repairMatrix {NMOF}

Repair an Indefinite Correlation Matrix

Description

The function ‘repairs’ an indefinite correlation matrix by replacing its negative eigenvalues by zero.

Usage

repairMatrix(C, eps = 0)

Arguments

C

a correlation matrix

eps

a small number

Details

The function ‘repairs’ a correlation matrix: it replaces negative eigenvalues with eps and rescales the matrix such that all elements on the main diagonal become unity again.

Value

Returns a numeric matrix.

Note

This function may help to cure a numerical problem, but it will rarely help to cure an empirical problem. (Garbage in, garbage out.)

See also the function nearPD in the Matrix package.

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. doi:10.1016/C2017-0-01621-X

Rebonato, R. and Jaeckel, P. (1999) The most general methodology to create a valid correlation matrix for risk management and option pricing purposes.

Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

Examples

## example: build a portfolio of three assets
C <- c(1,.9,.9,.9,1,.2,.9,.2,1)
dim(C) <- c(3L, 3L)
eigen(C, only.values = TRUE)

vols <- c(.3, .3, .3)      ## volatilities
S <- C * outer(vols,vols)  ## covariance matrix
w <- c(-1, 1, 1)           ## a portfolio
w %*% S %*% w          ## variance of portfolio is negative!
sqrt(as.complex(w %*% S %*% w))

S <- repairMatrix(C) * outer(vols,vols)
w %*% S %*% w          ## more reasonable
sqrt(w %*% S %*% w)