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Finance[Duration] - calculate the duration of a set of cash flows or bonds
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Calling Sequence
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Duration(cashflows, rate, opts)
Duration(bond, rate, opts)
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Parameters
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cashflows
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cash flow data structure or a list of cash flow data structures; cash flows
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bond
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fixed- or floating-rate bond data structure; bond
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rate
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non-negative real number; interest rate
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opts
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equations of the form option = value where option is one of evaluation, compounding, or daycounter; specify options for the Duration command
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Description
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The Duration command calculates the duration of a set of cash flows or a portfolio of bonds.
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For a set of cash flows  the simple duration is defined as
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![(Sum(t*C(t)*P[t], t))/(Sum(C(t)*P[t], t))](/support/helpjp/helpview.aspx?si=8829/file01614/math102.png)
where ![P[t]](/support/helpjp/helpview.aspx?si=8829/file01614/math105.png) is the discount at time  implied by the given interest rate. There are at least two ways to calculate ![P[t]](/support/helpjp/helpview.aspx?si=8829/file01614/math109.png) . 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.
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A bond's duration is defined in a similar way. It can also be interpreted as the weighted first derivative of the price:
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Duration is useful as a measure of sensitivity of a bond's or cash flows' price to interest rate movements.
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The parameter cashflows is a cash flow data structure or a list of cash flow data structures.
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The parameter bond must be a fixed- or floating-rate bond data structure.
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Options
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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.
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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.
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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).
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Compatibility
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The Finance[Duration] command was introduced in Maple 15.
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Examples
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![cashflow1 := [seq(SimpleCashFlow(100, AdvanceDate(paymentdate, i, Years)), i = 1 .. 10)]](/support/helpjp/helpview.aspx?si=8829/file01614/math246.png)
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![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`]](/support/helpjp/helpview.aspx?si=8829/file01614/math249.png)
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Here is another example.
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![cashflow2 := [seq(FixedRateCoupon(nominalamt, rate, startdate, AdvanceDate(startdate, i, Years)), i = 1 .. 10)]](/support/helpjp/helpview.aspx?si=8829/file01614/math290.png)
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![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`]](/support/helpjp/helpview.aspx?si=8829/file01614/math293.png)
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Compute the value of this cash flow on January 1, 2005.
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Compute the Macaulay duration for the previous cash flow.
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Here is an example using bonds.
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![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'`]](/support/helpjp/helpview.aspx?si=8829/file01614/math334.png)
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| (14) |
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| (15) |
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