Dollar Duration

The dollar duration expresses a bond’s duration in dollar terms: the number of dollars (or cents) the bond’s price will change for every basis point move in yield. It converts abstract time-weighted duration into a concrete figure that tells you the immediate stakes of a rate move.

From abstract to concrete

Duration is elegantly abstract: a 5-year Treasury bond has a duration of roughly 4.7 years. But what does that mean in your pocket?

Dollar duration answers precisely. That 4.7-year bond, priced at $98, has a dollar duration of about $4.60. If yields rise 1 basis point, its price falls to $97.9954—a loss of roughly $0.0046, or 0.46 cents per $100 of face value. For a $1 million position, that’s a $46 loss.

For a portfolio manager holding hundreds of millions, that granular number is not academic—it dictates real risk exposure and hedge sizing.

The mathematics

The formula is straightforward:

Dollar Duration = Duration × Bond Price ÷ 10,000

The division by 10,000 converts basis points (which are hundredths of a percent) to a decimal scale.

Alternatively, you can express it per $100 of par:

Dollar Duration (per $100 par) = Duration × 100 ÷ 10,000 = Duration ÷ 100

A 7-year coupon bond with duration of 6.2 years and priced at $103 per $100 of par has:

• Dollar Duration = 6.2 × 103 ÷ 10,000 = $0.0638 per basis point
• Or: $6.38 per 1 basis point move on a $1 million position

Real-world application

Fixed-income traders use dollar duration constantly:

Position sizing — If a trader wants to hedge a portfolio of corporate bonds with Treasury futures contracts, she needs to know the futures contract’s dollar duration and size the hedge accordingly. If her portfolio has a dollar duration of $100 and each futures contract has a dollar duration of $50, she might short two contracts.

Risk reporting — Portfolio managers report daily risk to clients and risk committees. “We have $500,000 of duration risk” is far more meaningful than “6.3 years of duration” when the portfolio size is $50 billion.

Marking the portfolio — In fixed income, market-to-market P&L is relentless. If you own $10 million of a bond and yields move 5 basis points, dollar duration tells you instantly whether you’ve just gained or lost money: multiply dollar duration by 5 and you have your approximate loss.

Dollar duration vs. DV01

The terms are often used interchangeably by traders, and the concepts are nearly identical. Strictly speaking:

• Dollar Duration is the product of duration and price: it expresses the bond’s mathematical interest-rate sensitivity in dollars.
• DV01 (“dollar value of one basis point”) is empirically computed: you bump the yield by 1 basis point, reprice the bond, and measure the difference.

For bonds without embedded options (straight corporates, Treasuries), the two are mathematically equivalent. For callable bonds or mortgage-backed securities, DV01 can diverge because the bond’s cash flows themselves change with rates—a phenomenon duration doesn’t capture directly.

In practice, when a trader says “the DV01 is $400,” they usually mean the DV01; when a quant says “dollar duration is $400,” they’re computing it from duration and price. The result is the same for plain-vanilla bonds.

Why it matters more than duration

A bond’s duration is timeless—it describes the shape of the bond’s cash-flow stream. But its dollar duration changes as the bond’s price changes. A bond bought at par has a different dollar duration than the same bond bought at a premium or discount, even though its duration is nearly identical.

This matters because portfolio risk is always measured in dollars. You don’t care that your bond has 4.5 years of duration if it costs you $500,000 when rates rise 1 basis point. Dollar duration is the language of actual loss and gain.

The hedge arithmetic

A hedge works when you match dollar durations. Suppose you own $100 million of 10-year corporates with a dollar duration of $750,000 per basis point. Yields rise 10 basis points and you lose $7.5 million.

To offset that risk, you could short $750 million of 2-year Treasury bills (which have a much lower dollar duration per dollar notional—say $50,000 per basis point) or sell Treasury futures sized to exactly $750,000 of duration. If done correctly, your long corporate and short Treasury exposure offset, and the portfolio becomes duration-neutral.

Dollar duration makes that algebra transparent.

Limitations

Dollar duration assumes a parallel yield curve shift. If the 5-year yield rises but the 10-year stays flat, your actual loss may differ from what dollar duration predicts. For precise risk under non-parallel moves, you need key rate duration, which decomposes duration into sensitivities at each maturity point.

Also, dollar duration breaks down for bonds with embedded options. A callable bond bought at a high price has less downside duration than a straight bond (because if rates fall and the bond rallies, the issuer is more likely to call it), but standard dollar duration doesn’t account for that optionality. DV01 becomes more reliable because it’s computed from actual repricing.

See also