tawny (version 1.0)

optimizePortfolio: Optimize a portfolio using the specified correlation filter

Description

Performs basic minimum variance optimization on the given portfolio over the given window returning a zoo object of portfolio weights. The window must be less than or equal to the number of observations in h (s.t. if they are equal then only one resultant weight vector will be returned).

A number of preconfigured correlation matrix filters are available: getCorFilter.RMT for using random matrix theory, getCorFilter.Shrinkage returns a function for filltering the correlation matrix using a shrinkage estimator. A raw version is provided for comparison. These functions provide reasonable configurability, for example with getCorFilter.RMT, one can choose whether a histogram or a kernel density estimator is used to calculate the probability density function. With getCorFilter.Shrinkage one can select a constant correlation model or the identity as the model.

Usage

optimizePortfolio(h, window, cor.gen, ...)
getCorFilter.Shrinkage(prior.fun = cov.prior.cc, ...)
getCorFilter.RMT(hint = c(4,1), ...)
getCorFilter.raw()
p.optimize(h, c.denoised)

Arguments

h

A zoo object representing a portfolio with dimensions T x M

window

The size of the window to use when generating a correlation matrix

cor.gen

A function that takes a portfolio with window observations and generates a correlation matrix

prior.fun

The function that generates the prior/model covariance matrix for shrinkage estimation

hint

A hint for the correct value of Q and sigma for random matrix theory

c.denoised

A cleaned correlation matrix

...

Additional parameters to pass to the cor.gen function

Value

• A weights zoo object with T - t + 1 dates and M assets. The dates are aligned to the end date.

Details

This is the primary entry point to using the tawny package. This function calculates the portfolio weights over the portfolio based on a rolling window. Given M assets in the portfolio, T total observations, and a window of length t, the resulting weights object will have dimensions T - t + 1 x M.

The weights matrix can then be analyzed to calculate standard portfolio performance metrics. A simple analytics function is provided so that cumulative returns can be easily viewed, although for more sophisticated analysis other packages should be used.

In theory any compatible correlation matrix generator can be used (and has in practice to test against proprietary risk models) and the function will generate portfolio weights accordingly. To leverage the remainder of the package, the getCorFilter.RMT function or getCorFilter.Shrinkage should be called. These wrappers are somewhat superfluous but do provide some utility by ensuring compatibility with the underlying RMT code that uses transposed matrices (pre-zoo integration). Additionally, by way of closures these functions are used to store hints to the optimizer and any final data massaging, potentially cleaning up code but admittedly can be serviced via the normal dots mechanism.

In the future, the default will be a direct handle to the underlying function once the rest of the code is converted to zoo.

The secondary function optimizePortfolio.RMT exists to optimize the correlation matrix using RMT exclusively. This is a more direct route to accessing the RMT functionality and might be more convenient to use. The intention is that the base optimizePortfolio function becomes a generic function that passes on to specific implementations, but the mechanics haven't been worked out yet. It is also possible to extract the optimizer and pass that in explicitly as a function.

Examples

data(sp500.subset)
h <- sp500.subset
ws <- optimizePortfolio(h, 190, getCorFilter.RMT() )
ws <- optimizePortfolio(h, 190, getCorFilter.Shrinkage() )