Duration is often referred to as the approximate percentage change in the price for a 1% change in rates. Now, we will see some other definitions or interpretations of duration.

Duration is the "First Derivative" 

Duration is also referred to as the "first derivative of the price/yield function". A derivative used in this context is obtained by differentiating a mathematical function. When a bond is written in the form of a mathematical equation, the value arrived at by differentiating the equation for the first time is known as the first derivative. While it is the correct interpretation of duration, this interpretation does not help us to understand the concept of the interest rate risk of a bond. Thus, it is an operationally meaningless interpretation. 

Duration is Some Measure of Time

When Macaulay introduced the measure duration he used it as a measure of time for a bond that was outstanding. He defined duration as the weighted average of the time to each coupon and principal payment of a bond. The drawbacks of this interpretation are:

• The proper way to interpret a duration is as the price volatility of a zero-coupon bond with a number of years to maturity. For example, when we say that a bond has a duration of 5 years, it means that the bond has the price sensitivity to rate changes of a 5-year zero-coupon bond.

• When we explain duration in terms of years, then it is very difficult to understand the duration of some complex securities.