# 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?

• You may find this related question useful quant.stackexchange.com/questions/59989 – Dimitri Vulis Jan 21 at 23:45
• Quick answer, in addition to the link that Dimitri posted: (i) the forward curve is not a great predictor of the "future" (historical backtests show very poor relationship indeed) (ii) The entire idea of carry & roll down is to get an idea how much your trade will cost you (or accumulate money for you) if you enter the trade and "everything stays constant": this is an important metric for a trader, because even if you somehow believe that the future spot curve will change you want to understand what will happen if your "belief about the future" is wrong & in fact the curve will stay unchanged. – Jan Stuller Jan 22 at 13:05
• Thanks for link and explanation. What I miss in the carry and roll down story is how pull to par fits in. The value of the bond will be pulled to par as time passes. So for a premium bond its negative. So how does it fit into carry. – Kanivan Jan 23 at 22:22