Show how interest rate futures, forwards and swaps can reshape the risk and return of a portfolio
The idea
Duration is the lever. Futures needed = (target BPV − portfolio BPV) ÷ futures BPV, where futures BPV is roughly the cheapest-to-deliver bond's BPV ÷ its conversion factor. A portfolio with BPV 50,000, target 30,000 and futures BPV 100 sells 200 contracts. A receive-fixed swap adds duration, like owning a fixed-rate bond funded at a floating rate. Paying fixed shortens it, with notional = BPV gap ÷ swap BPV per unit of notional. Forward rate agreements lock in a future borrowing or lending rate. Futures are liquid and margined daily; swaps are tailored but bring counterparty and collateral demands. Traps: the sign, since shortening means selling futures or paying fixed, and basis risk from non-parallel curve shifts.
Formulas
Futures needed to change a bond portfolio's duration
futures needed = (target BPV − portfolio BPV) ÷ futures BPV
- target BPV
- the basis point value wanted
- portfolio BPV
- the portfolio's basis point value now
- futures BPV
- the basis point value of one contract, usually the cheapest-to-deliver bond's divided by its conversion factor
BPV is money duration per basis point: duration × value × 0.0001. A positive answer means buying futures to lengthen duration, a negative one selling them to shorten it.
In the app: 1 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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