Tag Archives: Ledoit-Wolf shrinkage

Variance matrix differences

Torturing portfolios to give different volatilities between a factor model and Ledoit-Wolf shrinkage. Previously There have been posts on: “What the hell is a variance matrix?” factor models Ledoit-Wolf shrinkage Question Two of the several ways to produce an estimate of the variance matrix of asset returns is a statistical factor model and Ledoit-Wolf shrinkage.  … Continue reading

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Predicted correlations and portfolio optimization

What effect do predicted correlations have when optimizing trades? Background A concern about optimization that is not one of “The top 7 portfolio optimization problems” is that correlations spike during a crisis which is when you most want optimization to work. This post looks at a small piece of that question.  It wonders if increasing predicted … Continue reading

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Variability of predicted portfolio volatility

A prediction of a portfolio’s volatility is an estimate — how variable is that estimate? Data The universe is 453 large cap US stocks. The variance matrices are estimated with the daily returns in 2012. Variance estimation was done with Ledoit-Wolf shrinkage (shrinking towards equal correlation). Two sets of random portfolios were created.  In both … Continue reading

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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

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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Three things factor models do

Factor models are heavily used in finance to create variance matrices. Here’s why. Factor models: Provide non-degenerate estimates Save space Quantify sources of risk Non-degenerate estimates First off, what does this mean? The technical term is that you want your estimate of the variance matrix to be positive definite.  In practical terms what that means … Continue reading

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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

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

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

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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