calculate the duration of a set of cash flows or bonds
Duration(cashflows, rate, opts)
Duration(bond, rate, opts)
cash flow data structure or a list of cash flow data structures; cash flows
fixed- or floating-rate bond data structure; bond
non-negative real number; interest rate
equations of the form option = value where option is one of evaluation, compounding, or daycounter; specify options for the Duration command
compounding = Simple, Continuous, Annual, Semiannual, EveryFourthMonth, Quarterly, Bimonthly, Monthly, SimpleThenAnnual, SimpleThenSemiannual, SimpleThenEveryFourthMonth, SimpleThenQuarterly, SimpleThenBimonthly, or SimpleThenMonthly -- This option specifies the compounding type for the given interest rate.
daycounter = Actual360, Actual365Fixed, AFB, Bond, Euro, Historical, ISDA, ISMA, OneDay, Simple, Thirty360BondBasis, Thirty360EuroBondBasis, Thirty360European, Thirty360Italian, Thirty360USA, or a day counter data structure created using the DayCounter constructor -- This option provides a day counter that will be used to represent the period between two dates as a fraction of the year. The default day count convention can be set using the Settings command.
evaluationdate = a string containing a date specification in a format recognized by ParseDate or a Date data structure -- This option specifies the evaluation date. This is set to the global evaluation date by default (see EvaluationDate).
The Duration command calculates the duration of a set of cash flows or a portfolio of bonds.
For a set of cash flows C⁡t the simple duration is defined as
where Pt is the discount at time t implied by the given interest rate. There are at least two ways to calculate Pt. One can either use a yield term structure or an internal rate of return of the set of cash flows. In the latter case one would obtain the Macaulay duration.
A bond's duration is defined in a similar way. It can also be interpreted as the weighted first derivative of the price:
Duration is useful as a measure of sensitivity of a bond's or cash flows' price to interest rate movements.
The parameter cashflows is a cash flow data structure or a list of cash flow data structures.
The parameter bond must be a fixed- or floating-rate bond data structure.
SetEvaluationDate⁡January 1, 2005:
paymentdate ≔ January 1, 2007
paymentdate≔January 1, 2007
cashflow1 ≔ seq⁡SimpleCashFlow⁡100,AdvanceDate⁡paymentdate,i,Years,i=1..10
cashflow1≔100. on January 1, 2008,100. on January 1, 2009,100. on January 1, 2010,100. on January 1, 2011,100. on January 1, 2012,100. on January 1, 2013,100. on January 1, 2014,100. on January 1, 2015,100. on January 1, 2016,100. on January 1, 2017
Duration⁡cashflow1,0.03,evaluationdate=January 1, 2005
Duration⁡cashflow1,0.03,evaluationdate=January 1, 2004
Here is another example.
nominalamt ≔ 100
rate ≔ 0.05
startdate ≔ January 1, 2006
startdate≔January 1, 2006
cashflow2 ≔ seq⁡FixedRateCoupon⁡nominalamt,rate,startdate,AdvanceDate⁡startdate,i,Years,i=1..10
cashflow2≔5. on January 1, 2007,10. on January 1, 2008,15. on January 1, 2009,20. on January 1, 2010,25. on January 1, 2011,30. on January 1, 2012,35. on January 1, 2013,40. on January 1, 2014,45. on January 1, 2015,50. on January 1, 2016
Compute the value of this cash flow on January 1, 2005.
Duration⁡cashflow2,0.03,evaluationdate=January 1, 2005
Compute the Macaulay duration for the previous cash flow.
irr ≔ InternalRateOfReturn⁡cashflow2,15
Here is an example using bonds.
bond ≔ FixedCouponBond⁡100,5,Years,0.05
cflows ≔ CashFlows⁡bond
cflows≔5. on 'January 1, 2006',5. on 'January 1, 2007',5. on 'January 1, 2008',5. on 'January 1, 2009',5. on 'January 1, 2010',100. on 'January 1, 2010'
Duration⁡bond,0.03,evaluationdate=January 5, 2000
Duration⁡cflows,0.03,evaluationdate=January 5, 2000
The Finance[Duration] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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