GARCH Toolbox

price2ret

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.

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.

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