Type: Package
Title: Black-Litterman and Copula Opinion Pooling Frameworks
Version: 0.3.3
Description: An implementation of the Black-Litterman Model and Attilio Meucci's copula opinion pooling framework as described in Meucci, Attilio (2005) <doi:10.2139/ssrn.848407>, Meucci, Attilio (2006) <doi:10.2139/ssrn.872577> and Meucci, Attilio (2008) <doi:10.2139/ssrn.1117574>.
License: MIT + file LICENSE
LazyData: true
NeedsCompilation: no
URL: https://github.com/mangothecat/BLCOP
BugReports: https://github.com/mangothecat/BLCOP/issues
Imports: methods, MASS, quadprog, RUnit (≥ 0.4.22), timeSeries, fBasics, fMultivar, fPortfolio (≥ 3011.81), rmarkdown, knitr
Suggests: sn, corpcor, mnormt
VignetteBuilder: knitr
Packaged: 2021-01-25 15:30:56 UTC; jrussell
Author: Francisco Gochez [aut], Richard Chandler-Mant [aut], Suchen Jin [aut], Jinjing Xie [aut], Ava Yang [ctb] (Previous maintainer), Joe Russell [cre]
Maintainer: Joe Russell <jrussell@mango-solutions.com>
Repository: CRAN
Date/Publication: 2021-01-25 23:00:02 UTC

Monthly equity returns

Description

A matrix holding time series of monthly returns (calculated from closing prices) for six stocks. The returns span the period from Jaunary 1998 through December 2003.

Usage

monthlyReturns

Format

A matrix with 6 columns and 71 rows. The names of the rows hold the dates of each series entry, and the column names are the names of the six equities from which the return series are taken.

Examples

CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB)

Global package options

Description

This function can be used to set or get global options for the BLCOP package.

Usage

BLCOPOptions(opt, setting)

Arguments

opt

A string with the name of an option

setting

The new setting for the option

Details

If setting is omitted, the current setting for opt is returned. If both arguments are omitted, a list with all of the settings is returned. The following settings may be changed: regFunc:Function used to perform the regression in CAPMalphas numSimulations:Number of monte-carlo simulations to perform in copula opinion pooling functions unitTestPath: Path where unit tests are located.

Value

If both arguments omitted, a list. If setting is omitted, value of an individual setting.

Author(s)

Francisco Gochez <fgochez@mango-solutions>

Examples

    BLCOPOptions("numSimulations")

BLposterior

Description

BLposterior

Usage

BLPosterior(returns, views, tau = 1, marketIndex, riskFree = NULL,
  kappa = 0, covEstimator = "cov")

Arguments

returns

A matrix of time series of returns. The columns should correspond to individual assets.

views

An object of class BLViews

tau

The "tau" parameter in the Black-Litterman model.

marketIndex

A set of returns of a market index.

riskFree

A time series of risk-free rates of return. Defaults to 0

kappa

if greater than 0, the confidences in each view are replaced. See the online help for details

covEstimator

A string holding the name of the function that should be used to estimate the variance-covariance matrix. This function should simply return a matrix.

Value

An object of class BLResult

Author(s)

Francisco

Class "BLResult": posterior of a market distribution in the Black-Litterman sense

Description

This class holds the posterior market mean and variance-covariance matrix calculated from some prior and set of views. The original views are also returned.

Objects from the Class

Objects can be created by calls of the form new("BLResult", ...). However, it is intended that they be created by the function posteriorEst(or wrappers to that function).

Slots

views:

Object of class "BLViews". These are the original views used to calculate this posterior

tau:

Object of class "numeric". The value of "tau" used

priorMean:

Object of class "numeric": prior vector of market means

priorCovar:

Object of class "matrix": prior of the variance-covariance

posteriorMean:

Object of class "numeric": posterior mean

posteriorCovar:

Object of class "matrix": posterior variance-covariance

kappa:

Object of class "logical": logical flag indicating whether or not confidences-in-views were ignored.

Methods

denityPlots

signature(result = "BLResult"): Plots the marginal distributions of the asset returns under the prior and posterior distributions

show

signature(object = "BLResult"): Displays the contents of a result

optimalPortfolios.fPort

signature(result = "BLResult"): Generates optimal prior and posterior portfolios using fPortfolio package routines

Author(s)

Francisco Gochez

Class "BLViews" (Black-Litterman views)

Description

An object that holds a set of analyst views, in the Black-Litterman sense, on a set of assets

Objects from the Class

Objects can be created by calls of the form new("BLViews", ...) or with the BLViews function.

Slots

P:

Object of class "matrix". The "pick" matrix

qv:

Object of class "numeric". Means of the views

confidences:

Object of class "numeric". Holds the confidence in each of the individual views

assets:

Object of class "character": Name of the asset "universe" to which these views apply

Methods

deleteViews

signature(views = "BLViews", viewsToDel = "numeric"): Deletes a vector of views from the object, where the vector entries correspond to rows of the pick matrix

show

signature(object = "BLViews"): Prints views in a user-friendly manner

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Create or add to a BLViews object

Description

BLViews and COPViews are "constructors" for BLViews and COPViews objects respectively. addBLViews and addCOPViews allow one to easily add more views to a pre-existing views objects. newPMatrix is a utility function for creating pick matrices.

Usage

	
addBLViews(pickMatrix, q, confidences, views)
addCOPViews(pickMatrix, viewDist, confidences, views) 
BLViews(P, q, confidences, assetNames)
COPViews(pickMatrix, viewDist, confidences, assetNames) 
newPMatrix(assetNames, numViews, defaultValue = 0)

Arguments

P

"Pick" matrix with columns named after assets to which views correspond

pickMatrix

"Pick" matrix with columns named after assets to which views correspond

q

"q" vector of views

confidences

Vector of confidences in views. Note that confidences are recipricols of standard deviations

viewDist

A list of marginal distributions of the views

views

A BLViews object

assetNames

Names of the assets in the universe

numViews

Number of views in the pick matrix

defaultValue

Default value to use to fill the new pick matrix

Value

A BLViews or COPViews class object as appropriate. newPMatrix creates a matrix.

Author(s)

Francisco Gochez

See Also

createBLViews, updateBLViews

Examples

    ### example from T. M. Idzorek's paper "A STEP-BY-STEP GUIDE TO THE 
	### BLACK-LITTERMAN MODEL"
 	## Not run: 
	    pick <- newPMatrix(letters[1:8], 3)
	    pick[1,7] <- 1
	    pick[2,1] <- -1 
	    pick[2,2] <- 1
	    pick[3, 3:6] <- c(0.9, -0.9, .1, -.1)
	    confidences <- 1 / c(0.00709, 0.000141, 0.000866)
	    myViews <- BLViews(pick, q = c(0.0525, 0.0025, 0.02), confidences, letters[1:8])
	    myViews
	    
	    ### Modified COP example from Meucci's "Beyond Black-Litterman: Views on
		### non-normal markets" 
	    dispersion <- c(.376,.253,.360,.333,.360,.600,.397,.396,.578,.775) / 1000
	    sigma <- BLCOP:::.symmetricMatrix(dispersion, dim = 4)
	    caps <- rep(1/4, 4)
	    mu <- 2.5 * sigma 
	    dim(mu) <- NULL
	    marketDistribution <- mvdistribution("mt", mean = mu, S = sigma, df = 5 )
	    pick <- newPMatrix(c("SP", "FTSE", "CAC", "DAX"), 1)
	    pick[1,4] <- 1
	    vdist <- list(distribution("unif", min = -0.02, max = 0))
	    views <- COPViews(pick, vdist, 0.2, c("SP", "FTSE", "CAC", "DAX"))
    
## End(Not run)

Compute CAPM alphas for a set of assets

Description

CAPMList is a helper function that computes the "alphas" and "betas" in the sense of the CAPM for series of asset returns. It is meant to be used for computing "prior" means for the Black-Litterman model.

Usage

CAPMList(returns, marketIndex, riskFree = NULL, regFunc = BLCOPOptions("regFunc"), 
         coeffExtractFunc = NULL, ...)

Arguments

returns

A matrix or data.frame of asset returns, with different columns corresponding to different assets

marketIndex

A time series of returns for some market index (e.g. SP500)

riskFree

Risk-free rate of return

regFunc

The name of the function to used to regress the asset return series against the market index. This is set in the BLCOP options, and is lm by default.

coeffExtractFunc

A function that extracts the intercept (alpha) and coefficient of the market index (beta) from the results of a call to the regression function. It should return a vector containing these two elements.

...

Additional arguments to the regression function

Details

coeffExtractFun is needed because some regression functions such as gls from the nlme package don't return their results in the same format as lm does. If it is not supplied, a default that works with lm results is used.

Value

A data.frame with one column for the "alphas" and another for the "betas"

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Examples

    library(MASS)
    CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB, regFunc = "rlm")

Calculate the posterior distribution of the market using copula opinion pooling

Description

COPPosteior uses Attilio Meucci's copula opinion pooling method to incorporate an analyst's subjective views with a prior "official" market distribution. Both the views and the market may have an arbitrary distribution as long as it can be sampled in R. Calculations are done with monte-carlo simulation, and the object returned will hold samples drawn from the market posterior distribution.

Usage

    COPPosterior(marketDist, views, numSimulations = BLCOPOptions("numSimulations"))

Arguments

marketDist

An object of class mvdistribution which describes the prior "official" distribution of the market.

views

An object of class COPViews which describe the subjective views on the market distribution

numSimulations

The number of monte carlo samples to draw during calculations. Each asset in one's universe will have numSimulations samples from the posterior.

Value

An object of class COPResult.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

References

Attilio Meucci, "Beyond Black-Litterman:Views on Non-normal Markets". See also Attilio Meucci, "Beyond Black-Litterman in Practice: a Five-Step Recipe to Input Views on non-Normal Markets."

See Also

BLPosterior

Examples

    
    ## Not run:     
        # An example based on one found in "Beyond Black-Litterman:Views on Non-normal Markets"
        dispersion <- c(.376,.253,.360,.333,.360,.600,.397,.396,.578,.775) / 1000
        sigma <- BLCOP:::.symmetricMatrix(dispersion, dim = 4)
        caps <- rep(1/4, 4)
        mu <- 2.5 * sigma 
        dim(mu) <- NULL
        marketDistribution <- mvdistribution("mt", mean = mu, S = sigma, df = 5 )
        pick <- matrix(0, ncol = 4, nrow = 1, dimnames = list(NULL, c("SP", "FTSE", "CAC", "DAX")))
        pick[1,4] <- 1
        vdist <- list(distribution("unif", min = -0.02, max = 0))
    
        views <- COPViews(pick, vdist, 0.2, c("SP", "FTSE", "CAC", "DAX"))
        posterior <- COPPosterior(marketDistribution, views)
    
## End(Not run)

Class "COPResult"

Description

A class that holds the posterior distribution produced with the COP framework

Objects from the Class

Objects can be created by calls of the form new("COPResult", ...). In general however they are created by the function COPPosterior

Slots

views:

Object of class "COPViews". These are the views that led to the result

marketDist:

Object of class "mvdistribution". Prior distribution of the market

posteriorSims:

Object of class "matrix". Matrices holding the simulations of the posteriors with a column for each asset.

Methods

densityPlots

signature(result = "COPResult"): Generates density plots of the marginal prior and posterior distributions of each asset.

show

signature(result = "COPResult"): Displays basic information about the posterior results

optimalPortfolios.fPort

signature(result = "COPResult"): Generates optimal prior and posterior portfolios using fPortfolio package routines

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

COPPosterior, BLResult-class

Class "COPViews" (copula opinion pooling views)

Description

An object that holds a set of analyst views, in the copula opinion pooling sense, on a set of assets

Objects from the Class

Objects can be created by calls of the form new("COPViews", ...) or with the COPViews function.

Slots

pick:

Object of class "matrix". The pick matrix

viewDist:

Object of class "list". List of probability distributions of the views

confidences:

Object of class "numeric".

assets:

Object of class "character". Name of the asset "universe" to which these views apply.

Methods

deleteViews

signature(views = "COPViews", viewsToDel = "numeric"): Deletes a vector of views from the object, where the vector entries correspond to rows of the pick matrix

show

signature(object = "COPViews"): Prints views in a user-friendly manner

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

BLViews, COPViews, addCOPViews, createCOPViews

Examples

    showClass("COPViews")

Create or add to a view object using a graphical interface

Description

These helper functions allow one to easily create or add to an object of class BLViews or COPViews through the use of R's built-in data editor.

Usage

createBLViews(allAssets, numAssetViews = 1, assetSubset = NULL, 
              mode = c("editor", "Window"))
updateBLViews(views, includeNullViews = FALSE, numNewViews = 0, assets = NULL)
createCOPViews (allAssets, numAssetViews = 1, assetSubset = NULL, 
                mode = c("editor", "Window"))

Arguments

allAssets

A character vector holding the names of all of the assets in one's "universe"

numAssetViews

The number of views to form. Should be less than or equal to the total number of assets

assetSubset

A character vector of assets that is a subset of allAssets. Views will be formed only on this subset. By default, assetSubset = allAssets

.

mode

Mode of GUI. Currently unused

views

Object of class BLViews

assets

Set of assets to form or modify views on. If NULL, will use the full set of assets

includeNullViews

When updating views, should the 0 columns of the pick matrix be included?

numNewViews

In updateViews, this is the number of new views to add

Details

createCOPViews does not allow one to specify the distributions of the views at the moment. Such a feature may be added later through another GUI. At the moment the object returned by this function has its distribution set to a default. updateViews allows one to modify pre-existing views

Value

An object of class BLViews or COPViews that holds all of the views created.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

addBLViews, addCOPViews, COPViews, BLViews

Examples

    
    ## Not run: 
        views <- createBLViews(colnames(monthlyReturns), 2)
    
## End(Not run)

Constructors for distribution and mvdistribution class objects

Description

These functions create objects of class distribution and mvdistribution

Usage

mvdistribution(RName, ...)
distribution(RName, ...)

Arguments

RName

A string holding the R suffix corresponding to the distribution, e.g. "pois" for the Poisson distribution

...

Additional parameters that parametrize the distribution

Details

In general any distribution with a corresponding sampling function can be used. This function should have the name given in RName but preceded with an "r", e.g. rnorm for the normal distribution. When the constructors are called, they check that the given sampling function exists and that it takes the arguments that were passed in the ....

Value

An object of class distribution or mvdistribution.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

sampleFrom

Examples

    ## Not run: 
	    # create a uniform distribution object and sample from it
	    myUnif <- distribution("unif", min = -0.1, max = 0.1)
	    hist(sampleFrom(myUnif, 1000))
	    
	    mvNormal <- mvdistribution("mnorm", mean = c(1, 5), varcov = diag(c(2, 0.1)))
	    x <- sampleFrom(mvNormal, 1000)
	    plot(x[,1] ~ x[,2])
    
## End(Not run)

Get prior and posterior estimators stored in package scope

Description

These functions are not intended to be called directly by the user but exist to allow third party optimizer routines to access prior and posterior estimators calculated as part of the portfolio optimisation.

Usage

getPriorEstim(x, spec=NULL, ...)
getPosteriorEstim(x, spec=NULL, ...)

Arguments

x

multivariate time series

spec

optional portfolio specification

...

additional arguments

Value

A list with 2 elements:

mu

estimate of mean

Sigma

estimate of covariance

Author(s)

Richard Chandler-Mant <rchandler-mant@mango-solutions.com>

Extract various fields of view or posterior objects

Description

A collection of functions to extract several fields of BLViews, COPViews, COPPosterior and BLPosterior objects.

Usage

assetSet(views)
viewMatrix(views, dropZeroColumns = TRUE)
PMatrix(views)
confidences(views)
posteriorMeanCov(posterior)
posteriorSimulations(posterior)
numSimulations(posterior)
priorViews(posterior)

Arguments

views

An object of class BLViews or COPViews

posterior

An object of class BLPosterior (posteriorMeanCov) or COPPosterior (posteriorSimulations, priorViews) , as appropriate

dropZeroColumns

Logical flag. If TRUE, columns of "view matrix" which only have zeros are dropped

Value

assetSet

The names of the assets in the view object's universe

confidences

The set of confidences in each view.

PMatrix

The 'pick' matrix

viewMatrix

The pick matrix augmented with the q vector of the BL model

posteriorMeanCov

The posterior mean and covariance (in a list) of a BLPosterior object

posteriorSimulations

Matrix of posterior distribution simulations held in a COPPosterior object

numSimulations

Number of simulations in posterior COP distribution

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Examples

    pick <- matrix(0, ncol = 4, nrow = 1, dimnames = list(NULL, c("SP", "FTSE", "CAC", "DAX")))
    pick[1,4] <- 1
    vdist <- list(distribution("unif", min = -0.02, max = 0))
    views <- COPViews(pick, vdist, 0.2, c("SP", "FTSE", "CAC", "DAX"))
    assetSet(views)
    confidences(views)
    PMatrix(views)

Various functions for modifying fields of view objects

Description

These functions allow for direct replacement of fields of view objects such as the pick matrix and vector of confidences.

Usage

PMatrix(views) <- value
confidences(views) <- value
qv(views) <- value

Arguments

views

An object of class BLViews or COPViews, except in the case of qv<- which applies only to BLViews

value

A vector in confidences<- and qv<- or a matrix in PMatrix<-.

Value

The object is modified directly

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Examples


## example from Thomas M. Idzorek's paper "A STEP-BY-STEP GUIDE TO THE BLACK-LITTERMAN MODEL"
x <- c(0.001005,0.001328,-0.000579,-0.000675,0.000121,0.000128,-0.000445,-0.000437 ,
     0.001328,0.007277,-0.001307,-0.000610,-0.002237,-0.000989,0.001442,-0.001535 ,
     -0.000579,-0.001307,0.059852,0.027588,0.063497,0.023036,0.032967,0.048039 ,
    -0.000675,-0.000610,0.027588,0.029609,0.026572,0.021465,0.020697,0.029854 ,
     0.000121,-0.002237,0.063497,0.026572,0.102488,0.042744,0.039943,0.065994 ,
     0.000128,-0.000989,0.023036,0.021465,0.042744,0.032056,0.019881,0.032235 ,
    -0.000445,0.001442,0.032967,0.020697,0.039943,0.019881,0.028355,0.035064 ,
    -0.000437,-0.001535,0.048039,0.029854,0.065994,0.032235,0.035064,0.079958 )

    varCov <- matrix(x, ncol = 8, nrow = 8)
    mu <- c(0.08, 0.67,6.41, 4.08, 7.43, 3.70, 4.80, 6.60) / 100
    pick <- matrix(0, ncol = 8, nrow = 3, dimnames = list(NULL, letters[1:8]))
    pick[1,7] <- 1
    pick[2,1] <- -1; pick[2,2] <- 1
    pick[3, 3:6] <- c(0.9, -0.9, .1, -.1)
    confidences <- 1 / c(0.000709, 0.000141, 0.000866)
    myViews <- BLViews(pick, c(0.0525, 0.0025, 0.02), confidences, letters[1:8])
    myPosterior <- posteriorEst(myViews, tau = 0.025, mu, varCov )
    myPosterior
    # increase confidences
   	confidences(myViews) <-  1 / c(0.0001, 0.0001, 0.0005)
    myPosterior2 <- posteriorEst(myViews, tau = 0.025, mu, varCov )
    myPosterior2

Risk free rate of return

Description

The monthly rate of return of the US 13 week Treasury Bill for the period 30/1/1998 through 30/11/2003.

Usage

US13wTB

Format

A one-column matrix with 71 rows.

Examples

ts.plot(US13wTB)

Delete individual views from view objects

Description

A generic function that allows one to delete individual views from objects of class BLViews or COPViews. The inputs are a view object and a numeric vector of views to delete, where the entires of the vector map to rows of the pick matrix.

Usage

deleteViews(views, viewsToDel)

Arguments

views

An object of class BLViews or COPViews

viewsToDel

A numeric vector of views to delete, as described above

Value

The original object with the indicated views deleted

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

BLViews-class, COPViews-class

Examples

    stocks <- colnames(monthlyReturns)
    pick <- matrix(0, ncol = 6, nrow = 2, dimnames = list(NULL, stocks))
    pick[1,"IBM"] <- 1
    pick[1, "DELL"] <- 0.04
    pick[2, "C"] <- 1
    pick[2, "JPM"] <- 0.6

    confidences <- 1 / c(0.7, 0.1)

    views <- BLViews( P = pick, q = c(0.1,0.1) , confidences = confidences,stocks)
    deleteViews(views, 1)

Density plots of prior and posterior distributions

Description

This generic function generates density plots of the marginal posterior and prior distributions of a set of assets in an object of class BLResult or COPResult for comparative purposes.

Usage

densityPlots(result, assetsSel = NULL, numSimulations = BLCOPOptions("numSimulations"), 
             ...)

Arguments

result

Object of class

assetsSel

A numeric vector of assets to plot

numSimulations

For COPResult class objects, the number of simulations to use for the market posterior distribution

...

Additional arguments passed to plot

Details

For COPResults objects, density kernel estimates from the samples are used

Value

None

Author(s)

Francisco Gochez, <fgochez@mango-solutions>

Examples

    ## Not run: 
        dispersion <- c(.376,.253,.360,.333,.360,.600,.397,.396,.578,.775) / 1000
        sigma <- BLCOP:::.symmetricMatrix(dispersion, dim = 4)
        caps <- rep(1/4, 4)
        mu <- 2.5 * sigma 
        dim(mu) <- NULL
        marketDistribution <- mvdistribution("mt", mean = mu, S = sigma, df = 5 )
        pick <- matrix(0, ncol = 4, nrow = 1, dimnames = list(NULL, c("SP", "FTSE", "CAC", "DAX")))
        pick[1,4] <- 1
        vdist <- list(distribution("unif", min = -0.02, max = 0))
    
        views <- COPViews(pick, vdist, 0.2, c("SP", "FTSE", "CAC", "DAX"))
        posterior <- COPPosterior(marketDistribution, views)
        densityPlots(posterior, 4)
        
## End(Not run)

Class "distribution"

Description

A class that describes univariate distributions

Objects from the Class

Objects can be created by calls of the form new("distribution", ...). There is also a constructor which is also named distribution.

Slots

RName:

Object of class "character". This is the R "suffix" of the distirbution.

parameters:

Object of class "numeric". A named numeric vector that holds the parameters of the distribution

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

distribution, mvdistribution, mvdistribution

Examples

    showClass("distribution")

Class "mvdistribution"

Description

A class that describes multivariate distributions

Objects from the Class

Objects can be created by calls of the form new("distribution", ...). There is also a constructor which is also named mvdistribution.

Slots

RName:

Object of class "character". This is the R "suffix" of the distirbution.

parameters:

A named list of parameters that characterize the distribution

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

See Also

distribution, mvdistribution, distribution-class

Examples

      showClass("mvdistribution")

Calculates optimal portfolios under prior and posterior distributions

Description

These are wrapper functions that calculate optimal portfolios under the prior and posterior return distributions. optimalPortfolios works with a user-supplied optimization function, though simple Markowitz minimum-risk optimization is done with solve.QP from quadprog if none is supplied. optimalPortfolios.fPort is a generic utility function which calculates optimal portfolios using routines from the fPortfolio package.

Usage

optimalPortfolios(result, optimizer = .optimalWeights.simpleMV, ..., doPlot = TRUE, 
                  beside = TRUE)
optimalPortfolios.fPort(result, spec = NULL, constraints = "LongOnly", 
                        optimizer = "minriskPortfolio", inputData = NULL, 
                        numSimulations = BLCOPOptions("numSimulations"))

Arguments

result

An object of class BLResult

optimizer

For optimalPortfolios, An optimization function. It should take as arguments a vector of means and a variance-covariance matrix, and should return a vector of optimal weights. For optimalPortfolios, the name of a fPortfolio function that performs portfolio optimization

spec

Object of class fPORTFOLIOSPEC. If NULL, will use a basic mean-variance spec for Black-Litterman results, and a basic CVaR spec for COP results

inputData

Time series data (any form that can be coerced into a timeSeries object)

constraints

String of constraints that may be passed into fPortfolio optimization routines

numSimulations

For COP results only - the number of posterior simulations to use in the optimization (large numbers here will likely cause the routine to fail)

...

Additional arguments to the optimization function

doPlot

A logical flag. Should barplots of the optimal portfolio weights be produced?

beside

A logical flag. If a barplot is generated, should the bars appear side-by side? If FALSE, differences of weights will be plotted instead.

Details

By default, optimizer is a simple function that performs Markowitz optimization via solve.QP. In addition to a mean and variance, it takes an optional constraints parameter that if supplied should hold a named list with all of the parameters that solve.QP takes.

Value

optimalPortfolios will return a list with the following items:

priorPFolioWeights

The optimal weights under the prior distribution

postPFolioWeights

The optimal weights under the posterior distribution

optimalPortfolios.fPort will return a similar list with 2 elements of class fPORTFOLIO.

Note

It is expected that optimalPortfolios will be deprecated in future releases in favour of optimalPortfolios.fPort.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

References

Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009); Portfolio Optimization with R/Rmetrics, Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.

Examples

	## Not run: 
	    entries <- c(0.001005,0.001328,-0.000579,-0.000675,0.000121,0.000128,
                    -0.000445, -0.000437, 0.001328,0.007277,-0.001307,-0.000610,
                    -0.002237,-0.000989,0.001442,-0.001535, -0.000579,-0.001307,
                    0.059852,0.027588,0.063497,0.023036,0.032967,0.048039,-0.000675,
                    -0.000610,0.027588,0.029609,0.026572,0.021465,0.020697,0.029854,
                    0.000121,-0.002237,0.063497,0.026572,0.102488,0.042744,0.039943,
                    0.065994 ,0.000128,-0.000989,0.023036,0.021465,0.042744,0.032056,
                    0.019881,0.032235 ,-0.000445,0.001442,0.032967,0.020697,0.039943,
                    0.019881,0.028355,0.035064 ,-0.000437,-0.001535,0.048039,0.029854,
                    0.065994,0.032235,0.035064,0.079958 )
	    
	    varcov <- matrix(entries, ncol = 8, nrow = 8)
	    mu <- c(0.08, 0.67,6.41, 4.08, 7.43, 3.70, 4.80, 6.60) / 100
	    pick <- matrix(0, ncol = 8, nrow = 3, dimnames = list(NULL, letters[1:8]))
	    pick[1,7] <- 1
	    pick[2,1] <- -1; pick[2,2] <- 1
	    pick[3, 3:6] <- c(0.9, -0.9, .1, -.1)
	    confidences <- 1 / c(0.00709, 0.000141, 0.000866)
	    views <- BLViews(pick, c(0.0525, 0.0025, 0.02), confidences, letters[1:8])
	    posterior <- posteriorEst(views, tau = 0.025, mu, varcov )
	    optimalPortfolios(posterior, doPlot = TRUE)
    
    	optimalPortfolios.fPort(posterior, optimizer = "tangencyPortfolio")
    	
    	# An example based on one found in "Beyond Black-Litterman:Views on Non-normal Markets"
        dispersion <- c(.376,.253,.360,.333,.360,.600,.397,.396,.578,.775) / 1000
        sigma <- BLCOP:::.symmetricMatrix(dispersion, dim = 4)
        caps <- rep(1/4, 4)
        mu <- 2.5 * sigma 
        dim(mu) <- NULL
        marketDistribution <- mvdistribution("mt", mean = mu, S = sigma, df = 5 )
        pick <- matrix(0, ncol = 4, nrow = 1, dimnames = list(NULL, c("SP", "FTSE", "CAC", "DAX")))
        pick[1,4] <- 1
        vdist <- list(distribution("unif", min = -0.02, max = 0))
    
        views <- COPViews(pick, vdist, 0.2, c("SP", "FTSE", "CAC", "DAX"))
        posterior <- COPPosterior(marketDistribution, views)
    
        optimalPortfolios.fPort(myPosterior, spec = NULL, optimizer = "minriskPortfolio", 
		                        inputData = NULL, numSimulations  = 100	)
	
    
## End(Not run)

This function performs the "core" calculation of the Black-Litterman model.

Description

This function performs the "core" calculation of the Black-Litterman model.

Usage

posteriorEst(views, mu, tau = 0.5, sigma, kappa = 0)

Arguments

views

An object of class BLViews

mu

A vector of mean equilibrium returns

tau

The "tau" parameter in the Black-Litterman model.

sigma

The variance-covariance matrix of the returns of the assets

kappa

if greater than 0, the confidences in each view are replaced. See the online help for details

Value

An object of class BLResult holding the updated Black-Litterman posterior

Author(s)

Francisco

Calculate the "feasibility" of the (Black-Litterman) posterior mean

Description

Attilio Meucci and Gianluca Fusai have suggested using the Mahalanobis distance to assess the feasibility of a set of Black-Litterman views. This function calculates this distance, along with a "feasibility" measure based on this distance and the sensitivity of the measure to changes in the "q" vector.

Usage

posteriorFeasibility(result)

Arguments

result

An object of class BLResult

Details

The feasibility measure proposed by Meucci and Fusai (see the references below) is 1 - F(m), where m is the Mahalanobis distance from from the prior mean calculated with respect to the prior distribution. F is the chi-squared CDF of n-degrees of freedom, where n is the number assets in one's universe. It should be noted that in Meucci and Fusai's paper, a version of Black-Litterman is used in which the tau parameter is always set to 1.

Value

mahalDist

Mahalonobis distance of posterior mean vector from prior mean

mahalDistProb

1 - F(mahalDist), where F is the CDF of the Chi-squared distribution with n = \#assets degrees of freedom

sensitivities

Derivatives of mahalDistProb with respect to the elements of the "q" vector in the set of views. Not yet implemented

Warning

It is not clear that the results produced by this routine are entirely sensible, though the calculation is very straightforward and seems to match the one discussed in the source paper. Use with caution.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

References

Fusai, Gianluca and Meucci, Attilio. "Assessing Views", 2002. http://www.symmys.com/AttilioMeucci/Research/PublFinance/PublFinance.html

Examples

    pickMatrix <- matrix(c(rep(1/2, 2), -1,  rep(0, 3)), nrow = 1, ncol = 6 )
    views <- BLViews(P = pickMatrix, q = 0.08,confidences =  100, 
	                 assetNames = colnames(monthlyReturns))
    marketPosterior <- BLPosterior(monthlyReturns, views, marketIndex = sp500Returns, 
        riskFree = US13wTB)
    posteriorFeasibility(marketPosterior)

Execute the BLCOP unit tests

Description

Uses the RUnit package to execute a series of unit tests.

Usage

runBLCOPTests(testPath = BLCOPOptions("unitTestPath"), protocolFile = "BLCOPTests.html", 
    writeProtocol = FALSE)

Arguments

testPath

Location of the unit tests.

protocolFile

Name of the html report file generated by the RUnit function printHTMLProtocol

writeProtocol

Logical flag. Should the above html report be produced?

Value

The summary of an object returned by RUnit's runTestSuite

Warning

These unit tests are in need of additional test cases, and should not be regarded as exhaustive in their current state.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Examples

## Not run: 
    runBLCOPTests()
    
## End(Not run)

Sample from a distribution object

Description

Generates samples from a distribution held by an object of class distribution or mvdistribution. Intended mainly for internal use.

Usage

sampleFrom(dstn, n = 1)

Arguments

dstn

an object of class distribution or mvdistribution.

n

Number of samples to generate

Value

A vector or matrix of samples.

Author(s)

Francisco Gochez <fgochez@mango-solutions.com>

Examples

    x <- distribution("pois", lambda = 5)
    hist(sampleFrom(x, 1000), col = "blue", prob = TRUE)

S\&P500 Returns

Description

Monthly returns of the S&P 500 index for the period 2/2/1998 through 1/12/2003

Usage

sp500Returns

Format

A matrix with 1 column and 71 rows.

Examples

    ts.plot(sp500Returns)