Quant finance

The guts of a statistical factor model

November 12, 2012 | Pat

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...]

An easy mistake with returns

November 5, 2012 | Pat

When aggregating over both time and assets, the order of aggregation matters. Task We have the weights for a portfolio and we want to use those and a matrix of returns over time to compute the (long-term) portfolio return. “A tale of two returns” tells us that aggregation over time ...
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Volatility from daily or monthly: garch evidence

October 29, 2012 | Pat

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...]

S&P 500 sector strengths

October 10, 2012 | Pat

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...]

S&P 500 correlations up to date

October 8, 2012 | Pat

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...]

How to add a benchmark to a variance matrix

October 1, 2012 | Pat

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 ...
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Variance targeting in garch estimation

September 24, 2012 | Pat

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...]

garch estimation on impossibly long series

September 20, 2012 | Pat

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...]

Variability of garch estimates

September 17, 2012 | Pat

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...]

garch and long tails

August 27, 2012 | Pat

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...]

Highlights of R in Finance 2012

August 13, 2012 | Pat

I unfortunately was not there, but we can vicariously enjoy it via the presentations that are posted on the conference website. Below is my take on the highlights (in chronological order). Peter Carl and Brian Peterson “Constructing Strategic Hedge Fund Portfolios” is wonderful from my perspective.  Promoting random portfolios is ...
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Returns with negative net asset values

July 30, 2012 | Pat

How are returns calculated when net asset value goes negative? Previously In “A tale of two returns” we highlighted the similarities and differences of log returns versus simple returns. Positive valuation We create — in R — an example of net asset value at four times: __ nav1 nav1 … Continue reading →
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2 dimensions of portfolio diversity

July 16, 2012 | Pat

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...]

A practical introduction to garch modeling

July 6, 2012 | Pat

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...]

Cross sectional spread of stock returns

June 18, 2012 | Pat

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...]

Variability in maximum drawdown

June 4, 2012 | Pat

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...]

Jackknifing portfolio decision returns

May 28, 2012 | Pat

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...]

Correlations and postive-definiteness

May 22, 2012 | Pat

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...]

Portfolio diversity

May 7, 2012 | Pat

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...]
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