R/optimal_contrib_uniroot.R

In veldanie/SuraInvestmentAnalytics: Investment Analytics

#' optimal contribution to reach target.
#'
#' Takes the risk aversion coefficient, the covariance matrix and the market cap weights.
#' @param pr_simul Price Simul.
#' @param port Portfolio.
#' @param rc_1 Contrib rate year 1.
#' @param rc_2 Contrib rate year 2.
#' @param rc_3 Contrib rate year 3 onwards.
#' @param L_contrib Contribution years.
#' @param L Fund Horizon
#' @param B Param distribution over time.
#' @param Y Yield.
#' @param gr_1 Growth rate 2nd year onwards.
#' @param gr_2 Growth rate 2nd year onwards.
#' @param pe_target PE target.
#' @return optimal contribution to reach target.
#' @export

optimal_contrib_uniroot <- function(pr_simul, port, rc_1 = 0.25, rc_2 = 0.333 , rc_3 = 0.5, L_contrib = NA, L = 12, B = 2.5, Y = 0,
                                    gr_1, gr_2, pe_target = c(0.1,0.2,0.3)){
  dim_pr <- dim(pr_simul)
  N <- dim_pr[1]
  M <- dim_pr[2]
  V <- dim_pr[1]
  n_assets <- ncol(port) - 1
  n_port <- nrow(port)
  cc_port <- matrix(0, nrow = n_port, ncol = M)
  #ptm <- proc.time()
  for (k in 1:n_port){
    weights_mat <- as.matrix(port[k,-1])
    for(m in 1:M){
      obj_cc <- function(cc){
        pe_simul <- private_equity_simul_const_contrib(cc, 1, V, rc_1, rc_2 , rc_3, L_contrib, L, B, Y,
                                                       gr_1 = gr_1[,m], gr_2 = gr_2[,m])
        port_val <- rep(0, nrow = L)
        pe_ti <- pe_t(pe_simul, 1)
        port_val[1] <- 100 + pe_ti$cf + pe_ti$nav
        for (i in 2:L){
          dist_asset <- ((port_val[i - 1] - pe_ti$nav) %*% t(rep(1, n_assets)))  * weights_mat
          asset_units <- dist_asset/pr_simul[i - 1,m,]
          pe_ti <- pe_t(pe_simul, i)

          port_val[i] <- rowSums(asset_units * pr_simul[i,m,]) + pe_ti$cf + pe_ti$nav
        }
        port_val_L <- tail(port_val, 1)
        pe_val <- pe_consol(pe_simul)$nav[L,]
        pe_part <- pe_val / port_val_L - pe_target[k]
        return(pe_part)
      }
      cc_m =  try(uniroot(obj_cc, c(0,50))$root, silent = TRUE)
      if(class(cc_m)=='try-error'){
        cc_port[k,m] <- 0
      }else{
        cc_port[k,m] <- cc_m
      }
    }
    print(paste('Portfolio ',k, ': ', round(mean(cc_port[k,]),2)))
  }
  cc_avg_port <- apply(cc_port,1,mean)
  #proc.time() - ptm
  return(list(cc_port=cc_port, cc_avg_port=cc_avg_port))
}