Bond Future

A bond future is a standardised contract to buy or sell government bonds at a set price on a set date — the Treasury future in the US, the Bund future in Europe. It's how most of the world actually trades interest-rate risk: enormous liquidity, tiny margins, one click.

Twist one: the seller doesn't deliver one specific bond, but may choose from a basket of eligible bonds. Twist two: because those bonds differ, each has a conversion factor meant to put them on equal footing — imperfectly, which creates the famous "cheapest-to-deliver" game.

For most users none of this matters: they trade the future as a pure bet or hedge on government bond prices — rates up, future down; rates down, future up — and roll it before delivery ever happens.

Contract design

• Notional: e.g. $100k (Treasuries) / €100k (Bund) of a notional 6% bond.
• Delivery basket: bonds within a maturity window (e.g. 8.5–10.5y for the Bund) are deliverable.
• Conversion factor (CF): approximately the bond's price at a 6% yield — the seller receives futures price × CF + accrued.
• Delivery month options: the short chooses which bond and (in the US) when in the month — free options that shave the fair futures price.

Cheapest-to-deliver (CTD)

Conversion factors would be perfect only if all yields were 6%; since they aren't, one bond is always cheapest for the short to buy and deliver. The future tracks that bond — its duration, its yield — and when yields cross 6% or the basket changes, the CTD can jump, abruptly changing the future's personality.

Uses

• Duration management: adjust a portfolio's rate risk instantly with futures rather than trading bonds.
• Basis trading: cash bond vs. future — the "basis trade" that grew into a multi-hundred-billion-dollar hedge-fund strategy (and a financial-stability talking point).
• Curve trades: 2y vs 10y futures spreads, etc., in one liquid package.

Pricing: carry and the short's options

Fair futures price ≈ forward price of the CTD divided by its conversion factor, minus the value of the delivery options:

where carry = financing cost − coupon accrual (repo-driven), and DOV (delivery option value) prices the short's switch/timing/wildcard rights — computed by scenario analysis over yield shifts that change the CTD.

The basis

Gross basis \(= S - F \times CF\); net basis subtracts carry, leaving ≈ DOV. Basis trades short the rich leg and finance the bond in repo; profitability lives in repo specialness and option mispricing. The strategy's leverage (50–100x via repo) is why regulators monitor it — the March 2020 unwind moved the entire Treasury market.

Risk metrics through the CTD lens

The future's DV01 = CTD's forward DV01 / CF; its "yield" is the CTD's forward yield. Near CF-yield (6%) crossovers, effective duration becomes state-dependent — the future embeds a switch option, giving it negative convexity versus holding the CTD outright.

Cross-market plumbing

Invoice spreads (futures vs. matched-maturity swaps) and futures-implied repo vs. GC define the richness/cheapness map that rates RV desks live on.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.