Separating Treasury Curve and Credit Spread Duration
Summary
The note explains why a corporate bond can show different sensitivities to Treasury-rate shifts and option-adjusted spread shifts. It distinguishes duration measured by moving the Treasury curve while holding the OAS fixed from spread duration measured by moving the OAS while holding the curve fixed. The example reports Bloomberg measures for one bond and asks why spread duration is higher than curve duration.
The response attributes the gap to the embedded option and the model assumptions: a tree models stochastic Treasury rates, while the spread is treated as constant. This option treatment can reduce measured Treasury-rate sensitivity, whereas spread duration is computed under a separate constant-spread comparison. The explanation highlights that these measures arise from different assumptions and should not be read as a single additive decomposition of total yield sensitivity. The note offers intuition rather than a derivation, and its conclusion depends on the pricing model and bond features.
Key ideas
- Treasury curve duration shifts rates while keeping the option-adjusted spread fixed.
- Spread duration shifts the OAS while holding the Treasury curve fixed.
- The two sensitivities can differ because the pricing model treats rate and spread risks differently.
- An embedded option can lower modeled Treasury-rate sensitivity.
- The reported measures depend on model assumptions and are not necessarily additive components of one yield sensitivity.
Tags
Full text
# Duration split: treasury curve vs spread duration # Duration split: treasury curve vs spread duration I am looking at corporate bond (FR0013367620) in Bloomberg for which I have these values: DUR_ADJ_MID (modified duration performed using the yield to worst): 6.649 DUR_ADJ_OAS_MID (security's price/yield sensitivity calculated by shifting the entire yield curve): 4.48 OAS_SPREAD_DUR_MID (price sensitivity calculated by shifting the OAS - keeping the yield curve fixed): 6.647 The current yield is 1.041 (YLD_CNV_MID in Bloomberg). My understanding is that if this yield goes from 1.041 to 1.051 (1.041 + 1%) the price of this bond will go down by 6.649%. Now how if DUR_ADJ_OAS_MID and OAS_SPREAD_DUR_MID are the sensitivity to the treasury curve and to the spread respectively (as explained by a Bloomberg rep) how can this bond be more sensitive only to the spread (OAS) than the full curve (treasury + spread)? ## Answer by Rodolfo Oviedo (score 1) https://quant.stackexchange.com/a/42325 DUR_ADJ_OAS_MID = 4.48 is the security's price/yield sensitivity calculated by shifting the Treasury yield curve while keeping the OAS constant. Anyway you may want to have an intuition of why this number es lower than the sensitivity to changes in the OAS: 6.647. Well, the model behind the aforementioned numbers assumes that the Treasury rates are stochastic and modelled with a tree, and that the spread is constant. Yes, the model assumes that the spread in constant. Therefore, the spread duration is computed by assuming another constant spread, and comparing the bond price for each spread. If you complain that this is not coherent, you are entitled to do so. Now, what explains the different durations? The option owned by the bondholder decreases the price risk of the bond, which is generated by the change in both the Treasury rates and the spread. However, the only risk modelled by the tree is the Treasury rates risk. That is why the sensitivity to changes in those rates appears to be lower than the sensitivity to changes in the spread. The model does not assume that the bondholder can react to changes in the spread just because it is assumed to be constant. If this is not the answer to your question, please comment on my answer and reword your question.
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