FRM® DV01 versus effective duration: which risk measure?

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DV01 turns a small yield movement into an approximate money change for a specific position; effective duration expresses the same local sensitivity relative to the position’s value. For an FRM® Part I calculation, use duration to compare proportional exposure and DV01 to size or aggregate dollar exposure. Convert with the full position value and keep the yield change in the correct units.

Start with the question each measure answers

Suppose two holdings have identical cash flows but different face amounts. They should have the same effective duration if the same valuation assumptions apply. The larger holding has the larger DV01 because a given percentage price movement affects more money. This simple comparison is often enough to choose the measure before touching a calculator.

Effective duration estimates the percentage response of a price to a small change in the yield or curve input used in a repricing model. It is a ratio: the dollar change divided by the starting full value, scaled by the yield change. DV01, also called the value of a basis point, instead reports the magnitude of the money change associated with one basis point. It carries the currency and position scale that duration omits.

GARP places valuation and risk models within its FRM study materials. A CFA Institute fixed income reference gives the familiar price, duration and basis-point relationship. The conversion is a local approximation, so a candidate should identify both the relevant price and the rate shock before using it.

Convert percentage sensitivity into money sensitivity

One basis point is a change of one ten-thousandth in a yield written as a decimal. Thus multiply effective duration by the full market value of the position and divide by ten thousand. The result is the approximate absolute value of a price change for a one-basis-point parallel yield movement, in the currency of the position. The negative sign belongs to the estimated price response to a rise in yield, not necessarily to the quoted DV01 magnitude.

The value input must match the object whose risk is being measured. A per-unit bond price yields a per-unit DV01. A whole position value yields a whole position DV01. Mixing the duration of one security with the par amount, or using a clean quote where the calculation calls for full value, breaks the units even if the arithmetic is tidy.

Work a complete position example

The following figures are invented for illustration. A fixed-rate position has a full market value of £2,000,000 and an effective duration of four. Its estimated price loss for a one-percentage-point upward shift is four per cent of the full value, or £80,000. Divide that result across one hundred basis points: the DV01 magnitude is £800 per basis point. Direct multiplication gives the same answer: four times £2,000,000 divided by ten thousand equals £800.

If the same curve moves upward by five basis points, the first-order estimate is a £4,000 fall. A five-basis-point fall gives a £4,000 rise under the same symmetric linear approximation. Neither outcome is an observed market result. The amounts merely demonstrate how sign and scale enter the calculation.

Now double only the holding size. Its full value becomes £4,000,000, its effective duration remains four under the identical repricing assumptions, and its DV01 becomes £1,600. If instead the duration changes while value stays fixed, both proportional and money sensitivity change. This two-step thought experiment separates scale from underlying interest-rate exposure.

Move from one security to a portfolio

For a small parallel movement under consistent risk assumptions, signed dollar sensitivities can be combined across positions. A portfolio with an illustrative positive £800 DV01 from one long bond and a negative £300 signed exposure from a hedge has approximately £500 net sensitivity to that common shock. Saying the portfolio has duration four plus the hedge’s duration would be meaningless: durations are ratios that require value weights and consistent signs.

To recover a portfolio duration from net DV01, divide its signed money sensitivity by the portfolio’s net starting value and undo the basis-point scaling. This is straightforward only when the denominator and risk convention are coherent. A hedge can have a small market value but substantial rate exposure, so a casual average of durations weighted by face amount may produce a misleading number.

A single parallel-shift DV01 is also a compression of the yield curve. Cash flows at different maturities may respond to different key rates. Two positions with similar headline DV01 need not offset if one reacts mainly to short maturities and the other to long maturities. A hedge decision needs matching of the actual rate factors, cash-flow dates and instrument conventions, not just equality of two totals.

Know when the estimate becomes weak

Duration and DV01 are first-order descriptions around a starting valuation. A larger rate movement exposes curvature, so multiplying one DV01 by a large number of basis points becomes less reliable. The original price-yield relationship may bend, and embedded options can change expected cash flows as rates move. Effective duration is especially useful for securities with rate-dependent cash flows because it can be calculated through repricing, but its meaning then depends on the model and shock chosen.

Different spread and benchmark assumptions also matter. A quoted DV01 may refer to a government yield, a swap curve, a credit spread, or a modelled parallel shift. These are not interchangeable risks. Before comparing two quoted figures, ask which market input moved, what was held fixed and whether both values are stated per security, per contract or per entire position.

A reliable exam routine

First name the output unit. If the question asks for pounds per basis point, you need DV01; if it asks for the approximate percentage price response, you need duration. Second identify the full starting value and write the yield change as a decimal. Third carry the sign only when reporting a price gain or loss. Fourth make a reasonableness check: multiplying a per-basis-point exposure by one hundred should match the rough money move implied by a one-percentage-point rate shift.

The common error is to multiply by one hundredth as though it represented one basis point. That yields an answer one hundred times too large. Another is to treat a duration of four as a price change of four per cent for a one-basis-point move; four per cent corresponds to a one-percentage-point move in the local linear interpretation. Distinguishing a basis point from a percentage point is the central unit check.

When comparing positions, duration alone answers which is proportionally more sensitive under the stated assumptions. DV01 answers which contributes more currency exposure to the same shock. Both can be correct descriptions of the same holding; choosing between them depends on the decision. The FRM programme overview and Omni methodology provide context for organising the topic within revision, while the official sources above anchor the financial definition.

Separate effective and modified duration

The conversion works when the duration and DV01 refer to the same small yield perturbation and the same valuation base. For a conventional fixed-cash-flow bond, modified duration describes sensitivity to its yield to maturity. Effective duration is generally obtained by repricing for upward and downward changes in the relevant benchmark rate and is more suitable when an option may alter cash flows. A numerical value from one definition should not be silently relabelled as the other. The CFA Institute reference derives the DV01 relation with modified duration for its bond example; using an effective-duration input is the analogous local calculation only when the repricing shock is defined consistently.

In a callable bond, falling rates may prompt earlier redemption, limiting upside relative to an otherwise similar option-free bond. The two-sided revaluation can capture that behaviour under the model’s assumptions. If the upward and downward repriced values are far apart, one duration number can still conceal asymmetric outcomes. State what moved and what price was re-estimated before comparing such securities.

A final check is to reverse the conversion: divide the position DV01 by the full position value and multiply by ten thousand. The result should return the original duration. If it does not, the likely causes are a mismatch of price basis, basis-point scaling, currency unit or position size. That diagnostic is faster than repeating a long chain of arithmetic.