What it means
Duration is the standard way of describing interest rate sensitivity. A bond with an effective duration of 6 is expected to lose roughly 6% of its value if yields rise by one percentage point, and gain roughly 6% if yields fall by the same amount.
Effective duration exists because ordinary duration measures assume the bond's cash flows are fixed. That assumption breaks down for callable bonds, putable bonds and mortgage-backed securities, where a change in rates changes the timing of the cash flows themselves.
The calculation is empirical rather than algebraic. A pricing model revalues the bond after a small upward rate shift and a small downward one, and effective duration is derived from how far the price moved in each direction relative to the size of the shift.
Portfolio managers use it constantly, because duration adds up neatly across holdings. A fund's overall effective duration is the weighted average of its individual positions, which makes it straightforward to dial the interest rate risk of a whole portfolio up or down.
The nuance is that duration is a first approximation and becomes less accurate for large rate moves. Convexity, which measures how duration itself changes as yields change, is the second-order correction applied when the move is substantial.
In practice
Real-world examples.
Example
A pension fund holds a bond portfolio with an effective duration of 8.4 and expects rates to rise. It sells long-dated holdings and buys short-dated ones, bringing portfolio duration down to 4.1 and roughly halving its rate exposure.
Example
An insurer matches a book of liabilities with an effective duration of 11 against assets with a duration of 7. The mismatch means falling rates hurt the liabilities more than they help the assets, so the insurer buys long-dated bonds to close the gap.
Example
A treasury team compares two corporate bonds with identical yields. The callable one shows an effective duration of 3.2 against 6.1 for the non-callable equivalent, revealing that the call feature substantially changes the risk being taken.
Formula
Calculation
Effective duration = (P- minus P+) / (2 x P0 x change in yield)
where P- is the bond price if yields fall, P+ is the price if yields rise, P0 is the current price and the change in yield is expressed as a decimal.
Take a callable corporate bond currently priced at $100.00 per $100 of face value. The pricing model is run with a 50 basis point downward shift, giving a price of $103.10, and a 50 basis point upward shift, giving a price of $97.20. The yield change is 0.005.
Effective duration = ($103.10 - $97.20) / (2 x $100.00 x 0.005) = $5.90 / $1.00 = 5.9.
The interpretation is that a one percentage point rise in yields would reduce the bond's price by approximately 5.9%, so a $2,000,000 holding would be expected to lose around $118,000 of value. Note the asymmetry in the model prices: the bond gained $3.10 on the way down but lost $2.80 on the way up, which reflects the call feature limiting the upside.Case study
Seen in the real world.
This case is illustrative and fictional. Vellacott Mutual, an invented insurance company, held a $400,000,000 bond portfolio it described internally as low risk because most holdings were investment grade. The risk committee had never separated credit risk from interest rate risk.
A new chief investment officer calculated effective duration across the portfolio and found a weighted average of 9.2. That implied a one percentage point rise in yields would cut portfolio value by roughly 9.2%, or about $36,800,000, which was more than the company's annual underwriting profit.
In this fictional example Vellacott set a duration policy limit of 6.0 and moved roughly $90,000,000 from long-dated bonds into shorter maturities to reach it. The portfolio yield fell slightly, but the committee gained a measure it could monitor and a limit it could act on.
Watch out
Common mistakes.
- Reading duration as a time period. Although it is quoted in years, in practice it should be read as a price sensitivity: a duration of 5.9 means about 5.9% per percentage point.
- Using modified duration for callable or mortgage-backed bonds. Those instruments have cash flows that shift with rates, and only effective duration accounts for that behaviour.
- Applying duration to very large rate moves. Beyond roughly one percentage point the estimate drifts, and convexity is needed to correct it.
Questions
People also ask.
What is the difference between effective and modified duration?
Modified duration assumes fixed cash flows, while effective duration is calculated by repricing the bond under rate shifts and so captures embedded options.
Can effective duration be negative?
Yes, for some mortgage-backed and structured securities, where prepayment behaviour can cause prices to fall as rates fall.
How is portfolio duration calculated?
It is the market-value-weighted average of each holding's effective duration, which is why duration is such a practical portfolio management tool.
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