# date2time

Time and frequency from dates

## Syntax

## Description

`[`

computes
time factors appropriate to compounded rate quotes between the `TFactors`

,`F`

]
= date2time(___,`Compounding`

,`Basis`

,`EndMonthRule`

)`Settle`

and `Maturity`

dates
using optional input arguments for `Compounding`

, `Basis`

,
and `EndMonthRule`

. `date2time`

is
the inverse of `time2date`

.

## Examples

### Compute `date2time`

Using an actual/actual Basis

To get the `date2time`

period between '31-Jul-2015' and '30-Sep-2015' using an actual/actual basis:

date2time(datetime(2015,7,31),datetime(2015,9,30), 2, 0, 1)

ans = 0.3333

When using `date2time`

quasi coupon, two quasi coupon dates are computed for a bond with a maturity corresponding to the `Dates`

input. In this case, that would be "30-Sep-2015". Assuming that the compounding frequency is `2`

, the other quasi coupon date is six months prior to this date. Assuming the end of month rule is in place, then the other quasi coupon date is "31-Mar-2015". You can use these two dates to compute the total number of actual days in a period (which is 183). Given this, the fraction of time between the start and end date for the actual/actual basis is computed as follows.

`(Actual Days between Start Date and End Date)/(Actual Number of Days between Quasi Coupon Dates)`

There are 61 days between 31-Jul-2015 and 30-Sep-2015 and 183 days between the quasi coupon dates ("31-Mar-2015" and "30-Sep-2015") which leads to a final result of 61/183 or exactly 1/3.

## Input Arguments

`Settle`

— Settlement date

datetime scalar | string scalar | date character vector

Settlement date, specified as a scalar datetime, string, or date character vector.

To support existing code, `date2time`

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 a scalar or `N`

-by-`1`

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

To support existing code, `date2time`

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

**Data Types: **`char`

| `string`

| `datetime`

`Compounding`

— Rate at which input zero rates are compounded when annualized

`2`

(Semiannual compounding) (default) | scalar with numeric values of `0`

, `1`

, `2`

, `3`

, `4`

, `5`

, `6`

, `12`

, `365`

, `–1`

Rate at which input zero rates are compounded when annualized,
specified as a scalar with numeric values of: `0`

, `1`

, `2`

, `3`

, `4`

, `5`

, `6`

, `12`

, `365`

,
or `–1`

. Allowed values are defined as:

`0`

— Simple interest (no compounding)`1`

— Annual compounding`2`

— Semiannual compounding (default)`3`

— Compounding three times per year`4`

— Quarterly compounding`6`

— Bimonthly compounding`12`

— Monthly compounding`365`

— Daily compounding`-1`

— Continuous compounding

The optional `Compounding`

argument determines
the formula for the discount factors (`Disc`

):

`Compounding`

=`0`

for simple interest`Disc = 1/(1 + Z * T)`

, where`T`

is time in years and simple interest assumes annual times`F = 1`

.

`Compounding`

=`1`

,`2`

,`3`

,`4`

,`6`

,`12`

`Disc = (1 + Z/F)^(-T)`

, where`F`

is the compounding frequency,`Z`

is the zero rate, and`T`

is the time in periodic units, for example,`T = F`

is one year.

`Compounding`

=`365`

`Disc = (1 + Z/F)^(-T)`

, where`F`

is the number of days in the basis year and`T`

is a number of days elapsed computed by basis.

`Compounding`

=`-1`

`Disc = exp(-T*Z)`

, where`T`

is time in years.

`Basis`

— Day-count basis

`0`

(actual/actual) (default) | numeric with value `0`

through `13`

| vector of numerics with values `0`

through `13`

Day-count basis, specified as an integer with a value `0`

through `13`

or
a `N`

-by-`1`

vector of integers
with values `0`

through `13`

.

0 = actual/actual (default)

1 = 30/360 (SIA)

2 = actual/360

3 = actual/365

4 = 30/360 (BMA)

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: **`single`

| `double`

`EndMonthRule`

— End-of-month rule flag for month having 30 or fewer days

`1`

(in effect) (default) | nonnegative integer `[0,1]`

End-of-month rule flag for month having 30 or fewer days, specified
as scalar nonnegative integer [`0`

, `1`

]
or a using a `N`

-by-`1`

vector of
values. 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 payment date is always the same numerical day of the month.`1`

= Set rule on, meaning that a payment date is always the last actual day of the month.

**Data Types: **`logical`

## Output Arguments

## More About

### Difference Between `yearfrac`

and `date2time`

The difference between `yearfrac`

and `date2time`

is
that `date2time`

counts full periods as a whole
integer, even if the number of actual days in the periods are different. `yearfrac`

does
not count full periods.

For example,

yearfrac('1/1/2000', '1/1/2001', 9)

ans = 1.0167

`yearfrac`

for `Basis`

`9`

(ACT/360
ICMA) calculates 366/360 = 1.0167. So, even if the dates have the
same month and date, with a difference of 1 in the year, the returned
value may not be exactly 1. On the other hand, `date2time`

calculates
one full year period:

date2time('1/1/2000', '1/1/2001', 1, 9)

ans = 1

## Version History

**Introduced before R2006a**

### R2022b: Serial date numbers not recommended

Although `date2time`

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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