# floatdiscmargin

Discount margin for floating-rate bond

## Syntax

## Description

calculates the discount margin or zero discount margin for a floating-rate
bond.`Margin`

= floatdiscmargin(`Price`

,`Spread`

`Settle`

,`Maturity`

,`RateInfo`

,`LatestFloatingRate`

)

The input `RateInfo`

determines whether the discount margin or
the zero discount margin is calculated. Principal schedules are supported using
`Principal`

.

adds optional name-value pair arguments. `Margin`

= floatdiscmargin(___,`Name,Value`

)

## Examples

### Compute the Zero Discount Margin Using a Yield Curve

Use `floatdiscmargin`

to compute the discount margin and zero discount margin for a floating-rate note.

Define data for the floating-rate note.

Price = 99.99; Spread = 50; Settle = datetime(2011,1,20); Maturity = datetime(2012,1,15); LatestFloatingRate = 0.05; StubRate = 0.049; SpotRate = 0.05; Reset = 4; Basis = 2;

Compute the discount margin.

dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... [StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)

dMargin = 48.4810

Usually you want to set `AdjustCashFlowsBasis`

to `true`

, so cash flows are calculated with adjustments on accrual amounts.

Create an annualized zero-rate term structure to calculate the zero discount margin.

Rates = [0.0500; 0.0505; 0.0510; 0.0520]; StartDates = [datetime(2011,1,20); datetime(2011,4,15); datetime(2011,7,15); datetime(2011,11,15)]; EndDates = [datetime(2011,4,15); datetime(2011,7,15); datetime(2011,11,15); datetime(2012,1,15)]; ValuationDate = datetime(2011,1,20); RateSpec = intenvset('Compounding', Reset, 'Rates', Rates,... 'StartDates', StartDates, 'EndDates', EndDates,... 'ValuationDate', ValuationDate, 'Basis', Basis);

Calculate the zero discount margin using the previous yield curve.

dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ... RateSpec, LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ... 'AdjustCashFlowsBasis', true)

dMargin = 46.0689

## Input Arguments

`Price`

— Bond prices where discount margin is to be computed

matrix

Bond prices where discount margin is to be computed, specified as a
`NINST`

-by-`1`

matrix.

**Note**

The spread is calculated against the clean price (the function
internally does not add the accrued interest to the price specified by
the `Price`

input). If the spread is required against
the dirty price, the price of a bond that includes the accrued interest,
you must supply the dirty price for the `Price`

input.

**Data Types: **`double`

`Spread`

— Number of basis points over the reference rate

numeric

Number of basis points over the reference rate, specified as a
`NINST`

-by-`1`

matrix.

**Data Types: **`double`

`Settle`

— Settlement date of the floating-rate bonds

datetime array | string array | date character vector

Settlement date of the floating-rate bonds, specified as a scalar or a
`NINST`

-by-`1`

vector using a datetime
array, string array, or date character vectors. If supplied as a
`NINST`

-by-`1`

vector of dates, all
settlement dates must be the same (only a single settlement date is
supported)

To support existing code, `floatdiscmargin`

also
accepts serial date numbers as inputs, but they are not recommended.

**Data Types: **`char`

| `string`

| `datetime`

`Maturity`

— Maturity date of the floating-rate bond

datetime array | string array | date character vector

Maturity date of the floating-rate bond, specified as a
`NINST`

-by-`1`

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

To support existing code, `floatdiscmargin`

also
accepts serial date numbers as inputs, but they are not recommended.

**Data Types: **`char`

| `string`

| `datetime`

`RateInfo`

— Interest-rate information

numeric

interest-rate information, specified as
`NINST`

-by-`2`

vector where the:

First column is the stub rate between the settlement date and the first coupon rate.

Second column is the reference rate for the term of the floating coupons (for example, the 3-month LIBOR from settlement date for a bond with a

`Reset`

of`4`

).

**Note**

If the `RateInfo`

argument is an annualized
zero-rate term structure created by `intenvset`

(Financial Instruments Toolbox),
the zero discount margin is calculated.

**Data Types: **`double`

`LatestFloatingRate`

— Rate for next floating payment set at last reset date

numeric

Rate for the next floating payment set at the last reset date,
specified as `NINST`

-by-`1`

vector.

**Data Types: **`double`

### 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: **```
Margin =
floatdiscmargin(Price,Spread,Settle,Maturity,RateInfo,LatestFloatingRate,'Reset',2,'Basis',5)
```

`Reset`

— Frequency of payments per year

`1`

(default) | numeric

Frequency of payments per year, specified as
`NINST`

-by-`1`

vector.

**Data Types: **`double`

`Basis`

— Day-count basis used for time factor calculations

`0`

(actual/actual) (default) | integers of the set `[0...13]`

| vector of integers of the set `[0...13]`

Day-count basis used for time factor calculations, specified as a
`NINST`

-by-`1`

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.

**Data Types: **`double`

`Principal`

— Notional principal amounts

`100`

(default) | numeric

Notional principal amounts, specified as a
`NINST`

-by-`1`

vector or a
`NINST`

-by-`1`

cell array
where each element is a
`NUMDATES`

-by-`2`

cell array
where the first column is dates and the second column is the
associated principal amount. The date indicates the last day that
the principal value is valid.

**Data Types: **`double`

| `cell`

`EndMonthRule`

— End-of-month rule flag

`1`

(in effect) (default) | nonnegative integer `0`

or
`1`

End-of-month rule flag, specified as a
`NINST`

-by-`1`

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`

`AdjustCashFlowsBasis`

— Adjust cash flows according to accrual amount

`0`

(not in effect) (default) | nonnegative integer `0`

or
`1`

Adjusts cash flows according to the accrual amount, specified as a
`NINST`

-by-`1`

vector of logicals.

**Note**

Usually you want to set
`AdjustCashFlowsBasis`

to
`1`

, so cash flows are calculated with
adjustments on accrual amounts. The default is set to
`0`

to be consistent with `floatbyzero`

(Financial Instruments Toolbox).

**Data Types: **`logical`

`Holidays`

— Dates for holidays

`holidays.m`

used (default) | datetime array | string array | date character vector | serial date number

Dates for holidays, specified as
`NHOLIDAYS`

-by-`1`

vector using a
datetime array, string array, or date character vectors. Holidays are
used in computing business days.

To support existing code, `floatdiscmargin`

also
accepts serial date numbers as inputs, but they are not recommended.

**Data Types: **`char`

| `string`

| `datetime`

`BusinessDayConvention`

— Business day conventions

`'actual'`

(default) | character vector with values`'actual'`

,
`'follow'`

,
`'modifiedfollow'`

, `'previous'`

or
`'modifiedprevious'`

Business day conventions, specified as a
`NINST`

-by-`1`

cell array of
character vectors of business day conventions to be used in
computing payment dates. The selection for business day convention
determines how nonbusiness days are treated. Nonbusiness days are
defined as weekends plus any other date that businesses are not open
(for example, statutory holidays). Values are:

`'actual'`

— Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.`'follow'`

— Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.`'modifiedfollow'`

— Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.`'previous'`

— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.`'modifiedprevious'`

— Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

**Data Types: **`char`

| `cell`

## Output Arguments

`Margin`

— Discount margin

numeric

Discount margin, returned as a
`NINST`

-by-`1`

vector of the
discount margin if `RateInfo`

is specified as a
`NINST`

-by-`2`

vector of stub and
spot rates.

If `RateInfo`

is specified as an annualized zero
rate term structure created by `intenvset`

(Financial Instruments Toolbox),
`Margin`

is returned as a
`NINST`

-by-`NCURVES`

matrix of the
zero discount margin.

## References

[1] Fabozzi, Frank J., Mann, Steven V. *Floating-Rate
Securities.* John Wiley and Sons, New York, 2000.

[2] Fabozzi, Frank J., Mann, Steven V. *Introduction to Fixed Income
Analytics: Relative Value Analysis, Risk Measures and Valuation.*
John Wiley and Sons, New York, 2010.

[3] O'Kane, Dominic, Sen, Saurav. *“Credit Spreads
Explained.”* Lehman Brothers Fixed Income Quantitative
Research, March 2004.

## Version History

**Introduced in R2012b**

### R2022b: Serial date numbers not recommended

Although `floatdiscmargin`

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.

## See Also

`floatmargin`

| `floatbyzero`

(Financial Instruments Toolbox) | `bndspread`

| `intenvset`

(Financial Instruments Toolbox) | `datetime`

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