Where you are. You have every piece of the machine: backing, cage, business model, disclosure, and the mint and burn path with its vetted dealers. Nothing so far explains why the price on an exchange is a dollar.
Ask most people what holds a stablecoin at a dollar and they say the reserve assets. That answer is incomplete in a way that matters, and the whole of the next two lessons turns on it.
The reserve assets are not connected to the exchange. Nobody at the exchange can see them, and no mechanism forces a buyer to pay a dollar because a bill exists in a custody account somewhere. Demand rises, the price on the exchange goes to 1.03, and the reserve assets have done nothing about it.
The idea in one paragraph
The price returns to a dollar because somebody profits from returning it. When the token trades above par, a dealer mints new tokens from the issuer at exactly one dollar each and sells them into the market above that, which adds supply and pushes the price down. When it trades below par, a dealer buys cheap in the market and redeems with the issuer at exactly a dollar, which removes supply and pushes the price up. The reserve assets matter because they are what makes the redemption side of that trade possible, but the mechanism that acts is the trade, not the assets. A token can be perfectly backed and drift a long way from a dollar if nobody can execute that loop, which is the entire subject of the next lesson.
What the simulation shows
The exercise starts the price three percent above par, which is a large but plausible premium under a demand surge, and runs forty rounds.
With the redemption path open, the premium closes inside three rounds and the price then sits within a fraction of a percent of a dollar for the rest of the run. With the same shock and the same noise but nobody able to mint or redeem, the price drifts around three percent above par indefinitely: there is no force pulling it anywhere, because the only force was the trade.
The band in the middle is worth noticing too. Arbitrage stops when the gap is smaller than the cost of the round trip, so the price settles inside a band rather than exactly on the dollar. That band is the wires, the fees and the capital tied up for a day, and it is why real tokens trade at 0.9997 or 1.0002 rather than at a clean one.
The dealer is a market maker with a guarantee
Module 4 built a market maker: a firm quoting both sides, earning the spread, and carrying inventory risk because the price can move against it while it holds a position.
An authorised dealer is that firm with one enormous advantage. It has a counterparty who will always trade at exactly one dollar, in whatever size, in both directions. That is not a normal market maker’s position; the whole difficulty of quoting a market is that nobody is obliged to take the other side of your inventory at a known price.
The advantage explains the behaviour. A dealer will act on a gap of a few basis points, repeatedly, all day, because the trade is close to riskless: the price it exits at is contractual rather than hoped for. That willingness to act on tiny gaps is what keeps the band narrow, and it evaporates the moment the guaranteed side stops answering.
Why this is the module’s hinge
Everything before this lesson was about the issuer’s balance sheet. Everything after it is about what happens when the loop is impaired.
That framing is the most useful thing to take from this module, because it applies far beyond tokens. A promise is enforced by whoever profits from enforcing it. If nobody profits, or the people who would profit cannot act, the promise is decoration however well capitalised its maker.
Check yourself
1. The token trades at 1.03. Describe the trade that fixes it, and who does it.
An authorised dealer wires dollars to the issuer, mints tokens at exactly one dollar each, and sells them into the market above a dollar. That adds supply and pushes the price down. The dealer does it because it is profitable, not because anybody instructed them to.
2. Why is “the reserve assets hold the peg” an incomplete answer?
Because the reserve assets are not connected to the exchange and no mechanism forces a buyer to pay a dollar because a bill exists in custody. The assets make redemption possible; the trade is what acts on the price. Backing without a working redemption path is a promise with no mechanism.
3. Why does the price settle inside a band rather than exactly on a dollar?
Because the round trip has a cost: wires, fees and capital committed for a day. Inside that band there is no profit in acting, so nobody acts. The band’s width is the cost of arbitrage, which is why real tokens quote a hair either side of one rather than exactly at it.
4. An issuer holds ten billion of bills and repairs a gap slowly. How?
Because capacity is a rate rather than a total: how much a dealer can move per day through wires, a redemption desk and free capital. The size of the portfolio sets whether redemption is possible at all; the throughput of the path sets how fast a gap actually closes.
Do this
Run the shock with the loop open and with it shut.
python3 code/peg_arbitrage.pyThe starter leaves you arbitrage, which decides whether the profitable action at a given price is to mint, to redeem, or to wait because the gap is inside the round-trip cost. The driver sizes each action to the room between the price and the band’s edge, capped at what one dealer can push through in a round. The assertions check that the shock starts clearly above par and that the price settles inside half a percent of it.
The completed version is in solutions/peg_arbitrage.py.
What you can now do. You can explain the peg as a loop rather than a property, name what makes it act, and show a simulation where the same shock resolves or persists depending only on whether the loop can run. The next lesson breaks the loop two different ways.