问题
I am trying to use the chart.EfficientFrontier function in the portfolioanalytics package in R to chart an efficient frontier object that I have created but it keeps failing. Basically I am trying to find a frontier that will minimize annaulized standard deviation. Eventually once I get this working I would also like to maximize annualized return.
Firstly I created an annualized standard deviation function using this code
pasd <- function(R, weights){
as.numeric(StdDev(R=R, weights=weights)*sqrt(12)) # hardcoded for monthly data
# as.numeric(StdDev(R=R, weights=weights)*sqrt(4)) # hardcoded for quarterly data
}
I imported a csv file with monthly returns and my portfolio object looks like this:
> prt
**************************************************
PortfolioAnalytics Portfolio Specification
**************************************************
Call:
portfolio.spec(assets = colnames(returns))
Number of assets: 3
Asset Names
[1] "Global REITs" "Au REITs" "Au Util and Infra"
Constraints
Enabled constraint types
- leverage
- long_only
Objectives:
Enabled objective names
- mean
- pasd
Now I successfully create an efficient frontier object using this line:
prt.ef <- create.EfficientFrontier(R = returns, portfolio = prt, type = "DEoptim", match.col = "pasd")
But when I try to plot it I am getting the following error messages.
> chart.EfficientFrontier(prt.ef, match.col="pasd")
Error in StdDev(R = R, weights = weights) :
argument "weights" is missing, with no default
In addition: There were 26 warnings (use warnings() to see them)
Error in StdDev(R = R, weights = weights) :
argument "weights" is missing, with no default
Error in StdDev(R = R, weights = weights) :
argument "weights" is missing, with no default
Error in xlim[2] * 1.15 : non-numeric argument to binary operator
Anyone know why this is the case? When I use summary(prt.ef) I can see the weights, but why is the chart.EfficientFrontier function failing?
回答1:
As @WaltS suggested, you need to be consistent in implementing functions to annualize mean and risk returns.
But actually to get annualized statistics you have two options, you are not using any:
1) Make the optimization with monthly data, with the original risk return functions in the specification. For plotting you can anualize making
Port.Anua.Returns=prt.ef$frontier[,1]*12
Port.Anua.StDev=prt.ef$frontier[,2]*12^.5
The weights will be the same for monthly or annualized portfolios.
prt.ef$frontier[,-(1:3)]
2) Transform your monthly returns in annualized returns multiplying by 12. Then do the optimization with the usual procedure, all risk and return will be already annualized in prt.ef$frontier.
Related to the jagged line in EF. Using your portfolio specification I was also able to recreate the same behavior. For the following plot I used edhec data, your specification with original mean and StdDev in the objectives:
data(edhec)
returns <- edhec[,1:3]
That behavior must be influenced by the specification or the optimization algorithm you are using. I did the same optimization with solve.QP from package quadprog. This is the result.
Update
The code is here:
require(quadprog)
#min_x(-d^T x + 1/2 b^T D x) r.t A.x>=b
MV_QP<-function(nx, tarRet, Sig=NULL,long_only=FALSE){
if (is.null(Sig)) Sig=cov(nx)
dvec=rep(0,ncol(Sig))
meq=2
Amat=rbind(rep(1,ncol(Sig)),
apply(nx,2,mean) )
bvec=c(1,tarRet )
if (long_only) {
meq=1
Amat=Amat[-1,]
Amat=rbind(Amat,
diag(1,ncol(Sig)),
rep(1,ncol(Sig)),
rep(-1,ncol(Sig)))
bvec=bvec[-1]
bvec=c(bvec,
rep(0,ncol(Sig)),.98,-1.02)
}
sol <- solve.QP(Dmat=Sig, dvec, t(Amat), bvec, meq=meq)$solution
}
steps=50
x=returns
µ.b <- apply(X = x, 2, FUN = mean)
long_only=TRUE
range.bl <- seq(from = min(µ.b), to = max(µ.b)*ifelse(long_only,1,1.6), length.out = steps)
risk.bl <- t(sapply(range.bl, function(targetReturn) {
w <- MV_QP(x, targetReturn,long_only=long_only)
c(sd(x %*% w),w) }))
weigthsl=round(risk.bl[,-1],4)
colnames(weigthsl)=colnames(x)
weigthsl
risk.bl=risk.bl[,1]
rets.bl= weigthsl%*%µ.b
fan=12
plot(x = risk.bl*fan^.5, y = rets.bl*fan,col=2,pch=21,
xlab = "Annualized Risk ",
ylab = "Annualized Return", main = "long only EF with solve.QP")
回答2:
Adding to Robert's comments, the optimization calculation with monthly returns is a quadratic programming problem with linear constraints. When mean is the return objective and StdDev or var is the risk objective, optimize.portfolio and create.EfficientFrontier select the ROI method as the solver which uses solve.QP, an efficient solver for these sorts of problems. When the risk objective is changed to pasd, these functions don't recognize this as a QP problem so use DEoptim a general nonlinear problem solver perhaps better suited to solving nonconvex problem rather than convex QP ones. See Differential Evolution with DEoptim . This seems to be the cause of the jagged efficient frontier.
In order to have create.EfficientFrontier use solve.QP, which is much more efficient and accurate for this type of problem, you can make a custom moment function to compute the mean and variance and then specify it with the argument momentFUN. However, create.EfficientFrontier at least in part uses means computed directly from the returns rather than using mu from momentFUN. To deal with that, multiply the returns and divide the variance by 12 as shown in the example below.
library(PortfolioAnalytics)
data(edhec)
returns <- edhec[,1:3]
# define moment function
annualized.moments <- function(R, scale=12, portfolio=NULL){
out <- list()
out$mu <- matrix(colMeans(R), ncol=1)
out$sigma <- cov(R)/scale
return(out)
}
# define portfolio
prt <- portfolio.spec(assets=colnames(returns))
prt <- add.constraint(portfolio=prt, type="long_only")
# leverage defaults to weight_sum = 1 so is equivalent to full_investment constraint
prt <- add.constraint(portfolio=prt, type="leverage")
prt <- add.objective(portfolio=prt, type="risk", name="StdDev")
# calculate and plot efficient frontier
prt_ef <- create.EfficientFrontier(R=12*returns, portfolio=prt, type="mean-StdDev",
match.col = "StdDev", momentFUN="annualized.moments", scale=12)
xlim <- range(prt_ef$frontier[,2])*c(1, 1.5)
ylim <- range(prt_ef$frontier[,1])*c(.80, 1.05)
chart.EfficientFrontier(prt_ef, match.col="StdDev", chart.assets = FALSE,
labels.assets = FALSE, xlim=xlim, ylim=ylim )
points(with(annualized.moments(12*returns, scale=12), cbind(sqrt(diag(sigma)), mu)), pch=19 )
text(with(annualized.moments(12*returns, scale=12), cbind(sqrt(diag(sigma)), mu)),
labels=colnames(returns), cex=.8, pos=4)
chart.EF.Weights(prt_ef, match.col="StdDev")
The means and standard deviations of the assets also need to be adjusted and so are plotted outside of chart.EfficientFrontier and shown on the chart below.
At the end of the day it would be simpler, as Robert suggests, to compute the weights for the efficient frontier using the monthly returns and then compute the portfolio returns and standard deviations using annualized asset means and standard deviations and the monthly weights which are the same in both cases. However, perhaps this example is useful to show the use of custom moment and objective functions.
回答3:
Does not find the reason of the error, but setting the limits it partially works!
prt.ef$frontier #see the EF
xylims=apply(prt.ef$frontier[,c(2,1)],2,range)*c(.98,1.01)
chart.EfficientFrontier(prt.ef, match.col="pasd",
main="Portfolio Optimization",
xlim=xylims[,1], ylim=xylims[,2])
#or
plot(prt.ef$frontier[,c(2,1)],col=2)
回答4:
ok so I tried the pasd function that WaltS suggested, and the chart.EfficientFrontier seemed to work but it gave me a jagged line and not a smooth line.
I have now created an annualized return function using this code:
pamean <- function(R, weights=NULL){Return.annualized(apply(as.xts(t(t(R) * weights)),1,sum))}
and added this as an objective to my portfolio prt.
> prt
**************************************************
PortfolioAnalytics Portfolio Specification
**************************************************
Call:
portfolio.spec(assets = colnames(returns))
Number of assets: 3
Asset Names
[1] "Global REITs" "Au REITs" "Au Util and Infra"
Constraints
Enabled constraint types
- long_only
- leverage
Objectives:
Enabled objective names
- pamean
- pasd
I then create the efficient frontier again using this line:
> prt.ef <- create.EfficientFrontier(R=returns, portfolio=prt, type="DEoptim", match.col="pasd")
but when I use the summary function I see that only 1 frontier point has been generated. What does the error msg mean and why was only 1 point generated?
> summary(prt.ef)
**************************************************
PortfolioAnalytics Efficient Frontier
**************************************************
Call:
create.EfficientFrontier(R = returns, portfolio = prt, type = "DEoptim",
match.col = "pasd")
Efficient Frontier Points: 1
Error in `colnames<-`(`*tmp*`, value = character(0)) :
attempt to set 'colnames' on an object with less than two dimensions
来源：https://stackoverflow.com/questions/30614457/r-portfolio-analytics-chart-efficientfrontier-function