A repo margin call is not the mark-to-market loss: when the lender raises the haircut on the same morning, the cash demanded is more than twice the loss.
A repo margin call is the loan outstanding less what the lender will now lend against the collateral: call = loan − new collateral value × (1 − new haircut). On 200 of bonds financed at a 5 per cent haircut, an 8 per cent price fall with the haircut raised to 15 per cent produces a call of 33.6, 2.10 times the 16.0 the bonds actually lost, and 5.60 per cent of the fund's net assets, payable the same morning.
Worked in full in Financial Risk Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The fund is illustrative: a credit fund with 600 of net assets that finances part of its investment-grade sleeve through repo. All amounts are in millions.
| Item | Value |
|---|---|
| Fund net asset value | 600 |
| Bonds delivered as repo collateral, market value | 200 |
| Initial haircut | 5.0% |
| Cash borrowed: 200 × (1 − 5.0%) | 190.0 |
| Fund's own equity in the position | 10.0 |
| Leverage on that equity | 20.00x |
| Unencumbered liquid assets available for calls | 45 |
The stress: the bonds fall 8.0 per cent and the lender, reviewing its terms the same week, lifts the haircut from 5.0 to 15.0 per cent. Neither is extreme on its own. They are the two halves of one scenario, because lenders raise haircuts when prices are falling, not when they are calm.
Collateral after the fall = 200 × (1 − 8.0%) = 184.0
Lendable value at the old haircut = 184.0 × (1 − 5.0%) = 174.8 → call 190.0 − 174.8 = 15.2
Lendable value at the new haircut = 184.0 × (1 − 15.0%) = 156.4 → call 190.0 − 156.4 = 33.6
In one line: call = V0 × [(1 − h0) − (1 − d)(1 − h1)] = 200 × (0.950 − 0.782) = 33.6
In Excel: =Loan - Collateral*(1-PriceFall)*(1-NewHaircut)
Split the call into its two causes. The price move, at the old haircut, accounts for 15.2, or 45.2 per cent. The haircut increase on the reduced collateral, 184.0 × 10 points, accounts for 18.4, or 54.8 per cent. The larger part of the call has nothing to do with the bonds' value: it is the lender changing the terms.
| Measure | Amount | % of NAV |
|---|---|---|
| Mark-to-market loss on the bonds | 16.0 | 2.67% |
| Margin call from the price fall alone | 15.2 | |
| Margin call from the haircut increase | 18.4 | |
| Total margin call | 33.6 | 5.60% |
The loss is 2.67 per cent of net assets, a figure a stress report would show without alarm. The cash demanded is 33.6, which is 74.7 per cent of the 45 of unencumbered liquid assets, leaving 11.4 for anything else that morning, including redemptions. The NAV-based stress and the liquidity stress are describing different events.
The instinct is to sell some of the pledged bonds to repay part of the loan. Each unit sold repays one unit of loan but removes one unit of collateral, so it cuts the deficit only by the haircut: 15 per cent of what is sold.
Pledged bonds to sell to cure the call = 33.6 / 15.0% = 224.0, against 184.0 held
Extra bonds of the same kind to post instead = 190.0 / (1 − 15.0%) − 184.0 = 39.53
So the fund has three choices: post 33.6 of cash, post 39.53 of other bonds that are themselves then encumbered, or close the repo entirely by selling all 184.0 of bonds into a falling market and paying the remaining 6.0 from cash. The first two keep the position and consume liquidity; the third consumes the position and crystallises the loss. There is no choice that does neither.
| New haircut | No price fall | −4% | −8% | −12% |
|---|---|---|---|---|
| 5% (unchanged) | 0.0 | 7.6 | 15.2 | 22.8 |
| 10% | 10.0 | 17.2 | 24.4 | 31.6 |
| 15% | 20.0 | 26.8 | 33.6 | 40.4 |
| 20% | 30.0 | 36.4 | 42.8 | 49.2 |
Read down the first column: a haircut change with no price move at all calls 20.0 at 15 per cent. Read across the first row: an 8 per cent fall at an unchanged haircut calls 15.2. Each 5 points of haircut costs about 9 to 10 of cash, roughly what a 5 per cent price fall costs. The haircut is the larger lever and the one the fund does not control.
Term repo with a locked haircut moves the risk to the maturity date: the haircut is reset on the rollover, which can fall in the worst week. Record the roll dates in the liquidity report beside the haircut grid.
Compute the call as loan less new collateral value times one minus the new haircut, and run the price and haircut shocks together. On 200 of bonds at a 5 per cent haircut, an 8 per cent fall and a haircut moving to 15 per cent call 33.6, more than twice the 16.0 loss and three quarters of the fund's free liquidity. The stress book, with its financing sheet and the collateral call that competes with the redemption for the same cash, is in the free workbooks for this book.
The loss is what the bonds lost; the call is what the lender needs to stay covered at its new haircut. On 200 of bonds falling 8 per cent the loss is 16.0, but at a 5 per cent haircut the call is already 15.2, and with the haircut raised to 15 per cent it is 33.6, 2.10 times the loss. The haircut part, 18.4, arrives even if prices recover.
Only by shrinking the position, because each unit of pledged bonds sold cuts the deficit by the haircut alone. At a 15 per cent haircut, curing a 33.6 call by sales needs 224.0 of bonds, more than the 184.0 held. In practice the choice is between posting 33.6 of other cash or unwinding the whole repo, selling 184.0 into a stressed market and paying the 6.0 shortfall.
Run the price shock and the haircut shock together, because lenders raise haircuts in the same conditions that move prices. A grid of price falls against haircuts shows the call: on a 190.0 loan, 15.2 for an 8 per cent fall at 5 per cent, 33.6 at 15 per cent, 42.8 at 20 per cent. Set it against the unencumbered liquid assets, not against NAV.
This article is one calculation from Financial Risk Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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