# Pseudo Delta Neutral Yield Farming- How Important is Rebalancing?

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Pseudo Delta-Neutral (PDN) Yield Farming / Liquidity Mining is a really interesting way of trying to harvest yield without having to take on the price risk of the tokens (a risk you have to take when regular yield farming or hodling). I am not going to get into the specifics here. Check out my story on PDN Yield Farming, and how your delta changes as the price changes. Here are another two great articles on the process by DarkRay (article 1, article 2) (give him a follow, he puts out some really great stuff on Solana DeFi).

In order to truly stay delta neutral, you would need to continuously rebalance your assets and debt, so that your total supply of risky token (A) is equal to the total amount borrowed of that risky token (A). However, continuously rebalancing is practically impossible. So I was curious if I could come up with a basic model to test a couple different rebalancing strategies.

# 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.

To model the price of the risky asset (A), I choose to use Geometric Brownian Motion with Z = standard normal random variable.

I choose to let the price of the risky token A start at 100, and change each day based on that equation above, for 365. For the main section below, I used an expected return of 20% annualized and an expected standard deviation of 100%, along with a normal distribution for the randomness. However, in the appendix there are summary tables with different assumptions for those curious.

# 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.

Let’s compare the “No Rebalance” to the “Daily Rebalance” and the “5% Threshold”. Starting with the median (50th percentile), the “No Rebalancing” strategy has better P&L versus the “5% Threshold” and “Daily Rebalance”. However, we can really see why rebalancing your PDN strategy matters in the cases below the median. In the 10% worst trials, the “No Rebalance” strategy actually produced a loss of 10%, versus a gain of 46% for the “Daily Rebalance” and a gain of 42% for the “5% Threshold”). Amazingly, no rebalancing strategy has a negative return even in the 1st percentile (the 10 worst trials!). Its pretty obvious that the standard deviation of your P&L (Profit/Loss) is highest with “No Rebalancing”/“Hodling”/“Yield Farming”, and the more frequently you rebalance, the lower that volatility is. Also interesting, the mean of the 3 strategies we compared are very similar even though the median (50% Percentile) is different. This just shows that the price distribution is not normally distributed (maybe it looks lognormal?). *Note, this analysis doesn’t take into account the fees to swap and any transaction fees.*

Below is the evolution of the average price over the 1000 trials during each day in the 365 day period. It ends at 118.5 (the mean of price A above). Below that is the evolution of the average percent profit for each of the strategies over the 1000 trials, for each day in the 365 day period.

Below is a snapshot of a random trial. This is just to give you an idea of the volatility of price, and how price can take one of many paths, and how the different strategies performed based on this specific price path.

# 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.

So maybe holding yourself to some sort of threshold makes the most sense. I just used assets/equity in this analysis, but you could easily do something similar saying if my total tokens A (or value of tokens A) is greater than or less than my total debt in tokens A (or value of debt A) by some percentage, or if the price has changed by some percentage, rebalance. Something else to think about is your personal view. If I am super bullish on an asset, as it goes down, my delta increases and I have more price exposure to that asset… maybe I am okay with leaving that risk on.

I hope this helps you think about the importance of rebalancing, and why you should definitely rebalance a PDN strategy. There are many different ways of doing it, and there were a lot of assumptions built into this model. But overall, my findings make me believe you don’t need to rebalance constantly, and you can still have low volatility in your P&L.

Good luck and happy degening!

# 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.

“No Rebalancing” works when prices move and then come back and land somewhere slightly above the initial price (end around 150 when they started at 100, but had some decent moves in between). This is why I believe the ‘10% Threshold’ rebalancing tends to show better than the “Daily Rebalancing” on average. Prices are so volatile there is some mean reversion you capture when you don’t rebalance daily. But you can get bit in the a** by massively trending prices (see next graph below).

“No Rebalancing” performs the worst when prices just trend. The worst worst is when prices skyrocket. But continually trending down has poor performance as well. This is why the more you rebalance, the less volatile your P&L is. In those bad cases where prices massively trend, “Daily Rebalancing” can outperform less frequent rebalancing.

# 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 🐰.

I am invested in SOL, ADA, ETH, DOT, ALGO, MIOTA along with plenty of other tokens.

This is not Financial Advice!

I would love to hear your feedback/questions/comments. Reach out to me on Twitter… Marco_112358, or Discord… marco_112358 in Wonderland#2400