Quantitative Portfolio Management: with Applications in Python by Pierre Brugiere

Quantitative Portfolio Management: with Applications in Python by Pierre Brugiere

1

Returns and the Gaussian Hypothesis

In this book, the problem of finding optimal portfolios is mathematically solved
under the assumption that the returns of the risky assets follow a Gaussian
distribution. In this section, we give the definition of a price return and of a total
return and describe some tools to analyse these returns and to statistically test the
hypothesis of normality on them. The hypothesis does not always appear to be
satisfied, depending on the stock or on the period considered, nevertheless, even
in these cases, the methods of portfolio optimisation may still teach some useful
lessons.
1.1 Measure of the Performance
1.1.1 Return
We consider an economy with two instants of observations 0 and T . The investment
decisions are made at time 0, which is today, and the result of the investment is
observed at a future time T . The notion of return is defined as follows:

Quantitative Portfolio Management: with Applications in Python by Pierre Brugiere