# 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)?

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.