Rachev Ratio — RachevRatio • PerformanceAnalytics

RachevRatio computation with standard errors.

Usage

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