fPortfolio (version 240.10068)

TwoAssetsPortfolio: Two Assets Portfolio

Description

A collection and description of functions to investigate the efficient frontier for a two assets portfolio from a given return series in the mean-variance and CVaR sense when short selling is forbidden. The functions are: ll{ twoAssetsMarkowitz Efficient frontier for Markowitz PF, twoAssetsCVaR Efficient frontier for CVaR PF. }

Usage

frontierTwoAssetsMarkowitz(x, length = 100, 
    title = NULL, description = NULL) 
frontierTwoAssetsCVaR(x, length= 100, alpha = 0.05,
    title = NULL, description = NULL) 
    
## S3 method for class 'fPFOLIO2':
print(x, \dots)
## S3 method for class 'fPFOLIO2':
plot(x, \dots)
## S3 method for class 'fPFOLIO2':
summary(object, \dots)

Arguments

alpha

a numeric value, the confidence interval, by default 0.05.

description

a character string, assigning a brief description to an "fPFOLIO" object.

length

the number of equidistand return points on the efficient frontier.

object

[summary] - cr an object of class "fPFOLIO2".

title

a character string, assigning a title to an "fPFOLIO" object.

x

[frontier*] - a numeric matrix or multivariate time series consisting of a series of returns. [print][plot] - cr an object of class "fPFOLIO2".

...

optional arguments to be passed.

Value

• frontierTwoAssetsMarkowitz frontierTwoAssetsCVaR return a S4 object class of class "fPFOLIO2", with the following slots:
• @call
  the matched function call.
• @data
  the input data in form of a data.frame.
• @description
  allows for a brief project description.
• @pfolio
  the results as a list returned from the underlying analytical results.
• @method
  the selected method used by the optimization algorithm, here "Exact Analytical Solution".
• @model
  the model used for the optimization, here "Two Assets Markowitz Portfolio" or "Two Assets CVaR Portfolio.
• @title
  a title string.
• The @pfolio slot is a list with the following compontents: (Note, not all are documented here).
• pm, ps
  the portfolios mean (the return) and standard deviation (the risk) values .

References

Elton E.J., Gruber M.J. (1991); Modern Portfolio Theory and Investment Analysis, 4th Edition, Wiley, NY, pp. 65--93.

Examples

## SOURCE("fPortfolio.102B-TwoAssetsPortfolio")

## berndtInvest -
   xmpPortfolio("\nStart: Load monthly data set of returns > ")
   data(berndtInvest)
   # Select "IBM" and "DEC"
   twoAssets = berndtInvest[, c("IBM", "DEC")]
   rownames(twoAssets) = berndtInvest[, 1]
   head(twoAssets)
   
## Compute Efficient Frontier:
   myPortfolio = frontierTwoAssetsMarkowitz(twoAssets)
   
## Print Efficient Frontier:
   print(myPortfolio)
    
## Plot Efficient Frontier:
   plot(myPortfolio)
   
## Compute Efficient Frontier:
   myPortfolio = frontierTwoAssetsCVaR(twoAssets)
   
## Print Efficient Frontier:
   print(myPortfolio)
    
## Plot Efficient Frontier:
   plot(myPortfolio)
   
  
  
    show = function(i, j) { 
        w = (0:100)/100 
        alpha = 0.04
        par(mfrow = c(2, 2), cex = 0.5)
        
        print(c(i, j))
        twoAssets = cbind(berndtInvest[, i], berndtInvest[, j])
        print(head(twoAssets))
        
        means = apply(twoAssets, 2, mean)
        x.Return = y.VaR = y.CVaR = y.CVaRplus = NULL
        for (k in 1:101) {
            weights = c(w[k], 1-w[k])
            x.Return = c(x.Return, weights            y.VaR = c(y.VaR, -VaR(twoAssets, weights, alpha))
            y.CVaR = c(y.CVaR, -CVaR(twoAssets, weights, alpha))
            y.CVaRplus = c(y.CVaRplus, -CVaRplus(twoAssets, weights, alpha))
        }
        plot(x = range(x.Return), y = range(c(y.VaR, y.CVaR, y.CVaRplus)), 
            xlab = as.character(i), ylab = as.character(j), type = "n")
        lines(x.Return, as.vector(y.VaR), col ="red")
        lines(x.Return, as.vector(y.CVaR), col = "green")
        lines(x.Return, as.vector(y.CVaRplus), col = "blue")
    }

    par(mfrow = c(1,1)) 
    w = (0:200)/200
    alpha = 0.04
    for (i in 2:17) {
        for (j in (i+1):18) {    
            twoAssets = cbind(berndtInvest[, i], berndtInvest[, j])   
            means = apply(twoAssets, 2, mean)
            x = NULL
            y = NULL
            for (k in 1:201) {
                weights = c(w[k], 1-w[k])
                x = c(x, weights                y = c(y, -CVaRplus(twoAssets, weights, alpha))
            }
            s = round(100*abs( y[201] - y[1] ) / ( max(y) - min(y)))
            print(c(i, j, s))
            plot(x, y, main = paste(as.character(i), as.character(j)))
        }
    }
    
    i = 5; j = 13
    twoAssets = cbind(berndtInvest[, i], berndtInvest[, j])     
    means = apply(twoAssets, 2, mean)
    x = y = NULL
    for (k in 1:201) {
        weights = c(w[k], 1-w[k])
        x = c(x, weights        y = c(y, -VaR(twoAssets, weights, alpha)) 
    }
    s = round(100*abs( y[201] - y[1] ) / ( max(y) - min(y)))
    plot(x, y, main = paste(as.character(i), as.character(j)))