DURATION
A bond's Macaulay duration, in years.
Group: Financial. Compatible with DAX.
Syntax
DURATION ( <settlement>, <maturity>, <coupon>, <yld>, <frequency> [, <basis>] )| Parameter | Type | Description |
|---|---|---|
settlement | Date | The day the buyer takes the security over; later than its issue. |
maturity | Date | The day the security ends and its face value is repaid. |
coupon | Number | The coupon rate a year, as a decimal. |
yld | Number | The yield a year the buyer earns, as a decimal. |
frequency | Whole number | Coupons a year: 1 for yearly, 2 for half-yearly, 4 for quarterly. |
basis | Whole number optional | The day count, by number: US 30/360 (0, when left out), actual/actual (1), actual/360 (2), actual/365 (3) or European 30/360 (4). |
Returns
Number. The Macaulay duration in years.
Remarks
- The average time until the bond's payments arrive, each coupon and the redemption weighted by its present value at the yield. A bond with no coupon has a duration equal to its time to maturity.
- It is worked out from the yield alone; no price is needed.
- A coupon or yield below 0, or settlement on or after maturity, is an error.
- The dates are taken as whole days. frequency and basis are rounded to whole numbers first; a frequency other than 1, 2 or 4, or a basis outside 0 to 4, is an error.
Examples
A 30-year bond and a zero-coupon bond
The first pays 8 % half-yearly coupons for almost 30 years and is valued at a 9 % yield. The second pays nothing until it matures, 5 years after settlement.
EVALUATE
ROW (
"8 % coupons", DURATION ( DATE ( 2018, 7, 1 ), DATE ( 2048, 1, 1 ), 0.08, 0.09, 2, 1 ),
"Zero coupon", DURATION ( DATE ( 2026, 11, 2 ), DATE ( 2031, 11, 2 ), 0, 0.04, 1, 1 )
)| 8 % coupons | Zero coupon |
|---|---|
| 10.9191452815919 | 5 |