Functionally Generated Portfolio Objects

Description

The function fgport is used to create functionally generated portfolio objects.

Usage

fgp(name, gen.function, weight.function)

Arguments

Details

The function fgp is used to create functionally generated portfolio objects. Detailed treatments of functionally generated portfolios can be found in Chapter 3 of Fernholz (2002) as well as Pal and Wong (2014). In brief, a functionally generated portfolio is determined by a generating function (gen.function) and the weight function (weight.function).

Some common functionally generated portfolios are provided in the package. For example, EntropyPortfolio is the entropy-weighted, DiversityPortfolio is a constructs fgp objects for the diversity-weigthed portfolio, and ConstantPortfolio defines constant-weighted portfolios.

The most important operation concerning fgp objects is Fernholz's decomposition. See FernholzDecomp for more details.

Value

References

Fernholz, E. R. (2002) Stochastic portfolio theory. Springer.

Pal, S. and T.-K. L. Wong (2014). The geometry of relative arbitrage. arXiv preprint arXiv:1402.3720.

See Also

FernholzDecomp

Examples

# Example 1: The diversity-weighted portfolio with p = 0.5
# This has the same effect has DiversityPortfolio(p = 0.5)
my.portfolio <- fgp("Diversity-Weighted Portfolio, p = 0.5",
                    function(x) (sum(sqrt(x)))^2,
                    function(x) sqrt(x) / sum(sqrt(x)))
                    
                    
# Example 2: A quadratic Gini coefficient
# See Example 3.4.7 of Fernholz (2002)

# Generating function
gen.function <- function(x) {
  n <- length(x)
  return(1 - sum((x - 1/n)^2)/2)
}

# Weight function
weight.function <- function(x) {
  n <- length(x)
  S <- gen.function(x) 
  return(((1/n - x)/S + 1 - sum(x*(1/n - x)/S))*x)
}

# Define fgp object
my.portfolio <- fgp("Quadratic Gini",
                    gen.function, weight.function)

# Its performance in the apple-starbucks market
data(applestarbucks)
market <- toymkt(applestarbucks)
result <- FernholzDecomp(market, my.portfolio, plot = TRUE)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(RelValAnalysis)
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/RelValAnalysis/fgp.Rd_%03d_medium.png", width=480, height=480)
> ### Name: fgp
> ### Title: Functionally Generated Portfolio Objects
> ### Aliases: fgp
> 
> ### ** Examples
> 
> # Example 1: The diversity-weighted portfolio with p = 0.5
> # This has the same effect has DiversityPortfolio(p = 0.5)
> my.portfolio <- fgp("Diversity-Weighted Portfolio, p = 0.5",
+                     function(x) (sum(sqrt(x)))^2,
+                     function(x) sqrt(x) / sum(sqrt(x)))
>                     
>                     
> # Example 2: A quadratic Gini coefficient
> # See Example 3.4.7 of Fernholz (2002)
> 
> # Generating function
> gen.function <- function(x) {
+   n <- length(x)
+   return(1 - sum((x - 1/n)^2)/2)
+ }
> 
> # Weight function
> weight.function <- function(x) {
+   n <- length(x)
+   S <- gen.function(x) 
+   return(((1/n - x)/S + 1 - sum(x*(1/n - x)/S))*x)
+ }
> 
> # Define fgp object
> my.portfolio <- fgp("Quadratic Gini",
+                     gen.function, weight.function)
> 
> # Its performance in the apple-starbucks market
> data(applestarbucks)
> market <- toymkt(applestarbucks)
Warning message:
In toymkt(applestarbucks) :
  Since initial.weight is not given, the benchmark is assumed to be equal-weighted initially.
> result <- FernholzDecomp(market, my.portfolio, plot = TRUE)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>