rportfolios (version 1.0-1)

portfolio.difference: Portfolio Difference Measure

Description

This function computes a measure of the difference between one or more portfolios and a benchmark portfolio.

Usage

portfolio.difference(portfolios, x.b, method = c("relative", "absolute"))

Arguments

portfolios

A numeric vector or matrix that defines the portfolio exposures

x.b

A numeric vector that defines the benchmark exposures

method

A character value that defines the difference measure

Value

A single numeric measure for one portfolio or a numeric vector for a collection of portfolios

Details

The absolute deviation between a portfolio $\bf{x}$ and a benchmark $\bf{x}_b$ is denoted by ${D_a}\left({{\bf{x}},{{\bf{x}}_b}} \right)$ and is computed as ${D_a}\left( {{\bf{x}},{{\bf{x}}_b}} \right) = \frac{1}{2}\sum\limits_{i = 1}^n {\left| {{x_i} - {x_{b,i}}} \right|}$. The relative deviation between a portfolio and a benchmark is denoted by ${D_r}\left( {{\bf{x}},{{\bf{x}}_b}} \right)$ and is computed as ${D_r}\left( {{\bf{x}},{{\bf{x}}_b}} \right) = \frac{1}{n}\sum\limits_{i = 1}^n {\frac{{\left| {{x_i} - {x_{b,i}}} \right|}}{{{x_i} + {x_{b,i}}}}}$. The private function vector.difference performs the actual calculation of the difference based on the given method.

References

Worthington, A. C., 2009. Household Asset Portfolio Diversification: Evidence from the Household, Income and Labour Dynamics in Australia (Hilda) Survey, Working Paper, Available at SSRN: http://ssrn.com/abstract=1421567.

Examples

onePortfolio <- random.longonly( 100, 75 )
aBenchmark <- rep( 0.01, 100 )
portfolio.difference( onePortfolio, aBenchmark, method="absolute" )
portfolio.difference( onePortfolio, aBenchmark, method="relative" )