# bnddury

Bond duration given yield

## 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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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

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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 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 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)```

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

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 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`

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`

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`

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 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

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

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