Quant finance

Asynchrony in market data

November 21, 2011 | Pat

Be careful if you have global daily data. The issue Markets around the world are open at different times.  November 21 for the Tokyo stock market is different from November 21 for the London stock market.  The New York stock market has yet a different November 21. The effect The major effect is ... [Read more...]

Another look at autocorrelation in the S&P 500

November 11, 2011 | Pat

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 ... [Read more...]

The mystery of volatility estimates from daily versus monthly returns

November 8, 2011 | Pat

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 ... [Read more...]

Variability of volatility estimates from daily returns

November 3, 2011 | Pat

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 ... [Read more...]

Risk parity

October 31, 2011 | Pat

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 ... [Read more...]

How to compute portfolio returns badly

October 24, 2011 | Pat

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 ... [Read more...]

Does the S&P 500 exhibit seasonality through the year?

October 20, 2011 | Pat

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&... [Read more...]

Predictability of kurtosis and skewness in S&P constituents

October 3, 2011 | Pat

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 ... [Read more...]

Time series equivalence of brains and markets

September 27, 2011 | Pat

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 ... [Read more...]

Beta and expected returns

September 16, 2011 | Pat

Some pictures to explore the reality of the theory that stocks with higher beta should have higher expected returns. Figure 2 of “The effect of beta equal 1″ shows the return-beta relationship as downward sloping.  That’s a sample of size 1.  In this post we add six more datapoints. Data The exact ... [Read more...]

A brief history of S&P 500 beta

September 8, 2011 | Pat

Data The data are daily returns starting at the beginning of 2007.  There are 477 stocks for which there is full and seemingly reliable data. Estimation The betas are all estimated on one year of data. The times that identify the betas mark the point at which the estimate would become available.  ... [Read more...]

Realized beta and beta equal 1

August 30, 2011 | Pat

What does beta look like in the out-of-sample period for the portfolios generated to have beta equal to 1? In the comments Ian Priest wonders if the results in “The effect of beta equal 1″ are due to a shift in beta from the estimation period to the out-of-sample period.  (The current ... [Read more...]

The effect of beta equal 1

August 29, 2011 | Pat

Investment Performance Guy had a post about beta equal 1.  It made me wonder about the properties of portfolios with beta equal 1.  When I looked, I got a bigger answer than I expected. Data I have some S&P 500 data lying about from the post ‘On “Stock correlation has been rising”‘.  ... [Read more...]

More S&P 500 correlation

July 28, 2011 | Pat

Here are some additions to the previous post on S&P 500 correlation. Correlation distribution Before we only looked at mean correlations.  However, it is possible to see more of the distribution than just the mean.  Figures 1 and 2 show several quantiles: 10%, 25%, 50%, 75%, 90%. Figure 1: Quantiles of 50-day rolling correlation of … Continue reading → [Read more...]

On “Stock correlation has been rising”

July 17, 2011 | Pat

Ticker Sense posted about the mean correlation of the S&P 500. The plot there — similar to Figure 1 — shows that correlation has been on the rise after a low in February. Figure 1: Mean 50-day rolling correlation of S&P 500 constituents to the index. For me, this post raised a whole lot ... [Read more...]

Selections from the R/Finance conference

June 2, 2011 | Pat

The R/Finance conference happened in Chicago at the end of April.  If, like me, you weren’t there, you can still benefit from it because slides from many of the talks are now online. Here is a quick synopsis (in chronological order) of some of the talks I found ...
[Read more...]

Specific differences between Ledoit-Wolf and factor models

May 22, 2011 | Pat

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 ... [Read more...]

Again with Ledoit-Wolf and factor models

May 4, 2011 | Pat

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 ... [Read more...]

A test of Ledoit-Wolf versus a factor model

April 27, 2011 | Pat

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 ... [Read more...]

Risk fraction constraints and volatility

April 21, 2011 | Pat

What is the effect on predicted and realized volatility of substituting risk fraction constraints for weight constraints? Previously This post depends on two previous blog posts: “Unproxying weight constraints” “Weight compared to risk fraction” The exact same sets of random portfolios are used in this post that were generated in ... [Read more...]
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