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bnddury

Bond duration given yield

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In R2017b, the specification of optional input arguments has changed. While the previous ordered inputs syntax is still supported, it may no longer be supported in a future release. Use the optional name-value pair inputs: Period, Basis, EndMonthRule, IssueDate,FirstCouponDate, LastCouponDate, StartDate,Face, CompoundingFrequency, DiscountBasis, and LastCouponInterest.

Syntax

[ModDuration,YearDuration,PerDuration] = bnddury(Yield,CouponRate,Settle,Maturity)
[ModDuration,YearDuration,PerDuration] = bnddury(___,Name,Value)

Description

example

[ModDuration,YearDuration,PerDuration] = bnddury(Yield,CouponRate,Settle,Maturity) computes the Macaulay and modified duration of NUMBONDS fixed income securities given yield to maturity for each bond.

bnddury determines the Macaulay and modified duration for a bond whether the first or last coupon periods in the coupon structure are short or long (that is, whether the coupon structure is synchronized to maturity). bnddury also determines the Macaulay and modified duration for a zero coupon bond.

example

[ModDuration,YearDuration,PerDuration] = bnddury(___,Name,Value) adds optional name-value pair arguments.

Examples

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Open Live Script

This example shows how to compute the duration of a bond at three different yield values.

Yield = [0.04; 0.055; 0.06];  
CouponRate = 0.055; 
Settle = '02-Aug-1999'; 
Maturity = '15-Jun-2004'; 
Period = 2; 
Basis = 0; 

[ModDuration,YearDuration,PerDuration]=bnddury(Yield,... 
CouponRate, Settle, Maturity, Period, Basis)
ModDuration = 3×1

    4.2444
    4.1924
    4.1751


YearDuration = 3×1

    4.3292
    4.3077
    4.3004


PerDuration = 3×1

    8.6585
    8.6154
    8.6007
Open Live Script

This example shows how to use datetime inputs to compute the duration of a bond at three different yield values. 

Yield = [0.04; 0.055; 0.06];
CouponRate = 0.055;
Settle = datetime('02-Aug-1999','Locale','en_US');
Maturity = datetime('15-Jun-2004','Locale','en_US');
Period = 2;
Basis = 0;
[ModDuration,YearDuration,PerDuration]=bnddury(Yield,...
CouponRate, Settle, Maturity, Period, Basis)
ModDuration = 3×1

    4.2444
    4.1924
    4.1751


YearDuration = 3×1

    4.3292
    4.3077
    4.3004


PerDuration = 3×1

    8.6585
    8.6154
    8.6007

Input Arguments

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Yield to maturity on a semiannual basis, specified as a decimal value using a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

Annual percentage rate used to determine the coupons payable on a bond, specified as decimal value using a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

Settlement date for the certificate of deposit, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays. The Settle date must be before the Maturity date.

Data Types: double | char | datetime

Maturity date for the certificate of deposit, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: double | char | datetime

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [ModDuration,YearDuration,PerDuration] = bnddury(Yield,CouponRate,Settle,Maturity,'Period',4,'Basis',7)

Number of coupon payments per year, specified as the comma-separated pair consisting of 'Period' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using the values: 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Day-count of the instrument, specified as the comma-separated pair consisting of 'Basis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a supported value:

  • 0 = actual/actual

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (PSA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see Basis.

Data Types: double

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.

  • 0 = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: logical

Bond Issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify an IssueDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

Irregular or normal first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

Irregular or normal last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays. The StartDate is when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date.

If you do not specify a StartDate, the effective start date is the Settle date.

Data Types: double | char | datetime

Face value of the bond, specified as the comma-separated pair consisting of 'Face' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

Compounding frequency for yield calculation, specified as the comma-separated pair consisting of 'CompoundingFrequency' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

  • 1 — Annual compounding

  • 2 — Semiannual compounding

  • 3 — Compounding three times per year

  • 4 — Quarterly compounding

  • 6 — Bimonthly compounding

  • 12 — Monthly compounding

Note

By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ICMA bases (8-12) use an annual compounding convention.

Data Types: double

Basis used to compute the discount factors for computing the yield, specified as the comma-separated pair consisting of 'DiscountBasis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. Values are:

  • 0 = actual/actual

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (PSA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see Basis.

Note

If a SIA day-count basis is defined in the Basis input argument and there is no value assigned for DiscountBasis, the default behavior is for SIA bases to use the actual/actual day count to compute discount factors.

If an ICMA day-count basis or BUS/252 is defined in the Basis input argument and there is no value assigned for DiscountBasis, the specified bases from the Basis input argument are used.

Data Types: double

Compounding convention for computing the yield of a bond in the last coupon period, specified as the comma-separated pair consisting of 'LastCouponInterest' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. LastCouponInterest is based on only the last coupon and the face value to be repaid. Acceptable values are:

  • simple

  • compound

Data Types: char | cell

Output Arguments

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Modified duration in years reported on a semiannual bond basis (in accordance with SIA convention), returned as a NUMBONDS-by-1 vector.

Macaulay duration in years, returned as a NUMBONDS-by-1 vector.

Periodic Macaulay duration reported on a semiannual bond basis (in accordance with SIA convention), returned as a NUMBONDS-by-1 vector.

References

[1] Krgin, D. Handbook of Global Fixed Income Calculations. Wiley, 2002.

[2] Mayle, J. "Standard Securities Calculations Methods: Fixed Income Securities Formulas for Analytic Measures." SIA, Vol 2, Jan 1994.

[3] Stigum, M., Robinson, F. Money Market and Bond Calculation. McGraw-Hill, 1996.

Version History

Introduced before R2006a

See Also

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