Implied Repo Rate
The implied repo rate (IRR) is the rate of return that can be earned by buying the cheapest-to-deliver (CTD) Treasury bond in the cash market, financing the purchase through a repurchase agreement (repo), and simultaneously selling the corresponding Treasury futures contract — with all cash flows structured so as to lock in a known rate of return over the futures delivery period. When the implied repo rate exceeds the actual repo rate, the cash-and-carry arbitrage is profitable; when it falls below, the reverse cash-and-carry (buying the future, delivering the bond) becomes attractive.
Key takeaways
- The implied repo rate is the synthetic borrowing rate embedded in the relationship between a Treasury bond's cash price and the futures contract price for the same bond's delivery.
- It is calculated from the bond's full price (clean price plus accrued interest), the futures price adjusted for the conversion factor, and the net carry (coupon income minus financing cost) over the holding period to futures delivery.
- The CTD bond — the specific Treasury bond that the futures short is most likely to deliver to satisfy the contract — has the highest implied repo rate among all eligible deliverable bonds, reflecting its optimal economics in the futures-to-cash relationship.
- When IRR > actual repo rate: buy the bond, repo it, short the future (cash-and-carry) is profitable. When IRR < actual repo rate: buy the future, short the bond, invest proceeds (reverse cash-and-carry) is profitable.
- The implied repo rate is central to CTD bond identification, Treasury basis trading, and the delivery option pricing embedded in Treasury futures contracts.
Explanation
The implied repo rate is derived from the no-arbitrage relationship that must hold between Treasury bond prices in the cash market and Treasury futures prices. If the cash-and-carry strategy — buying a bond, financing it via repo, delivering it against the short futures position — generates a return that exactly equals the actual repo rate, then no arbitrage profit exists. The IRR is the return that the cash-and-carry strategy would generate if executed exactly; deviations between IRR and actual market repo rates signal potential arbitrage opportunities.
The calculation of the implied repo rate begins with the delivery mechanics of Treasury futures contracts. The short position in a Treasury futures contract has the right to choose which eligible bond to deliver (within the contract's specified maturity range) and when to deliver within the delivery month. The delivered bond's invoice price — the amount the long position pays — is computed as the futures settlement price multiplied by the delivered bond's conversion factor (a CBOT-defined adjustment to make bonds of different coupon and maturity roughly equivalent in price) plus accrued interest. The conversion factor system ensures that multiple bonds are eligible for delivery, but at any point in time one bond will be 'cheapest to deliver' — the bond for which the cost of acquisition plus financing is minimized relative to the invoice price received upon delivery.
The formal IRR calculation for a given deliverable bond is: IRR = [(Invoice Price − Full Cash Price + Coupon Income) / (Full Cash Price × Days to Delivery / 360)]. Here, the Invoice Price is the futures settlement price × conversion factor + accrued interest at delivery. The Full Cash Price (dirty price) is the bond's current market price plus accrued interest. Coupon Income is any coupon paid between today and delivery, adjusted for reinvestment to the delivery date. Days to Delivery is the number of calendar days from today to the futures delivery date. The resulting rate is annualized on an actual/360 basis consistent with U.S. money market conventions.
The CTD bond is identified as the bond with the highest implied repo rate among all eligible deliverable bonds, because the short futures holder will always deliver the bond that maximizes the net proceeds received minus the cost of acquisition — i.e., the bond with the highest effective yield on the cash-and-carry strategy. When yields are high (bond prices are low), longer-duration, lower-coupon bonds tend to be CTD; when yields are low, shorter-duration, higher-coupon bonds tend to be CTD. This CTD switching as yield levels change creates the delivery option embedded in Treasury futures, which has positive value to the short and must be priced accordingly.
For fixed-income relative value hedge funds, IRR analysis is central to Treasury basis trading — the strategy of taking long or short positions in the Treasury basis (cash bond price minus futures-equivalent price) to exploit deviations from fair value. When the IRR is substantially above the actual repo rate across all deliverable bonds, the basis is 'cheap' — the futures are underpriced relative to cash — and a long basis trade (buy the bond, sell the futures) is attractive. Conversely, when IRR is below actual repo, the basis is 'rich' and a short basis trade (sell the bond, buy the futures) is appropriate. The delivery option's value, special repo rates for specific bonds, and financing constraints around delivery dates all complicate the analysis, making Treasury basis trading a technically demanding but well-established relative value strategy.
Formula
IRR = [(Invoice Price − Full Cash Price + Coupon Income) / (Full Cash Price × Days to Delivery / 360)]; Invoice Price = Futures Price × Conversion Factor + Accrued Interest at Delivery; Arbitrage Signal: If IRR > Actual Repo Rate → Cash-and-Carry Long Basis; If IRR < Actual Repo Rate → Reverse Cash-and-Carry Short Basis
Example
A fixed-income hedge fund analyzes the 10-year Treasury futures contract expiring in 90 days. The CTD bond is a 3.875% coupon Treasury maturing in 9.5 years, trading at a full price of $104.250 per $100 face value. The futures contract is trading at $100.500, and the bond's conversion factor is 1.0380. The invoice price at delivery (assuming no interim coupon) = $100.500 × 1.0380 + accrued interest = $104.319 + $1.750 = $106.069. No coupon is paid before delivery. IRR = ($106.069 − $104.250) / ($104.250 × 90/360) = $1.819 / $26.063 = 6.98% annualized. The actual 90-day repo rate for this bond is 5.25%. Since IRR (6.98%) > Repo Rate (5.25%), a cash-and-carry trade is profitable: borrow at 5.25% to buy the bond, repo it, short the futures at $100.500, deliver the bond at expiry, and lock in 173 bps of annualized risk-free spread.
Related terms
Accrued Interest Arbitrage Basis Bond Carry Trade Cheapest To Deliver Coupon Rate Credit Spread Delivery Dirty Price Duration Face Value