How is the conversion factor calculated and why does it matter for delivery?

Question

AcadiFi · Accepted Answer

The conversion factor (CF) is the clean price per dollar of face value of a deliverable bond priced to yield 6% at the first day of the delivery month, with maturity rounded down to the nearest three months. For a 3.5% coupon bond maturing in 18 years 7 months (rounded to 18.5 years), the CF is computed by discounting all cash flows at 6% yield and dividing by face. This gives roughly 0.7516. The invoice price the short receives equals Futures Settle * CF + accrued interest.

Because CF is a mechanical function of coupon and maturity, it imperfectly equates bonds. Above 6% yields, low-coupon long bonds have a CF that's relatively too generous (from the long's perspective), making them CTD. Below 6%, the opposite occurs. Kestrel Fixed Income uses CFs published by CME each delivery cycle and recomputes when the contract specifications change. CF rounding to the nearest three months creates small quirks in which specific CUSIPs are CTD, something sophisticated desks exploit.

```mermaid
flowchart LR
  Coupon[Coupon Rate] --> PV[Discount at 6%]
  Maturity[Maturity Rounded] --> PV
  PV --> CF[Conversion Factor]
  CF --> Invoice[Invoice Price]
  Invoice --> Short[Short Receives]
```

How is the conversion factor calculated and why does it matter for delivery?

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