Publications by Pat
Time series equivalence of brains and markets
fMRI data from 90 locations in the brain look somewhat like daily closing prices on 116 stocks if you squint just right. Marginal Revolution was nice enough to point to “Topological isomorphisms of human brain and financial market networks”. I’ve only just glanced through the paper. I find it interesting, but I’m fairly skeptical. The...
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Predictability of kurtosis and skewness in S&P constituents
How much predictability is there for these higher moments? Data The data consist of daily returns from the start of 2007 through mid 2011 for almost all of the S&P 500 constituents. Estimates were made over each half year of data. Hence there are 8 pairs of estimates where one estimate immediately follows the other. What is more important than ...
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Does the S&P 500 exhibit seasonality through the year?
Are there times of the year when returns are better or worse? Abnormal Returns prompted this question with “SAD and the Halloween indicator” in which it is claimed that the US market tends to outperform from about Halloween until April. Data The data consisted of 15,548 daily returns of the S&P 500 starting in 1950. Then the point along the...
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How to compute portfolio returns badly
For those who naturally compute portfolio returns correctly here are some lessons in how to do it wrong. The data Random portfolios were generated from constituents of the S&P 500 with constraints: long-only exactly 20 assets in the portfolio no more than 10% weight for any asset (just for fun) the sum of the 5 largest weights no more than 40% ...
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Introduction to “Numerical Methods and Optimization in Finance”
The book is by Manfred Gilli, Dietmar Maringer and Enrico Schumann. I haven’t actually seen the book, so my judgement of it is mainly by the cover (and knowing the first two authors). The parts of the book closest to my heart are optimization, particularly portfolio optimization, and particularly particularly portfolio optimization via heuris...
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Risk parity
Some thoughts and resources regarding a popular fund management buzzword. The idea Given asset categories (like stocks, bonds and commodities) create a portfolio where each category contributes equally to the portfolio variance. Two operations There are two cases in creating a risk parity portfolio: the universe is the asset categories the unive...
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Variability of volatility estimates from daily returns
Investment Performance Guy has a post “Periodicity of risk statistcs (and other measures)” in which it is wondered how valid volatility estimates are from a month of daily returns. Here is a quick look. Figure 1 shows the variability (and a 95% confidence interval) of volatility estimates for the S&P 500 index in January 2011. Figure 2 is...
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The mystery of volatility estimates from daily versus monthly returns
What drives the estimates apart? Previously A post by Investment Performance Guy prompted “Variability of volatility estimates from daily data”. In my comments to the original post I suggested that using daily data to estimate volatility would be equivalent to using monthly data except with less variability. Dave, the Investment Performance...
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Another look at autocorrelation in the S&P 500
Casting doubt on the possibility of mean reversion in the S&P 500 lately. Previously A look at volatility estimates in “The mystery of volatility estimates from daily versus monthly returns” led to considering the possibility of autocorrelation in the returns. I estimated an AR(1) model through time and added a naive confidence interval to ...
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Performance measurement is about decisions
The return of a hypothetical fund was 17.9% in 2010. We want to know if that is good or bad. The benchmark method The assets in the portfolio are constituents of the S&P 500, so we can compare our fund return to the return of the index. Figure 1: 2010 returns of: the fund and the S&P 500. That looks pretty good for the fund. But is it? One pr...
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