Where you are. Module 5 followed collateral down a pledge chain and found it had been reused three times. Module 1 built repo. This lesson asks what changes when the collateral is a token that moves in a message.
A bank needs cash from ten in the morning until two in the afternoon. Four hours.
In the ordinary market it borrows overnight, because the machinery of pledging, confirming and returning collateral takes long enough that a four-hour loan is not worth arranging. It pays for a night and uses a third of it.
The idea in one paragraph
When collateral is a token, pledging it is a ledger transfer rather than a process, which makes the minimum sensible term of a secured loan collapse from a night to minutes. That unlocks genuinely new things: repo priced by the hour, collateral rebalanced between two ledgers as an atomic swap using lesson 13’s locks, and margin met in one place with collateral held in another. It also does something less comfortable. The same speed that lets a firm rescue itself in minutes lets a problem propagate in minutes, and a margin engine that depends on a cross-ledger message about collateral is an engine that is blind exactly when that message is delayed.
What four hours costs
The exercise prices the same million borrowed for four hours and for a night.
Four hours costs 18.26. A night costs 109.59, exactly six times as much, because a night is six times four hours and the rate is the rate. There is nothing subtle in the arithmetic; the point is that the four-hour price was never available before, so the borrower paid the overnight number for an intraday need.
| term | interest |
|---|---|
| four hours, 10:00 to 14:00 | 18.26 |
| overnight | 109.59 |
n = 2 trials · one million borrowed at four percent
Multiply that gap across a treasury desk’s daily funding and it is a real saving, and it is the least interesting consequence.
The margin engine goes blind
The second half of the exercise is the one worth sitting with.
A position is margined on ledger A. Its collateral sits on ledger B. That arrangement is a direct consequence of everything this module has built: collateral can be anywhere, because moving it is cheap.
Then the crash. The collateral is genuinely worth 700,000 rather than a million, so the position needs a 300,000 call. The engine, reading collateral state that has not yet arrived from ledger B, computes the requirement against the old value and asks for nothing at all.
| the engine reads | collateral value | margin call made |
|---|---|---|
| current state | 700,000 | 300,000 |
| state one message behind | 1,000,000 | 0 |
n = 1 trial · position of ten million, ten percent requirement, collateral on another ledger
The rescue and the run travel together
The honest summary of collateral mobility is that it is symmetric, and the symmetry is not something a better design removes.
A firm that can move collateral in minutes can meet a call it would otherwise have failed, and a market that can reallocate collateral in minutes can rescue a shortage before it becomes a default. The same market can also withdraw it just as fast, and the run that used to take days because the paperwork took days can now happen in an afternoon.
Every improvement in mobility is an improvement in both directions, and no amount of engineering makes it one-directional.
Check yourself
1. Why was a four-hour secured loan not available before?
Because pledging, confirming and returning collateral was an operational process measured in hours or days, so the minimum sensible term was a night. Tokenised collateral makes the pledge a transfer, and the term can then be as short as the need.
2. The engine asks for nothing when 300,000 is needed. What went wrong?
Nothing broke. The collateral is on another ledger and the message carrying its new value has not arrived, so the engine computed the requirement correctly from state that was one message old. Being correct about stale information is the failure.
3. Why is the delay worst exactly when it matters?
Because a crash is when values move fastest and cross-ledger traffic is heaviest, so the message is most likely to be late precisely when lateness is most expensive. The correlation is structural rather than bad luck.
4. In what sense is collateral mobility symmetric?
It speeds the rescue and the run by the same amount. A firm can meet a call it would have failed, and a market can withdraw collateral just as quickly, so a run that took days because the paperwork took days can now happen in an afternoon. No design removes the symmetry.
Do this
Price the four hours, then blind the engine.
python3 code/collateral_mobility.pyThe starter provides the margin call calculation and the crash, and leaves you repo_interest: charge the annual rate for the fraction of a year the money is actually borrowed, counting a year as 365 times 24 hours. The assertions check the four-hour figure to the penny, that a night costs exactly six times as much, and that the engine reading stale collateral state makes no call when 300,000 is due.
The completed version is in solutions/collateral_mobility.py.
What you can now do. You can price a secured loan by the hour, explain what tokenised collateral makes newly possible, and demonstrate a margin engine acting correctly on state that is already wrong. The next lesson hands the whole apparatus to software.