Why bad trading strategies may perform well? Mathematical explanation

You probably know that even a trading strategy which is actually no different from a random walk (RW henceforth) can perform very well. Perhaps you chalk it up to short-run volatility. But in fact there is a deeper reason for this to happen, in force. If you insist on using and continuously testing a RW strategy, you will find, at some point with certainty, that it has significant outperformance.

This post explains why is that.

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Why statistical bootstrap

I often write about bootstrap (here an example and here a critique). I refer to it here as one of the most consequential advances in modern statistics. When I wrote that last post I was searching the web for a simple explanation to quickly show how useful bootstrap is, without boring the reader with the underlying math. Since I was not content with anything I could find, I decided to write it up, so here we go.

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Omitted Variable Bias

Frequently, we see the term ‘control variables’. The researcher introduces dozens of explanatory variables she has no interest in. This is done in order to avoid the so-called ‘Omitted Variable Bias’.

What is Omitted Variable Bias?

In general, OLS estimator has great properties, not the least important is the fact that for a finite number of observations you can faithfully retrieve the marginal effect of X on Y, that is E(\widehat{\beta}) = \beta. This is very much not the case when you have a variable that should be included in the model but is left out. As in my previous posts about Multicollinearity and heteroskedasticity, I only try to provide the intuition since you are probably familiar with the result itself.

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