Matrixx0070 Bond Futures Basis Analysis
When to use
Use this to decompose the relationship between a cash government bond and the bond-future that can deliver it: to compute gross and net basis, carry, and the implied repo rate, to identify the cheapest-to-deliver (CTD) issue, and to reason about whether the future is rich or cheap versus cash. Applies to Bund/Bobl/Schatz, Gilt, UST, JGB futures — any physically-settled bond future with a delivery basket and conversion factors.
Not for: outright duration positioning across a portfolio (lseg-fixed-income-portfolio), or curve-shape trades on the swap curve (lseg-swap-curve-strategy). This skill is about one future against its deliverable basket.
This is educational market analysis, not investment advice. Nothing here is a recommendation to trade.
Method
- Pin the contract mechanics. Note the delivery month, the delivery basket, each bond's conversion factor (CF), the notional coupon of the contract, and the day-count convention. The CF normalizes each deliverable to the notional coupon.
- Compute the gross basis for each candidate:
Gross basis = Clean price of bond − (Futures price × CF). Quote in price points; it is always ≥ 0 near delivery for the CTD by no-arbitrage. - Compute carry to the delivery date:
Carry = coupon income accrued over the holding period − financing cost (repo) over the same period. Positive when the coupon yield exceeds the repo rate (the normal upward-sloping case). - Compute net basis:
Net basis = Gross basis − Carry. Net basis is the cost of the delivery option plus any richness; it is the number to compare across the basket. - Compute the implied repo rate (IRR) — the return from buying the bond, selling the future, and delivering:
IRR = [(Futures × CF + accrued at delivery − (bond price + accrued now)) / (bond price + accrued now)] × (360 or 365 / days). The bond with the highest IRR is the CTD. - Cross-check CTD two ways: highest IRR and lowest net basis should agree. If they disagree, re-check accrued-interest dates and the day-count. Note that CTD shifts with yield level (a rule of thumb: at yields above the notional coupon the market tends toward longer-duration/lower-CF issues; below, toward shorter).
- Interpret. A large positive net basis on the CTD signals the future is cheap to cash (or the delivery option is valuable); near-zero net basis signals fair. State the delivery-option component you cannot strip out analytically as a residual to be aware of.
Example
Bund future price 133.50, delivery in 60 days. Candidate bond: clean price 128.20, CF 0.945000, coupon 2.30% (semi-annual), current accrued 0.85, repo 3.40% (act/360).
- Gross basis = 128.20 − (133.50 × 0.945000) = 128.20 − 126.1575 = 2.0425.
- Carry (60 days): coupon income = 2.30% × (60/365) × 100 ≈ 0.378; financing = (128.20 + 0.85) × 3.40% × (60/360) ≈ 0.731. Carry = 0.378 − 0.731 = −0.353 (negative — repo exceeds running yield, an inverted-carry regime).
- Net basis = 2.0425 − (−0.353) = 2.3955. Interpretation: net basis is clearly positive, so the future is cheap to this bond and/or the delivery option is being priced. To confirm CTD, compute IRR for every basket bond and pick the max; do not declare CTD from one issue.
Pitfalls
- Wrong accrued-interest dates. Basis is dominated by accrued at both the trade date and the delivery date — use the contract's exact last-delivery day, not month-end.
- Mixing day-counts. Repo is usually act/360, the bond coupon act/act or 30/360 — a mismatch silently corrupts carry.
- Calling the CTD from gross basis. Gross basis ignores carry; the CTD is the highest-IRR / lowest-net-basis issue, which can differ.
- Ignoring the delivery option. Net basis embeds the short's timing and quality (switch) option; a positive net basis is not pure "richness" you can arbitrage away.
- Assuming CTD is static. A parallel yield move can switch the CTD and break a basis position — re-run the basket after large rate moves.
- Sign confusion on carry in an inverted regime — when repo > running yield, carry is negative and widens net basis.
Output format
Contract: <future> <delivery month> | Futures price: <..> | Days to delivery: <..>
Basket (per bond):
| bond | clean px | CF | accrued | gross basis | carry | net basis | IRR% |
CTD: <bond> (highest IRR = <..>%, lowest net basis = <..>) [both criteria agree? yes/no]
Regime: carry <positive/negative>, repo <..>% vs running yield <..>%
Read: future <rich/cheap/fair> vs cash; delivery-option caveat: <..>
NOT investment advice — educational analysis only.
Reference
The core identities
- Gross basis = P_bond − (F × CF), in price points.
- Carry = accrued coupon over holding period − repo financing over holding period.
- Net basis = Gross basis − Carry = the delivery-option value + residual richness.
- Implied repo rate (IRR) = annualized return of the cash-and-carry: buy bond, sell CF futures, deliver. The CTD maximizes IRR.
Implied repo rate, expanded
Invoice at delivery = F × CF + accrued_at_delivery
Cost today = P_bond + accrued_now
IRR = (Invoice − Cost) / Cost × (basis_days_per_year / days_to_delivery)
Use act/360 for euro/USD repo, act/365 for GBP. IRR > actual term repo ⇒ cash-and-carry is profitable (future cheap); IRR < repo ⇒ reverse cash-and-carry.
Conversion factor intuition
CF ≈ price of the bond at delivery if it yielded the contract's notional coupon. CF > 1 for coupons above the notional, < 1 below. The CF is fixed by the exchange for the contract; use the published value, do not re-derive it casually.
Why the CTD changes with yields
The CTD is the bond that is cheapest to buy and deliver. Because CFs are computed at a single notional yield, when market yields rise above the notional coupon, higher-duration (typically longer-maturity, lower-CF) bonds become relatively cheaper to deliver; when yields fall below it, the shorter/higher-CF end becomes cheapest. This is the embedded switch option the short owns.
Delivery options (why net basis isn't free money)
The short position in the future holds: the quality/switch option (deliver whichever bond is cheapest at expiry), the timing option (choose the delivery day in the month), and the wildcard option (deliver after the futures settlement price is fixed). These options have positive value to the short, which is why the CTD's net basis is positive even in a fair market — it is the price of the options, not an arbitrage.
Duration hedging with the future
To hedge a cash bond position with the future:
Number of contracts = (BPV_position / BPV_CTD) × CF_CTD
where BPV is the basis-point value (DV01). Hedge on the CTD because that is what drives the future near delivery. Re-hedge if the CTD switches.