Calculate Uryasev's proposed Conditional Drawdown at Risk (CDD or CDaR) measure

For some confidence level \(p\), the conditional drawdown is the mean of the worst \(p\%\) drawdowns.

Usage

CDD(
  R,
  weights = NULL,
  geometric = TRUE,
  invert = TRUE,
  p = 0.95,
  method = c("discrete", "average", "quantile"),
  ...
)

Arguments

R

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns

weights

portfolio weighting vector, default NULL, see Details

geometric

utilize geometric chaining (TRUE) or simple/arithmetic chaining (FALSE) to aggregate returns, default TRUE

invert

TRUE/FALSE whether to invert the drawdown measure. see Details.

p

confidence level for calculation, default p=0.95

method

one of "discrete", "average", or "quantile". See Details.

...

any other passthru parameters

Details

The method parameter allows for three mathematical variations of CDD/CDaR:

discrete

(Default) Computes the Expected Shortfall of the discrete, isolated peak-to-trough drawdown sequences. This isolates major discrete events without penalizing the prolonged duration of shallow drawdowns.

average

Computes the mean of the continuous sample path of drawdowns that exceed the threshold. This strictly adheres to the Chekhlov (2003) continuous definition but can be heavily autocorrelated, mathematically overweighting long, shallow drawdowns over sharp, brief crashes.

quantile

(Deprecated) A legacy implementation that merely computed the VaR (quantile) of the discrete drawdowns, rather than the Expected Shortfall (mean).

References

Chekhlov, A., Uryasev, S., and M. Zabarankin. Portfolio Optimization With Drawdown Constraints. B. Scherer (Ed.) Asset and Liability Management Tools, Risk Books, London, 2003 https://www.ise.ufl.edu/uryasev/drawdown.pdf

See also

ES maxDrawdown

Author

Brian G. Peterson

Examples

data(edhec)
t(round(CDD(edhec), 4))
#>                        Conditional Drawdown 95%
#> Convertible Arbitrage                    0.1487
#> CTA Global                               0.1087
#> Distressed Securities                    0.1760
#> Emerging Markets                         0.2910
#> Equity Market Neutral                    0.0692
#> Event Driven                             0.1537
#> Fixed Income Arbitrage                   0.1151
#> Global Macro                             0.0528
#> Long/Short Equity                        0.1455
#> Merger Arbitrage                         0.0583
#> Relative Value                           0.0928
#> Short Selling                            0.7687
#> Funds of Funds                           0.1224