如何解决R 中的递归 optim() 函数导致错误
我正在尝试使用 R 中的 optim() 函数来最小化矩阵运算的值。在这种情况下，我试图将一组股票的波动性降至最低，这些股票的单个回报彼此共变。被最小化的目标函数是 calculate_portfolio_variance。
library(quantmod)
filter_and_sort_symbols <- function(symbols)
{
# Name: filter_and_sort_symbols
# Purpose: Convert to uppercase if not
# and remove any non valid symbols
# Input: symbols = vector of stock tickers
# Output: filtered_symbols = filtered symbols
# convert symbols to uppercase
symbols <- toupper(symbols)
# Validate the symbol names
valid <- regexpr("^[A-Z]{2,4}$",symbols)
# Return only the valid ones
return(sort(symbols[valid == 1]))
}
# Create the list of stock tickers and check that they are valid symbols
tickers <- filter_and_sort_symbols(c("AAPL","NVDA","MLM","AA"))
benchmark <- "SPY"
# Set the start and end dates
start_date <- "2007-01-01"
end_date <- "2019-01-01"
# Gather the stock data using quantmod library
getSymbols(Symbols=tickers,from=start_date,to=end_date,auto.assign = TRUE)
getSymbols(benchmark,auto.assign = TRUE)
# Create a matrix of only the adj. prices
price_matrix <- NULL
for(ticker in tickers){price_matrix <- cbind(price_matrix,get(ticker)[,6])}
# Set the column names for the price matrix
colnames(price_matrix) <- tickers
benchmark_price_matrix <- NULL
benchmark_price_matrix <- cbind(benchmark_price_matrix,get(benchmark)[,6])
# Compute log returns
returns_matrix <- NULL
for(ticker in tickers){returns_matrix <- cbind(returns_matrix,annualReturn(get(ticker)))}
returns_covar <- cov(returns_matrix)
colnames(returns_covar) <- tickers
rownames(returns_covar) <- tickers
# get average returns for tickers and benchmark
ticker_avg <- NULL
for(ticker in tickers){ticker_avg <- cbind(ticker_avg,colMeans(annualReturn(get(ticker))))}
colnames(ticker_avg) <- tickers
benchmark_avg <- colMeans(annualReturn(get(benchmark)))
# create the objective function
calculate_portfolio_variance <- function(allocations,returns_covar,ticker_avg,benchmark_avg)
{
# Name: calculate_portfolio_variance
# Purpose: Computes expected portfolio variance,to be used as the minimization objective function
# Input: allocations = vector of allocations to be adjusted for optimality; returns_covar = covariance matrix of stock returns
# ticker_avg = vector of average returns for all tickers,benchmark_avg = benchmark avg. return
# Output: Expected portfolio variance
# get benchmark volatility
benchmark_variance <- (sd(annualReturn(get(benchmark))))^2
# scale allocations for 100% investment
allocations <- as.matrix(allocations/sum(allocations))
# get the naive allocations
naive_allocations <- rep(c(1/ncol(ticker_avg)),times=ncol(ticker_avg))
portfolio_return <- sum(t(allocations)*ticker_avg)
portfolio_variance <- t(allocations)%*%returns_covar%*%allocations
# constraints = portfolio expected return must be greater than benchmark avg. return and
# portfolio variance must be less than benchmark variance (i.e. a better reward at less risk)
if(portfolio_return < benchmark_avg | portfolio_variance > benchmark_variance)
{
allocations <- naive_allocations
}
portfolio_variance <- t(allocations)%*%returns_covar%*%allocations
return(portfolio_variance)
}
# Specify lower and upper bounds for the allocation percentages
lower <- rep(0,ncol(returns_matrix))
upper <- rep(1,ncol(returns_matrix))
# Initialize the allocations by evenly distributing among all tickers
set.seed(1234)
allocations <- rep(1/length(tickers),times=length(tickers))
> calculate_portfolio_variance(allocations,benchmark_avg)
[,1]
[1,] 0.1713439
> optim_result <- optim(par=allocations,fn=calculate_portfolio_variance(allocations,benchmark_avg),lower=lower,upper=upper,method="L-BFGS-B")
Error in t(allocations) %*% returns_covar : non-conformable arguments
我不确定原因，但可能与 optim() 递归使用 allocations 变量的方式有关。我该怎么做才能解决这个问题？
编辑：FWIW，其他优化策略有效（差分进化、模拟退火）但我更喜欢使用梯度下降，因为它要快得多
解决方法
如果第一个参数重命名为 par 并且您将 t() 应用于该侧翼矩阵乘法运算中使用的参数向量的顺序切换，则不会发生错误：
cpv <- function(par,returns_covar=returns_covar,ticker_avg,benchmark_avg)
{
# Name: calculate_portfolio_variance
# Purpose: Computes expected portfolio variance,to be used as the minimization objective function
# Input: allocations = vector of allocations to be adjusted for optimality; returns_covar = covariance matrix of stock returns
# ticker_avg = vector of average returns for all tickers,benchmark_avg = benchmark avg. return
# Output: Expected portfolio variance
# get benchmark volatility
benchmark_variance <- (sd(annualReturn(get(benchmark))))^2
# scale allocations for 100% investment
par <- as.matrix(par/sum(par))
# get the naive allocations
naive_allocations <- rep(c(1/ncol(ticker_avg)),times=ncol(ticker_avg))
portfolio_return <- sum(t(par)*ticker_avg);print(par)
portfolio_variance <- t(par)%*%returns_covar%*%par
# constraints = portfolio expected return must be greater than benchmark avg. return and
# portfolio variance must be less than benchmark variance (i.e. a better reward at less risk)
if(portfolio_return < benchmark_avg | portfolio_variance > benchmark_variance)
{
par <- naive_allocations
}
portfolio_variance <- t(par)%*%returns_covar%*%par
return(portfolio_variance)
}
我在代码中留下了par的调试打印，并显示了运行结果的顶部
optim_result <- optim(par=allocations,fn=cpv,lower=lower,upper=upper,ticker_avg=ticker_avg,benchmark_avg=benchmark_avg,method="L-BFGS-B")
[,1]
[1,] 0.25
[2,] 0.25
[3,] 0.25
[4,] 0.25
[,] 0.2507493
[2,] 0.2497502
[3,] 0.2497502
[4,] 0.2497502
[,] 0.2492492
[2,] 0.2502503
[3,] 0.2502503
[4,] 0.2502503
#--- snipped output of six more iterations.
...结果：
> optim_result
$par
[1] 0.25 0.25 0.25 0.25
$value
[1] 0.1713439
$counts
function gradient
1 1
$convergence
[1] 0
$message
[1] "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL"
正如我在对一个无关问题的评论中所说的那样，优化函数首先尝试升高然后降低 par 中的第一个元素，然后尝试对第二个、第三个和第四个元素执行相同的操作。在这一点上，它没有发现任何改进，它“决定”它收敛于局部最小值并宣布收敛。
我应该指出，optim 的代码是 rather old and the author of the original algorithm,Dr Nash，它以 the optimx package 的形式在 CRAN 上放置了一个更新版本。他说 optim 在当时很好，但他认为如果不成功，应该尝试其他程序。
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