Как насчет этого?
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)
)
Это также должно помочь.
https://www.r-bloggers.com/a-gentle-introduction-to-finance-using-r-efficient-frontier-and-capm-part-1/