DivRatios function

Diversification Measures

These functions compute the diversification ratio, the volatility weighted average correlation and concentration ratio of a portfolio.

dr(weights, Sigma)
cr(weights, Sigma)
rhow(weights, Sigma)

Arguments

• weights: Vector: portfolio weights.
• Sigma: Matrix: Variance-covariance matrix of portfolio assets.

Details

The diversification ratio of a portfolio is defined as:

for a portfolio of $N$ assets and $\omega_i$ signify the weight of the i-th asset and $\sigma_i$ its standard deviation and $\Sigma$ the variance-covariance matrix of asset returns. The diversification ratio is therefore the weighted average of the assets' volatilities divided by the portfolio volatility.

The concentration ration is defined as:

and the volatility-weighted average correlation of the assets as:

The following equation between these measures does exist:

Returns

numeric, the value of the diversification measure.

References

Choueifaty, Y. and Coignard, Y. (2008): Toward Maximum Diversification, Journal of Portfolio Management, Vol. 34, No. 4, 40--51.

Choueifaty, Y. and Coignard, Y. and Reynier, J. (2011): Properties of the Most Diversified Portfolio, Working Paper, http://papers.ssrn.com

Author(s)

Bernhard Pfaff

See Also

PMD

Examples

data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE)
w <- Weights(PMD(Rets))
V <- cov(Rets)
DR <- dr(w, V)
CR <- cr(w, V)
RhoW <- rhow(w, V)
test <- 1 / sqrt(RhoW * (1 - CR) + CR)
all.equal(DR, test)