仅使用平均收益向量和协方差矩阵进行 R 中的投资组合优化

我看到的每个包似乎都需要我的资产的时间序列回报。

例如，我喜欢 PortfolioAnalytics 包，并且我需要提供的许多约束（框约束、组约束等）。然而，据我所知，它需要某种时间序列的回报，即使我指定了我自己的时刻（我可能是错的）。

我所拥有的只是 14 项资产中每项资产的预期回报和协方差矩阵。

我如何以此为出发点进行各种形式的优化？最终，我希望建立一个完全有效的边界，并且能够在给定的风险水平（标准差）给定的限制下最大化回报。如果我有一个时间序列，这不会是一个问题......但可惜我没有。

谢谢。我觉得这应该很容易，但我一直在兜圈子。

最坏的情况是我可以构建一个适合 E(R) 和协方差矩阵参数的假时间序列..如果您认为这是我的解决方案，您能为我提供一种简单的方法来做到这一点...但这就是原因我在这里 ：）

这个怎么样？

library(stockPortfolio)
library(quadprog)
library(ggplot2)
stocks <- c("SPY",  "EFA",  "IWM",  "VWO",  "LQD",  "HYG")

returns <- getReturns(stocks, freq = "week")

eff.frontier <-  function (returns,
                           short = "no",
                           max.allocation = NULL,
                           risk.premium.up = .5,
                           risk.increment = .005) {
  covariance <- cov(returns)
  print(covariance)
  n <- ncol(covariance)

  # Create initial Amat and bvec assuming only equality constraint (short-selling is allowed, no allocation constraints)
  Amat <- matrix (1, nrow = n)
  bvec <- 1
  meq <- 1

  # Then modify the Amat and bvec if short-selling is prohibited
  if (short == "no") {
    Amat <- cbind(1, diag(n))
    bvec <- c(bvec, rep(0, n))
  }

  # And modify Amat and bvec if a max allocation (concentration) is specified
  if (!is.null(max.allocation)) {
    if (max.allocation > 1 | max.allocation < 0) {
      stop("max.allocation must be greater than 0 and less than 1")
    }
    if (max.allocation * n < 1) {
      stop("Need to set max.allocation higher; not enough assets to add to 1")
    }
    Amat <- cbind(Amat, -diag(n))
    bvec <- c(bvec, rep(-max.allocation, n))
  }

  # Calculate the number of loops based on how high to vary the risk premium and by what increment
  loops <- risk.premium.up / risk.increment + 1
  loop <- 1

  # Initialize a matrix to contain allocation and statistics
  # This is not necessary, but speeds up processing and uses less memory
  eff <- matrix(nrow = loops, ncol = n + 3)
  # Now I need to give the matrix column names
  colnames(eff) <-
    c(colnames(returns), "Std.Dev", "Exp.Return", "sharpe")

  # Loop through the quadratic program solver
  for (i in seq(from = 0, to = risk.premium.up, by = risk.increment)) {
    dvec <-
      colMeans(returns) * i # This moves the solution up along the efficient frontier
    sol <-
      solve.QP(
        covariance,
        dvec = dvec,
        Amat = Amat,
        bvec = bvec,
        meq = meq
      )
    eff[loop, "Std.Dev"] <-
      sqrt(sum(sol$solution * colSums((
        covariance * sol$solution
      ))))
    eff[loop, "Exp.Return"] <-
      as.numeric(sol$solution %*% colMeans(returns))
    eff[loop, "sharpe"] <-
      eff[loop, "Exp.Return"] / eff[loop, "Std.Dev"]
    eff[loop, 1:n] <- sol$solution
    loop <- loop + 1
  }

  return(as.data.frame(eff))
}

eff <-
  eff.frontier(
    returns = returns$R,
    short = "yes",
    max.allocation = .45,
    risk.premium.up = .5,
    risk.increment = .001
  )


eff.optimal.point <- eff[eff$sharpe == max(eff$sharpe),]

ealred  <- "#7D110C"
ealtan  <- "#CDC4B6"
eallighttan <- "#F7F6F0"
ealdark  <- "#423C30"
ggplot(eff, aes(x = Std.Dev, y = Exp.Return)) + geom_point(alpha = .1, color =
                                                             ealdark) +
  geom_point(
    data = eff.optimal.point,
    aes(x = Std.Dev, y = Exp.Return, label = sharpe),
    color = ealred,
    size = 5
  ) +
  annotate(
    geom = "text",
    x = eff.optimal.point$Std.Dev,
    y = eff.optimal.point$Exp.Return,
    label = paste(
      "Risk: ",
      round(eff.optimal.point$Std.Dev * 100, digits = 3),
      "\nReturn: ",
      round(eff.optimal.point$Exp.Return * 100, digits =
              4),
      "%\nSharpe: ",
      round(eff.optimal.point$sharpe * 100, digits = 2),
      "%",
      sep = ""
    ),
    hjust = 0,
    vjust = 1.2
  ) +
  ggtitle("Efficient Frontier\nand Optimal Portfolio") + labs(x = "Risk (standard deviation of portfolio variance)", y =
                                                                "Return") +
  theme(
    panel.background = element_rect(fill = eallighttan),
    text = element_text(color = ealdark),
    plot.title = element_text(size = 24, color = ealred)
  )

这也应该有帮助。

https://www.r-bloggers.com/a-gentle-introduction-to-finance-using-r-efficient-frontier-and-capm-part-1/ https://www.r-bloggers.com/a-gentle-introduction-to-finance-using-r-efficient-frontier-and-capm-part-1/