# Implied repo rate from carry component

Carry is coupon income + pull-to-par - financing cost. Pull to par is derived as ytm-coupon. So carry can be rewritten as ytm - financing costs. Carry cash value is the current dirty price minus the cash flows in period x discounted at the current yield to maturity. So let's say you have a bond with annual coupon $$2.5$$, $$5$$ years remaining maturity and a ytm of $$1\%$$. The dirty price of this bond is $$104.7826$$. The dirty price for the cashflows in 6m time is $$105.5656$$. So an increase of $$0.782945$$.Ytm for 6m equals a value of $$104.7826 \cdot 1.5\% \cdot 0.5 = 0.78587$$. Can you say that the difference of $$-0.00293$$ is the implied repo value which implied a repo rate of $$- 0.00293/104.7826/0.5 = -0.0058\%$$?

$$IR = \frac{CF\times P_{fut} - P_{bond} + (a_2-a_1)}{(P_{bond}+a_1)t}$$
where $$a_1$$ is the accrued at the spot and $$a_2$$ the accrued at the delivery date, $$CF$$ is the conversion factor and $$t$$ the day count fraction from spot to delivery date.