AssetsModelling {fPortfolio} | R Documentation |
A collection and description of functions which
generate multivariate artificial data sets of assets,
which fit the parameters to a multivariate normal,
skew normal, or (skew) Student-t distribution and
which compute some benchmark statistics. In addition
a function is provided which allows for the selection
and clustering of individual assets from portfolios
using hierarchical and k-means clustering approaches.
The functions are:
assetsSim | Simulates a data set of assets, |
assetsSelect | Asset Selection from Portfolios, |
assetsFit | Fits the parameter of a data set of assets, |
assetsStats | Computes benchmark statistics of asset sets, |
print | S3 print method for an object of class 'fASSETS', |
plot | S3 Plot method for an object of class 'fASSETS", |
summary | S3 summary method for an object of class 'fASSETS'. |
assetsSim(n, dim = 2, model = list(mu = rep(0, dim), Omega = diag(dim), alpha = rep(0, dim), df = Inf), assetNames = NULL) assetsSelect(x, method = c("hclust", "kmeans"), kmeans.centers = 5, kmeans.maxiter = 10, doplot = TRUE, ...) assetsFit(x, method = c("st", "snorm", "norm"), title = NULL, description = NULL, fixed.df = NA, ...) assetsStats(x) ## S3 method for class 'fASSETS': print(x, ...) ## S3 method for class 'fASSETS': plot(x, which = "ask", ...) ## S3 method for class 'fASSETS': summary(object, which = "all", ...)
assetNames |
[assetsSim] - a vector of character strings of length dim allowing
for modifying the names of the individual assets.
|
description |
[assetsFit] - a character string, assigning a brief description to an "fASSETS" object.
|
doplot |
[assetsSelect] - a logical, should a plot be displayed? |
fixed.df |
[assetsFit] - either NA , the default, or a numeric value assigning the
number of degrees of freedom to the model. In the case that
fixed.df=NA the value of df will be included in the
optimization process, otherwise not.
|
kmeans.centers |
[assetsSelect] - either the number of clusters or a set of initial cluster centers. If the first, a random set of rows in x are chosen as the
initial centers.
|
kmeans.maxiter |
[assetsSelect] - the maximum number of iterations allowed. |
method |
[assetsFit] - a character string, which type of distribution should be fitted? "st" a multivariate skew-Student-t, "snorm" a multivariate skew-normal, or "norm" a multivariate normel. By default a multivariate normal distribution will be fitted to the empirical market data. [assetsSelect] - a character string, which clustering method should be applied? Either hclust for hierarchical clustering of dissimilarities,
or kmeans for k-means clustering.
|
model |
[assetsSim] - a list of model parameters: mu a vector of mean values, one for each asset series, Omega the covariance matrix of assets, alpha the skewness vector, and df the number of degrees of freedom which is a measure for
the fatness of the tails (excess kurtosis). For a symmetric distribution alpha is a vector of zeros.
For the normal distributions df is not used and set to
infinity, Inf . Note that all assets have the same value
for df .
|
n, dim |
[assetsSim] - integer values giving the number of data records to be simulated, and the dimension of the assets set. |
object |
[summary] - An object of class fASSETS .
|
title |
[assetsFit] - a character string, assigning a title to an "fASSETS" object.
|
which |
which of the five plots should be displayed? which can
be either a character string, "all" (displays all plots)
or "ask" (interactively asks which one to display), or a
vector of 5 logical values, for those elements which are set
TRUE the correponding plot will be displayed.
|
x |
[assetsFit][assetsStats] - a numeric matrix of returns or any other rectangular object like a data.frame or a multivariate time series objects which can be transformed by the function as.matrix to an object of
class matrix .
[plot][print] - An object of class fASSETS .
|
... |
optional arguments to be passed. |
Data sets of assets x
can be expressed as multivariate
'timeSeries' objects, as 'data.frame' objects, or any other rectangular
object which can be transformed into an object of class 'matrix'.
The functions assetsFit
for the parameter estimation and
assetsSim
for the simulation of assets sets use code based on
functions from the mentioned package "mtvnorm"
and "sn"
.
The required functionality from the contributed R package "sn"
for fitting data to a multivariate Normal, skew-Normal, or skew-Student-t
is available from builtin functions, so it is not necessary to load
the packages "mtvnorm"
and "sn"
.
The function assetsStats
implements benchmark formulas and
statistics as reported in the help page of the hedge fund software
from www.AlternativeSoft.com. The computed statistics are listed
in the 'Value' section below. Note, that the functions were written for
monthly recorded data sets. Be aware of this when you use or generate
asset sets on different time scales, then you have them to scale
properly.
The function assetsSelect
calls the functions hclust
and kmeans
from R's "stats"
package. hclust
performs a hierarchical cluster analysis on the set of dissimilarities
hclust(dist(t(x)))
and kmeans
performs a k-means
clustering on the data matrix itself.
assetsSim
returns a matrix, the artifical data records represent the assets
of the portfolio. Row names and column names are not created, they
have to be added afterwards.
assetsSelects
if method="hclust"
was selected then the function returns a
S3 object of class "hclust", otherwise if method="kmeans"
was
selected then the function returns an obkject of class list. For
details we refer to the help pages of hclust
and kmeans
.
assetsFit
returns a S4 object class of class "fASSETS"
, 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. |
@fit |
the results as a list returned from the underlying fitting function. |
@method |
the selected method to fit the distribution, one
of "norm" , "snorm" , "st" .
|
@model |
the model parameters describing the fitted parameters in
form of a list, model=list(mu, Omega, alpha, df .
|
@title |
a title string. |
@fit$dp |
a list containing the direct parameters beta, Omega, alpha.
Here, beta is a matrix of regression coefficients with
dim(beta)=c(nrow(X), ncol(y)) , Omega is a
covariance matrix of order dim , alpha is
a vector of shape parameters of length dim .
|
@fit$se |
a list containing the components beta, alpha, info. Here, beta and alpha are the standard errors for the corresponding point estimates; info is the observed information matrix for the working parameter, as explained below. |
fit@optim |
the list returned by the optimizer optim ; see the
documentation of this function for explanation of its
components.
|
Note that the @fit$model
slot can be used as input to the
function assetsSim
for simulating a similar portfolio of
assets compared with the original portfolio data, usually market
assets.
assetsStats
returns a data frame with the following entries per column and asset:
Records
- number of records (length of time series),
paMean
- annualized (pa, per annum) Mean of Returns,
paAve
- annualized Average of Returns,
paVola
- annualized Volatility (standard Deviation),
paSkew
- Skewness of Returns,
paKurt
- Kurtosis of Returns,
maxDD
- maximum Drawdown,
TUW
- Time under Water,
mMaxLoss
- Monthly maximum Loss,
mVaR
- Monthly 99
mModVaR
- Monthly 99
mSharpe
- Monthly Sharpe Ratio,
mModSharpe
- Monthly Modified Sharpe Ratio, and
skPrice
- Skewness/Kurtosis Price.
Adelchi Azzalini for R's sn
package,
Torsten Hothorn for R's mtvnorm
package,
Alan Ganz and Frank Bretz for the underlying Fortran Code,
Diethelm Wuertz for the Rmetrics port.
The references are listed in the MultivariateDistribution
collection.
MultivariateDistribution
,
hclust
and kmeans
.
## SOURCE("fBasics.A0-SPlusCompatibility") ## SOURCE("fPortfolio.A2-AssetsModelling") ## berndtInvest - xmpPortfolio("\nStart: Load monthly data set of returns > ") data(berndtInvest) # Exclude Date, Market and Interest Rate columns from data frame, # then multiply by 100 for percentual returns ... berndtAssets = berndtInvest[, -c(1, 11, 18)] rownames(berndtAssets) = berndtInvest[, 1] head(berndtAssets) ## assetsSelect - xmpPortfolio("\nNext: Select 4 most dissimilar assets from hclust > ") clustered = assetsSelect(berndtAssets, doplot = FALSE) myAssets = berndtAssets[, c(clustered$order[1:4])] colnames(myAssets) # Scatter and time series plot: par(mfrow = c(2, 1), cex = 0.7) plot(clustered) myPrices = apply(myAssets, 2, cumsum) ts.plot(myPrices, main = "Selected Assets", xlab = "Months starting 1978", ylab = "Price", col = 1:4) legend(0, 3, legend = colnames(myAssets), pch = "----", col = 1:4, cex = 1) ## assetsStats - if (require(fBasics)) assetsStats(myAssets) ## assetsSim - xmpPortfolio("\nNext: Fit a Skew Student-t > ") fit = assetsFit(myAssets) # Show Model Slot: fit @model # Simulate set with same properties: set.seed(1953) simAssets = assetsSim(n = 120, dim = 4, model = fit@model) head(simAssets) simPrices = apply(simAssets, 2, cumsum) ts.plot(simPrices, main = "Simulated Assets", xlab = "Number of Months", ylab = "Simulated Price", col = 1:4) legend(0, 3, legend = colnames(simAssets), pch = "----", col = 1:4, cex = 1) ## plot - xmpPortfolio("\nNext: Show Simulated Assets Plots > ") if (require(fExtremes)) { # Show Scatterplot: par(mfrow = c(1, 1), cex = 0.7) plot(fit, which = c(TRUE, FALSE, FALSE, FALSE, FALSE)) # Show QQ and PP Plots: par(mfrow = c(2, 2), cex = 0.7) plot(fit, which = !c(TRUE, FALSE, FALSE, FALSE, FALSE)) }