Beanstalk is an algorithmic stablecoin protocol on Ethereum. The protocol creates a token called Beans and attempts to maintain the Beans at a pegged price of $1. Like the Empty Set Dollar protocol it was based on, Beanstalk will eventually fail and permanently unpeg and fall to a value near 0.
The Beanstalk whitepaper uses a lot of math, which can obscure the important mechanics of how it works. This post is an attempt to explain them simply. The Beanstalk protocol contains many moving parts, but only the mechanics critical to understanding the peg will be discussed here.
This post will describe why Beanstalk requires either continued exponential growth in demand for holding Beans over time or the expectation among at least some protocol participants that this growth will eventually occur, for the price to remain stable. This model is unsustainable in the long run and will eventually lead to a collapse.
How does bean maintain its peg?
The price of Beans is maintained by expanding or contracting the available supply. When the price is above the peg, new supply of Beans is created, and when it is below the peg, bean supply is decreased.
Price below peg
The bean supply is contracted by the issuing of a unit of debt by the protocol, called pods. When the price is below the peg, the protocol will offer to issue pods in exchange for Beans. Participants can buy Beans on the market and sell them to the protocol in exchange for pods thereby reducing the outstanding bean supply and bringing the price towards the peg.
Pods accrue interest over time at a rate set based on the current debt owed by the protocol and other parameters. The pods are “unharvestable“ when initially created meaning that they may not be redeemed for Beans until they become harvestable as described in the section below.
Price above peg
When the price is above the peg, additional bean supply is created and distributed to pod holders (by converting the unharvestable pods into harvestable ones) and to governance token holders [0]. This increases the supply and pushes the price back down.
Why the peg cannot be maintained forever
The bean protocol adjusts parameters to target some non-zero debt ratio. This means that in stable conditions, the amount of debt owed by the protocol will increase as interest accrues.
Note that this debt will only become redeemable when new money flows into Beans, pushing the price above the peg.
Therefore, the quantity of outstanding Beans must continue to increase to prevent the debt ratio from spiraling away from target. Increases to the supply of Beans lead in turn to an increased target debt level (assuming a constant debt ratio is targeted [1]) and an increasing target debt level means larger inflows of new money will be required. The amount of required inflows will continue to increase in proportion to the current supply i.e. it will require exponential growth in inflows.
Since exponential growth of new money into the protocol cannot be sustained forever (at least not with growth rates anywhere near the targeted interest rates), the protocol debt will eventually spiral to an unsustainable level where newly issued debt will be never paid off.
Under such conditions, no rational participant would be willing to purchase debt from the protocol. Without new buyers of debt, the protocol cannot contract the bean supply, and will be unable to maintain the peg.
An objection to the above argument is to point out that the protocol has already seen periods where net flows into the protocol are flat, and even sustained periods of net outflows and has still been able to return to its pegged value of $1.
The protocol was able to maintain its peg in these cases by issuing new debt to buyers. However---new debt will only be purchased by buyers if they expect either a sufficiently large growth in demand for holding Beans in the future or they are acting irrationally and are perhaps drawn in by the high APRs, (which they may never be able to withdraw).
Rational debt market participants will realize that at some point further increases to the demand for holding Beans will be impossible and will stop purchasing debt. The pool of capital controlled by the irrational debt buyers is finite and will eventually be exhausted.
It should therefore be clear, that although the bean peg may be sustained during some periods of outflows, eventually there will be no new debt buyers and this pattern will be unsustainable.
Additional stability mechanisms
The Beanstalk protocol makes several changes over the Empty Set Dollar, which seek to improve the stability of the peg.
One mechanism worth discussing is the “cross” targeting. In this mechanism, Beanstalk attempts to regularly cross the price of Beans above and below the $1 mark. The idea behind the crossing mechanism is that by committing to continually cross back and forth around the $1 mark, arbitrageurs will be willing to help stabilize the price. These arbitrageurs would be able to buy the token whenever it is below the $1 mark, and sell it when it crosses above, thereby helping stabilize the price.
This mechanism is unable to permanently prevent an unpegging however. Those who seek to buy below the peg and sell at or above it, face significant carry risk at times when unpegging of the protocol is likely. These participants will therefore be unwilling to buy the Beans below peg at these times when the stability is most needed, and so will do little to prevent a permanent unpegging.
The Beanstalk protocol also has other interesting changes to the Empty Set Dollar, such as its parameter adjustment mechanism inspired by control theory. These mechanisms are interesting and may help maintain the peg under some conditions in the short-run, but do not change the fundamental debt-based pegging mechanics of the protocol that make its collapse inevitable.
Conclusion
The Beanstalk protocol makes interesting changes to the Empty Set Dollar which it is based on but will suffer the same eventual fate of permanent unpegging.
At the time of writing this post, Beans are at about $0.94 and have been slightly below peg for a couple of weeks. The bean price may be able to recovery back to the pegged value from this dip, but eventaully it will fail to do so.
[0] And under some conditions by selling new supply directly onto Uniswap
[1] Several mechanisms not described here are used to target the debt ratio by adjusting the protocol parameters
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