Where you are. The peg is a loop: a dealer profits from closing the gap, and the reserve assets are what makes the redemption side possible. This lesson breaks the loop in the two ways it actually breaks.
It is Saturday. An issuer’s tokens are backed by a portfolio that is exactly what the last disclosure said it was, every instrument investment grade. Nothing about the backing has changed since Friday.
The price is 0.92 and falling.
Nothing is wrong with the reserve assets. What is wrong is that a slice of them sits at a bank that failed on Friday afternoon, the redemption desk cannot confirm anything until Monday, and the dealers who would normally buy at 0.92 and redeem at a dollar cannot redeem at all this weekend. The loop has no fuel and the price has nothing pulling it anywhere.
The idea in one paragraph
Two entirely different things produce a price below a dollar, and they need different responses. In the first, the reserve assets are sound and the redemption path is blocked or slow, so the token is illiquid rather than impaired: the price falls because nobody can execute the repair trade, and it returns to par as soon as they can. In the second, the reserve assets are genuinely worth less than the tokens outstanding, so the price settles near what a token is actually worth and no amount of open redemption brings it back, because redeeming at par is no longer something the issuer can afford to offer. On the first day these look the same from outside. That is the problem.
Running both
The exercise takes the lesson-7 simulator and adds two switches: whether the redemption window is open, and how much of the backing turned out not to be there.
Sound with the window open repairs to par within a few rounds, as lesson 7 showed. Sound with the window gated drifts down and keeps drifting, reaching about 0.87: the same figure the March 2023 episode printed, which is a coincidence of parameters rather than a calibration, but a reassuring one. Reserve assets impaired by ten percent settle at about 0.90 and stay there, wandering around the value of what is actually behind each token.
The detail worth staring at is the first fourteen rounds, where the gated run and the impaired run are the same line. They have to be: in both, nobody is repairing anything, for different reasons. An observer watching the price has no way to tell a solvent issuer with a shut window from an insolvent one until the window reopens and either it recovers or it does not.
| condition | lowest | closing | back to par |
|---|---|---|---|
| sound, window open | 0.9250 | 1.0035 | yes |
| sound, window gated throughout | 0.8682 | 0.8717 | no |
| reserve assets impaired 10% | 0.8944 | 0.9035 | no |
n = 3 trials · peg path under three conditions, 40 rounds
Why the impaired run settles where it does
The third run is worth understanding mechanically, because the number is not arbitrary.
If ten percent of the backing is gone, each token has ninety cents of assets behind it. A dealer will still buy below ninety cents and redeem, because that is profitable. Above ninety cents there is no trade, because redeeming would pay out more than the assets are worth and the issuer cannot honour it. So the repair mechanism still works, and it works towards ninety cents rather than towards a dollar.
The peg has not stopped functioning. It is functioning perfectly, against a promise the issuer can actually keep.
Try it
Check yourself
1. Two tokens both trade at 0.88 on Saturday. What is the difference that matters, and can you see it?
One has sound backing and a blocked redemption path; the other has backing worth less than its tokens. Not from the price, and not on the first day. The two paths are the same line until the window reopens, and only then does one recover while the other does not.
2. Why does pausing redemption make things worse rather than buying time?
Because redemption is the mechanism that repairs the price. Pausing it removes the only force pulling the price back, so the gap widens precisely when confidence is lowest, and the market reads the widening gap as evidence about the backing. It converts a liquidity problem into a public solvency signal.
3. With ten percent of the backing gone, why does the price settle near 0.90 rather than collapsing?
Because the arbitrage loop still works, against a lower target. Buying below ninety cents and redeeming is still profitable; buying above it is not, since the issuer cannot pay out more than the assets are worth. The mechanism is functioning correctly towards the promise the issuer can actually keep.
4. What does the word depeg tell you about an issuer’s solvency?
Nothing on its own. It describes a price, and this lesson’s whole point is that the same price is produced by a sound issuer with a shut window and by an issuer whose backing is short. Diagnosis needs the composition, the custodians and whether redemption is being honoured, which is what lesson 5 was for.
Do this
Break the loop both ways.
python3 code/peg_stress.pyThe starter leaves you the repair step: an arbitrageur only acts when the window is open and the price is below what a dollar of reserve assets is actually worth, and it redeems enough to close that gap without overshooting past it. The assertions check that sound reserve assets with an open window return to par, that gating produces a deeper low and no recovery, and that impaired backing settles near what the assets are worth however open the window is.
The completed version is in solutions/peg_stress.py.
What you can now do. You can reproduce both failure shapes from one simulator, explain why a price alone cannot separate them on the first day, and say why pausing redemption makes a liquidity problem look like an insolvency. The next lesson shows that this whole machine is thirty years old, and that the dangerous part is not the machine.