bnddury
Bond duration given yield
Syntax
Description
[
computes the Macaulay and modified duration of ModDuration
,YearDuration
,PerDuration
] = bnddury(Yield
,CouponRate
,Settle
,Maturity
)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.
[
adds optional name-value pair arguments. ModDuration
,YearDuration
,PerDuration
] = bnddury(___,Name,Value
)
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 compounding2
— Semiannual compounding3
— Compounding three times per year4
— Quarterly compounding6
— Bimonthly compounding12
— 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 R2006aR2022b: 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
.
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