optimalPortfolios: Calculates optimal portfolios under prior and posterior...
In BLCOP: Black-Litterman and copula-opinion pooling frameworks

Description Usage Arguments Details Value Note Author(s) References Examples

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.

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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 `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.

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 <fgochez@mango-solutions.com>

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)