What it means
Ordinary modified duration tells you the approximate percentage change in a bond's price for a 1% change in yield. That is useful for comparing bonds but useless for sizing risk across a portfolio, because a 1% move on a small holding and on a huge holding are the same in percentage terms and wildly different in dollars.
Dollar duration fixes this by multiplying duration by the position's market value. The result is expressed in currency, so positions of different sizes, maturities and coupons can be added together into a single portfolio exposure figure.
A closely related measure is DV01, sometimes called the price value of a basis point, which is simply the dollar duration scaled to a one basis point move rather than a full 1%. Traders quote DV01 because real daily rate moves are measured in basis points, not whole percentage points.
The practical use is hedging. If a portfolio has a dollar duration of $320,000 and the manager wants to neutralise half of it, the hedge instrument must supply an offsetting $160,000, which determines exactly how much of the hedge to buy or sell.
The main caveat is that dollar duration is a straight-line approximation of a curved relationship. It is accurate for small rate moves and increasingly wrong for large ones, which is why convexity is added as a second-order correction when moves get big.
In practice
Real-world examples.
Example
An insurance company measures the dollar duration of its bond portfolio at $4.2 million and of its liabilities at $5.1 million. The mismatch tells the actuary exactly how many dollars of extra long-dated bonds are needed to bring the two into line.
Example
A corporate treasurer holding a short-term investment portfolio reports DV01 rather than duration to the audit committee, because a figure of $18,000 per basis point communicates the exposure immediately without a lecture on bond mathematics.
Example
A fund manager wants to cut interest rate risk without selling holdings, so she sells bond futures sized by dollar duration. Matching the futures position's dollar duration to the amount she wants to hedge removes that exposure while leaving the credit positions intact.
Formula
Calculation
Dollar duration = Modified duration x Market value x 0.01 for a 1% yield move, and DV01 = Modified duration x Market value x 0.0001 for a one basis point move.
A pension fund holds a corporate bond position with a market value of $5,000,000 and a modified duration of 6.4 years. The dollar duration is 6.4 x 5,000,000 x 0.01 = $320,000, meaning a 1% rise in yields would cut the position's value by roughly that amount. The DV01 is 6.4 x 5,000,000 x 0.0001 = $3,200 per basis point. If yields rise by 25 basis points, the expected loss is 3,200 x 25 = $80,000, which matches 320,000 x 0.25 = $80,000. To offset the whole exposure with a shorter bond of modified duration 3.2, the manager would need a position of 320,000 / (3.2 x 0.01) = $10,000,000, twice the size, because each dollar of the shorter bond carries half the rate sensitivity.Case study
Seen in the real world.
Brightmoor Mutual is a fictional insurer invented for this illustrative case. Its investment committee had long reported interest rate risk as an average portfolio duration of 6.1 years, a number that appeared on every quarterly pack and that almost nobody on the board could interpret.
A new chief risk officer restated the same exposure in dollar duration terms. The portfolio's $840 million of bonds carried a dollar duration of about $5.1 million per 1% rate move, against liabilities whose dollar duration was closer to $6.4 million, leaving an unhedged gap of roughly $1.3 million per 1% move.
Nothing about the underlying risk had changed, but the conversation did. Presented as a cash figure the board could compare to earnings, the gap was closed within two quarters through a modest extension of maturities. The illustrative point is that the right unit of measurement is often what turns a technical exposure into a decision.
Watch out
Common mistakes.
- Confusing dollar duration with duration in years, when one is a cash amount and the other is a time-weighted percentage sensitivity.
- Adding the durations of several holdings directly, when only dollar durations add up properly across positions of different sizes.
- Relying on dollar duration for a large rate shock, where the ignored curvature of the price-yield relationship makes the estimate materially wrong.
Questions
People also ask.
Is dollar duration the same as DV01?
They measure the same thing at different scales, since DV01 is the dollar change for a one basis point move and dollar duration is usually quoted for a full 1% move.
Does dollar duration work for a portfolio containing derivatives?
Yes, and it is one of the few measures that does, because futures and swaps can be assigned a dollar duration and netted against cash bond positions.
Why is convexity needed if dollar duration already gives a dollar figure?
Because the relationship between price and yield is curved, so dollar duration overstates losses and understates gains on large moves, and convexity corrects for that.
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