest way to fix this is to prevent an LT from being bought if its pool share is above 25% or so.
