Conditional Diversification Benefit (CDB)

Compute the CDB (Christoffersen et al., 2012; 2018) for a two–asset portfolio at confidence level p, using normal–theory VaR/ES with plug-in means and standard deviations.

Usage

cdb(x, y, p, w)

Arguments

x: Numeric vector of returns for asset X.
y: Numeric vector of returns for asset Y.
p: Scalar in (0, 1): confidence level (e.g., 0.05 for 5% ES/VaR).
w: Scalar in [0, 1]: portfolio weight on X (Y is 1 - w).

Value

A single numeric value giving the Conditional Diversification Benefit for the specified weight and confidence level.

Details

The function computes $$ \mathrm{CDB}(w,p) = \frac{ w\,\mathrm{ES}_X(p) + (1-w)\,\mathrm{ES}_Y(p) - \mathrm{ES}_P(p) } { w\,\mathrm{ES}_X(p) + (1-w)\,\mathrm{ES}_Y(p) - \mathrm{VaR}_P(p) } $$ where ES and VaR are computed via cvar::ES() and cvar::VaR() using stats::qnorm (normal approximation). Portfolio mean/SD use plug-in means/SDs under an independence assumption (no covariance term).

References

Christoffersen, P., Errunza, V., Jacobs, K., & Langlois, H. (2012). Is the potential for international diversification disappearing? A dynamic copula approach. Review of Financial Studies, 25(12), 3711–3751. Christoffersen, P., Jacobs, K., Jin, X., & Langlois, H. (2018). Dynamic dependence and diversification in corporate credit. Review of Finance, 22(2), 521–560.

Examples

x <- rnorm(1000, 0.0005, 0.02)
y <- rnorm(1000, 0.0003, 0.015)
cdb(x, y, p = 0.05, w = 0.3)
#> [1] 0.6458706