The duration of the security directly relates to the extent to which a change in interest rate will impact the price. It is different from maturity. It calculates the expected change in the price as a result of a 1% change in interest rates. It approximates the price elasticity of demand. It is calculated by adding the product of the time period of cash flow and the respective weights, which are calculated on the basis of the present value of cash flows.

**Example**

**A five-year bond with a face value of $100 is issued with a coupon rate of 6%. It has a semi-annually compounded market yield of 8%. Calculate duration.**

**Solution:**

The coupon payment is made on a half-yearly basis. Hence, cash flow after every 6 months would be half of 6%, i.e., $3.

Hence, the duration of this bond is 3.599 years, whereas maturity is 4 years. The price of the bond is the sum total of the present value of all the cash flows, which is $93.27.

Change in price is proportional to the change in interest rate, which is calculated by using the following formula:

**Change in Price = - % Change in Interest Rate * Duration * Current Price**

So, if the % increase in interest rate is 0.1%, then in the above example, the change in the price would be: -0.1% * 3.599 * 93.27 = **-$0.34**

New price of the bond would be = $93.27 - $0.34 = $92.93.

You can refer to the above given excel template for the detailed calculation of interest rate risk.