Price of RAI: A “Dominant Fiat” Hypothesis

  • RAI is a non-pegged stablecoin that is collateralised by ETH.
  • I hypothesise that the price of RAI will follow that of the strongest fiat currency.

Problems with fiat-pegged stablecoins:

One issue with stablecoins is that they typically depend on the price of one single fiat currency. For example — USDC, DAI and LUSD all depend on the price of US dollars. If that fiat currency becomes weak relative to another currency, then the stablecoin also suffers that disadvantage.

A second issue with stablecoins is that they cannot earn “risk-free” interest as US dollars do. This issue has not been so pronounced because of recent interest rates being near zero. (Yes, there are money markets for USDC like Aave, but they involve lending/borrowing risk, so they are not risk free.) As interest rates rise, it will become penalising to hold USDC compared to holding US dollars in a bank account (or, equivalently, buying short dated US treasuries). Interestingly, this will benefit stablecoin issuers like Circle (USDC) and the issuer of Tether — since they collect the interest on the US dollars that are backing your USDC (plus they are building up a float that backs “lost” USDC!).

A brief Primer on RAI

RAI is a non-pegged stablecoin that tracks a redemption price. The redemption price is set using a PID controller (actually just PI as of May 2022) that aims to minimise the difference between the market price of RAI and the redemption price of RAI.

Very crudely, in the case of a P controller (forget the I and D for now), if the market price of RAI rises above the redemption price, then the controller lowers the redemption price. This results in market forces that drive down the market price of RAI and make the market and redemption prices equal again.

In short, the controller dampens movements in the market price of RAI.

The big question is, towards what does this move the price of RAI towards?

A “dominant fiat” hypothesis for the movement of RAI’s price

I specifically got this line of thinking from Vitalik’s recent post on stablecoins — in particular, the second bullet of this section:

I interpret and extend this second point as follows:

Start by assuming an expectation that RAI’s price remains constant when denominated in a “risk-free” fiat currency like the US dollar.

Now, if the US dollar is paying interest (e.g. at 4% annually) that is above the borrow rate fee of RAI (currently 2%), there would be a quasi-arbitrage opportunity whereby you could borrow RAI and sell it for US dollars on a centralised exchange. At any point, you could sell your dollars back for RAI, repay the loan, and pocket the interest.

This thinking can be further extended to allow the price of RAI to float and generally move towards the redemption rate (which is set by the controller). In this case (and I think subject to certain restrictions on PID controller performance, perhaps like avoiding overshoot), any time the interest rate on US dollars is larger than that the sum of the RAI borrow rate plus the RAI redemption rate (which can be positive or negative), there is a quasi-arbitrage. More accurately, perhaps, RAI price should move according to the price of short term US treasuries (less the effect of RAI’s 2% borrow rate).

Generalising this logic to a world with many “risk-free” currencies, there will always be an arbitrage — provided the price of RAI trails the strongest available short-dated government bonds.

Implications of this Hypothesis — if True

I don’t know if this hypothesis is true, and I’m sure it can be better formalised to help support or disprove it further.

If true, the implication is that RAI would track (with a small lag owning to fees) the strongest short-dated treasury bonds in the world. This would be better than holding a basket of currencies. It would be like always holding the strongest government bond.

In practise, there is not an open market between fiat currencies because there are capital controls. However, whatever country RAI can be accessed in, would result in RAI closing the arbitrage between that local currency and any other currencies (or, more technically, short dated bonds) that can readily be converted to RAI.

Borrow rate fees and risks aside, it would become optimal to hold RAI over any one single fiat currency.

Open Questions in My Head

What is the equlibrium RAI borrow rate?

This is currently 2% and serves to fill up a reserve buffer to protect against under-collateralisation events. 2% is quite high and would provide quite a lag in performance to holding US T-Bills.

RAI <> Eth interplay

One mental model for RAI’s price is a damped version of Ether’s price (in USD) — since RAI is collateralised by Eth:

  • RAI must always be collateralised by at least 150% of its value by Eth. This restricts RAI to never having a market cap of more than 66% of the value of Eth’s market cap.

Currently, RAI market cap is a tiny fraction of Eth market cap. If RAI were much bigger, one would have to think about how demand for RAI might affect the price of Eth. I haven’t thought this through fully.

RAI as a source of leverage

Another mental model is to think of the price of RAI as a reflection of the demand for leverage on “risky” assets (like stocks or Bitcoin, Ether).

Fiat currency is another source of leverage for traders.

I haven’t thought through whether RAI is disproportionately used for leverage and whether and how that would affect the hypothesis that its price should track the strongest fiat.

Formal Proof

I suspect there may be a formal way to prove (or disprove) that a system like RAI (that seeks to equalise the market price of a token with the a price reflecting a target level of collateralisation for issuance or redemption of RAI tokens) will move price — for reasons of arbitrage — towards that of the strongest risk-free asset.

If indeed the result is to disprove this hypothesis, I think there is strong promise in the idea of a collateralised stablecoin that tracks (owing to market forces, not owing to a direct peg) — at any given time — the strongest risk-free asset.

Then again, this line of thinking may be nonsense.


  • By “risk-free” I mean that there is no credit risk.
  • I say “quasi-arbitrage” because there may be Eth-collateralisation risks, smart contract risks, PID controller risks and other risks involved in holding RAI. There are also gas fees that need to be paid.


Of tokens referred to in this piece, I own ETH, FLX (RAI’s governance token), MKR and LQTY.



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