投资组合优化SOLVE.QP不等式约束 [英] Portfolio Optimization SOLVE.QP inequality constraints

问题描述

我的名字是Grégory，我试图计算一个具有以下约束的最小方差组合：

My name is Grégory and I am trying to compute a Minimum Variance portfolio with the following constraints:

1. 等于1（投资组合可以完全投资，但它不是一种义务）


2. 总和高于或等于0（投资组合可以完全是现金，但不是一个义务）



3. 0 <=资产重量<= 5％（不允许短期销售，最大资产重量为5％）

1. Sum of the weights lower or equal to 1 (the portfolio can be fully invested, but it's not an obligation)
2. Sum of the weights higher or equal to 0 (the portfolio can be fully in cash, but it's not an obligation)

3. 0<= Asset weight <= 5% (no short-sales are allowed, and the maximum asset weight is 5%)

MV <-function（Returns，percentage = TRUE，...）
{
if（is.null {
stop（'Returns'的参数必须为rectangle.\\\
）
}
call< - match.call（）
V&返回，...）
V< - make.positive.definite（V）
N< - ncol（返回）
a1< b $ b b1 < - -1
a2 < - diag（N）
b2 <-rep（0，N）
c1 <已经添加到模型中（说：min 5％）
c2 <-rep（-0.05，N）##这已被添加到模型中（说：min 5％）
c3 ; - rep（1，N）
c4 < - 0
Amat < - cbind（a1，c3，a2，c1）###对应于定义不同约束的矩阵
Bvec < - c（b1，c4，b2，c2）###对应于约束的向量
Dvec <-rep（0，N）###设置为0，因为例程的第一项必须等于0
＃meq <-c（1,1，rep（1，N），rep（1，N））
opt < dvc = Dvec，Amat = Amat，bvec = Bvec，meq = 0）
w_mv < - opt $ solution
names（w_mv）
w_mv< - w_mv * 100
return（w_mv）
}

当我查看MV投资组合权重时，所有资产权重都等于0，因此我不知道错误来自何处。

When I look at the MV portfolio weights, all the asset weights are equal to 0, so I don't know where the error comes from.

如果你能帮助我，我会非常感谢。

I would be very grateful if you could help me.

非常感谢，

Grégory

推荐答案

library(stockPortfolio) # Base package for retrieving returns
library(ggplot2) # Used to graph efficient frontier
library(reshape2) # Used to melt the data
library(quadprog) #Needed for solve.QP

# Create the portfolio using ETFs, incl. hypothetical non-efficient allocation
stocks <- c(
 "VTSMX" = .0,
 "SPY" = .20,
 "EFA" = .10,
 "IWM" = .10,
 "VWO" = .30,
 "LQD" = .20,
 "HYG" = .10)

# Retrieve returns, from earliest start date possible (where all stocks have
# data) through most recent date
returns <- getReturns(names(stocks[-1]), freq="week") #Currently, drop index

#### Efficient Frontier function ####
eff.frontier <- function (returns, short="no", max.allocation=NULL,
 risk.premium.up=.5, risk.increment=.005){
 # return argument should be a m x n matrix with one column per security
 # short argument is whether short-selling is allowed; default is no (short
 # selling prohibited)max.allocation is the maximum % allowed for any one
 # security (reduces concentration) risk.premium.up is the upper limit of the
 # risk premium modeled (see for loop below) and risk.increment is the
 # increment (by) value used in the for loop

 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
 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 along the EF
 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))
}

# Run the eff.frontier function based on no short and 50% alloc. restrictions
eff <- eff.frontier(returns=returns$R, short="no", max.allocation=.50,
 risk.premium.up=1, risk.increment=.001)

# Find the optimal portfolio
eff.optimal.point <- eff[eff$sharpe==max(eff$sharpe),]

# graph efficient frontier
# Start with color scheme
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)", y="Return") +
 theme(panel.background=element_rect(fill=eallighttan),
 text=element_text(color=ealdark),
 plot.title=element_text(size=24, color=ealred))
ggsave("Efficient Frontier.png")

下面的链接中有一个很好的解释。

There is a good explanation of how this works at the link below.

http：// economistatlarge。 com / portfolio-theory / r-optimized-portfolio

这篇关于投资组合优化SOLVE.QP不等式约束的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！