tawny (version 1.0)

tawny-package: Provides various portfolio optimization strategies including random matrix theory and shrinkage estimators

Description

Portfolio optimization typically requires an estimate of a covariance matrix of asset returns. There are many approaches for constructing such a covariance matrix, some using the sample covariance matrix as a starting point. This package provides implementations for two such methods: random matrix theory and shrinkage estimation. Each method attempts to clean or remove noise related to the sampling process from the sample covariance matrix. Random matrix theory does this by using the known eigenvalue distribution of a random matrix as the null hypothesis, scaling any eigenvalues below a threshold to a lower bound, thus eliminating the noise related to the idiosyncratic noise of the matrix. Shrinkage estimation shrinks the sample covariance matrix towards a so-called global average that theoretically represents a truer estimate of the covariance matrix. A single API is provided for generating asset weights based on the different approaches.

Details

ll{ Package: tawny Type: Package Version: 1.0 Date: 2009-03-02 License: GPL-2 } There are a number of ways to use this package. At a high level, the estimation techniques can be applied to a portfolio and optimized portfolio weights are returned. This is followed by calculation of basic portfolio statistics and comparison functions to provide a quick, visual check to the results. It is possible to embark on further study using other packages (e.g. PerformanceAnalytics). If a zoo object already exists, then this is as simple as calling optimizePortfolio and specifying an appropriate (and built-in) function for generating a correlation matrix.

In addition to these functions there are a number of convenience methods for constructing simple portfolios for a given date range via quantmod. This includes getPortfolioReturns and ensure.

To get started using the package, the only requirement is to have a history of returns for the assets in the portfolio. The length of the portfolio is the sum of the window selected and the time frame to optimize against,

For people interested in studying the core behavior of Random Matrix Theory, theunderlying mp.* functions are available. These functions provide direct control over eigenvalue density histogram plotting, theoretical distributions as specified by Marcenko and Pastur, and optimization functions for fitting the two. In most cases the functions are designed to be pluggable as they climb the tree of abstraction, meaning that an arbitrary optimization function can be plugged into the fitting function, and so on.

For people interested in studying shrinkage estimation techniques, these functions are primarily exposed as shrinkage.*.

References

Gatheral, Jim. "Random Matrix Theory and Covariance Estimation." 3 Oct. 2008. New York. 7 Oct. 2008 .

Potters, Marc; Bouchaud, Jean-Philippe; Laloux, Laurent. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces." Jul. 2005. Paris. 10 Dec. 2008

Olivier Ledoit and Michael Wolf. "Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection." Oct. 2001. London. 12 Feb. 2009

See Also

optimizePortfolio, filter.RMT, getPortfolioReturns

Examples

## High level use of package
# Select a portfolio using 200 total observations
data(sp500.subset)
h <- sp500.subset
# Optimize using a window of length 200 (there will be 51 total iterations)
ws <- optimizePortfolio(h, 150, getCorFilter.RMT() )
# Plot the performance of the resulting optimized portfolio
pf <- plotPerformance(h, ws, 150, y.min=-0.4)
# Compare the performance with a naive equal-weighted portfolio
ef <- compare.EqualWeighted(h, 150, y.min=-0.4)
# Also compare against the S&P 500
mf <- compare.Market('^GSPC',200,150, y.min=-0.4)

# Generate weights based on the constant correlation shrinkage estimator
ws <- optimizePortfolio(h, 150, getCorFilter.Shrinkage())
pf <- plotPerformance(h, ws, 150, y.min=-0.4)


## Low level use of the package
# View the theoretical Marcenko-Pastur distribution of eigenvalues of a
# random matrix
mp.theory(Q=4.2, sigma=1.1)

# Calculate the density of eigenvalues for a matrix of portfolio returns
h <- getRandomMatrix(20, 100)
hist <- mp.density.kernel(h)

# Fit an empirical distribution to a theoretical curve
hint <- c(6,2)
o <- optim(hint, mp.fit.kernel(hist))