Category Archives: Allgemein
A linear model using R (quality of life vs. crime)
Audio Mastering Techniques – Certificate of Completion
Audio Mixing Master Class – Certificate of Completion
A day full of mixing.
ECR 2023
Some impressions from the ECR Congress 2023.
Calculating simple portfolio statistics with R
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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # World Bank Data using WDI Package # path: ~/ownCloud/ # file_name: # files_used: # files_created # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # rm(list = ls(all = TRUE)) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # packages #install.packages("httr") #install.packages("XML") #install.packages('WDI') #install.packages("magrittr") #install.packages("tidyverse") #install.packages("quantmod") #install.packages("PerformanceAnalytics") #install.packages("tidyquant") library("httr") library("XML") library("magrittr") library("tidyverse") library("WDI") library("quantmod") library("PerformanceAnalytics") #library("tidyquant") # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # system("ls") # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # using quantmod to collect data # selecting the date while downloading MCD <- quantmod::getSymbols("MCD",src = "yahoo", auto.assign=FALSE, from = "2007-06-01", to = "2012-07-01" ) head(MCD) tail(MCD) # or download the available data and selecting later MCD <- quantmod::getSymbols("MCD",src = "yahoo", auto.assign=FALSE ) head(MCD) tail(MCD) MCD <- MCD["2007-06-01/2012-07-01"] head(MCD) tail(MCD) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # download monthly data MCD <- quantmod::getSymbols("MCD",src = "yahoo", auto.assign=FALSE, from = "2007-06-01", to = "2012-07-01", periodicity = "monthly" ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # alternative ways #stock_list <- c( "IBM", "MCD" ) # #stocks_weekly <- tq_get(stock_list, # from = start_date, # to = end_date, # periodicity = "weekly") #stocks_weekly #install.packages("BatchGetSymbols") #library(BatchGetSymbols) #stocks <- BatchGetSymbols( c( "IBM", "MCD" ), # first.date = "2007-06-01", # last.date = "2012-07-01", # freq.data = "monthly", # how.to.aggregate = 'first') #stocks # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # for now lets use the example time series IBM <- read.csv("IBM.csv") MCD <- read.csv("MCD.csv") head(IBM) IBM$Adj.Close MCD$Adj.Close data <- data.frame(IBM$Adj.Close,MCD$Adj.Close) data[,3] <- NA data[,4] <- NA data log( IBM$Adj.Close[2] / IBM$Adj.Close[1] ) # log computes logarithms, by default natural logarithms, # log10 computes common (i.e., base 10) logarithms, and # log2 computes binary (i.e., base 2) logarithms. for(i in 2: length(data[,1]) ){ data[i,3] <- ( log( data[i,1] / data[i-1,1] ) ) } data for(i in 2: length(data[,2]) ){ data[i,4] <- ( log( data[i,2] / data[i-1,2] ) ) } data colnames(data)[3] <- "IBM.Adj.roc" colnames(data)[4] <- "MCD.Adj.roc" head( data ) #in comparison: the ROC function from the quantmod package # computes the standard deviation of the values in x. If na.rm is TRUE # then missing values are removed before computation proceeds. ROC( data$IBM.Adj.Close ) str( as.numeric( data$IBM.Adj.roc[2] ) ) str( as.numeric( ROC( data$IBM.Adj.Close )[2] ) ) as.numeric( ROC( data$IBM.Adj.Close ) ) == as.numeric( data$IBM.Adj.roc ) as.numeric( ROC( data$IBM.Adj.Close )[2] ) == as.numeric( data$IBM.Adj.roc[2] ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # why are they not exactly the same? Starting with the 16th digit the # numbers differ. # the continuous formulation of ROC is : roc <- diff(log(x), n, na.pad = na.pad) # this gives the small difference compared to what we calculated first # log( t / (t-1) ) # lets try the same diff( log( data$IBM.Adj.Close ) ) ROC( data$IBM.Adj.Close )[2:length(data$IBM.Adj.Close)] == diff( log( data$IBM.Adj.Close ) ) # now it is exactly the same, but for practical reasons such # minuscule differences do not really matter. # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # if we use the first 5 digits the numbers are exactly the same print( ROC( data$IBM.Adj.Close )[2], digits = 20 ) print( as.numeric( data$IBM.Adj.roc )[2], digits = 20 ) round( as.numeric( data$IBM.Adj.roc ), 5) round( as.numeric( ROC( data$IBM.Adj.Close ) ), 5 ) round( as.numeric( data$IBM.Adj.roc ), 5) == round( as.numeric( ROC( data$IBM.Adj.Close ) ), 5 ) #options( digits = 10 ) # Modify global options # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # the data preparation phase is somewhat more intensive if using # a programming tool like R but in the long run i think # i pays off by having more accessible data that can be processed in a # much faster way especially if it comes to big data applications summary( data ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculating the mean with a function and out of the data mean( na.omit( data[,3] ) ) mean( na.omit( data[,4] ) ) sum( na.omit( data[,3] ) ) / length( na.omit( data[,3] ) ) sum( na.omit( data[,4] ) ) / length( na.omit( data[,4] ) ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex formulas # Mean = \frac{1}{N} \sum_{i=1}^{N} r_i # population and sample mean # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # var( na.omit( data[,3] ) ) data[,3] - mean( na.omit( data[,3] ) ) # demeaning ( data[,3] - mean( na.omit( data[,3] ) ) )^2 # power of 2 sum( na.omit( ( data[,3] - mean( na.omit( data[,3] ) ) )^2 ) ) # sum with drop NA sum( na.omit( ( data[,3] - mean( na.omit( data[,3] ) ) )^2 ) ) / ( length( na.omit( data[,3] ) ) - 1 ) # NA is also omitted for length and we use the sample variance # therefore we divide by (n-1) var( na.omit( data[,4] ) ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex formulas # Var.p = \frac{1}{N} \sum_{i=1}^{N} (r_i-\bar{r})^2 # Var.s = \frac{1}{N-1} \sum_{i=1}^{N} (r_i-\bar{r})^2 # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # # stats:: calls the package directly # this is not really necessary unless there are functions with the # same name in different packages. Then one might be masked be the other # SD IBM stats::sd( data[,3] , na.rm = TRUE ) sd( data[,3] , na.rm = TRUE ) # the squqre root of the variance gives us the standard deviation sqrt( var( na.omit( data[,3] ) ) ) # the long way: sqrt( sum( na.omit( ( data[,3] - mean( na.omit( data[,3] ) ) )^2 ) ) / ( length( na.omit( data[,3] ) ) - 1 ) ) # SD MCD stats::sd( data[,4] , na.rm = TRUE ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex formulas standard deviation #Stdev.p = \sqrt{ \frac{1}{N} \sum_{i=1}^{N} (r_i-\bar{r})^2 } #Stdev.s = \sqrt{ \frac{1}{N-1} \sum_{i=1}^{N} (r_i-\bar{r})^2 } # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculate covariance cov( na.omit(data$IBM.Adj.roc), na.omit(data$MCD.Adj.roc) ) # this gives the sample covariance # calculation by hand na.omit( data$IBM.Adj.roc ) - mean( na.omit( data$IBM.Adj.roc ) ) na.omit( data$MCD.Adj.roc ) - mean( na.omit( data$MCD.Adj.roc ) ) ( na.omit( data$IBM.Adj.roc ) - mean( na.omit( data$IBM.Adj.roc ) ) )* ( na.omit( data$MCD.Adj.roc ) - mean( na.omit( data$MCD.Adj.roc ) ) ) sum( ( na.omit( data$IBM.Adj.roc ) - mean( na.omit( data$IBM.Adj.roc ) ) )* ( na.omit( data$MCD.Adj.roc ) - mean( na.omit( data$MCD.Adj.roc ) ) ) ) / length( na.omit( data$IBM.Adj.roc ) ) * 60/59 # length( na.omit( data$IBM.Adj.roc ) ) == 60 # Population covariance # * (n-1)/n cov( na.omit(data$IBM.Adj.roc), na.omit(data$MCD.Adj.roc) ) * (60-1)/60 # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex formulas Covariances # Covariance.p = \frac{1}{N} \sum_{t=1}^{N} (r_{it}-\bar{r}_i)(r_{jt}-\bar{r}_j) # Covariance.s = \frac{1}{N-1} \sum_{t=1}^{N} (r_{it}-\bar{r}_i)(r_{jt}-\bar{r}_j) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculating correlation - sample correlation cor( na.omit(data$IBM.Adj.roc), na.omit(data$MCD.Adj.roc) ) cov( na.omit(data$IBM.Adj.roc), na.omit(data$MCD.Adj.roc) ) / ( sqrt( var( na.omit( data[,3] ) ) ) * sqrt( var( na.omit( data[,4] ) ) ) ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex formulas Correlation # Correl(i,j) = \frac{Covar.p(i,j)}{Stdev.p(i)*Stdev.p(j)} # the full formula # Correl(i,j) = \frac{Covariance.p = \frac{1}{N} \sum_{t=1}^{N} (r_{it}-\bar{r}_i)(r_{jt}-\bar{r}_j)}{Stdev.p_{(i)} = \sqrt{ \frac{1}{N} \sum_{t=1}^{N} (r_{it}-\bar{r}_i)^2 }*Stdev.p_{(j)} = \sqrt{ \frac{1}{N} \sum_{t=1}^{N} (r_{jt}-\bar{r}_j)^2 }} # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # ploting return series plot( na.omit(data$IBM.Adj.roc), na.omit(data$MCD.Adj.roc), xlab = "IBM", ylab = "MCD", frame.plot = FALSE, axes = TRUE, xgap.axis = 4, ygap.axis = 4,pch=2) model <- lm( na.omit(data$IBM.Adj.roc) ~ na.omit(data$MCD.Adj.roc) ) abline(model$coefficients, col="red") abline( h=0, v=0, lty = 3 ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculating portfolio performance data[,3:4] ratio.ibm <- 0.5 ratio.mcd <- (1 - ratio.ibm) data[,5] <- NA data for(i in 2: length(data[,3]) ){ data[i,5] <- ( data[i,3] * ratio.ibm ) + ( data[i,4] * ratio.mcd ) } colnames(data)[5] <- "portfolio.performance" data head( data ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # portfolio performance values mean( na.omit( data$portfolio.performance ) ) var( na.omit( data$portfolio.performance ) ) sqrt( var( na.omit( data$portfolio.performance ) ) ) # sd( na.omit( data$portfolio.performance ) ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculating different portfolios ratios <- seq( 0, 1, by = 0.1 ) result <- NULL for(i in 1:length(ratios) ) { ratio.ibm <- ratios[i] ratio.mcd <- (1 - ratio.ibm) data[,5] <- NA data for(i in 2: length(data[,3]) ){ data[i,5] <- ( data[i,3] * ratio.ibm ) + ( data[i,4] * ratio.mcd ) } colnames(data)[5] <- "portfolio.performance" m <- mean( na.omit( data$portfolio.performance ) ) s <- sqrt( var( na.omit( data$portfolio.performance ) ) ) frame <- data.frame( m, s ) result <- data.frame( rbind( result, frame ) ) } result # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # ploting values plot( result$s, result$m, type = "b", xlab = "PF-SD", ylab = "PF-Return", frame.plot = FALSE, axes = TRUE, xgap.axis = 4, ygap.axis = 4,pch=2) #model <- lm( result$m ~ result$s ) #abline(model$coefficients, col="red") plot( result$s, result$m, type = "b", xlim = c(0.035,0.06), ylim = c(0.0117,0.0122), xlab = "PF-SD", ylab = "PF-Return", frame.plot = FALSE, axes = TRUE, xgap.axis = 4, ygap.axis = 4, pch=2) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # calculating more portfolios values including the option for shorting ratios <- seq( -3, 3, by = 0.1 ) result <- NULL for(i in 1:length(ratios) ) { ratio.ibm <- ratios[i] ratio.mcd <- (1 - ratio.ibm) data[,5] <- NA data for(i in 2: length(data[,3]) ){ data[i,5] <- ( data[i,3] * ratio.ibm ) + ( data[i,4] * ratio.mcd ) } colnames(data)[5] <- "portfolio.performance" m <- mean( na.omit( data$portfolio.performance ) ) s <- sqrt( var( na.omit( data$portfolio.performance ) ) ) frame <- data.frame( m, s, ratio.ibm, ratio.mcd ) result <- data.frame( rbind( result, frame ) ) } result # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # ploting values plot( result$s, result$m, type = "b", xlab = "PF-SD", ylab = "PF-Return", frame.plot = FALSE, axes = TRUE, xgap.axis = 4, ygap.axis = 4,pch=2) which( round( result$s,4) == round(min( result$s ),4) ) sep.line <- result[which( round( result$s,4) == round(min( result$s ),4) ),1] abline( h = sep.line , lty = 3, col = "red") # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # The next step would be to calculate values for n asset portfolio min( result$s ) dplyr::filter( result, s == min( result$s ) ) # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # # latex vector notation # x=\begin{bmatrix} x_1 \\ x_2 \\ ... \\ x_N \end{bmatrix} |
D7 – Music
Engineering (FOH) at Starmania Tour 2021
Some Impressions from the Starmania Tour 2021. I operated the shows in Linz, Innsbruck and Vienna. It was a lot of fun to work with all the young talents at the show. 🙂
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A trip to Marchegg
