Where you are. The engine of the last lesson acts when equity falls below a level. This lesson asks who decides that level, and finds three answers with very different failure modes.
A trader is long a hundred thousand of spot and short ninety-five thousand of the perpetual against it. Almost perfectly hedged: if the price falls, the long loses and the short gains, and the two nearly cancel.
How much margin should that book post? The three answers differ by a factor of four, and the argument between them is the whole of modern margining.
The idea in one paragraph
Isolated margin treats each position as its own box with its own collateral, so a loss on one cannot reach the other, which contains damage and ignores the hedge entirely. Cross margin puts one pool of collateral behind both, so a gain on one funds a loss on the other, which stops the sillier liquidations without reducing what the book must post. Portfolio margin goes further and margins the risk of the book rather than the size of its positions, so a hedged position posts a fraction of what its notional would suggest. That fraction is calculated from an assumed relationship between the two legs, and the assumption is the whole of the risk being taken.
Three answers to one book
The exercise computes the requirement for that hedged book each way.
Isolated and cross both ask for 19,500, ten percent of the combined notional. Portfolio margin looks at the net exposure, sees a book that is very nearly flat, and asks for 5,000, which is 74 percent less. On a well-hedged book that saving is enormous and it is not fictitious: the book really is nearly flat, and requiring collateral against both legs really does tie up capital against a risk that mostly is not there.
Then the correlation halves. The hedge that was tracking the spot now only follows it halfway.
| regime | margin required |
|---|---|
| isolated | 19,500 |
| cross | 19,500 |
| portfolio, hedge holding | 5,000 |
| portfolio, correlation halved | 5,250 |
n = 4 trials · long 100,000 spot against short 95,000 perpetual
The model does react: the requirement rises when the assumed relationship weakens. It rises to 5,250, and a twenty percent fall with the hedge only half working loses 10,500. The margin was calculated correctly from the assumption, and the assumption was wrong, so the collateral covers half the loss.
Isolated margin, which ignored the hedge entirely and looked wastefully conservative all along, would have covered it.
Which one a venue chooses
The three regimes are not competitors so much as points on a line between containment and efficiency, and venues sit at different points on purpose.
A venue serving retail traders with high leverage leans isolated, because containment matters more than efficiency when the participants are numerous, anonymous and cannot be pursued for a debt. A venue serving professionals leans portfolio, because the participants genuinely do run hedged books and forcing them to post against both legs drives them elsewhere.
The uncomfortable part is that the participants who benefit most from portfolio margin are the ones whose failure would be largest, which is a design tension nobody in this field has resolved.
Check yourself
1. What does each regime margin against?
Isolated margins each position separately in its own box. Cross puts one pool of collateral behind them all, so gains fund losses, without reducing the total required. Portfolio margins the net risk of the book, so offsetting positions require far less.
2. Portfolio margin asks 74 percent less for this book. Is that a discount?
No, it is a calculation. The book really is nearly flat, and collateral against both legs really does secure a risk that is mostly not present. The saving is genuine for as long as the assumed relationship between the legs holds.
3. The correlation halves and the requirement rises only slightly. What went wrong?
Nothing in the arithmetic: the model reacted correctly to its input. The input was an assumption about how the two legs move together, and it was wrong. The margin covers about half the loss the broken hedge actually produced, while the conservative regime would have covered all of it.
4. Why is the failure worse than a single mispriced book suggests?
Because the capital saving is what allowed the position to be that large in the first place. A quarter of the collateral supports four times the position, so the correlation breaks against a book that portfolio margin itself made possible.
Do this
Compute all three, then break the hedge.
python3 code/margin_types.pyThe starter provides the isolated and cross calculations and the stress path, and leaves you portfolio: margin the net exposure, long minus short times the correlation, with a floor so that a perfectly hedged book still posts something. The assertions check that the saving exceeds seventy percent, that less correlation demands more margin, and that the broken-hedge loss exceeds what portfolio margin posted while staying inside what isolated would have.
The completed version is in solutions/margin_types.py.
What you can now do. You can compute a book’s requirement under three regimes, say what each one is protecting against, and show why the most efficient one fails hardest. The next lesson leaves margin behind and returns to the gap between the two ledgers.