Implied Repo Rate
The implied repo rate is the annualized financing rate implied by the relationship between a Treasury bond's spot price and the futures contract into which it is deliverable, representing the return earned by buying the bond in the cash market, holding it, and delivering it into the futures contract at expiration.
The implied repo rate measures the return to a specific arbitrage strategy: purchase a Treasury bond today in the cash market, finance it overnight in the repo market, and deliver it into the corresponding futures contract at expiration. If the implied repo rate exceeds the actual general collateral repo rate available in the market, the strategy is profitable, and the bond is attractive for delivery — it is likely the cheapest to deliver. If the implied repo rate falls below the actual repo rate, owning the bond and delivering it into futures does not cover financing costs.
The formula for the implied repo rate is derived from the futures pricing relationship. For a bond with spot price P, the futures settlement price F, conversion factor CF, accrued interest AI at spot settlement and at futures delivery, and days from settlement to delivery D:
Implied Repo Rate = [(F x CF + AI_delivery) / (P + AI_spot) - 1] x (360 / D)
This annualized rate represents the effective yield on the carry trade of buying the bond and delivering it into futures. When implied repo rates are computed for all bonds in the deliverable basket, the bond with the highest implied repo rate is the CTD bond — it offers the best return in the delivery arbitrage and is therefore the bond the market assumes will be delivered, anchoring futures pricing.
Implied repo rates are also used to identify delivery option value. In a world with a single eligible delivery bond, the theoretical futures price would equal the forward price of that bond exactly, and the implied repo rate would equal the actual repo rate. In practice, the optionality of choosing from multiple basket members gives the short holder a quality option, causing the futures to trade slightly cheap to the CTD forward price. This cheapness translates into a slightly lower implied repo rate on the CTD than the actual repo rate, with the difference representing the quality option premium.
For rate trading desks at banks and hedge funds, monitoring implied repo rates across the basket is a continuous activity. Significant dislocations between implied and actual repo rates signal either mispricing of the futures contract or unusual supply-demand dynamics in the cash Treasury or repo market. These signals drive cash-futures arbitrage activity, which helps keep the two markets in alignment.