使用Optimize R优化向量 [英] Optimizing for Vector Using Optimize R

问题描述

我想使用R的优化函数构造自己的优化.

I want to construct my own optimization using R's optimization function.

目标函数是分散率，以使其最大化(希望其正确):

The objective function is the diversification ratio, to maximize it (hope its correct):

div.ratio<-function(weight,vol,cov.mat){
  dr<-(t(weight) %*% vol) / (sqrt(t(weight) %*% cov.mat %*% (weight)))  
  return(-dr)
}

一个例子:

rm(list=ls())
require(RCurl)
sit = getURLContent('https://github.com/systematicinvestor/SIT/raw/master/sit.gz',     binary=TRUE, followlocation = TRUE, ssl.verifypeer = FALSE)
con = gzcon(rawConnection(sit, 'rb'))
source(con)
close(con)
load.packages('quantmod')


data <- new.env()

tickers<-spl("VTI,VGK,VWO,GLD,VNQ,TIP,TLT,AGG,LQD")
getSymbols(tickers, src = 'yahoo', from = '1980-01-01', env = data, auto.assign = T)
for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T)

bt.prep(data, align='remove.na', dates='1990::2013')

prices<-data$prices[,-10]  #don't include cash
ret<-na.omit(prices/mlag(prices) - 1)
vol<-apply(ret,2,sd)
cov.mat<-cov(ret)

optimize(div.ratio,
     weight,
     vol=vol,
     cov.mat=cov.mat,
     lower=0, #min constraints
     upper=1, #max 
     tol = 0.00001)$minimum 

我收到以下错误消息，似乎是优化程序包没有进行矢量优化.我做错了什么?

I get the following error message which seems to be it that optimization package doesn't do vector optimization. What did I do wrong?

Error in t(weight) %*% cov.mat : non-conformable arguments

推荐答案

首先，如果您要进行优化，则weight没有理由进入Optimize调用. 然后，optimize用于一维优化，同时您尝试求解权重向量.您可以改为使用optim函数.

First of all, weight has no reason to be in the optimize call if that's what you are trying to optimize. Then, optimize is for one-dimensional optimization while you are trying to solve for a vector of weights. You could use the optim function instead.

关于注释中的第二个问题，如何为函数设置一个总和为1的约束?您可以使用此处提出的技巧:如何在约束优化中将参数的总和设置为1 ，即按如下所示重写目标函数:

Regarding your second question in the comments, how do you set a constraint that it sums to 1 for the function? You can use the trick proposed here: How to set parameters' sum to 1 in constrained optimization, i.e, rewrite your objective function as follows:

div.ratio <- function(weight, vol, cov.mat){
  weight <- weight / sum(weight)
  dr <- (t(weight) %*% vol) / (sqrt(t(weight) %*% cov.mat %*% (weight)))  
  return(-dr)
}

这给出了:

out <- optim(par     = rep(1 / length(vol), length(vol)),  # initial guess
             fn      = div.ratio,
             vol     = vol,
             cov.mat = cov.mat,
             method  = "L-BFGS-B",
             lower   = 0,
             upper   = 1)

您的最佳体重:

opt.weights <- out$par / sum(out$par)
# [1] 0.154271776 0.131322307 0.073752360 0.030885856 0.370706931 0.049627627
# [7] 0.055785740 0.126062746 0.007584657

pie(opt.weights, names(vol))

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