# cftimes

Time factors corresponding to bond cash flow dates

## Description

determines the time factors corresponding to the cash flows of a bond or set of
bonds.`TFactors`

= cftimes(`Settle`

,`Maturity`

)

`cftimes`

computes the time factor of a cash flow, which is the
difference between the settlement date and the cash flow date, in units of
semiannual coupon periods. In computing time factors, use SIA actual/actual day
count conventions for all time factor calculations.

specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax. `TFactors`

= cftimes(___,`Name,Value`

)

## Examples

### Compute the Time Factor of a Cash Flow

This example shows how to calculate a cash flow time factor.

Settle = datetime(1997,3,15); Maturity = datetime(1999,9,1); Period = 2; TFactors = cftimes(Settle, Maturity, Period)

`TFactors = `*1×5*
0.9239 1.9239 2.9239 3.9239 4.9239

## Input Arguments

`Settle`

— Settlement date

datetime array | string array | date character vector

Settlement date, specified as an
`NINST`

-by-`1`

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

must be earlier than `Maturity`

.

To support existing code, `cftimes`

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

**Data Types: **`char`

| `string`

| `datetime`

`Maturity`

— Maturity date

datetime array | string array | date character vector

Maturity date, specified as an
`NINST`

-by-`1`

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

date is the date on which the cash flows are
priced.

To support existing code, `cftimes`

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: **```
TFactors =
cftimes(Settle,Maturity,'Period',4)
```

`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

`0`

(actual/actual) (default) | positive integers of the set `[1...13]`

| vector of positive integers of the set
`[1...13]`

Day-count basis, specified as the comma-separated pair consisting of
`'Basis'`

and a positive integer using a
`NINST`

-by-`1`

vector.

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, `cftimes`

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.

`cftimes`

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.

`cftimes`

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.

`cftimes`

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

**Data Types: **`char`

| `string`

| `datetime`

`CompoundingFrequency`

— Compounding frequency for yield calculation

SIA bases uses`2`

, 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
`'CompundingFrequency'`

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`

## Output Arguments

`TFactors`

— Time to cash flow

matrix

Time to cash flow, returned as an `NUMBONDS`

rows. The
number of columns is determined by the maximum number of cash flow payment
dates required to hold the bond portfolio. `NaN`

s are
padded for bonds which have less than the maximum number of cash flow
payment dates.

## References

[1] Krgin, Dragomir.
*Handbook of Global Fixed Income Calculations.* John Wiley
& Sons, 2002.

[2] Mayle, Jan.
*“Standard Securities Calculations Methods: Fixed Income Securities
Formulas for Analytic Measures.”* SIA, Vol 2, Jan
1994.

[3] Stigum, Marcia, and Franklin
Robinson. *Money Market and Bond Calculations.* McGraw-Hill, 1996.

## Version History

**Introduced before R2006a**

### R2022b: Serial date numbers not recommended

Although `cftimes`

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.

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