Portfolio Frontier 不适用于大型数据集
Portfolio Frontier not Working for large dataset
自 2012 年以来，我有一个包含股票 returns 的时间序列对象。在我将数据集扩展到超出月数之前，portfolioFrontier 函数可以很好地创建我的效率边界。例如，我正在查看 39 个月，38 只股票一切正常。但是一旦我添加了第 39 只股票（和第 40 只等），我就得到了一个错误。代码和错误如下。
输入：
returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275,
0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251,
0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002,
0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117,
0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162,
0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136,
0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039,
0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044,
0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132,
0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("Stock.A", "Stock.B",
"Stock.C", "Stock.D", "Stock.E", "Stock.F", "Stock.G", "Stock.H",
"Stock.I", "Stock.J")))
, units = c("Stock.A", "Stock.B", "Stock.C", "Stock.D", "Stock.E", "Stock.F",
"Stock.G", "Stock.H", "Stock.I", "Stock.J")
, positions = c(1327968000, 1330473600, 1333152000, 1335744000, 1338422400,
1341014400, 1343692800, 1346371200)
, format = "%Y-%m-%d"
, FinCenter = "GMT"
, recordIDs = structure(list(), .Names = character(0), row.names = integer(0), class = "data.frame")
, title = "Time Series Object"
, documentation = "Tue Jun 23 13:48:36 2015"
)
代码：
library(timeSeries)
library(fPortfolio)
# returns <- read.csv("Not Working Excel File.csv")
#lct <- Sys.getlocale("LC_TIME"); Sys.setlocale("LC_TIME", "C")
#returns[,1] = as.Date(as.character(returns[,1]),format="%d-%b-%y")
#Sys.setlocale("LC_TIME", lct)
#returns = timeSeries(returns[,-1], charvec = returns[,1])
Frontier <- portfolioFrontier(returns)
错误：
Error in `colnames<-`(`*tmp*`, value = c("AAPL", :
attempt to set 'colnames' on an object with less than two dimensions
我该如何解决这个问题，以便在不添加日期的情况下添加我想要的股票数量？
编辑：这是数据集的快照。 http://i.imgur.com/i0hkBdY.png
所以在这个有 8 个月数据和只有四只股票的例子中，我上面发布的代码工作正常。但是一旦我再添加 5 只股票（总共 9 只），我就会收到上面列出的错误。
将数据框更改为矩阵会产生相同的错误。
添加更多的月份可以让我添加更多的股票，但我不想要更多的月份。
问题
您无法在不添加更多月（年）的情况下添加更多股票的原因似乎与最小化均值方差的问题有关。
来自 Cochrane "Asset Pricing" 第 81-83 页：
Theorem: So long as the variance-covariance matrix of returns is non-singular, there is a mean-variance frontier.
The problem “choose a portfolio to minimize variance
for a given mean” is then
min{w} w0 Σw s.t. w0
您可以使用书中概述的拉格朗日乘数法来解决这个问题。然而，有趣的是 returns 的协方差矩阵必须是非奇异的，这意味着协方差矩阵必须是 Positive Definite。如果您提供的用于计算边界的协方差矩阵是奇异的，那么边界将不存在。
一个例子
输入：
returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275,
0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251,
0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002,
0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117,
0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162,
0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136,
0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039,
0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044,
0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132,
0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("StockA", "StockB",
"StockC", "StockD", "StockE", "StockF", "StockG", "StockH",
"StockI", "StockJ")))
, units = c("StockA", "StockB", "StockC", "StockD", "StockE", "StockF",
"StockG", "StockH", "StockI", "StockJ")
, positions = c(1327968000, 1330473600, 1333152000, 1335744000, 1338422400,
1341014400, 1343692800, 1346371200)
, format = "%Y-%m-%d"
, FinCenter = "GMT"
, recordIDs = structure(list(), .Names = character(0), row.names = integer(0), class = "data.frame")
, title = "Time Series Object"
, documentation = "Tue Jun 23 13:48:36 2015"
)
代码块 1：
# Load Matrix Checks
library(matrixcalc)
# Get dimensions and check if positive definite
dim(returns)
is.positive.definite(cov(returns))
### Results ###
# > dim(returns)
# [1] 8 10
# > is.positive.definite(cov(returns))
# [1] FALSE
如您所见，协方差矩阵不是正定的，如果您尝试使用 portfolioFrontier() 它将引发错误。
> portfolioFrontier(returns)
Error in `colnames<-`(`*tmp*`, value = c("StockA", "StockB", "StockC", :
attempt to set 'colnames' on an object with less than two dimensions
代码块 2：
# Remove first three columns to fit n (obs) > m (stocks)
returns <- returns[,4:10]
dim(returns)
#Check if positive definite
is.positive.definite(cov(returns))
### Results ###
# > dim(returns)
# [1] 8 7
# > is.positive.definite(cov(returns))
# [1] TRUE
现在检查portfolioFrontier()
输出：
Title:
MV Portfolio Frontier
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints: LongOnly
Portfolio Points: 5 of 50
Portfolio Weights:
StockD StockE StockF StockG StockH StockI StockJ
1 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
13 0.0000 0.0000 0.0000 0.1452 0.5016 0.2566 0.0966
25 0.0000 0.0000 0.0000 0.0000 0.1345 0.6738 0.1917
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.4758 0.5242
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Covariance Risk Budgets:
StockD StockE StockF StockG StockH StockI StockJ
1 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
13 0.0000 0.0000 0.0000 0.1417 -0.0570 0.4871 0.4282
25 0.0000 0.0000 0.0000 0.0000 -0.0455 0.5865 0.4589
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.2196 0.7804
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Target Returns and Risks:
mean Cov CVaR VaR
1 0.0001 0.0056 0.0080 0.0080
13 0.0048 0.0037 0.0025 0.0025
25 0.0094 0.0092 0.0122 0.0122
37 0.0141 0.0158 0.0238 0.0238
50 0.0191 0.0237 0.0370 0.0370
似乎正在工作。因此，让我们绘制有效边界：
portfolio <- portfolioFrontier(returns)
plot(portfolio)
自 2012 年以来，我有一个包含股票 returns 的时间序列对象。在我将数据集扩展到超出月数之前，portfolioFrontier 函数可以很好地创建我的效率边界。例如，我正在查看 39 个月，38 只股票一切正常。但是一旦我添加了第 39 只股票（和第 40 只等），我就得到了一个错误。代码和错误如下。
输入：
returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275,
0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251,
0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002,
0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117,
0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162,
0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136,
0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039,
0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044,
0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132,
0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("Stock.A", "Stock.B",
"Stock.C", "Stock.D", "Stock.E", "Stock.F", "Stock.G", "Stock.H",
"Stock.I", "Stock.J")))
, units = c("Stock.A", "Stock.B", "Stock.C", "Stock.D", "Stock.E", "Stock.F",
"Stock.G", "Stock.H", "Stock.I", "Stock.J")
, positions = c(1327968000, 1330473600, 1333152000, 1335744000, 1338422400,
1341014400, 1343692800, 1346371200)
, format = "%Y-%m-%d"
, FinCenter = "GMT"
, recordIDs = structure(list(), .Names = character(0), row.names = integer(0), class = "data.frame")
, title = "Time Series Object"
, documentation = "Tue Jun 23 13:48:36 2015"
)
代码：
library(timeSeries)
library(fPortfolio)
# returns <- read.csv("Not Working Excel File.csv")
#lct <- Sys.getlocale("LC_TIME"); Sys.setlocale("LC_TIME", "C")
#returns[,1] = as.Date(as.character(returns[,1]),format="%d-%b-%y")
#Sys.setlocale("LC_TIME", lct)
#returns = timeSeries(returns[,-1], charvec = returns[,1])
Frontier <- portfolioFrontier(returns)
错误：
Error in `colnames<-`(`*tmp*`, value = c("AAPL", :
attempt to set 'colnames' on an object with less than two dimensions
我该如何解决这个问题，以便在不添加日期的情况下添加我想要的股票数量？
编辑：这是数据集的快照。 http://i.imgur.com/i0hkBdY.png 所以在这个有 8 个月数据和只有四只股票的例子中，我上面发布的代码工作正常。但是一旦我再添加 5 只股票（总共 9 只），我就会收到上面列出的错误。
将数据框更改为矩阵会产生相同的错误。 添加更多的月份可以让我添加更多的股票，但我不想要更多的月份。
问题
您无法在不添加更多月（年）的情况下添加更多股票的原因似乎与最小化均值方差的问题有关。
来自 Cochrane "Asset Pricing" 第 81-83 页：
Theorem: So long as the variance-covariance matrix of returns is non-singular, there is a mean-variance frontier.
The problem “choose a portfolio to minimize variance for a given mean” is then
min{w} w0 Σw s.t. w0
您可以使用书中概述的拉格朗日乘数法来解决这个问题。然而，有趣的是 returns 的协方差矩阵必须是非奇异的，这意味着协方差矩阵必须是 Positive Definite。如果您提供的用于计算边界的协方差矩阵是奇异的，那么边界将不存在。
一个例子
输入：
returns <- new("timeSeries", .Data = structure(c(-0.0108, 0.005, -0.0059, 0.0067, -0.0069, -0.0275,
0.0226, 0.0089, 0.0469, 0.0193, -5e-04, -0.03, -0.0483, 0.0251,
0.013, 0.0202, 0.019, 0.015, 0.0091, 0.002, -0.014, 0.0046, 0.002,
0.025, 0.008, 0.0177, -0.0023, 0.0023, -0.0217, 0.0045, 0.0117,
0.0081, 0.0345, 0.0332, 0.0098, 0.0086, -0.0362, -0.0137, 0.0162,
0.0276, 0.0749, 0.0691, 0.0275, -0.0278, -0.0442, 0.0226, -0.0136,
0.0305, 0.0178, 0.0061, 0.0034, 0.0039, -0.0042, -0.0017, 0.0039,
0.0083, -0.008, -0.0044, 7e-04, 0.0018, 0.008, -0.0057, 0.0044,
0.0043, 0.012, 0.0134, 0.003, 0.0078, -0.0092, 0.0113, 0.0132,
0.0168, 0.032, 0.037, 0.033, 0.017, -0.037, 0.027, 0.026, 0.018
), .Dim = c(8L, 10L), .Dimnames = list(NULL, c("StockA", "StockB",
"StockC", "StockD", "StockE", "StockF", "StockG", "StockH",
"StockI", "StockJ")))
, units = c("StockA", "StockB", "StockC", "StockD", "StockE", "StockF",
"StockG", "StockH", "StockI", "StockJ")
, positions = c(1327968000, 1330473600, 1333152000, 1335744000, 1338422400,
1341014400, 1343692800, 1346371200)
, format = "%Y-%m-%d"
, FinCenter = "GMT"
, recordIDs = structure(list(), .Names = character(0), row.names = integer(0), class = "data.frame")
, title = "Time Series Object"
, documentation = "Tue Jun 23 13:48:36 2015"
)
代码块 1：
# Load Matrix Checks
library(matrixcalc)
# Get dimensions and check if positive definite
dim(returns)
is.positive.definite(cov(returns))
### Results ###
# > dim(returns)
# [1] 8 10
# > is.positive.definite(cov(returns))
# [1] FALSE
如您所见，协方差矩阵不是正定的，如果您尝试使用 portfolioFrontier() 它将引发错误。
> portfolioFrontier(returns)
Error in `colnames<-`(`*tmp*`, value = c("StockA", "StockB", "StockC", :
attempt to set 'colnames' on an object with less than two dimensions
代码块 2：
# Remove first three columns to fit n (obs) > m (stocks)
returns <- returns[,4:10]
dim(returns)
#Check if positive definite
is.positive.definite(cov(returns))
### Results ###
# > dim(returns)
# [1] 8 7
# > is.positive.definite(cov(returns))
# [1] TRUE
现在检查portfolioFrontier()
输出：
Title:
MV Portfolio Frontier
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints: LongOnly
Portfolio Points: 5 of 50
Portfolio Weights:
StockD StockE StockF StockG StockH StockI StockJ
1 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
13 0.0000 0.0000 0.0000 0.1452 0.5016 0.2566 0.0966
25 0.0000 0.0000 0.0000 0.0000 0.1345 0.6738 0.1917
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.4758 0.5242
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Covariance Risk Budgets:
StockD StockE StockF StockG StockH StockI StockJ
1 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
13 0.0000 0.0000 0.0000 0.1417 -0.0570 0.4871 0.4282
25 0.0000 0.0000 0.0000 0.0000 -0.0455 0.5865 0.4589
37 0.0000 0.0000 0.0000 0.0000 0.0000 0.2196 0.7804
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
Target Returns and Risks:
mean Cov CVaR VaR
1 0.0001 0.0056 0.0080 0.0080
13 0.0048 0.0037 0.0025 0.0025
25 0.0094 0.0092 0.0122 0.0122
37 0.0141 0.0158 0.0238 0.0238
50 0.0191 0.0237 0.0370 0.0370
似乎正在工作。因此，让我们绘制有效边界：
portfolio <- portfolioFrontier(returns)
plot(portfolio)