Year fraction - Financial definition
Concise definition of the term year fraction
In finance, a year fraction represents a portion of an interest period, expressed as a decimal figure. It is calculated by dividing the number of days of the portion through the number of days in the interest period.
Comprehensive definition of the term year fraction
Year fractions are frequently used in interest calculations, like for example the calculation of the price of a bond. When calculating the price of a bond, all of the security's future cash flows are discounted at the bond's yield using the time span between the value date for the bond price calculation and each of the cash flows' payment date. Whenever the value date is not an anniversary date of the bond's maturity date, the discounting period will comprise a year fraction.
Example:
Let's consider a bond which matures on Dec 15th, 2016 and bears a 3% coupon. The bond redeems at par, has an actual/actual day count convention and the value date used for calculating the price shall be July 15th, 2015.
The bond will pay three cash flows until maturity, one coupon on Dec 15th 2015 and the final coupon and the principal both on Dec 15th, 2016.
The discount period for the first coupon is calculated by dividing the number of remaining days between the value date (July 15th) and the coupon date (Dec 15th) by the number of days for the interest period: 153 / 365 = 0.419178082. The result is the year fraction which we will also use for determining the discount period of the two cashflows on Dec 15th, 2016.
As these cash flows are a full year later, we simply add 1, which gives us a discount period of 1.419178082 for the last coupon and the bond's principal.