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# bndyield

Yield to maturity for fixed-income security

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

``Yield = bndyield(Price,CouponRate,Settle,Maturity)``
``Yield = bndyield(___,Name,Value)``

## Description

example

````Yield = bndyield(Price,CouponRate,Settle,Maturity)` given `NUMBONDS` bonds with SIA date parameters and clean prices (excludes accrued interest), returns the bond equivalent yields to maturity.```

example

````Yield = bndyield(___,Name,Value)` adds optional name-value arguments. ```

## Examples

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

```Price = [95; 100; 105]; CouponRate = 0.05; Settle = '20-Jan-1997'; Maturity = '15-Jun-2002'; Period = 2; Basis = 0; Yield = bndyield(Price, CouponRate, Settle,... Maturity, Period, Basis)```
```Yield = 3×1 0.0610 0.0500 0.0396 ```

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

```Price = [95; 100; 105]; CouponRate = 0.05; Settle = datetime('20-Jan-1997','Locale','en_US'); Maturity = datetime('15-Jun-2002','Locale','en_US'); Period = 2; Basis = 0; Yield = bndyield(Price, CouponRate, Settle,... Maturity, Period, Basis)```
```Yield = 3×1 0.0610 0.0500 0.0396 ```

Compute the yield of a Treasury bond.

```Price = [95; 100; 105]; CouponRate = 0.0345; Settle = '15-May-2016'; Maturity = '02-Feb-2026'; Period = 2; Basis = 1; format long Yield = bndyield(Price,CouponRate,Settle,Maturity,Period,Basis)```
```Yield = 3×1 0.040764403932618 0.034482347625316 0.028554719853118 ```

Using the same data, compute the yield of a Treasury bond using the same basis for discounting and generating the cash flows.

```DiscountBasis = 1; Yield = bndyield(Price,CouponRate,Settle,Maturity,'Period',Period,'Basis',Basis, ... 'DiscountBasis',DiscountBasis)```
```Yield = 3×1 0.040780176658036 0.034495592361619 0.028565614029497 ```

## Input Arguments

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Clean price of the bond (current price without accrued interest), specified as 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 using a scalar or a `NUMBONDS`-by-`1` or `1`-by-`NUMBONDS` vector.

Data Types: `double`

Settlement date of the bond, 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 of the bond, 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 Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Example: ```Yield = bndyield(Price,CouponRate,Settle,Maturity,'Period',4,'Basis',9)```

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.

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. Values are:

• `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. This 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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Yield to maturity with semiannual compounding, returned as a `NUMBONDS`-by-`1` vector.

## More About

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### Price and Yield Conventions

The `Price` and `Yield` are related to different formulae for SIA and ICMA conventions.

For SIA conventions, `Price` and `Yield` are related by the formula:

` Price + Accrued Interest = sum(Cash_Flow*(1+Yield/2)^(-Time)) `
where the sum is over the bond's cash flows and corresponding times in units of semiannual coupon periods.

For ICMA conventions, the `Price` and `Yield` are related by the formula:

` Price + Accrued Interest = sum(Cash_Flow*(1+Yield)^(-Time))`

## Algorithms

For SIA conventions, the following formula defines bond price and yield:

`$PV=\frac{CF}{{\left(1+\frac{z}{f}\right)}^{TF}},$`

where:

 PV = Present value of a cash flow. CF = The cash flow amount. z = The risk-adjusted annualized rate or yield corresponding to a given cash flow. The yield is quoted on a semiannual basis. f = The frequency of quotes for the yield. TF = Time factor for a given cash flow. Time is measured in semiannual periods from the settlement date to the cash flow date. In computing time factors, use SIA `actual/actual` day count conventions for all time factor calculations.

For ICMA conventions, the frequency of annual coupon payments determines bond price and yield.

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

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

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

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