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November 10, 2016 13:46
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Computing the efficient frontier in R
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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) | |
) |
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Hi! Where do you take the data from? Where is the point you download it? Thanks