Chapter 11. Statistics

I can prove anything by statistics except the truth.

George Canning

Statistics is a vast field. The tools and results the field provides have become indispensible for finance. This also explains the popularity of domain-specific languages like R in the finance industry. The more elaborate and complex statistical models become, the more important it is to have available easy-to-use and high-performing computational solutions.

A single chapter in a book like this one cannot do justice to the richness and the broadness of the field of statistics. Therefore, the approach—as in many other chapters—is to focus on selected topics that seem of paramount importance or that provide a good starting point when it comes to the use of Python for the particular tasks at hand. The chapter has four focal points:

Normality tests
A large number of important financial models, like the mean-variance portfolio theory and the capital asset pricing model (CAPM), rest on the assumption that returns of securities are normally distributed; therefore, this chapter presents some approaches to test a given time series for normality of returns.
Portfolio theory
Modern portfolio theory (MPT) can be considered one of the biggest successes of statistics in finance; starting in the early 1950s with the work of pioneer Harry Markowitz, this theory began to replace people’s reliance on judgment and experience with rigorous mathematical and statistical methods when it comes to the investment ...

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