modifiedDuration¶

Evaluates the modified Macauley duration of a security.

Synopsis¶

modifiedDuration (settlement, maturity, couponRate, t_yield, frequency, basis)

Required Arguments¶

date settlement (Input): The date on which payment is made to settle a trade. For a more detailed discussion on dates see the Usage Notes section of this chapter.
date maturity (Input): The date on which the bond comes due, and principal and accrued interest are paid. For a more detailed discussion on dates see the Usage Notes section of this chapter.
float couponRate (Input): Annual interest rate set forth on the face of the security; the coupon rate.
float t_yield (Input): Annual yield of the security.
int frequency (Input): Frequency of the interest payments. It should be one of ANNUAL, SEMIANNUAL or QUARTERLY. For a more detailed discussion on frequency see the Usage Notes section of this chapter.
int basis (Input): The method for computing the number of days between two dates. It should be one of DAY_CNT_BASIS_ACTUALACTUAL, DAY_CNT_BASIS_NASD, DAY_CNT_BASIS_ACTUAL360, DAY_CNT_BASIS_ACTUAL365, or DAY_CNT_BASIS_30E360. For a more detailed discussion on basis see the Usage Notes section of this chapter.

Return Value¶

The modified Macauley duration of a security is returned. The security has an assumed par value of $100. If no result can be computed, NaN is returned.

Description¶

Function modifiedDuration computes the modified Macauley duration for a security with an assumed par value of $100.

It is computed using the following:

\[\frac{\mathit{duration}}{1 + \left(\frac{\mathit{yield}}{\mathit{frequency}}\right)}\]

where duration is calculated from duration.

Example¶

In this example, modifiedDuration computes the modified Macauley duration of a security with the settlement date of July 1, 1995, and maturity date of July 1, 2005, using the Actual/365 day count method.

from __future__ import print_function
from numpy import *
from datetime import date
from pyimsl.math.modifiedDuration import modifiedDuration, DAY_CNT_BASIS_ACTUAL365, SEMIANNUAL

coupon = 0.075
yield_amt = 0.09
frequency = SEMIANNUAL
basis = DAY_CNT_BASIS_ACTUAL365

settlement = date(1995, 7, 1)
maturity = date(2005, 7, 1)

mduration = modifiedDuration(settlement, maturity,
                             coupon, yield_amt, frequency, basis)
print("The modified Macauley duration of the bond with ")
print("semiannual interest payments is %.4f." % (mduration))

Output¶

The modified Macauley duration of the bond with 
semiannual interest payments is 6.7387.