Coupon-Adjusted Treasury Curve Rolldown Using a Fitted Curve

# Roll down Treasury curve (Coupon effects)


# Roll down Treasury curve (Coupon effects)












I'm currently working on roll down calculations for the Treasury curve (3-month roll, 6-month roll, etc..). One of the senior guys (I just started out of college) asked me to adjust for the coupon effects for some of the long dated bonds. I understand that higher coupon bonds have lower yields than other bonds with the same maturity. However, I am not sure the proper way to adjust for the coupon effects.

I've read literature where people use asset swap spreads to observe the coupon effects.

## Answer by Helin (score 7, accepted)

https://quant.stackexchange.com/a/35798

To calculate rolldown that accounts for the coupon effect requires a fitted curve. Assuming such a curve is available, then the following procedure is usually followed:

First, calculate the z-spread of the bond in question relative to the fitted curve: $$ P = \sum_{i=1}^n c_i \cdot d(t_i) \cdot e^{-s t_i}, $$ where $P$ is the current quoted dirty price (inclusive of accrued interest), $c_i$ is the $i$th upcoming cash flow, $d(t_i)$ is the discount factor corresponding to the $i$th cash flow (obtained from the fitted curve), and $s$ is the z-spread we are solving for. Conceptually, we are looking for how much of a parallel shift we need to apply to the zero coupon curve, so that the shifted curve reprices the bond to its current market price. (I'm using continuous compounding here, but you can use semi-annual compounding if you want; doesn't really matter.)

Assuming that we are calculating 3-month rolldown, we then reprice the bond using discount factors that are three months shorter and using the same z-spread from the previous step: $$ P' = \sum_{i=1}^n c_i \cdot d(t_i - 0.25) \cdot e^{-s \cdot (t_i - 0.25)}. $$ (Note that "0.25" is me being lazy. In practice, you should get the correct day count fraction corresponding to the true "3 months.")

We can then calculate a new yield to maturity $y'$ from $P'$ (assuming that maturity has shortened by three months). The difference between the current market yield and $y'$ is rolldown – coupon adjusted.