Multivariate break test

In this tutorial, I explain how to implement, in a flexible way, the algorithm of Bai, Lumsdaine, and Stock (1998). Step 1: Lag variables. This function takes as argument a matrix of time series observations and lags it by an order (q). Code compute_lags <- function(Y #time series matrix Y , q) #lag order q { p <- dim(Y)[1] #get the dimensions n <- dim(Y)[2] myDates <- rownames(Y)[(q + 1) : p] #optional: keep the rownames dates of the data frame with final matching Y <- data.

Incremental efficient frontier

In this tutorial, I quickly describe how to compute and update an efficient frontier in adding stocks to an existing porfolio with R. Step 1: Efficient frontier First let’s write a simple code for an efficient frontier computation Code efficient_frontier = function(MRet #matrix of returns (MRet) , rangeMu) #range (sequence) of target expected returns (rangeMu) { uM <- dim(MRet)[1] #get the row (uM) and column (pM) dimensions of the matrix of returns pM <- dim(MRet)[2] expRet <- colMeans(MRet) #compute the portfolio's individual stocks expected returns Omega = var(MRet) #compute the sample var-covar matrix unityVec <- rep(1, pM) #define a constraints vector (weights of the portfolio must sum to one) A <- rbind(expRet, unityVec) #define a matrix of constraints (weights sum to one and variance will match a #target level of expected returns) n <- length(rangeMu) #get the length of the target range (sequence) myVar <- rep(NA, n) #define an empty variance vector myWeights <- matrix(data = NA, nrow = n, ncol = pM) #define an empty matrix of weights for each stock at each level of target #expected returns for(i in 1:n) #loop over the target expected returns range and compute variances and weights { b <- matrix(data = c(rangeMu[i], 1), nrow = 2) myVar[i] <- t(b) %*% solve(A %*% solve(Omega) %*% t(A)) %*% b myWeights[i,] <- solve(Omega) %*% t(A) %*% solve(A %*% solve(Omega) %*% t(A)) %*% b } mySd <- myVar^0.