Carry and Roll-Down: Spot Curves, Forward Curves, and Bond Returns

Summary

The document examines the convention of estimating fixed-income roll-down by moving a bond along today’s spot yield curve. It contrasts that practice with using a forward curve, which might seem more suitable as a predictor of yields at the investment horizon. The question also notes that a forward bond curve derived from spot bond prices may differ from a financing-based forward because repo costs and bond pricing affect the relationship.

To construct a forward yield curve, the proposed process is to fit the observed yield curve, bootstrap it into zero rates, derive forward zero rates and discount factors, and then reprice future bond cash flows to obtain forward yields. The discussion raises calculation effort as a possible reason for the simpler spot-curve convention, but does not provide a definitive explanation, empirical test, or recommendation. It therefore serves as a framing of curve-construction and carry assumptions rather than evidence that either roll-down estimate predicts realized returns better.

Key ideas

• Spot-curve roll-down estimates carry by moving a bond to a shorter maturity on the current curve.
• A forward curve may appear more predictive, but forward bond yields depend on curve construction and financing assumptions.
• Deriving forward yields involves fitting and bootstrapping curves, then projecting and repricing cash flows.
• The document poses, but does not resolve, why market practice favors the spot curve or which method forecasts returns better.

Tags

# Carry & Roll, roll down current curve valid assumption?


# Carry & Roll, roll down current curve valid assumption?












The assumption for calculating the roll of a fixed income instrument is that you roll down the current spot curve. So if 10y rate is 2% and 9.5y is 1.8% the carry for the coming 6 month horizon is 20bp. But why is it market practice to use rolling down the current spot curve? Why isn't the forward curve also used for the roll? Isn't the 6m forward curve in this case not a more suitable predictor than the spot curve?

Is the spot curve used because it's easier? In practice if you would use the forward bond curve for the roll, this forward bond curve would not be the same as the forward based on the coupon and financing costs as the relationship between repo financing costs and implied forward based on spot bond curve are distorted.

In order to calculate the forward bond 'ytm' curve you would first need to fit the current ytm curve and bonds on a curve in practice don't have equal maturity gaps. After fitting you can assume this is a par curve and bootstrap for 0.5 or 1 maturity gaps to get the zero curve. Then you can derive the 6m forward zero curve and forward discount factors. Then you need to discount the cashflows in 6m time of all the bonds to get a forward price and extract the forward ytm from this price. This takes some calculations so maybe that is why just the spot ytm curve is used?

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