bnddury

Bond duration given yield

Syntax

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

[ModDuration,YearDuration,PerDuration] = bnddury(___,Name,Value)

Description

[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.

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

Examples

Find Bond Duration Given Yield

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 = datetime(1999,8,2); 
Maturity = datetime(2004,6,15); 
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

Yield — Yield to maturity on a semiannual basis

decimal

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

CouponRate — Annual percentage rate used to determine coupons payable on a bond

decimal

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

Settle — Settlement date for certificate of deposit

datetime array | string array | date character vector

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

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Maturity — Maturity date for certificate of deposit

datetime array | string array | date character vector

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

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | 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)

Period — Number of coupon payments per year

2 (default) | numeric with values 0, 1, 2, 3, 4, 6 or 12

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

Basis — Day-count basis of instrument

0 (default) | numeric values: 0,1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13

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

EndMonthRule — End-of-month rule flag

1 (in effect) (default) | nonnegative integer 0 or 1

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

IssueDate — Bond issue date

datetime array | string array | date character vector

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 a datetime array, string array, or date character vectors.

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

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

FirstCouponDate — Irregular or normal first coupon date

datetime array | string array | date character vector

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 a datetime array, string array, or date character vectors.

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

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

LastCouponDate — Irregular or normal last coupon date

datetime array | string array | date character vector

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 a datetime array, string array, or date character vectors.

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

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

StartDate — Forward starting date of payments

datetime array | string array | date character vector

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 a datetime array, string array, or date character vectors. 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.

To support existing code, bnddury also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Face — Face value of bond

100 (default) | numeric

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

CompoundingFrequency — Compounding frequency for yield calculation

SIA bases uses2, ICMA bases uses 1 (default) | integer with value of 1, 2, 3, 4, 6, or 12

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

DiscountBasis — Basis used to compute the discount factors for computing the yield

SIA uses 0 (default) | integers of the set [0...13] | vector of integers of the set [0...13]

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

LastCouponInterest — Compounding convention for computing yield of a bond in last coupon period

compound (default) | values are simple or compound

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

ModDuration — Modified duration in years

numeric

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

YearDuration — Macaulay duration in years

numeric

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

PerDuration — Periodic Macaulay duration

numeric

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

R2022b: Serial date numbers not recommended

Although bnddury supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.

R2017b: Support for optional name-value input arguments

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.