Under the horns of Zen Bull
Disclaimer: This is automated content produced by GPT-3 trained on the Zen Bull Github repo and a catalogue of 1990s VCR manuals. It does not constitute investment advice or a solicitation to buy or sell any particular deltas, gammas, vegas, etc.
Zen Bull is a new Opyn strategy vault. It is made from two things:
- A 50% allocation to 2x leveraged USDC loan collateralized with ETH
- A 50% allocation to the Crab strategy (short oSQTH, long ETH, ETH delta neutral)
This gives Zen Bull a 100% exposure to ETH and a 50% exposure to short volatility through Crab. Zen Bull is bullish, but it also prefers calmer, more contemplative markets. Number go up, stress go down.
This note shows how the Bull gets its Zen, detailing:
- The crab component: The mechanism and payoff for the Crab vault
- The leverage component: The mechanism and payoff of the leveraged long ETH position created with a USDC loan
- The combined payoff and break-even return: The win condition and character of the combined Bull payoff
- Two rebalancing mechanisms: rebalance mechanisms for the vault to adjust to maintain the target delta and collateral.
The Crab Component
The Crab is an Opyn strategy vault made from two things:
- A 100% allocation to ETH (used as collateral)
- A 50% allocation to short oSQTH (the strategy mints and sells oSQTH)
Since oSQTH has a 2x delta to ETH, this combination has 0 ETH delta. The maximum payoff is achieved if ETH moves sideways (like a crab), and decreases with the square of ETH returns.
A typical payoff for crab between two rebalances (i.e from delta 0) is in in the figure 1.
Deriving the Crab payoff
The price of oSQTH can be expressed as
where 𝑁𝑡 is normalization factor (the accumulated funding for the contract since inception), 𝜎² is the annualized variance of ETH returns, and 𝑇 is the contract funding period in years (17.5/365).
The return between 𝑡 and 𝑡+Δ𝑡 is
where 𝑟 is the ETH/USD return. We show in the white paper that
where 𝑓 is the funding rate applied per funding period. Crab strategy is short squeeth with hedged delta, so
The leverage component
The leverage component borrows USDC in an Euler pool to buy ETH which it holds as collateral for the loan. Maintaining a 2:1 collateral to debt ratio gives a 2x exposure to ETH relative to the leverage component, or a 1x exposure relative to the total vault value.
Example:
Suppose the ETH price is $1200. The trade flow for a deposit is as follows:
- Deposit 1 ETH
- (Flash) borrow 1200 USDC
- Buy 1 additional ETH for 1200 USDC
The resulting position is long 2 ETH and short 1200 of USDC. The collateral ratio (the ratio of collateral to debt) is
Deriving the leverage payoff
Let 𝐸 be the amount of ETH in collateral and 𝐷 be the dollar amount of debt. The the loan equity is worth
After a change in price Δ𝑃 the return is
The collateral ratio is
so
Where 𝑟 is the ETH return.
The bull targets a CR of 2 so the payoff from a fully rebalanced state is
Including borrow and supply rate
The loan pays interest on the USDC loan at the Euler borrow rate and accrues interest on the ETH collateral at the Euler supply rate.
The combined bull payoff and break-even return
The bull strategy is 50% allocation each to crab and a loan with a 𝐶𝑅=2, so
Example:
Suppose we have:
- Funding rate per day: 0.2%
- ETH/USD return over two days: 5%
- Euler supply rate for ETH: 10%
- Euler borrow rate for USDC: 20%
Bull’s net return over two days is:
In this instance bull has out performed ETH because the funding was higher than squared ETH return.Looking at the whole payoff function is demonstrative. Bull will outperform long ETH if the funding is higher than squared return:
This payoff puts one in mind of a covered-call strategy (long asset, short call). A covered call outperforms a long position if the price does not increase too much before the option expiry. Bull outperforms a long position provided that the return is not too high or too low between rebalances.
Both Zen Bull and the covered call are long delta and short gamma.
Two rebalancing mechanisms
The Bull strategy must rebalance from time to time to achieve two goals:
- Collateral ratio target: The collateral ratio for the ETH loan (collateral value divided by debt value) should be 2
- Delta target: The delta for the whole strategy should be 1
Two types of rebalancing are used to hit these targets.
Leverage rebalance
A leverage rebalance trades some ETH for USDC within the loan to so that the value of ETH collateral is equal to the total value of Bull.
Example:
Suppose that the value of the Crab holding rises to to 1260 and the ETH price remains $1200. The delta is now not equal to the total value of the strategy:
To obtain the correct delta we need to buy 0.05 ETH financed by borrowing 60 USDC.
Now the total value and the ETH exposure are 2460, so the ETH delta is 1.
Full rebalance
A full rebalance adds an additional step, withdrawing from or depositing into crab to obtain a loan collateral ratio of 2.
The resulting USDC debt value will be the USD value of the crab component.
Example:
Suppose the ETH price is again 1200, we have 2 ETH in collateral, 1200 USDC in debt, and $1000 in crab value.
- Total value is 1000 + 2*1200–1200 = 2200
- To get delta=1 we need 2200/1200 = 1.833 ETH in collateral, so we sell 2–1.833 = 0.1667 ETH for 200 USDC
- To get CR = 2 we need to have debt = half the total value or 1100 USDC. We started with 1200 USDC of debt and got 200 UDSC from selling ETH so we have an extra 100 USDC to deposit into crab
Of the 200 received from selling ETH, 100 is repaid against the debt and 100 is deposited into Crab.
After these steps we have
- 1.83 ETH collateral valued at $2200
- 1100 USDC debt
- $1100 value in crab
Now check that the new portfolio is correct for delta and CR:
Rebalance transaction size
Bull rebalances in three ways:
- Indirectly through the Crab rebalance trading ETH for oSQTH
- A leverage rebalance exchanging ETH for USDC in the loan
- A full rebalance trading Crab and ETH/USDC
The Crab trades |2𝑟| of its size each rebalance. The Bull allocates 50% to crab, so
The leverage rebalance the trade size of ETH/USDC as a proportion of the portfolio is
For the full rebalance the trade size of crab as a proportion of the portfolio is
Example:
ETH return is −20% and crab return is −4%, the strategy return will be
For the rebalance, Bull will trade |−0.04/2|=2% of it’s value in ETH/USDC for the leverage trade
If it is a full rebalance it will trade an additional |−0.22∗(1/2−1)−0.2|=9% of its value in CRAB/USD
If it costs 0.05% to trade ETH/USD and 0.5% to trade CRAB/USD the total cost will be 0.1bps for the ETH/USDC rebalance trade and 4.5bps for the CRAB/USDC rebalance.
Analytic value for rebalance size
Simplifying the rebalance size expressions and ignoring funding rates gives simple expressions for each rebalance size as a proportion of Bull value:
- Delta hedge rebalance: rebalance size is |𝑟| of Bull value
- Leverage rebalance size : 0.5𝑟² of Bull value
- Full rebalance: |0.25𝑟²+0.5𝑟| of Bull value
These can be calculated directly from historical returns or computed from a distribution of returns. For normally distributed returns we have:
The last integral for full rebalance size we leave as an exercise for the reader ;)
Bull
Go bull some bull!
