Duration

Duration is a bond's life weighted by the present value of its cash flows: each coupon and the redemption itself count with a weight equal to that payment's share of the bond's current price. Duration is therefore measured in years, but it also acts as the coefficient that links a change in the bond's price to a shift in market yield.

How the calculation works

Each payment is weighted by its discounted value divided by the bond's price. The further out a payment falls, the more it pulls the average term towards itself, but the smaller its present-value weight. All of the measure's behaviour follows from this: duration lengthens as the time to maturity grows, shortens when the coupon is large, and shortens when market yields rise, because distant payments are discounted more heavily and lose weight.

There is Macaulay duration, expressed in years, and modified duration, which is obtained by dividing by the yield per coupon period and shows directly by what percentage the price will change for a small shift in yield. The same sensitivity expressed in money terms is DV01: the price response in roubles. Because the relationship between price and yield is not linear, duration alone is not enough for large moves in the key rate, and a correction for bond convexity is needed. For a set of bonds, portfolio duration is calculated as an average weighted by the value of the positions — this property is the basis of portfolio immunisation.

An example using the platform's data

In the list of the most liquid issues, long-dated OFZ sit next to short corporate bonds, and their durations are completely different even though their turnover is comparable:

For each issue, the bond's page shows the time to maturity, the coupon size and the payment frequency — these are exactly the inputs from which duration is built.

Where the measure misleads

Duration describes only interest-rate risk and says nothing about the issuer's ability to pay: the price of an issue with a long duration and the price of an issue with high credit risk fall for different reasons, and the two must not be confused. For a bond with a floating coupon, the standard calculation produces a meaninglessly long term — what applies there is floating-rate note duration. If an issue has a put option, duration is calculated to the put date; otherwise the term is overstated, as is the yield. The same distortion arises when the face value is repaid in instalments — see bond amortisation.