price2ret (GARCH Toolbox)

Convert a price series to a return series

Syntax

[RetSeries, RetIntervals] = price2ret(TickSeries, TickTimes, 
Method)

Arguments

TickSeries
Time series of price data. TickSeries can be a vector (row or column) or a matrix:
As a vector, TickSeries represents a univariate price series. The length of the vector is the number of observations (NUMOBS). The first element contains the oldest observation, and the last element the most recent.

As a matrix, TickSeries represents a NUMOBS-by-number of assets (NUMASSETS) matrix of asset prices. Rows correspond to time indices. The first row contains the oldest observations and the last row the most recent. price2ret assumes the observations across a given row occur at the same time for all columns, and each column is a price series of an individual asset.

TickTimes
(optional) A NUMOBS element vector of monotonically increasing observation times. Times are numeric and taken either as serial date numbers (day units), or as decimal numbers in arbitrary units (e.g., yearly). If TickTimes = [] or is not specified, then price2ret assumes sequential observation times from 1, 2, ..., NUMOBS.

Method
(optional) Character string indicating the compounding method to compute asset returns. If Method = 'Continuous', = [], or is not specified, then price2ret computes continuously compounded returns. If Method = 'Periodic', then price2ret assumes simple periodic returns. Method is case insensitive.

`TickSeries`	Time series of price data. `TickSeries` can be a vector (row or column) or a matrix: As a vector, `TickSeries` represents a univariate price series. The length of the vector is the number of observations (`NUMOBS`). The first element contains the oldest observation, and the last element the most recent. As a matrix, `TickSeries` represents a `NUMOBS`-by-number of assets (`NUMASSETS`) matrix of asset prices. Rows correspond to time indices. The first row contains the oldest observations and the last row the most recent. `price2ret` assumes the observations across a given row occur at the same time for all columns, and each column is a price series of an individual asset.
`TickTimes`	(optional) A `NUMOBS` element vector of monotonically increasing observation times. Times are numeric and taken either as serial date numbers (day units), or as decimal numbers in arbitrary units (e.g., yearly). If `TickTimes = []` or is not specified, then `price2ret` assumes sequential observation times from 1, 2, ..., `NUMOBS`.
`Method`	(optional) Character string indicating the compounding method to compute asset returns. If `Method` = '`Continuous`', `= []`, or is not specified, then `price2ret` computes continuously compounded returns. If `Method = 'Periodic',` then `price2ret` assumes simple periodic returns. `Method` is case insensitive.

Description

[RetSeries, RetIntervals] = price2ret(TickSeries, TickTimes, Method) computes asset returns for NUMOBS price observations of NUMASSETS assets.

RetSeries
Array of asset returns:
When TickSeries is a NUMOBS element row (column) vector, RetSeries is a NUMOBS-1 row (column) vector.

When TickSeries is a NUMOBS-by-NUMASSETS matrix, RetSeries is a (NUMOBS-1)-by-NUMASSETS matrix. price2ret quotes the ith return of an asset for the period TickTimes(i) to TickTimes(i+1) and normalizes it by the time interval between successive price observations.

Assuming that

then if Method = 'Continuous', = [], or is not specified, price2ret computes the continuously-compounded ith return of an asset as

If Method = 'Periodic', then price2ret computes the ith simple return as

RetIntervals
NUMOBS-1 element vector of interval times between observations. If TickTimes = [] or is not specified, price2ret assumes that all intervals are 1.

`RetSeries`	Array of asset returns: When `TickSeries` is a `NUMOBS` element row (column) vector, `RetSeries` is a `NUMOBS-1` row (column) vector. When `TickSeries` is a `NUMOBS`-by-`NUMASSETS` matrix, `RetSeries` is a (`NUMOBS-1`)-by-`NUMASSETS` matrix. `price2ret` quotes the ith return of an asset for the period `TickTimes(i)` to `TickTimes(i+1)` and normalizes it by the time interval between successive price observations. Assuming that then if `Method = 'Continuous'`, `= []`, or is not specified, `price2ret` computes the continuously-compounded ith return of an asset as If `Method` = '`Periodic`', then `price2ret` computes the ith simple return as
`RetIntervals`	`NUMOBS-1` element vector of interval times between observations. If `TickTimes = []` or is not specified, `price2ret` assumes that all intervals are `1`.

Example

Create a stock price process continuously compounded at 10 percent, then convert the price series to a 10 percent return series.

S = 100*exp(0.10 * [0:19]');   % Create the stock price series
R = price2ret(S);              % Convert the price series to a 
                               % 10 percent returns series
[S [R ; NaN]]                  % Pad the return series so vectors
                               % are of same length. price2ret
                               % computes the ith return from 
                               % the ith and i+1th prices.

ans =

  100.0000    0.1000
  110.5171    0.1000
  122.1403    0.1000
  134.9859    0.1000
  149.1825    0.1000
  164.8721    0.1000
  182.2119    0.1000
  201.3753    0.1000
  222.5541    0.1000
  245.9603    0.1000
  271.8282    0.1000
  300.4166    0.1000
  332.0117    0.1000
  366.9297    0.1000
  405.5200    0.1000
  448.1689    0.1000
  495.3032    0.1000
  547.3947    0.1000
  604.9647    0.1000
  668.5894       NaN

See Also
ret2price

parcorr ret2price