portsim (Financial Toolbox)

portsim
Random simulation of correlated asset returns

Syntax

RetSeries = portsim(ExpReturn, ExpCovariance, NumObs, RetIntervals, 
NumSim)

Arguments

ExpReturn
1 by number of assets (NASSETS) vector specifying the expected (mean) return of each asset.

ExpCovariance
NASSETS-by-NASSETS matrix of asset-asset covariances. The standard deviations of the returns are: ExpSigma = sqrt(diag(ExpCovariance)).

NumObs
(Optional) Number of consecutive observations in the return time series. If NumObs is entered as the empty matrix [], the length of RetIntervals is used.

RetIntervals
(Optional) Scalar or number of observations (NUMOBS) by 1 vector of interval times between observations. If RetIntervals is not specified, all intervals are assumed to have length 1.

NumSim
(Optional) Number of separate simulations of the NUMOBS observations to perform. Default = 1.

`ExpReturn`	1 by number of assets (`NASSETS`) vector specifying the expected (mean) return of each asset.
`ExpCovariance`	`NASSETS`-by-`NASSETS` matrix of asset-asset covariances. The standard deviations of the returns are: `ExpSigma = sqrt(diag(ExpCovariance))`.
`NumObs`	(Optional) Number of consecutive observations in the return time series. If `NumObs` is entered as the empty matrix `[]`, the length of `RetIntervals` is used.
`RetIntervals`	(Optional) Scalar or number of observations (`NUMOBS`) by 1 vector of interval times between observations. If `RetIntervals` is not specified, all intervals are assumed to have length 1.
`NumSim`	(Optional) Number of separate simulations of the `NUMOBS` observations to perform. Default = 1.

Description
portsim simulates returns of NASSETS assets over consecutive observation intervals. Returns are simulated as the increments of constant drift and volatility Brownian processes.

RetSeries is a NUMOBS-by-NASSETS-by-NUMSIM array of incremental return observations. The return over an interval of length DT is given by ExpReturn*DT + ExpSigma*sqrt(DT)*randn, where randn provides a random scalar whose value changes each time randn is referenced.

The returns realized from portfolios listed in PortWts are given by: PortReturn = PortWts * RetSeries(:,:,1)', where PortWts is a matrix in which each row contains the asset allocations of a portfolio. Each row of PortReturn corresponds to one of the portfolios identified in PortWts, and each column corresponds to one of the observations in RetSeries. See portopt and portstats for portfolio specification and optimization.

Examples
Create sample returns for three stocks over 10 periods.

ExpReturn = [0.1 0.2 0.15]; 

ExpCovariance = [0.005   -0.010    0.004 
                -0.010    0.040   -0.002 
                 0.004   -0.002    0.023];
  
NumObs = 10;

RetSeries = portsim(ExpReturn, ExpCovariance, NumObs)

RetSeries =

    0.1429    0.2626    0.2365
    0.0821    0.1599   -0.1796
    0.0054    0.6126    0.1072
    0.1719   -0.0669    0.1913
    0.1518   -0.0843    0.0442
    0.0112    0.2709    0.1501
    0.0409    0.1683    0.1932
    0.1485    0.2522    0.2774
    0.0463    0.3222    0.0954
    0.1990    0.1024    0.3843

Note: RetSeries is different each time this example is executed. The portsim function uses random number generation.

See Also
ewstats, portopt, portstats, randn, ret2tick

portrand portstats