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# Tag Archives: variance matrix

## 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

## 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

Posted in Quant finance, R language
Tagged Ledoit-Wolf shrinkage, statistical bootstrap, variance matrix
3 Comments

## 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

Posted in Quant finance, R language
Tagged benchmark, Ledoit-Wolf shrinkage, statistical factor model, variance matrix
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## A variance campaign that failed

they ought at least be allowed to state why they didn’t do anything and also to explain the process by which they didn’t do anything. First blush One of the nice things about R is that new statistical techniques fall into it. One such is the glasso (related to the statistical lasso) which converts degenerate … Continue reading

## 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

Posted in Quant finance, R language
Tagged Ledoit-Wolf shrinkage, statistical factor model, variance matrix
7 Comments

## Specific differences between Ledoit-Wolf and factor models

What can we learn about the difference in structure between a Ledoit-Wolf variance matrix and a corresponding factor model variance? Previously We’ve generated a set of random portfolios with constraints on the risk fractions of a Ledoit-Wolf variance matrix, and a corresponding set of random portfolios with risk fraction constraints from a statistical factor model. … Continue reading

Posted in Quant finance, R language
Tagged correlations, covariance matrix, Ledoit-Wolf shrinkage, risk fraction, variance matrix
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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

Posted in Quant finance, R language
Tagged covariance matrix, factor model, Ledoit-Wolf shrinkage, risk fraction, S&P 500, variance matrix
2 Comments

## 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

Posted in Quant finance, R language
Tagged covariance matrix, factor model, Ledoit-Wolf shrinkage, risk fraction, S&P 500, variance matrix
1 Comment

## Factor models of variance in finance

In “What the hell is a variance matrix?” I talked about the basics of variance matrices and highlighted challenges for estimating them in finance. Here we look more deeply at the most popular estimation technique. Models for variance matrices The types of variance estimates that are used in finance can be classified as: Sample estimate … Continue reading

Posted in R language, Risk
Tagged covariance matrix, factor model, risk model, variance matrix
10 Comments

## What the hell is a variance matrix?

When I first came to finance, I kept hearing about “risk models”. I wondered, “What the hell is a risk model?” Of course, I didn’t say this out loud — that would have given the game away. My wife has strict instructions that she is to be the only one to know that I’m an … Continue reading

Posted in R language, Risk, Statistics
Tagged covariance matrix, risk model, variance matrix
17 Comments