Does a lower overnight policy target guarantee a positive return on longer-duration bonds?
Hypothesis to test
A policy-rate cut is enough to establish that longer-duration bond prices will rise over the following weeks.
The dated evidence
| Observation | Date | Value |
|---|---|---|
| Federal funds target-range cut | 18 Sep 2024 | 50 basis points |
| New federal funds target range | 18 Sep 2024 | 4.75%–5.00% |
| 10-year Treasury constant-maturity yield | 18 Sep 2024 | 3.70% |
| 10-year Treasury constant-maturity yield | 6 Nov 2024 | 4.42% |
Reproduce the calculation
- The selected 10-year yield rose by 4.42 − 3.70 = 0.72 percentage point, or 72 basis points.
- Hypothetical example: modified duration 6 × a +0.005 yield change gives an approximate price change of −3%.
- For a hypothetical £1,000 bond, −3% is about −£30 before income, convexity, costs and other changes. This is not a measured return on a real bond or ETF.
What supports the hypothesis?
- The Federal Reserve did lower its overnight target range by 50 basis points on the stated date.
- For a given bond, a fall in its relevant yield generally supports its price, with other factors held constant.
What weakens it?
- The selected longer-maturity benchmark yield was higher on 6 November than on 18 September.
- The overnight target and a 10-year yield are different measures. The policy decision alone does not establish the subsequent longer-duration return.
1. Match the instrument to the claim
An overnight policy range does not describe every maturity on the yield curve. A constant-maturity Treasury yield is also an estimated benchmark, not the trade price of a particular bond.
An ETF holds a changing portfolio with its own duration, distributions and costs. Do not use two benchmark yield observations as if they were an ETF’s total return.
2. Use duration as a local approximation
Modified duration describes approximate price sensitivity to a small yield change, holding other factors constant. The hypothetical calculation states the duration, yield change and exclusions.
Larger changes, a non-parallel yield-curve move, credit spreads and convexity can change the result. A hypothetical duration calculation does not establish the maximum loss.
3. Avoid hindsight in the research note
These dates illustrate a counterexample; they are not a backtest or proof of what would have been predictable. The example does not establish why the longer yield moved.
Record what the original thesis required, what would invalidate it and which maturity, credit exposure and holding period it concerns. Retain contradictory evidence rather than redefining the thesis around the later outcome.
A hypothetical bond has modified duration 6 and its relevant yield rises by 50 basis points. What is the simple duration approximation, and what does it exclude?
Show the worked answer
Approximate price change ≈ −6 × 0.005 = −0.03, or −3%. It excludes income, convexity, non-parallel curve moves, credit changes, costs and portfolio changes. It is not an actual bond or ETF return and is not a maximum-loss estimate.
Primary sources
Prepared with AI assistance; numerical facts checked against the linked primary sources. Historical examples and hypothetical arithmetic do not establish what was predictable, a current valuation or a trade to take.