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...]

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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...]

The subtitle is: Adversaries in Art, Science and Philosophy. Executive Summary Genius or madness? I haven’t decided. Irreversibility of interpretation The book drives home that once we decide how something is we can’t go back to our state of innocence. Figures 1 through 3 exhibit this idea via a randomly ... [Read more...]

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...]

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...]

The title says “things” but conferences are mainly about people. Some of it can be serendipitous.  For example, one day I sat next to Jonathan Rougier at lunch because I had a question for him about climate models.  When Jonathan left, I started a conversation with the person on my ... [Read more...]

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The first 6 trading days of August have been bad for the major indices, but how variable is that across portfolios? To answer that, two sets of random portfolios were generated from the constituents of the S&P 500.  The trading days are 2011 August 1 — 5 and 8. The returns of the indices for … Continue ... [Read more...]

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...]

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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...]

If a particular prediction comes true, how surprised should we be? The prediction The page that sparked my curiosity tells of a prediction made a year ago that the S&P 500 would beat its historic high by the end of 2011.  It says that at the point the prediction was made, ... [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...]

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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...]

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