| Title: | Black-Litterman and Copula Opinion Pooling Frameworks |
|---|---|
| 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>. |
| Authors: | Francisco Gochez [aut], Richard Chandler-Mant [aut], Suchen Jin [aut], Jinjing Xie [aut], Ava Yang [ctb] (Previous maintainer), Joe Russell [cre] |
| Maintainer: | Joe Russell <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.3.3 |
| Built: | 2024-09-16 03:32:11 UTC |
| Source: | https://github.com/mangothecat/blcop |
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.
monthlyReturnsmonthlyReturns
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.
CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB)CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB)
This function can be used to set or get global options for the BLCOP package.
BLCOPOptions(opt, setting)BLCOPOptions(opt, setting)
opt |
A string with the name of an option |
setting |
The new setting for the option |
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.
If both arguments omitted, a list. If setting is omitted, value of an individual setting.
Francisco Gochez <fgochez@mango-solutions>
BLCOPOptions("numSimulations")BLCOPOptions("numSimulations")
BLposterior
BLPosterior(returns, views, tau = 1, marketIndex, riskFree = NULL, kappa = 0, covEstimator = "cov")BLPosterior(returns, views, tau = 1, marketIndex, riskFree = NULL, kappa = 0, covEstimator = "cov")
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. |
An object of class BLResult
Francisco
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 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).
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.
signature(result = "BLResult"): Plots the marginal distributions of the asset returns under the prior and posterior distributions
signature(object = "BLResult"): Displays the contents of a result
signature(result = "BLResult"): Generates optimal prior and posterior portfolios using fPortfolio package routines
Francisco Gochez
An object that holds a set of analyst views, in the Black-Litterman sense, on a set of assets
Objects can be created by calls of the form new("BLViews", ...) or with the BLViews function.
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
signature(views = "BLViews", viewsToDel = "numeric"): Deletes a vector of views from the object, where the vector entries correspond to rows of the pick matrix
signature(object = "BLViews"): Prints views in a user-friendly manner
Francisco Gochez <[email protected]>
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.
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)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)
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 |
A BLViews or COPViews class object as appropriate. newPMatrix creates a matrix.
Francisco Gochez
### 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)### 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)
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.
CAPMList(returns, marketIndex, riskFree = NULL, regFunc = BLCOPOptions("regFunc"), coeffExtractFunc = NULL, ...)CAPMList(returns, marketIndex, riskFree = NULL, regFunc = BLCOPOptions("regFunc"), coeffExtractFunc = NULL, ...)
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 |
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 |
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.
A data.frame with one column for the "alphas" and another for the "betas"
Francisco Gochez <[email protected]>
library(MASS) CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB, regFunc = "rlm")library(MASS) CAPMList(monthlyReturns, marketIndex = sp500Returns, riskFree = US13wTB, regFunc = "rlm")
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.
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"))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"))
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 |
.
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 |
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
An object of class BLViews or COPViews that holds all of the views created.
Francisco Gochez <[email protected]>
addBLViews, addCOPViews, COPViews, BLViews
## Not run: views <- createBLViews(colnames(monthlyReturns), 2) ## End(Not run)## Not run: views <- createBLViews(colnames(monthlyReturns), 2) ## End(Not run)
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.
COPPosterior(marketDist, views, numSimulations = BLCOPOptions("numSimulations"))COPPosterior(marketDist, views, numSimulations = BLCOPOptions("numSimulations"))
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. |
An object of class COPResult.
Francisco Gochez <[email protected]>
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."
## 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)## 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)
A class that holds the posterior distribution produced with the COP framework
Objects can be created by calls of the form new("COPResult", ...). In general however
they are created by the function COPPosterior
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.
signature(result = "COPResult"): Generates density plots of the marginal prior and posterior distributions of each asset.
signature(result = "COPResult"): Displays basic information about the posterior results
signature(result = "COPResult"): Generates optimal prior and posterior portfolios using fPortfolio package routines
Francisco Gochez <[email protected]>
An object that holds a set of analyst views, in the copula opinion pooling sense, on a set of assets
Objects can be created by calls of the form new("COPViews", ...) or with the COPViews function.
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.
signature(views = "COPViews", viewsToDel = "numeric"): Deletes a vector of views from the object, where the vector entries correspond to rows of the pick matrix
signature(object = "COPViews"): Prints views in a user-friendly manner
Francisco Gochez <[email protected]>
BLViews, COPViews, addCOPViews, createCOPViews
showClass("COPViews")showClass("COPViews")
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.
deleteViews(views, viewsToDel)deleteViews(views, viewsToDel)
views |
An object of class |
viewsToDel |
A numeric vector of views to delete, as described above |
The original object with the indicated views deleted
Francisco Gochez <[email protected]>
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)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)
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.
densityPlots(result, assetsSel = NULL, numSimulations = BLCOPOptions("numSimulations"), ...)densityPlots(result, assetsSel = NULL, numSimulations = BLCOPOptions("numSimulations"), ...)
result |
Object of class |
assetsSel |
A numeric vector of assets to plot |
numSimulations |
For |
... |
Additional arguments passed to |
For COPResults objects, density kernel estimates from the samples are used
None
Francisco Gochez, <fgochez@mango-solutions>
## 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)## 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)
These functions create objects of class distribution and mvdistribution
mvdistribution(RName, ...) distribution(RName, ...)mvdistribution(RName, ...) distribution(RName, ...)
RName |
A string holding the R suffix corresponding to the distribution, e.g. "pois" for the Poisson distribution |
... |
Additional parameters that parametrize the distribution |
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 ....
An object of class distribution or mvdistribution.
Francisco Gochez <[email protected]>
## 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)## 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)
A class that describes univariate distributions
Objects can be created by calls of the form new("distribution", ...). There is also
a constructor which is also named distribution.
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
Francisco Gochez <[email protected]>
distribution, mvdistribution, mvdistribution
showClass("distribution")showClass("distribution")
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.
getPriorEstim(x, spec=NULL, ...) getPosteriorEstim(x, spec=NULL, ...)getPriorEstim(x, spec=NULL, ...) getPosteriorEstim(x, spec=NULL, ...)
x |
multivariate time series |
spec |
optional portfolio specification |
... |
additional arguments |
A list with 2 elements:
mu |
estimate of mean |
Sigma |
estimate of covariance |
Richard Chandler-Mant <[email protected]>
A collection of functions to extract several fields of BLViews, COPViews, COPPosterior and BLPosterior objects.
assetSet(views) viewMatrix(views, dropZeroColumns = TRUE) PMatrix(views) confidences(views) posteriorMeanCov(posterior) posteriorSimulations(posterior) numSimulations(posterior) priorViews(posterior)assetSet(views) viewMatrix(views, dropZeroColumns = TRUE) PMatrix(views) confidences(views) posteriorMeanCov(posterior) posteriorSimulations(posterior) numSimulations(posterior) priorViews(posterior)
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 |
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 |
Francisco Gochez <[email protected]>
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)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)
A class that describes multivariate distributions
Objects can be created by calls of the form new("distribution", ...). There is also
a constructor which is also named mvdistribution.
RName:Object of class "character". This is the R "suffix" of the distirbution.
parameters:A named list of parameters that characterize the distribution
Francisco Gochez <[email protected]>
distribution, mvdistribution, distribution-class
showClass("mvdistribution")showClass("mvdistribution")
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.
optimalPortfolios(result, optimizer = .optimalWeights.simpleMV, ..., doPlot = TRUE, beside = TRUE) optimalPortfolios.fPort(result, spec = NULL, constraints = "LongOnly", optimizer = "minriskPortfolio", inputData = NULL, numSimulations = BLCOPOptions("numSimulations"))optimalPortfolios(result, optimizer = .optimalWeights.simpleMV, ..., doPlot = TRUE, beside = TRUE) optimalPortfolios.fPort(result, spec = NULL, constraints = "LongOnly", optimizer = "minriskPortfolio", inputData = NULL, numSimulations = BLCOPOptions("numSimulations"))
result |
An object of class |
optimizer |
For |
spec |
Object of class |
inputData |
Time series data (any form that can be coerced into a |
constraints |
String of constraints that may be passed into |
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 |
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.
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.
It is expected that optimalPortfolios will be deprecated in future releases in favour of
optimalPortfolios.fPort.
Francisco Gochez <[email protected]>
Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009); Portfolio Optimization with R/Rmetrics, Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.
## 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)## 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.
posteriorEst(views, mu, tau = 0.5, sigma, kappa = 0)posteriorEst(views, mu, tau = 0.5, sigma, kappa = 0)
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 |
An object of class BLResult holding the updated Black-Litterman posterior
Francisco
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.
posteriorFeasibility(result)posteriorFeasibility(result)
result |
An object of class BLResult |
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.
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 |
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.
Francisco Gochez <[email protected]>
Fusai, Gianluca and Meucci, Attilio. "Assessing Views", 2002. http://www.symmys.com/AttilioMeucci/Research/PublFinance/PublFinance.html
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)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)
These functions allow for direct replacement of fields of view objects such as the pick matrix and vector of confidences.
PMatrix(views) <- value confidences(views) <- value qv(views) <- valuePMatrix(views) <- value confidences(views) <- value qv(views) <- value
views |
An object of class BLViews or COPViews, except in the case of qv<- which applies only to BLViews |
value |
A vector in |
The object is modified directly
Francisco Gochez <[email protected]>
## 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## 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
Uses the RUnit package to execute a series of unit tests.
runBLCOPTests(testPath = BLCOPOptions("unitTestPath"), protocolFile = "BLCOPTests.html", writeProtocol = FALSE)runBLCOPTests(testPath = BLCOPOptions("unitTestPath"), protocolFile = "BLCOPTests.html", writeProtocol = FALSE)
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? |
The summary of an object returned by RUnit's runTestSuite
These unit tests are in need of additional test cases, and should not be regarded as exhaustive in their current state.
Francisco Gochez <[email protected]>
## Not run: runBLCOPTests() ## End(Not run)## Not run: runBLCOPTests() ## End(Not run)
Generates samples from a distribution held by an object of class distribution or
mvdistribution. Intended mainly for internal use.
sampleFrom(dstn, n = 1)sampleFrom(dstn, n = 1)
dstn |
an object of class |
n |
Number of samples to generate |
A vector or matrix of samples.
Francisco Gochez <[email protected]>
x <- distribution("pois", lambda = 5) hist(sampleFrom(x, 1000), col = "blue", prob = TRUE)x <- distribution("pois", lambda = 5) hist(sampleFrom(x, 1000), col = "blue", prob = TRUE)
Monthly returns of the S&P 500 index for the period 2/2/1998 through 1/12/2003
sp500Returnssp500Returns
A matrix with 1 column and 71 rows.
ts.plot(sp500Returns)ts.plot(sp500Returns)
The monthly rate of return of the US 13 week Treasury Bill for the period 30/1/1998 through 30/11/2003.
US13wTBUS13wTB
A one-column matrix with 71 rows.
ts.plot(US13wTB)ts.plot(US13wTB)