# 1.5.4 Duration

Modified duration is the approximate percentage change in price for a 100-basis-point change in interest rates, that is, the interest rate sensitivity. In general, the longer the modified duration, the more sensitive (higher fluctuations) the index is to changes in interest rates.

Given the price computed for an asset, modified duration is calculated as:

where:

is price change of an asset by an infinitesimal change in risk-free rate}().

is the cash flow at time .

represents the maturity of an asset.

represents the risk-free rate at time *t*.

represents a random change in the risk-free rate.