ret2price (GARCH Toolbox)

Convert a return series to a price series

Syntax

[TickSeries, TickTimes] = ret2price(RetSeries, StartPrice, 
RetIntervals, StartTime, Method)

Arguments

RetSeries
Time series array of returns. RetSeries can be a vector (row or column) or a matrix:
As a vector, RetSeries represents a univariate series of returns of a single asset. 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, RetSeries represents a NUMOBS-by-number of assets (NUMASSETS) matrix of asset returns. Rows correspond to time indices. The first row contains the oldest observations and the last row the most recent. ret2price assumes the observations across a given row occur at the same time for all columns, and each column is a return series of an individual asset.

StartPrice
(optional) A NUMASSETS element vector of initial prices for each asset, or a single scalar initial price applied to all assets. If StartPrice = [] or is not specified, all asset prices start at 1.

RetIntervals
(optional) A NUMOBS element vector of time intervals between return observations, or a single scalar interval applied to all observations. If RetIntervals = [] or is not specified, ret2price assumes all intervals have length 1.

StartTime
(optional) Scalar starting time for the first observation, applied to the price series of all assets. The default is 0.

Method
(optional) Character string indicating the compounding method used to compute asset returns. If Method = 'Continuous', = [], or is not specified, then ret2price computes continuously compounded returns. If Method = 'Periodic' then ret2price computes simple periodic returns. Method is case insensitive.

`RetSeries`	Time series array of returns. `RetSeries` can be a vector (row or column) or a matrix: As a vector, `RetSeries` represents a univariate series of returns of a single asset. 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, `RetSeries` represents a `NUMOBS`-by-number of assets (`NUMASSETS)` matrix of asset returns. Rows correspond to time indices. The first row contains the oldest observations and the last row the most recent. `ret2price` assumes the observations across a given row occur at the same time for all columns, and each column is a return series of an individual asset.
`StartPrice`	(optional) A `NUMASSETS` element vector of initial prices for each asset, or a single scalar initial price applied to all assets. If `StartPrice = []` or is not specified, all asset prices start at `1`.
`RetIntervals`	(optional) A `NUMOBS` element vector of time intervals between return observations, or a single scalar interval applied to all observations. If `RetIntervals = []` or is not specified, `ret2price` assumes all intervals have length `1`.
`StartTime`	(optional) Scalar starting time for the first observation, applied to the price series of all assets. The default is `0`.
`Method`	(optional) Character string indicating the compounding method used to compute asset returns. If `Method = 'Continuous', = []`, or is not specified, then `ret2price` computes continuously compounded returns. If `Method = 'Periodic'` then `ret2price` computes simple periodic returns. `Method` is case insensitive.

Description

[TickSeries, TickTimes] = ret2price(RetSeries, StartPrice, RetIntervals, StartTime, Method) generates a price series for each of NUMASSETS assets, given the asset starting prices and NUMOBS return observations for each asset.

TickSeries
Array of asset prices:
When RetSeries is a NUMOBS element row (column) vector, TickSeries is a NUMOBS+1 row (column) vector. The first element contains the starting price of the asset, and the last element the most recent price.

When RetSeries is a NUMOBS-by-NUMASSETS matrix, then RetSeries is a (NUMOBS+1)-by-NUMASSETS matrix. The first row contains the starting price of the assets, and the last row contains the most recent prices.

TickTimes
A NUMOBS+1 element vector of price observation times. The initial time is zero unless specified in StartTime.

`TickSeries`	Array of asset prices: When `RetSeries` is a `NUMOBS` element row (column) vector, `TickSeries` is a `NUMOBS+1` row (column) vector. The first element contains the starting price of the asset, and the last element the most recent price. When `RetSeries` is a `NUMOBS`-by-`NUMASSETS` matrix, then `RetSeries` is a (`NUMOBS+1`)-by-`NUMASSETS` matrix. The first row contains the starting price of the assets, and the last row contains the most recent prices.
`TickTimes`	A `NUMOBS`+1 element vector of price observation times. The initial time is zero unless specified in `StartTime`.

Example

Create a stock price process continuously compounded at 10 percent. Compute 10 percent returns for reference, then convert the resulting return series to the original price series and compare results.

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
P = ret2price(R, 100);         % Convert to the original price
                               % series
[S P]                          % Compare the original and 
                               % computed price series

ans =

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

See Also
price2ret

price2ret Glossary