GARCH Toolbox™

price2ret - Convert price series to return series

Syntax

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

Description

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

Input Arguments

TickSeries

Time series of price data. TickSeries can be a column vector 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 that the observations across a given row occur at the same time for all columns, where each column is a price series of an individual asset.

TickTimes

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 (for example, yearly). If TickTimes = [] or is unspecified, then price2ret assumes sequential observation times from 1, 2, ..., NUMOBS.

Method

Character string indicating the compounding method to compute asset returns. If Method = 'Continuous', = [], or is unspecified, then price2ret computes continuously compounded returns. If Method = 'Periodic', then price2ret assumes simple periodic returns. Method is case insensitive.

Output Arguments

RetSeries

Array of asset returns:

When TickSeries is a NUMOBS element column vector, RetSeries is a NUMOBS-1 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). It then normalizes it by the time interval between successive price observations.
Assuming that
RetIntervals(i) = TickTimes(i+1) – TickTimes(i)
then if Method is 'Continuous', [], or is unspecified, price2ret computes the continuously compounded returns as
RetSeries(i) = log [TickSeries(i+1)/TickSeries(i)]/RetIntervals(i)
If Method is 'Periodic', then price2ret computes the simple returns as
RetSeries(i) = [TickSeries(i+1)/TickSeries(i)] – 1 /RetIntervals(i)

RetIntervals

NUMOBS-1 element vector of times between observations. If TickTimes is [] or is unspecified, price2ret assumes that all intervals are 1.

Examples

Create a stock price process continuously compounded at 10 percent:
```
S = 100*exp(0.10 * [0:19]'); % Create the stock price series
```

Convert the price series to a 10 percent return series: