ewstats (Financial Toolbox)

Expected return and covariance from return time series.

Syntax

[ExpReturn, ExpCovariance, NumEffObs] = ewstats(RetSeries, 
DecayFactor, WindowLength)

Arguments


`RetSeries`	Return Series: number of observations (`NUMOBS`)-by- number of assets (`NASSETS`) matrix of equally spaced incremental return observations. The first row is the oldest observation, and the last row is the most recent.
`DecayFactor`	Controls how much less each observation is weighted than its successor. The `k`'th observation back in time has weight `DecayFactor^k`. `DecayFactor` must lie in the range: `0 < DecayFactor <= 1`. Default = `1`, the equally weighted linear moving average model (BIS).

`WindowLength`	Number of recent observations in the computation. Default = `NUMOBS`.

Description

[ExpReturn, ExpCovariance, NumEffObs] = ewstats(RetSeries, DecayFactor, WindowLength) computes estimated expected returns, estimated covariance matrix, and the number of effective observations.

ExpReturn is a 1-by-NASSETS vector of estimated expected returns.

ExpCovariance is an NASSETS-by-NASSETS estimated covariance matrix.The standard deviations of the asset return processes are given by:

     STDVec = sqrt(diag(ECov))

The correlation matrix is:

     CorrMat = VarMat./( STDVec*STDVec' )

NumEffObs is the number of effective observations = (1-DecayFactor^WindowLength)/(1-DecayFactor).

A smaller DecayFactor or WindowLength emphasizes recent data more strongly but uses less of the available data set.

Example

RetSeries = [ 0.24 0.08 
              0.15 0.13 
              0.27 0.06 
              0.14 0.13 ];
  DecayFactor = 0.98;
  [ExpReturn, ExpCovariance] = ewstats(RetSeries, DecayFactor)
ExpReturn =

    0.1995    0.1002
ExpCovariance =

    0.0032   -0.0017
   -0.0017    0.0010