demo/logToArithmeticCovariance.R

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

# Generate arithmetric returns and arithmetric covariance matrix given a distribution of log returns

# Example experiment with two assets

    # initialize with average log returns and log-based covariance matrix
    m1 <- c( .05 , .12 , .1 )
    S1 <- matrix( c( .1 , .05 , .02 , .05 , .1 , .03 , .02 , .03 , .1 ), nrow = 3 )

    # simulate log-return draws from log-based covariance matrix assuming normal distribution
        set.seed(1001)   
        library(MASS)
        logReturns <- MASS::mvrnorm(2000000,mu=m1,Sigma=S1)
    
        # convert to arithmetic returns
        arithmeticReturn = exp( logReturns ) - 1
        colMeans( arithmeticReturn )
        # create arithmetric based covariance matrix
        var( arithmeticReturn )

    # compare simulation results with linreturn function    
    linreturn( m1, S1 )