R/MinimumConnectednessPortfolio.R

In ConnectednessApproach: Connectedness Approach

#' @title Minimum connectedness portfolio
#' @description This function calculates the minimum connectedness portfolio
#' @param x zoo return matrix (in percentage)
#' @param H Pairwise connectedness matrix or alternatively variance-covariance or correlation matrix
#' @param method Cumulative sum or cumulative product 
#' @param long Allow only long portfolio position
#' @param statistics Hedging effectiveness statistic
#' @param metric Risk measure of Sharpe Ratio (StdDev, VaR, or CVaR)
#' @param digit Number of decimal places
#' @return Get portfolio weights
#' @examples
#' data("g2020")
#' fit = VAR(g2020, configuration=list(nlag=1))
#' dca = TimeConnectedness(Phi=fit$B, Sigma=fit$Q, nfore=10, generalized=TRUE)
#' mcp = MinimumConnectednessPortfolio(g2020/100, dca$PCI, statistics="Fisher")
#' mcp$TABLE
#' @references
#' Broadstock, D. C., Chatziantoniou, I., & Gabauer, D. (2022). Minimum connectedness portfolios and the market for green bonds: Advocating socially responsible investment (SRI) activity. In Applications in Energy Finance (pp. 217-253). Palgrave Macmillan, Cham.
#' 
#' 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
MinimumConnectednessPortfolio = function (x, H, method = c("cumsum", "cumprod"), statistics = c("Fisher", "Bartlett", "Fligner-Killeen", "Levene", "Brown-Forsythe"), long = TRUE, metric="StdDev", digit = 2) {
  message("The minimum connectedness portfolio is implemented according to:\n Broadstock, D. C., Chatziantoniou, I., & Gabauer, D. (2022). Minimum connectedness portfolios and the market for green bonds: Advocating socially responsible investment (SRI) activity. In Applications in Energy Finance (pp. 217-253). Palgrave Macmillan, Cham.\n\n          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.\n\n          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)
  if (!is(x, "zoo")) {
    stop("Data needs to be of type 'zoo'")
  }
  k = ncol(x)
  t = nrow(x)
  date = as.character(rownames(x))
  NAMES = colnames(x)
  I = matrix(1, k, 1)
  if (length(dim(H)) == 2) {
    H = array(H, c(k, k, 1))
  }
  if (dim(H)[[3]] == 1) {
    H = array(H, c(k, k, t), dimnames = list(NAMES, NAMES, date))
  }
  portfolio_weights = array(NA, c(t, k), dimnames = list(date, NAMES))
  for (i in 1:t) {
    V_inv = MASS::ginv(H[, , i])
    pw = (V_inv %*% I)/c(t(I) %*% V_inv %*% I)
    if (long) {
      pw = ifelse(pw < 0, 0, pw)
      pw = ifelse(pw > 1, 1, pw)
      pw = pw/sum(pw)
    }
    portfolio_weights[i, ] = pw
  }
  summary = NULL
  for (i in 1:k) {
    x_ = as.matrix(portfolio_weights[, 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%")
    summary = rbind(summary, summary_)
  }
  rownames(summary) = NAMES
  portfolio_return = array(NA, c(t, 1), dimnames = list(date))
  for (i in 1:t) {
    portfolio_return[i, ] = sum(portfolio_weights[i, ] *  as.numeric(x[i, ]))
  }
  if (method == "cumsum") {
    cumulative_portfolio_return = cumsum(portfolio_return)
  } else if (method == "cumprod") {
    cumulative_portfolio_return = cumprod(1 + portfolio_return) - 1
  }
  SR = HE = pvalue = array(NA, c(k, 1), dimnames = list(NAMES))
  for (i in 1:k) {
    HE[i, ] = 1 - var(portfolio_return)/var(x[, i])
    z = zoo::zoo(portfolio_return, order.by=zoo::index(x))
    SR[i,] = PerformanceAnalytics::SharpeRatio(z, FUN=(metric), annualize=TRUE)
    df = rbind(data.frame(val = x[, i], group = "A"), 
               data.frame(val = portfolio_return, group = "B"))
    pvalue[i, ] = VarianceTest(val ~ as.character(group), data = df, method = statistics)$p.value
  }
  TABLE = cbind(summary, HE, pvalue, SR)
  colnames(TABLE) = c("Mean", "Std.Dev.", "5%", "95%", "HE", "p-value", "SR")
  return = list(TABLE = format(round(TABLE, digit), nsmall = digit), 
                portfolio_weights = portfolio_weights, HE = HE, pvalue = pvalue, 
                portfolio_return = portfolio_return, cumulative_portfolio_return = cumulative_portfolio_return)
}