Posts Tagged ‘ Ledoit-Wolf shrinkage ’

How to add a benchmark to a variance matrix

October 1, 2012
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How to add a benchmark to a variance matrix

There is a good way and a bad way to add a benchmark to a variance matrix that will be used for optimization and similar operations.  Our examination sheds a little light on the process of variance matrix estimation in this realm. Role of benchmarks Investing Benchmarks are common in investment management.  It’s my opinion … Continue reading...

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Correlations and postive-definiteness

May 22, 2012
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Correlations and postive-definiteness

On the way to another destination, I found some curious behavior with average correlations. The data Daily log returns from almost all of the constituents of the S&P 500 for years 2006 through 2011. The behavior Figure 1 shows the actual mean correlation among stocks for the set of years and the mean correlation with … Continue reading...

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The quality of variance matrix estimation

March 12, 2012
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The quality of variance matrix estimation

A bit of testing of the estimation of the variance matrix for S&P 500 stocks in 2011. Previously There was a plot in “Realized efficient frontiers” showing the realized volatility in 2011 versus a prediction of volatility at the beginning of the year for a set of random portfolios.  A reader commented to me privately … Continue reading...

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Realized efficient frontiers

February 27, 2012
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Realized efficient frontiers

A look at the distortion from predicted to realized. The idea The efficient frontier is a mainstay of academic quant.  I’ve made fun of it before.  This post explores the efficient frontier in a slightly less snarky fashion. Data The universe is 474 stocks in the S&P 500.  The predictions are made using data from … Continue reading...

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The BurStFin R package

February 16, 2012
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The BurStFin R package

Version 1.01 of BurStFin is now on CRAN. It is written entirely in R, and meant to be compatible with S+. Functionality The package is aimed at quantitative finance, but the variance estimation functions could be of use in other applications as well. Also of general interest is threeDarr which creates a three-dimensional array out … Continue reading...

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Sensitivity of risk parity to variance differences

January 9, 2012
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Sensitivity of risk parity to variance differences

Equal risk contribution of assets determines the asset weights given the variance matrix.  How sensitive are those weights to the variance estimate? Previously The post “Risk parity” gave an overview of the idea. In particular it distinguished the cases: the assets have equal risk contribution groups of assets have equal risk contribution A key difference … Continue reading...

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Again with Ledoit-Wolf and factor models

May 4, 2011
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Again with Ledoit-Wolf and factor models

We come closer to a definitive answer on the relative merit of Ledoit-Wolf shrinkage versus a statistical factor model for variance matrices. Previously This post builds on the post entitled: A test of Ledoit-Wolf versus a factor model That post depended on some posts previous to it. New information Previously we generated random portfolios with … Continue reading...

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A test of Ledoit-Wolf versus a factor model

April 27, 2011
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A test of Ledoit-Wolf versus a factor model

Statistical factor models and Ledoit-Wolf shrinkage are competing methods for estimating variance matrices of returns.  So which is better?  This adds a data point for answering that question. Previously There are past blog posts on: the idea of variance matrices factor models of variance The data in this post are from the blog posts: “Weight … Continue reading...

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