Spread duration turns a scenario in basis points into a loss in money. The arithmetic is one line; the calibration and one duration decide the answer.
A credit spread stress loss is market value times spread duration times the spread shock in decimal, summed over positions. On Halverton, an 840M credit fund, shocks of 120, 450, 300 and 600 basis points on its four sleeves give a loss of 93,277,800, or 11.10 per cent of net assets, and take the net asset value per unit from 100.00 to 88.8955. The arithmetic is one line; which spread duration you use for floating-rate loans can move the answer by 17 million.
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, its sleeves, their spread durations and the scenario are those of Financial Risk Management: 840,000,000 of net assets in 8,400,000 units. The shocks are calibrated sleeve by sleeve rather than applied as one parallel move, which is the point of the scenario.
| Sleeve | Market value | Spread duration | Shock, bp |
|---|---|---|---|
| Investment-grade credit | 252,000,000 | 6.2 | 120 |
| High yield | 294,000,000 | 3.8 | 450 |
| Leveraged loans | 210,000,000 | 0.25 | 300 |
| Structured credit | 84,000,000 | 4.5 | 600 |
| Fund | 840,000,000 | 3.703 |
Spread duration is the percentage change in price for a one-point (100 basis point) change in spread. Divide by 10,000 to get the loss per basis point, the CS01. Summed, it is the fund's whole spread exposure in one number.
CS01 = market value × spread duration / 10,000
Investment grade: 252,000,000 × 6.2 / 10,000 = 156,240 per basis point
Excel: =SUMPRODUCT(MV,SDur)/10000
| Sleeve | Weight | CS01 | Per 100 bp | Share of CS01 |
|---|---|---|---|---|
| Investment-grade credit | 30% | 156,240 | 15,624,000 | 50.2% |
| High yield | 35% | 111,720 | 11,172,000 | 35.9% |
| Leveraged loans | 25% | 5,250 | 525,000 | 1.7% |
| Structured credit | 10% | 37,800 | 3,780,000 | 12.2% |
| Fund | 100% | 311,010 | 31,101,000 | 100.0% |
Investment grade carries half of the fund's spread sensitivity on 30 per cent of its assets, because its duration is long. Leveraged loans, a quarter of the fund, carry 1.7 per cent.
Loss = Σ market value × spread duration × shock (bp) / 10,000
High yield: 294,000,000 × 3.8 × 0.0450 = 50,274,000
Excel: =SUMPRODUCT(MV,SDur,ShockBp)/10000
| Sleeve | Shock, bp | Loss | Share of sleeve | Share of loss |
|---|---|---|---|---|
| Investment-grade credit | 120 | 18,748,800 | 7.44% | 20.1% |
| High yield | 450 | 50,274,000 | 17.10% | 53.9% |
| Leveraged loans | 300 | 1,575,000 | 0.75% | 1.7% |
| Structured credit | 600 | 22,680,000 | 27.00% | 24.3% |
| Fund | 93,277,800 | 11.10% | 100.0% |
Net assets fall to 746,722,200 and the value per unit to 88.8955. The loss is 12.88 times the fund's one-day 99 per cent VaR of 7,242,456, and 2.88 times the twenty-day VaR of 32,389,246. A VaR fitted to ordinary days does not contain this event; that is why the scenario is run separately.
Two shortcuts are common: a single parallel shock for every sleeve, and scaling a calibrated scenario up or down. Both are worth seeing side by side.
| Scenario | Investment grade | High yield | Fund loss | Share of NAV |
|---|---|---|---|---|
| Uniform 100 bp | 15,624,000 | 11,172,000 | 31,101,000 | 3.70% |
| Uniform 200 bp | 31,248,000 | 22,344,000 | 62,202,000 | 7.41% |
| Uniform 300 bp | 46,872,000 | 33,516,000 | 93,303,000 | 11.11% |
| Calibrated, as above | 18,748,800 | 50,274,000 | 93,277,800 | 11.10% |
| Calibrated × 0.5 | 46,638,900 | 5.55% | ||
| Calibrated × 1.5 | 139,916,700 | 16.66% |
A uniform 300 basis point shock lands within 25,200 of the calibrated total and describes a different fund. It puts 46,872,000 of loss on investment grade, two and a half times the calibrated figure, and 33,516,000 on high yield, two thirds of it. A board told that the stress costs 11.1 per cent would be right on the total and wrong about which sleeve to sell, hedge or stop buying. Report the sleeves, not just the sum.
The 0.25 on the loan sleeve is the reset period of the base rate, which is the right number for interest-rate risk. As a reading of spread risk it is the lowest possible one, and in a stress usually too low. The margin on a leveraged loan is fixed for the life of the loan; what keeps the price near par is the borrower's option to reprice or refinance, and in a stress that option is worth nothing because no borrower can refinance. Below par, a loan's price responds to spread roughly in proportion to its expected remaining life.
| Loan spread duration | Loan loss | Fund loss | Share of NAV | NAV per unit |
|---|---|---|---|---|
| 0.25 | 1,575,000 | 93,277,800 | 11.10% | 88.90 |
| 1.0 | 6,300,000 | 98,002,800 | 11.67% | 88.33 |
| 2.0 | 12,600,000 | 104,302,800 | 12.42% | 87.58 |
| 3.0 | 18,900,000 | 110,602,800 | 13.17% | 86.83 |
At three years the loans go from 1.7 to 17.1 per cent of the stress loss, and the fund loses 17,325,000 more. Neither figure is the truth; the point is that the duration is a modelling choice with a range, and the range belongs in the report next to the number.
The mark-to-market is only the first door. In the same scenario the fund's repo haircut widens and a collateral call arrives on the morning of the redemptions. Running a stress backwards, to the redemption a fund cannot meet, is worked on a different fund in how to compute a reverse stress level.
The stress book, with the shock in basis points by sleeve and the financing call beside it, is in the free workbook for this case.
CS01 is the change in value for a one basis point widening in credit spread: market value times spread duration divided by 10,000. On a 252,000,000 investment-grade sleeve with a spread duration of 6.2 it is 156,240. Across the four sleeves of the fund here CS01 totals 311,010, so a parallel 100 basis point widening costs 31,101,000, or 3.70 per cent of net assets.
Modified duration measures sensitivity to the risk-free rate; spread duration measures sensitivity to the credit spread. For a fixed-rate bond they are close. For a floating-rate loan they diverge: the base rate resets every quarter, so rate duration is about 0.25, but the margin is fixed for the life of the loan. Raising the loans' spread duration from 0.25 to 3.0 here adds 17,325,000 to the stress loss.
It answers a different question and is usually far larger. The scenario here costs 93,277,800, which is 12.88 times the fund's one-day 99 per cent VaR of 7,242,456 and 2.88 times its twenty-day VaR. VaR describes ordinary days fitted to history; a calibrated stress describes a specific bad event that history may not contain.
Spread duration by sleeve and the calibrated shock are worked in the stress book that goes with chapter 9 of 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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