Duration calculation formula:
If the market interest rate is y, the duration of Macaulay cash flow (X 1, X2, ..., Xn) is defined as:
d(y)=[ 1 * x 1/( 1+y) 1+2 * x2/( 1+y)2+...+n * xn/( 1)
Among them, PVXi represents the present value of the first cash flow, and D represents the duration. So duration is a way to measure the average duration of bond cash flow.
Extended data:
Some theorems about duration;
1, only zero coupon bond's Macaulay term is equal to their expiration time.
2. The Macaulay term of direct bonds is less than or equal to its maturity date.
3. The Macaulay duration of unified bonds is equal to (1+ 1/y), where y is the discount rate used to calculate the present value.
4. Under the same term, the higher the coupon rate, the shorter the duration.
5. Under the condition that coupon rate remains unchanged, the longer the term, the longer the duration.
6. Other things being equal, the lower the yield to maturity of a bond, the longer its duration.