Pseudo Delta Neutral Yield Farming- How Important is Rebalancing?

My Experiment

Coming from a TradFi background, I really struggle to rely on strictly historical data. The path that the price of an asset takes is only one of infinitely many it could have taken. So just relying on the one path of history for any specific token didn’t make sense to me (especially for a path dependent analysis). Instead, I decided to use some Monte Carlo simulations.

Price at time ‘t’ depends on: the price at time ‘t-1’, the expected return (mu), the expected standard deviation (sigma) , and a random variable (Z)
Z is just the standard normal random variable

Rebalancing Strategies Tested

  • No Rebalance — This one is simple, set it and forget it. This strategy initially set up a delta-neutral position at time 0 and let it go for the entire 365 days for every trial
  • Daily Rebalance — This is simply rebalancing at the end of the day ‘t-1’ (or you could think of it as beginning of the day ‘t’). This rebalance occurs every day for 364 days
  • Weekly Rebalance — This is rebalancing each 7 days, starting on day 7, then 14, etc.
  • 5% Threshold — This is basically rebalancing of you Assets / Equity (leverage) is outside of the band 2.85–3.15 (3+/-( 5% * 3)). This is very similar to rebalancing when the price of the risky assets has changed by 10% relative to the last time you rebalanced
  • 1% Threshold — This is basically rebalancing of you Assets / Equity (leverage) is outside of the band 2.97–3.03 (3+/- (1% * 3))
  • Hodl — This is just hodling 50% of your total equity in the risky token and 50% in the stablecoin (so if initial equity is $200, $100 in risky and $100 in stablecoin)
  • Yield Farming — This is just normal unlevered yield farming using the same initial equity amount (so if initial equity is $200, $100 in risky and $100 in stablecoin).

Model Assumptions

  • Yield = 40% (unlevered), Borrowing Rate on both tokens A and B = 20% (unlevered).
  • The expected return of token A is 20% annualized.
  • The expected standard deviation of token A is 100% annualized.
  • Token B is a stablecoin pegged to the US with an expected return and expected standard deviation of 0% (perfectly stable).
  • Token A starts at $100 USD and token B starts at $1 USD.
  • 1000 trials are run, and in each trial: each day new profit/loss is calculated for the entire 365 day period.
  • You initially supply $200 USD worth of token B (200 token B).
  • You initially apply 3x leverage (so borrow $400 worth of both tokens, which leaves you with $600 of total assets). You apply leverage so that 75% of your borrowings are in token A (borrow 3 tokens) and 25% in token B (100 token).
  • No fees are taken into account, no swap fees or transaction fees. (This is important, because fees would eat into your rebalancing P&L… shame on this author).
  • There is no liquidations. P&L can be negative.

Results

This is, in my opinion, the most important table. This is your Profit or Loss in percentage terms for each of the strategies, along with the prices for the tokens, across all 1000 trials ran with the above assumptions.

Histogram of Token A prices at the end of the period (t=365) across all 1000 trials

Summary

Overall, I think its fairly obvious that PDN can work to lower your exposure to the price of the risky token. And its obvious that rebalancing can drastically reduce the volatility of your profit/loss. However, is it really necessary to rebalance that frequently, like daily? I am not sure. Because there is so much volatility in digital assets, sitting on some positive delta (when price declines), or negative delta (when price increases) may not be a bad thing. If the price reverts back (like a mean reversion concept), you would be better off not rebalancing. Said another way, the more frequently you rebalance, the better you do in the worst case scenarios, but the worse you do in the best case scenarios, relative to less frequent rebalancing.

Appendix A

Let’s take a look at different expected returns and standard deviations and see how they affect the output.

Expected Return 0%, Expected Standard Deviation 100%

As the expected return assumption decreases, more frequent rebalancing is marginally more beneficial than it was with a higher expected return.

Expected Return 20%, Standard Deviation 50%

As the standard deviation decreases, all of the strategies tend to look a lot more similar. Interestingly the 5% threshold rebalances fewer times than it did versus the higher volatile model, but the performance across all the rebalancing models is very similar, even with different amounts of rebalances in the year.

Expected Return 20%, Expected Standard Deviation 150%

As the standard deviation increases, there is even a more drastic difference between the P&Ls. Rebalancing plays an even more important role.

Expected Return 40%, Expected Standard Deviation 100%

The higher expected return really only changes the “No Rebalancing”, “Hodling”, and “Yield Farming” columns, making them all more attractive relative to the lower expected return trials… but rebalancing in general still shows better.

Expected Return 0%, Expected Standard Deviation 100%, Yield Farming Yield increased to 80%

As the yield from farming increases, more frequent rebalancing is marginally more beneficial than it was with a higher expected return. Rebalancing overall is even more important.

Expected Return -20%, Expected Standard Deviation 100%

As the expected return goes negative, daily rebalancing has a better downside performance.

Appendix B

I took a look at using different rebalancing triggers based on the ‘rebalance threshold’. Using a price trigger (if price changes by +/- 10% from the last time you rebalanced) is eerily similar to the 5% Assets/Equity rebalancing trigger.

Appendix C

Just one extra bit of information I found interesting. When does “No Rebalancing” work best, and when does is fail the most? Below is a slice of the price path for the 10 best and 10 worst trials for “No Rebalancing” P&L.

About the Author

For full disclosure I mostly use Solana for DeFi, because I don’t have enough assets to justify Ethereum gas fees. I have a little bit in Algorand, Cardano and Polkadot DeFi. I am actively involved in multiple Friktion volts and a contributor in their Discord, and am beta testing Dappio Wonderland 🐰.

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Marco_112358

Marco_112358

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TradFi background, DeFi Degen. Love SOL, ADA, ETH, DOT, NEAR, Aurora, ALGO, MIOTA plus NFTs