There is many flavors of artificial intelligence (AI), however I want to show practical example of the cluster analysis. It is very applicable in finance. For example, one of stylized facts of volatility is, that it moves in clusters, meaning that today’s volatility will be more likely as yesterday’... [Read more...]

Winsorization replaces extreme data values with less extreme values. But why Extreme values sometimes have a big effect on statistical operations.  That effect is not necessarily a good effect.  One approach to the problem is to change the statistical operation — this is the field of robust statistics. An alternative solution ... [Read more...]

[Read more...]

If returns had infinite variance, would there be a problem bootstrapping information ratios? Background There is a discussion on the Quant Finance group of LinkedIn with the title: “How do you measure the confidence intervals of performance ratios?” One suggestion was to use the statistical bootstrap. This resulted in a ... [Read more...]

Graphs like Figure 1 are reasonably common.  But they are not reasonable. Figure 1: A (log) price series with an explicit guide line. Some have the prices on a logarithmic scale, which is an improvement on the raw prices. The problem with this sort of plot is that two particular data points ... [Read more...]

[Read more...]

bout half a year ago, I wrote a post on the configuration of (pgf)Sweave and LyX, which was intended to save us some efforts in going through all the details during the configuration. Now many things have changed: LyX 2.0 has internal support for Sweave, and fortunately I have been ... [Read more...]

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...]

While investigating Intraday patterns in FX returns and order flow paper I have faced the problem with timezone. I had 3 data sources with different timezones (GMT, CET, CEST). Most confusing thing was, that I didn’t know, how to deal with summer time. But why did I have the data ... [Read more...]

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...]

[Read more...]

I remember a few weeks ago, there was a challenge in the R-help list to make the prime symbol in R graphics. In LaTeX, we simply write $X'$ or $X^\prime$. R has a rough support for math expressions (see demo(plotmath)) and they are certainly unsatisfactory for LaTeX users. ... [Read more...]

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...]

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...]

Transaction cost analysis (TCA) is the framework to achieve best execution in trading context. TCA can be split into three groups: pre-trade analysis, intraday analysis, and post-trade measurement. Pre-trade analysis allows us to get insight about the future volatility of the price, forecast intra-day and daily volumes, market impact. It ... [Read more...]

How well do asset weight constraints constrain risk? The setup In “Unproxying weight constraints” I claimed that many constraints on asset weights are really a proxy for constraining risk. That is not a problem if weights are a good proxy for risk.  So the question is: how good of a ... [Read more...]

All my recent plots are built using ggplot2 package. I don’t know if my dear readers have noticed the difference, but from my point of view, ggplot2 allows to create nice looking and aesthetics plots. I was using this package before, but the real boost came after reading this ... [Read more...]

Overfitting is a problem when trying to predict financial returns.  Perhaps you’ve heard that before.  Some simple examples should clarify what overfitting is — and may surprise you. Polynomials Let’s suppose that the true expected return over a period of time is described by a polynomial. We can easily ... [Read more...]

I came up with an idea to draw correlation network to get a grasp about relationship between a list of stocks. An alternative way to show correlation matrix would be head map, which can have limitations with big matrices (__100). Unfortunately,  ggplot2 package doesn’t have a easy way to draw ... [Read more...]

[Read more...]