Python for Finance: Analyze Big Financial Data

Conclusions

Statistics is not only an important discipline in its own right, but also provides

indispensible tools for many other disciplines, like finance and the social sciences. It is

impossible to give a broad overview of statistics in a single chapter. This chapter therefore

concentrates on four important topics, illustrating the use of Python and several statistics

libraries on the basis of realistic examples:

Normality tests

The normality assumption with regard to financial market returns is an important one

for many financial theories and applications; it is therefore important to be able to

test whether certain time series data conforms to this assumption. As we have seen —

via graphical and statistical means — real-world return data generally is not normally

distributed.

Modern portfolio theory

MPT, with its focus on the mean and variance/volatility of returns, can be considered

one of the major conceptual and intellectual successes of statistics in finance; the

important concept of investment diversification is beautifully illustrated in this

context.

Principal component analysis

PCA provides a pretty helpful method to reduce complexity for factor/component

analysis tasks; we have shown that five principal components — constructed from

the 30 stocks contained in the DAX index — suffice to explain more than 95% of the

index’s variability.

Bayesian regression

Bayesian statistics in general (and Bayesian regression in particular) has become a

popular tool in finance, since this approach overcomes shortcomings of other

approaches, as introduced in Chapter 9; even if the mathematics and the formalism

are more involved, the fundamental ideas — like the updating of

probability/distribution beliefs over time — are easily grasped intuitively.