DMDPS2.R

# install.packages("ggplot2")
# install.packages("reshape")
# install.packages("gridextra")

require(ggplot2)
require(reshape)
library(gridextra)

### ASSUMPTIONS ###

aReturn <- 0.15
bReturn <- 0.20
aStd <- 0.05
bStd <- 0.06

# correlations that we want to test 
corrs = seq(from=-0.6, to=0.6, by=0.3)


### FUNCTIONS ###

# dmd "namespace"
dmd = new.env()

dmd$ValidateRatio <- function(ratio){
  # Ratios of asset a to asset b need to be pairs of numbers that add to 1 (100%) 
  if( length(ratio) != 2 || ratio[1] + ratio[2] != 1 ){
    stop("Ratios need to be pairs of values that add to 1.")
  }
}

dmd$GetRatioLabel <- function(ratio){
  # concatenate ratio values to create a label
  # Args:
  #   ratio between asset a and asset b, list of two values whose sum is 1  b<-ratio[2]
  dmd$ValidateRatio(ratio)
  a<-ratio[1]
  b<-ratio[2]
  paste(round(a,2),":",round(b,2))
}

dmd$GetExpectedReturn <- function(ratio, aReturn, bReturn){
  # finds the mean (expectation) for a given asset ratio
  # Args:
  #   ratio: Ratio between asset a and asset b, list with two values whose sum is 1
  #   aReturn: Expected return on asset a
  #   bReturn: Expected return on asset b
  dmd$ValidateRatio(ratio)
  a<-ratio[1]
  b<-ratio[2]
  a*aReturn+b*bReturn
}

dmd$GetCombinedStd<-function(ratio, aReturn, bReturn, aStd, bStd, corr){
  # find the standard deviation for a given asset ratio combination and correlation
  # Args:
  #   ratio: Ratio between asset a and asset b, list with two values whose sum is 1
  #   aReturn: Expected return on asset a
  #   bReturn: Expected return on asset b
  #   aStd: Standard deviation of asset a
  #   bStd: Standard deviation of asset b
  #   corr: Correlation between asset a and asset b
  dmd$ValidateRatio(ratio)
  a<-ratio[1]
  b<-ratio[2]
  
  # standard deviation is square root of the combined variances
  sqrt( a^2*aStd^2 + b^2*bStd^2 + 2*a*b*aStd*bStd*corr )
}


### DATA ###

# set up ratios of asset A to asset B.
aamt=seq(from=0,to=1,by=0.05)

# As percentages, these ratios will always combine to equal 1
bamt=1-aamt

# merge ratio values into a single vector
assets = cbind(aamt, bamt)

# add labels for ratios (to display alongside data and in graph)
ratioLabels <- apply( assets, 1, dmd$GetRatioLabel )

# create a data frame combinedData to contain data, with ratio labels as the first column
combinedData <- data.frame( label = ratioLabels )

# find the expected return for each asset blend
expectedReturns = apply(assets, 1, dmd$GetExpectedReturn, aReturn, bReturn)

# add expected returns to the combinedData data frame as the "mean" column
combinedData <- cbind(combinedData, mean = expectedReturns)

# iterate through correlations to test each at every asset ratio
for(corr in corrs){
  
  # add data for each correlation to our data frame
  combinedData <- cbind(combinedData, apply(assets, 1, dmd$GetCombinedStd, aReturn, bReturn, aStd, bStd, corr))
  
  # label the column with the correlation value
  idx = length(combinedData)
  colnames(combinedData)[idx] <- paste("Std @",corr, " Corr")
}

grid.table(combinedData,gp=gpar(fontsize=6, lwd=2))


### GRAPHING ###

# melt data for graphing
melted = melt(combinedData, id.vars="label")

# ...and graph it!
ggplot() + geom_line(data=melted, aes(label,value,group=variable,color=variable)) + theme(axis.text.x = element_text(hjust=1, angle=45)) + xlab("Ratio of asset a to asset b")