# optimizePortfolio: Optimize a portfolio using the specified correlation filter In tawny: Clean Covariance Matrices Using Random Matrix Theory and Shrinkage Estimators for Portfolio Optimization

## 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: RandomMatrixDenoiser for using random matrix theory, ShrinkageDenoiser 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 RandomMatrixDenoiser, one can choose whether a histogram or a kernel density estimator is used to calculate the probability density function. With ShrinkageDenoiser one can select a constant correlation model or the identity as the model.

## Usage

 ```1 2 3``` ```optimizePortfolio(...) p.optimize(h, c.denoised) ```

## Arguments

 `h` A zoo object representing a portfolio with dimensions T x M `c.denoised` A cleaned correlation matrix `...` Additional parameters

## Details

optimizePortfolio(h, window, cor.gen, ...)

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 RandomMatrixDenoiser function or ShrinkageDenoiser 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.

## Value

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

## Author(s)

Brian Lee Yung Rowe

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```require(tawny.types) data(sp500.subset) p <- TawnyPortfolio(sp500.subset, window=190) ws <- optimizePortfolio(p, SampleDenoiser() ) ws <- optimizePortfolio(p, EmpiricalDenoiser() ) ws <- optimizePortfolio(p, RandomMatrixDenoiser() ) ws <- optimizePortfolio(p, ShrinkageDenoiser() ) ## Not run: # This is computationally faster although the convenient approach is to pass # in the character symbol directly: ShrinkageDenoiser(market='^GSPC') m <- getPortfolioReturns('^GSPC', obs=1000, end='2009-02-27') ws <- optimizePortfolio(p, ShrinkageDenoiser(market=m) ) ## End(Not run) ```

tawny documentation built on April 21, 2018, 1:05 a.m.