Lesson 18 of 25 · 7 min

Duration as a sensitivity, applied outside bonds

Measure how far something fell per point of rate and you have the one number that converts a policy path into a headroom figure.

Duration is usually met as a bond measure — Track 8 lesson 3 used it to explain why short-dated government paper sits at the top of an advance-rate schedule. Read as a plain sensitivity, it applies to anything valued by discounting, which includes an equity portfolio and therefore includes collateral.

effective duration = −(percentage change in value) ÷ (change in rate, in points)

effective duration: How many percent the asset moves for each percentage point of rate change.
percentage change in value: What the asset actually did, measured over the same window as the rate move.
change in rate, in points: The move in the relevant rate, usually a long one, in percentage points rather than basis points.

The useful thing is that it can be estimated from what already happened rather than from a model. Across one period a long rate rose 1.18 points. Holding A fell 8.3 percent, so its effective duration was 8.3 ÷ 1.18 = 7.03. Holding B fell 26.7 percent, giving 26.7 ÷ 1.18 = 22.63. Two numbers, from price history already on the page.

Those two numbers do more work than the history they came from, because they convert a future rate move into a value. If the long rate rises a further 0.45 of a point, holding B is expected to fall 22.63 × 0.45 = 10.18 percent. On $1,180,000 of it, that is $120,150. At a 55 percent advance rate, $66,082.50 of lending value, which drops straight into the headroom calculation.

The caveats belong on the page with the number. An estimate from one period is a single observation and the next period may behave differently. The relationship is not linear, so the estimate degrades for large moves. And an asset's duration itself changes as rates change. Duration is a scaling rule rather than a law — and used as a scaling rule it is the only tool in this track that turns a rate path into a collateral number.

Key terms

Effective duration: The percentage an asset's value moves for each percentage point of rate change. A sensitivity, estimable from history, not restricted to bonds.
Linear approximation: Using one sensitivity figure for moves of any size. Accurate for small moves and increasingly wrong as the move grows.
Realised sensitivity: A duration estimated from what an asset actually did over a past window, rather than derived from a model of its cash flows.

Worked example

From a move that happened to a number that has not

A long rate rose 1.18 points over one period. Two holdings, then a further 0.45-point rise. Illustrative.

Holding A fell 8.3%: Effective duration 7.03
Holding B fell 26.7%: Effective duration 22.63
Further rate rise: +0.45 points
Expected fall in holding B: 10.18%
On $1,180,000 of holding B: −$120,150
Lending value lost at a 55% advance rate: $66,082.50

Two divisions turned a price history into a forward estimate of borrowing capacity. The estimate is rough, and it is the only one available without the lender's system.

Check yourself

Over a period a long rate rose 0.86 of a point and a holding fell 14.2 percent. What is its effective duration, and what does a further 0.30-point rise imply for $2,420,000 of it at a 60 percent advance rate?

Saved in this browser only. No account, nothing sent anywhere.

Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.