RachevRatio computation with standard errors.

RachevRatio(
  R,
  alpha = 0.1,
  beta = 0.1,
  rf = 0,
  SE = FALSE,
  SE.control = NULL,
  ...
)

Arguments

R

Data of returns for one or multiple assets or portfolios.

alpha

Lower tail probability.

beta

Upper tail probability.

rf

Risk-free interest rate.

SE

TRUE/FALSE whether to ouput the standard errors of the estimates of the risk measures, default FALSE.

SE.control

Control parameters for the computation of standard errors. Should be done using the RPESE.control function.

...

Additional parameters.

Value

A vector or a list depending on se.method.

Details

The Rachev ratio, introducted in Rachev et al. (2008), is a non-parametric estimator of the upper tail reward potential relative to the lower tail risk in a non-Gaussian setting, and as such, it is particularly useful when returns have a fat-tailed and possibly skewed distribution. For small \(\alpha\) and \(\beta\), it is a measure of the potential of extreme positive returns to risk of extremel negative returns.

For lower tail parameter \(\alpha\) and lower tail parameter \(\beta\), the Rachev ratio is given by

$$\frac{ETL_{\alpha}(R_{f}-R_{a})}{ETL_{\beta}(R_{a}-R_{f})}$$.

References

Rachev, Svetlozar T. et al. (2008). Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization (1st ed.)

Author

Anthony-Alexander Christidis, anthony.christidis@stat.ubc.ca

Examples

# Loading data from PerformanceAnalytics
data(edhec, package = "PerformanceAnalytics")
class(edhec)
#> [1] "xts" "zoo"
# Changing the data colnames
names(edhec) = c("CA", "CTA", "DIS", "EM", "EMN",
                 "ED", "FIA", "GM", "LS", "MA",
                 "RV", "SS", "FOF")
# Compute Rachev ratio for managers data
RachevRatio(edhec)
#>                   CA      CTA      DIS        EM      EMN       ED      FIA
#> RachevRatio 1.179419 1.338008 1.139389 0.9967392 1.514187 1.089176 1.135164
#>                   GM       LS     MA       RV       SS      FOF
#> RachevRatio 2.014378 1.238694 1.5023 1.159463 1.134508 1.225545