Asset Return and Distributions

This post talks about asset return and distributions, covering various definitions of returns and the relationship among them, return distributions and tests of returns.

1  Asset returns

Most financial studies involves returns, instead of prices, for two reasons:

1. Return is a complete and scale-free summary of investment opportunity;
2. Return has more attractive statistical properties than price.

Mathematics Underlying Principal Component Analysis

This tutorial covers mathematics underlying principal component analysis, including definition of PCs, how to find PCs, and derivation of PCs.

1  Introduction to Principal Component Analysis

1.1  Main idea of Principal Component Analysis

The central idea of principal component analysis (PCA) is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set.

This is achieved by transforming the original set of variables to a new set of variables, the principal components (PCs), which are uncorrelated, and which are ordered so that the first a few retain most of the variation present in all the original variables. Read more Mathematics Underlying Principal Component Analysis