Specifics of statistical factor models and of a particular implementation of them. Previously Posts that are background for this one include: Three things factor models do Factor models of variance in finance The BurStFin R package The quality of variance matrix estimation The problem Someone asked me some questions about ... [Read more...]

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Should you use daily or monthly returns to estimate volatility? Does garch explain why volatility estimated with daily data tends to be bigger than if it is estimated with monthly data? Previously There are a number of previous posts — with the variance compression tag — that discuss the phenomenon of volatility ... [Read more...]

Which sectors are coherent, and which aren’t? Previously The post “S&P 500 correlations up to date” looked at rolling mean correlations among stocks.  In particular it looked at rolling mean correlations of stocks within sectors. Of importance to this post is that the sectors used are taken from Wikipedia. ... [Read more...]

I haven’t heard much about correlation lately.  I was curious about what it’s been doing. Data The dataset is daily log returns on 464 large cap US stocks from the start of 2006 to 2012 October 5. The sector data were taken from Wikipedia. The correlation calculated here is the mean correlation ... [Read more...]

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What is variance targeting in garch estimation?  And what is its effect? Previously Related posts are: A practical introduction to garch modeling Variability of garch estimates garch estimation on impossibly long series The last two of these show the variability of garch estimates on simulated series where we know the ... [Read more...]

The variability of garch estimates when the series has 100,000 returns. Experiment The post “Variability of garch estimates” showed estimates of 1000 series that were each 2000 observations long.  Here we do the same thing except that the series each have 100,000 observations. That would be four centuries of daily data.  It’s not ... [Read more...]

Not exactly pin-point accuracy. Previously Two related posts are: A practical introduction to garch modeling garch and long tails Experiment 1000 simulated return series were generated.  The garch(1,1) parameters were alpha=.07, beta=.925, omega=.01.  The asymptotic variance for this model is 2.  The half-life is about 138 days. The simulated series used a Student’... [Read more...]

Previously This book and the associated R package were introduced before. Executive Summary A very nice — and enlightening — discussion of a wide range of topics. Principles The Introduction to the book sets out 5 principles.  This is probably the most important part of the book.  The principles are: We don’t ... [Read more...]

How much does garch shorten long tails? Previously Pertinent blog posts include: “A practical introduction to garch modeling” “The distribution of financial returns made simple” “Predictability of kurtosis and skewness in S&P constituents” Induced tails Part of the reason that the distributions of returns have long tails is because ... [Read more...]

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Portfolio diversity is a balancing act. Previously The post “Portfolio diversity” talked about the role of the correlation between assets and the portfolio.  The current post fills a hole in that post. The 2 dimensions asset-portfolio correlation Each asset in the universe has a correlation with the portfolio.  If there are ... [Read more...]

We look at volatility clustering, and some aspects of modeling it with a univariate GARCH(1,1) model. Volatility clustering Volatility clustering — the phenomenon of there being periods of relative calm and periods of high volatility — is a seemingly universal attribute of market data.  There is no universally accepted explanation of it. ... [Read more...]

A look at a simplistic measure of stock-picking opportunity. Motivation The interquartile range (the spread of the middle half of the data) has recently been added to the market portrait plots.  Putting those numbers into historical context was the original impulse. However, this led to thinking about change in stock-picking ... [Read more...]

Maximum drawdown is blazingly variable. Psychology Probably the most salient feature that an investor notices is the amount lost since the peak: that is, the maximum drawdown. Just because drawdown is noticeable doesn’t mean it is best to notice. Statistics The paper “About the statistics of the maximum drawdown ... [Read more...]

A look at return variability for portfolio changes. The problem Suppose we make some change to our portfolio.  At a later date we can see if that change was good or bad for the portfolio return.  Say, for instance, that it helped by 16 basis points.  How do we properly account ... [Read more...]

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 ... [Read more...]

How many baskets are your eggs in? Meucci diversity Attilio Meucci directly addresses the adage: Don’t put all your eggs in one basket. His idea is to think of your portfolio as a set of  subportfolios that are each uncorrelated with the rest.  If your portfolio can be configured ... [Read more...]