R中的投资组合优化仅使用平均回报和协方差矩阵的向量 [英] Portfolio Optimize in R with ONLY a vector of mean returns and covariance matrix

问题描述

我查看的每个包似乎都需要我的资产的时间序列回报.

Every package that I look at seems to require time series returns for my assets.

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).

For example I like the PortfolioAnalytics package, and I require many of the constraints offered (box constraints, group constraints, etc.). However, as far as I can tell it requires some sort of time series of returns, even if I specify my own moments (I could be wrong).

我所拥有的只是我的 14 种资产中每一种的预期回报和协方差矩阵.

如何以此为起点进行各种形式的优化?最终，我想建立一个完整的有效边界，并能够在给定的风险水平(标准差)下最大化回报给我的限制.如果我有一个时间序列，这将不是问题……但可惜我没有.

How can I do various forms of optimizations with that as my starting point? Ultimately I'd like to build a full efficient frontier as well as be able to maximize return at a given level of risk (standard deviation) given my constraints. If I had a time series this wouldn't be a problem...but alas I do not.

谢谢.我觉得这应该很容易，但我一直在兜圈子.

Thanks. I feel like this should be quite easy but I've been running in circles.

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.这就是我在这里的原因:)

Worst case scenario is I could build a fake time series that fits the parameters of the E(R) and covariance matrix..if you think this is my solution can you offer me an easy way to do that...but that is why I am here :)

推荐答案

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/

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