Quant finance

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...]

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...]

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 ...

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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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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...]

Were stock returns really better in 2007 than 2008?

November 22, 2010 | Pat

We know that the S&P 500 was up a little in 2007 and down a lot in 2008. So on the surface the question seems really stupid. But randomness played a part. Let’s have a go at deciding how much of a part. Figure 1: Comparison of 2007 and 2008 for the S&P 500. ... [Read more...]

American TV does cointegration

October 18, 2010 | Pat

Fringe provides an excellent example of cointegration. This is a television show in which there are two adjacent universes. The universes are almost alike but not exactly. Now, everyone knows that history is chaotic. If a butterfly does an extra flap of its wings, then that difference spreads out to ...

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A tale of two returns

October 4, 2010 | Pat

It was the best of times, it was the worst of times. As you may have guessed, this is a mashup of a novel by Charles Dickens and an explanation of financial returns. The key plot element of A Tale of Two Cities is that there are two men, Charles ...