RAI System Simulations: Part 3 — RAI Behavior
This is part 3 of a series of posts on RAI system simulations.
In Part 1, we introduced SAFE owners and observed how they influence RAI’s market and redemption prices. We observed the mint/selling and buy/repaying of SAFE owners ultimately caused the RAI market and redemption prices to follow ETH/USD.
In Part 2, we discussed RAI traders and showed their impact on the system. We saw that RAI traders profit from the volatility that SAFE owners create and they provide long-term stability to RAI.
In this post, we simulate how various behaviors and capital allocations of the SAFE owners and RAI traders define RAI’s final behavior as an asset.
The Cost of Leverage
One major feature of the RAI system is the non-zero redemption rate, which changes the value of a SAFE’s debt. With this non-zero rate, the overall cost of leverage is based on the rising or falling expected future value of the debt. Therefore, when making leverage/de-leverage decisions, SAFE Owners must consider not just the expected yield on their debt, but also the changing value of that debt.
If SAFE owners expect high yield, they will tolerate higher redemption rates.
Consider the bullish ETH example with minting and selling of RAI. If the increasing redemption rate gets larger than the expected ETH or yield farming return, the SAFE owner will not leverage any more. Debt is becoming too expensive.
If SAFE owners expect lower yield, they will tolerate lower redemption rates.
When de-leveraging, a SAFE owner will cease repayment of debt when the redemption rate is much lower than expected yield of their minted RAI. Debt is appreciating less than their leveraged asset, so they should wait to repay.
An Example
If you expect your leveraged ETH to achieve -5% and the redemption rate is -20%, your debt is getting cheaper faster than ETH is depreciating. It makes sense to keep your position open, wait to rebuy RAI at a lower price, and then repay your debt.
Setting the SAFE owner’s redemption rate limits
As we mentioned, the expected yield on minted RAI determines the acceptable redemption rates a SAFE Owner will tolerate when respectively leveraging and de-leveraging.
In simulations, we can set the following limits on SAFE Owners:
Max Redemption Rate: The maximum redemption rate a SAFE Owner will tolerate when leveraging. A SAFE Owner will not leverage when the redemption rate is higher than this value.
Min Redemption Rate: The minimum redemption rate a SAFE Owner will tolerate when de-leveraging. A SAFE Owner will not de-leverage when the redemption rate is lower than this value.
Example:
Let max redemption rate = 30%, min redemption rate = -30%
- if redemption rate > 30%, then SAFE owner will not leverage
- if redemption rate < -30%, then SAFE owner will not de-leverage
Simulation Caveat: For simplicity, we’ve set the min/max redemption rates to be symmetrical in the following simulations, ie.
if max redemption rate = 30%, then min redemption rate = -30% implicitly.
In the future we can explore asymmetrical and even dynamic redemption rate bounds based on market conditions.
Different min/max redemption rates affect the behavior of the SAFE owners
Consider the following Ethereum dataset, this time with a bullish market: ETH’s price just keeps going up and up! An excellent market condition to go long ETH!
Let’s use our previous RAI/ETH Uniswap Pool size of 5M RAI. We will run three simulations, each with different redemption rate limits.
As we can see in the charts, a larger redemption rate limit produces a redemption price that follows ETH/USD more closely. In this bullish case where ETH/USD gains about 50%, this means a larger % redemption price change.
SAFE owners with larger redemption rate limits will leverage more than those with lower limits. The controller then responds more strongly to move the redemption price.
Below are the redemption rates(APY) produced by the four simulations. A larger RRE causes the redemption rate to achieve larger values.
Now with RAI Traders
Let’s add RAI traders to the simulation and observe the response for the different redemption rate limits.
We see with RAI traders present, the redemption and market prices are relatively stable.
Also, the redemption rates seen have much less magnitude. The RAI traders perform arbitrage, keeping the market close to the redemption price and thus the controller produces lower rates.
With Less RAI Trader Capital
Let’s reduce the RAI trader capital to 1/4th of the previous value.
With less capital, the RAI market price is slightly more volatile, but overall the redemption price is still stable.
What if there is less faith in the redemption price?
Along with less capital, let’s increase the mean deviation used for RAI trader entry/exits. Re-visit Part 2 for a refresher if you need to.
This effectively reduces faith in the redemption price and the RAI traders allow the market to deviate more before acting.
With less faith in the redemption price by the RAI traders, the redemption price starts to follow ETH/USD.
What if RAI traders have even less capital?
Instead of reducing faith in the redemption price, let’s reduce RAI trader capital even further, down to 1M.
By keeping the faith, but reducing trader capital even more, the redemption price also starts to follow ETH/USD.
The Effects of Redemption Rate Limits and RAI Trader Faith
Let’s look at the effects of various redemption rate limits and Rate trader faith with changing trader capital allocations.
We will perform simulations under three scenarios of capital allocation.
- SAFE Owner: 20M, RAI trader: 20M
- SAFE Owner: 20M, RAI trader: 5M
- SAFE Owner: 20M, RAI trader: 1M
SAFE Owner: 20m, RAI trader: 20m
These simulations show that with adequate RAI trader capital, the RAI/USD market price is relatively stable under various redemption rate limits and RAI trader faith values.
SAFE Owner: 20m, RAI trader: 5m
With RAI trader capital reduced, the general relationship between redemption rate limits, RAI trader faith and RAI/USD’s behavior becomes clear.
Higher willingness to leverage(redemption rate limits) — -> RAI/USD follows ETH/USD more
Less RAI trader faith(mean deviation) in redemption price — -> RAI/USD follows ETH/USD more
SAFE Owner: 20m, RAI trader: 1m
With even less RAI trader capital, the previous correlations become even stronger.
Conclusion
Given enough RAI trader capital, RAI/USD is relatively stable against USD.
In lieu of adequate RAI trader capital, the system’s behavior depends on the SAFE owners’ willingness to leverage and RAI traders’ faith in the redemption price.
Summary
In these posts, we’ve performed agent-based simulations of the RAI system in order to reason about RAI’s behavior as an asset. We’ve seen how SAFE owners and RAI traders can participate in the system, achieve profits, and influence the RAI market and redemption prices.
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