Bond Carry and Roll-Down from a Zero-Coupon Yield Curve

Summary

The document explains the two components of a bond’s carry and roll-down over a holding period. Carry is the net income earned, such as coupon income after financing costs, and can be related to the difference between forward and spot yield. Roll-down is the price change that arises as a bond ages and moves to a shorter maturity point on the yield curve, assuming the curve’s shape is otherwise unchanged.

To estimate roll-down, the answer suggests pricing bonds from a zero-coupon curve and comparing their values at the current and future maturities. It cautions that market-observed bond prices and yields may include effects from liquidity premiums, repo specialness, or coupon characteristics, so a simple shift along observed yields may be misleading. The source gives a conceptual method, not a QuantLib implementation or a worked numerical example; accurate results require curve and financing assumptions suited to the bond and horizon.

Key ideas

• Carry is the net income from holding a bond over a chosen horizon, including financing costs.
• Roll-down estimates the price effect of the bond moving to a shorter maturity point on the curve.
• A zero-coupon curve can provide consistent prices for estimating roll-down.
• Observed bond yields can be distorted by liquidity, repo, and coupon effects.

Tags

# How to compute the Carry + Roll-down of a bond with QuantLib?


# How to compute the Carry + Roll-down of a bond with QuantLib?












I’m new using QuantLib (I have no idea how to use it) and I would like to know how to calculate the C+R of a bond, say the current 30Y.

The textbook definition of C+R is the P&L due to the passage of time, given that the term structure turns out to be as expected. How is this done in QuantLib? How to simulate the passage of time (and the P&L)? How to express our expected term structure?

I would appreciate your help a lot.

## Answer by VanillaCall (score 1)

https://quant.stackexchange.com/a/44963

You have to understand two concepts:

Carry: net income (coupon less financing) that you earn over some horizon. This is essentially Forward Yield - Spot Yield. I won't go into the details of calculating this since you can quickly search it on this forum.

Roll-down: Change in the price of the bond as it rolls down the yield curve assuming its upwards sloping. For example, a 30y bond would roll down to the 29.5y point on the yield curve in six-months. However, it's not as simple as that and you may need to make adjustments. You can express your term structure by pricing all the bonds off a zero-coupon yield curve to get the fair price/yields of the bonds then get your roll-down from there. Otherwise, market observed yields/prices of bonds may be distorted by liquidity premium/repo specialness/coupon effects.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.