R/wtdpapb.R

In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

#' Creates input for the stochastic dominance function stochdom2
#' 
#' Stochastic dominance is a sophisticated comparison of two distributions of
#' stock market returns.  The dominating distribution is superior in terms of
#' mean, variance, skewness and kurtosis respectively, representing dominance
#' orders 1 to 4, without directly computing four moments.  Vinod(2008) sec. 4.3
#' explains the details.  The `wtdpapb' function creates the input
#' for stochdom2 which in turn computes the stochastic dominance.
#' See Vinod (2004) for details about quantitative stochastic dominance.
#' 
#' @note  Function is needed before using stochastic dominance
#' 
#' @param xa {Vector of (excess) returns for the first investment option A or
#' values of any random variable being compared to another.}
#' @param xb Vector of returns for the second option B
#' @return 
#' \item{wpa}{Weighted vector of probabilities for option A} 
#' \item{wpb}{Weighted vector of probabilities for option B} 
#' \item{dj}{Vector of interval widths (distances) when both sets of data are forced on a common support} 

#' @note In Vinod (2008) where the purpose of \code{wtdpapb} is to map from standard
#' `expected utility theory' weights to more sophisticated `non-expected utility
#' theory' weights using Prelec's (1998, Econometrica, p. 497) method.  These
#'  weights are not needed here. Hence we provide the function \code{prelec2}
#'  which does not use Prelec weights at all, thereby simplifying and speeding up
#'  the R code provided in Vinod (2008). This function avoids sophisticated `non-expected'
#'  utility theory which incorporates commonly observed human behavior favoring
#'  loss aversion and other anomalies inconsistent with precepts of the
#'  expected utility theory. Such weighting is not needed for our application.
#' @author Prof. H. D. Vinod, Economics Dept., Fordham University, NY
#' @seealso See Also \code{\link{stochdom2}}
#' @references Vinod, H. D.', 'Hands-On Intermediate Econometrics 
#' Using R'  (2008) World Scientific Publishers: Hackensack, NJ.
#' \url{https://www.worldscientific.com/worldscibooks/10.1142/12831}
#'
#' @references Vinod, H. D. 'Ranking Mutual Funds Using 
#' Unconventional Utility Theory and Stochastic Dominance,'
#' Journal of Empirical Finance Vol. 11(3) 2004, pp. 353-377.
#' 
#' @concept stochastic dominance
#' @examples
#' 
#'  \dontrun{
#'  set.seed(234);x=sample(1:30);y=sample(5:34)
#'  wtdpapb(x,y)}
#' 
#' @export

wtdpapb <- function(xa, xb) {
  # input: excess returns for mutual fund A & B output is a weighted pa and pb
  # vectors (wpa, wpb) and dj vector
  Ta = length(xa)
  Tb = length(xb)
  k = Ta + Tb
  pa0 = rep(1/Ta, Ta)
  pb0 = rep(1/Tb, Tb)
  xpapb = matrix(0, k, 3)
  for (i in 1:Ta) {
    xpapb[i, 1] = xa[i]
    xpapb[i, 2] = pa0[i]
  }
  for (i in 1:Tb) {
    xpapb[Ta + i, 1] = xb[i]
    xpapb[Ta + i, 3] = pb0[i]
  }
  pra = prelec2(n = Ta + Tb)
  sm = sort_matrix(xpapb, 1)  #sort on first col of excess returns
  pa = sm[, 2]
  pb = sm[, 3]
  wpa = pa * pra$pdif
  wpb = pb * pra$pdif
  dj=sm[,1]-sm[1,1]  #deviations from the minimum
  #at sm[1,1] (sm is sorted)
  list(wpa = wpa, wpb = wpb, dj = dj)
}