Articles by Pat

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...]

The R Inferno revised

May 1, 2011 | Pat

Hell is new and improved. The R Inferno has been revised.  If you don’t know of it, it is a short explanation of a few trouble spots when using the R language.  Somehow the short explanation grew to approach book-length. It can be found at the usual place: http://...
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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...]

Weight compared to risk fraction

April 18, 2011 | Pat

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...]

The devil of overfitting

March 27, 2011 | Pat

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...]

Factor models of variance in finance

March 7, 2011 | Pat

In “What the hell is a variance matrix?” I talked about the basics of variance matrices and highlighted challenges for estimating them in finance.  Here we look more deeply at the most popular estimation technique. Models for variance matrices The types of variance estimates that are used in finance can ...
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4 and a half myths about beta in finance

February 8, 2011 | Pat

Much of what has been said and thought about beta in finance is untrue. Myth 1: beta is about volatility This myth is pervasive. Beta is associated with the stock’s volatility but there is more involved.  Beta is the ratio of the volatility of the stock to the volatility of ... [Read more...]

Review of “R Graphs Cookbook” by Hrishi Mittal

January 24, 2011 | Pat

Executive summary: Extremely useful for new users, informative to even quite seasoned users. Refereeing Once upon a time a publisher asked if I would referee a book (unspecified) about R.  In an instance that can only be described as psychotic I said yes.  That bit of insanity turned out to ...
[Read more...]

Paying interest and the number e

January 24, 2011 | Pat

Suppose I borrow a dollar from you and I’ll pay you 100% interest at the end of the year.  How much money will you have then? $1 * (1 + 1) = $2 What happens if instead the interest is calculated as  50% twice in the year? $1 * (1.5 * 1.5) = $2.25 After … Continue reading →
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Normal market accidents

January 17, 2011 | Pat

We think of accidents as abnormal events, but there is “normal accident” theory.  We don’t think of accidents happening in markets, but they do.  That’s why it’s called a market crash. For normal accidents to come into play, two conditions need to hold: the system is complex ...
[Read more...]

The number 1 novice quant mistake

January 12, 2011 | Pat

It is ever so easy to make blunders when doing quantitative finance.  Very popular with novices is to analyze prices rather than returns. Regression on the prices When you want returns, you should understand log returns versus simple returns. Here we will be randomly generating our “returns” (with R) and ...
[Read more...]

Some market predictions

January 6, 2011 | Pat

We look at a few forecasts for the year 2011 that we’ve run across, and compare them with the prediction distributions presented in Revised market prediction distributions. FTSE 100 There is a “range forecast” on an Interactive Investor page of 5350 to 6565.  It isn’t clear (to me at least) what this ...
[Read more...]

Revised market prediction distributions

January 4, 2011 | Pat

This provides revised plots of the prediction distributions published yesterday.  The previous plots of prediction distributions should be ignored — they are not doing as advertised. We show the prediction distribution of levels of several equity indices (plus oil price) at the end of 2011 assuming nothing happens.  That is, we’ve ...
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Creating prediction distributions

January 4, 2011 | Pat

Here we give details and code for the prediction distributions exhibited in yesterday’s blog post Tis the season to predict. Eight years of returns The equity indices use daily closing levels from the start of 2003.  This data comes from Yahoo. A roughly equivalent technique of selecting the last 2000 daily ...
[Read more...]

Blog year 2010 in review

December 30, 2010 | Pat

The blog year started in August and consists of 30-something posts.  Here is a summary. Quant concepts backtesting: Backtesting — almost wordless cointegration: American TV does cointegration efficient frontier: Anomalies meet volatility implied alpha: Implied alpha — almost wordless portfolio theory: Ancient portfolio theory random walk: The tightrope of the random walk ...
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The tightrope of the random walk

December 27, 2010 | Pat

We’re really interested in markets, but we’ll start with a series of coin tosses.  If the coin lands heads, then we go up one; if it lands tails, we go down one. Figure 1: A coin toss path.Figure 1 is the result of one thousand coin flips.  It is ...
[Read more...]

Some quibbles about “The R Book” by Michael Crawley

December 13, 2010 | Pat

A friend recently bought The R Book and I said I would tell him of problems that I’ve noticed with it.  You can eavesdrop. Page 4 The word “library” is used instead of “package”.  This (common)  error substantially raises the blood pressure of some people — probably to an unwarranted extent. ...
[Read more...]

Bear hunting

December 6, 2010 | Pat

When were there bear and bull markets in US stocks since 1950? Smoothing While we’d really like to estimate the expected return at each point in time, finding bear markets is ambitious enough.  The plan starts by smoothing the daily returns through time, as in Figure 1. Figure 1: Smoothed returns with ... [Read more...]
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