R/BivariatePortfolio.R

In YiffyGuo/GabauerDavid-ConnectednessApproach: Connectedness Approach

#' @title Kroner and Ng (1998) optimal bivariate portfolio weights
#' @description This function calculates the optimal portfolio weights according to Kroner and Ng (1998)
#' @param x zoo return matrix (in percentage)
#' @param H Residual variance-covariance, correlation or pairwise connectedness matrix
#' @param method Cumulative sum or cumulative product
#' @param long Allow only long portfolio position
#' @param statistics Hedging effectiveness statistic
#' @param digit Number of decimal places
#' @return Get bivariate portfolio weights
#' @importFrom stats var.test
#' @importFrom onewaytests bf.test
#' @importFrom onewaytests homog.test
#' @examples
#' data("g2020")
#' fit = VAR(g2020, configuration=list(nlag=1))
#' bpw = BivariatePortfolio(g2020, fit$Q, method="cumsum", statistics="Fisher")
#' bpw$TABLE
#' @references
#' Kroner, K. F., & Ng, V. K. (1998). Modeling asymmetric comovements of asset returns. The Review of Financial Studies, 11(4), 817-844.\\
#' Ederington, L. H. (1979). The hedging performance of the new futures markets. The Journal of Finance, 34(1), 157-170.\\
#' Antonakakis, N., Cunado, J., Filis, G., Gabauer, D., & de Gracia, F. P. (2020). Oil and asset classes implied volatilities: Investment strategies and hedging effectiveness. Energy Economics, 91, 104762.
#' @author David Gabauer
#' @export
BivariatePortfolio = function(x, H, method=c("cumsum", "cumprod"), long=TRUE, statistics=c("Fisher", "Bartlett", "Fligner-Killeen", "Levene", "Brown-Forsythe"), digit=2) {
  message("The optimal bivariate portfolios are computed according to:\n Kroner, K. F., & Ng, V. K. (1998). Modeling asymmetric comovements of asset returns. The Review of Financial Studies, 11(4), 817-844.")
  message("Hedging effectiveness is calculated according to:\n Ederington, L. H. (1979). The hedging performance of the new futures markets. The Journal of Finance, 34(1), 157-170.")
  message("Statistics of the hedging effectiveness measure are implemented according to:\n Antonakakis, N., Cunado, J., Filis, G., Gabauer, D., & de Gracia, F. P. (2020). Oil and asset classes implied volatilities: Investment strategies and hedging effectiveness. Energy Economics, 91, 104762.")
  
  method = match.arg(method)
  statistics = match.arg(statistics)
  x = x / 100
  if (class(x)!="zoo") {
    stop("Data needs to be of type 'zoo'")
  }
  k = ncol(x)
  t = nrow(x)
  date = as.character(rownames(x))
  NAMES = colnames(x)

  summary = NULL
  portfolio_weights = array(0.5, c(k, k, t), dimnames=list(NAMES,NAMES,date))
  for (i in 1:k) {
    for (j in 1:k) {
      pw = (H[j,j,]-H[i,j,]) / (H[i,i,]-2*H[i,j,]+H[j,j,])
      pw[which(is.na(pw))] = 0.5
      if (long) {
        pw = ifelse(pw>1,1,pw)
        pw = ifelse(pw<0,0,pw)
      }
      portfolio_weights[j,i,] = pw
      portfolio_weights[i,j,] = 1 - pw
      x_ = as.matrix(portfolio_weights[j,i,])
      summary_ = matrix(NA, nrow=ncol(x_), ncol=4)
      for (ij in 1:ncol(x_)){
        summary_[ij,] = matrix(c(mean(x_[,ij]), stats::sd(x_[,ij]), stats::quantile(x_[,ij],0.05), stats::quantile(x_[,ij],0.95)), nrow=1)
      }
      colnames(summary_) = c("Mean", "Std.Dev.", "5%", "95%")
      rownames(summary_) = paste0(NAMES[i], "/", NAMES[j])
      summary = rbind(summary, summary_)
    }
  }

  pvalue = HE = array(NA, c(k,k), dimnames=list(NAMES, NAMES))
  portfolio_return = cumulative_portfolio_return = cumulative_asset_return = array(NA,c(k,k,t), dimnames=list(NAMES,NAMES,date))
  for (i in 1:k) {
    for (j in 1:k) {
      portfolio_return[j,i,] = portfolio_weights[j,i,]*x[,i] + (1-portfolio_weights[j,i,])*x[,j]
      HE[j,i] = 1 - var(portfolio_return[j,i,])/var(x[,i])
      df = rbind(data.frame(val=portfolio_return[j,i,], group="A"), data.frame(val=x[,i], group="B"))
      if (statistics=="Fisher") {
        pvalue[i,j] = stats::var.test(x=portfolio_return[j,i,],y=x[,i],ratio=1)$p.value
      } else if (statistics=="Bartlett") {
        pvalue[i,j] = onewaytests::homog.test(val~as.character(group), data=df, method="Bartlett", verbose=F)$p.value
      } else if (statistics=="Fligner-Killeen") {
        pvalue[i,j] = onewaytests::homog.test(val~as.character(group), data=df, method="Fligner", verbose=F)$p.value
      } else if (statistics=="Levene") {
        pvalue[i,j] = onewaytests::homog.test(val~as.character(group), data=df, method="Levene", verbose=F)$p.value
      } else if (statistics=="Brown-Forsythe") {
        pvalue[i,j] = onewaytests::bf.test(val~as.character(group), data=df, verbose=F)$p.value
      } else {
        stop("No valid hedging effectiveness statistics have been chosen.")
      }

      if (method=="cumsum") {
        cumulative_asset_return[j,i,] = cumsum(x[,i])
        cumulative_portfolio_return[j,i,] = cumsum(portfolio_return[j,i,])
      } else if (method=="cumprod") {
        cumulative_asset_return[j,i,] = cumprod(1+x[,i])
        cumulative_portfolio_return[j,i,] = cumprod(1+portfolio_return[j,i,])
      }
    }
  }
  TABLE = cbind(summary,c(HE),c(pvalue))
  TABLE = TABLE[-which(TABLE[,1]==0.5),]
  colnames(TABLE) = c("Mean","Std.Dev.","5%","95%","HE","p-value")

  return = list(TABLE=format(round(TABLE,digit),nsmall=digit), portfolio_weights=portfolio_weights, portfolio_return=portfolio_return, cumulative_portfolio_return=cumulative_portfolio_return)
}