Duration is sensitivity, not a repayment date.
Maturity dates the final contractual payment; duration measures sensitivity. Neither gives a recovery deadline. An ongoing fund has duration without a final unit repayment date.
Modified duration measures sensitivity to the bond’s own YTM with unchanged cash flows. Keep its precise name and assumptions.
Why two duration figures need not be comparable
The CFA distinguishes yield-based measures from sensitivity to a benchmark yield curve. Similar numbers can describe different calculations, especially with changing payments. Keep the reporting date.
Translate sensitivity into money at risk.
Invented €20,000 holding, modified duration 6. Yield rises from 4% to 4.5% → estimated price change −3% → about €600 lower, or €19,400. This local estimate holds cash flows and other factors fixed; it excludes coupons, reinvestment, costs, tax and currency moves.
These are scenarios, not predictions or maximum-loss limits. The yield change is half a percentage point, not half a percent of the old yield.
Calculate all three local price scenarios
Approximate proportional change = −modified duration × decimal yield change. From 4% to 4.5%, enter 0.005: −6 × 0.005 = −0.03, or −3%. Applied to €20,000, about €600 is lost.
- Yield falls 0.5 percentage points
- +3%, about €20,600.
- Yield rises 0.5 percentage points
- −3%, about €19,400.
- Yield rises 1 percentage point
- −6%, about €18,800.
The same local approximation applies.
The price–yield relationship curves.
Separate two-year bond: the previous lesson’s year 1 €50 → year 2 €1,050, not the duration-6 holding above. Annual discounting; no call, default, costs or currency changes.
Compare exact prices with the local line
Price = €50/(1+y) + €1,050/(1+y)²; the local line uses its slope at 5%.
| YTM | Exact price | Local line |
|---|---|---|
| 0% | €1,100.00 | €1,092.97 |
| 5% | €1,000.00 | €1,000.00 |
| 10% | €913.22 | €907.03 |
| 15% | €837.43 | €814.06 |
Discounting the same payments at different yields produces the curve. The straight line is only local. Different maturities’ yields need not move together, and credit or callable payments can change. Duration 6 does not cap loss at 6%.
Fixed payments further in the future and lower coupons generally increase sensitivity, other things equal; maturity alone cannot rank every pair. An ongoing fund can replace maturing bonds to maintain exposure.
Why an ongoing fund does not simply count down
A plain bond approaches its final payment. A fund can replace it with later payments; five years of ownership need not reduce an initial duration 6 to a duration of one. An aggregate figure also hides differing curve shifts and borrower conditions.
Lower prices and better reinvestment can coexist.
Higher yields can lower current prices while allowing future receipts to earn more; lower yields can do the reverse. An imminent sale allows little time for reinvestment to offset a loss.
Reading duration as a recovery deadline leaves out later yields, credit events, withdrawals, changing holdings and the assumptions used. A longer horizon changes the balance without guaranteeing recovery by a date.
Put sensitivity beside the spending deadline.
Translate plausible price changes into a possible cash shortfall. Check currency, credit and access too. Short duration is not deposit insurance or default protection; low-default-risk long government debt can still fluctuate substantially.
For an ongoing allocation, assess sensitivity with the rest of the portfolio. Keep the measure/date and revisit after mandate or goal changes; understanding exposure requires no rate forecast.