A credit position's rate risk and its spread risk are separate sensitivities that happen to be computed by similar arithmetic. Spread duration is the price sensitivity to a change in the bond's own spread, holding the government curve fixed, and for a fixed-rate bullet bond it comes out close to the modified duration. On the rupee state development loan in Worked Example 1, a one basis point bump in the spread gives a spread duration of 3.419638 at horizon against a modified duration of 3.408001, and the small gap comes from the spread bump changing the discounting of every cash flow rather than only the yield.
Why does equal spread duration not mean equal risk?
Now the sizing problem. Two US bonds:
| Spread duration | OAS | DTS | |
|---|---|---|---|
| Aurora Grid Corp (BBB, synthetic) | 5.00 | 120 bp | 600 |
| Bracken Retail Inc (BB, synthetic) | 5.00 | 420 bp | 2,100 |
Identical spread duration. A manager who sizes on spread duration, or on market value, holds the same amount of each and believes the two positions carry the same risk. They do not, and the reason is an empirical regularity rather than a definition: spread changes are approximately proportional to spread levels, so a wide-spread bond moves in absolute terms by roughly the same multiple of its own spread as a tight one. Ben Dor, Dynkin, Hyman, Houweling, van Leeuwen and Penninga set that finding out in the Journal of Portfolio Management in 2007 and gave the resulting risk unit its name: duration times spread, the product of spread duration and spread, in basis-point-years.
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How is duration times spread used, and what are its limits?
The product is what equalises. Bracken's DTS is 3.5000 times Aurora's, so $10,000,000 of Aurora pairs with $2,857,143 of Bracken. Put a 20% proportional widening through both and the arithmetic closes:
- Aurora widens 24 basis points, loses 1.2000% of price, and on $10m that is -$120,000.
- Bracken widens 84 basis points, loses 4.2000% of price, and on $2.857m that is -$120,000.
Size them at $10m each instead and Bracken loses $420,000 against Aurora's $120,000, which is the 3.5 ratio arriving as a surprise in the profit and loss rather than as a decision in the sizing.
The unit also works in the other direction, and that case is the one people find harder. Corniche Utilities (A, synthetic) has a spread duration of 8.00 at 90 basis points, giving a DTS of 720. Dunlin Energy (B, synthetic) has a spread duration of 2.50 at 300 basis points, giving 750. The two differ by more than three times in spread duration and more than three times in spread, and their systematic spread risk differs by 4.17%. A long-dated high-grade bond and a short-dated high-yield bond can be the same position.
Two limits belong next to the metric. DTS measures systematic spread risk, the part that moves proportionally; it says nothing about idiosyncratic risk, so a single name's default is not in it. And the proportionality is an empirical average, so it degrades badly for distressed names, where spreads stop behaving like spreads and the bond starts trading on a recovery estimate.