A Practitioner's Guide to Asset Allocation

CHAPTER 18Statistical and Theoretical Concepts

This chapter provides a brief introduction to concepts in statistics and portfolio theory. We include a fair amount of math, but we do our best to avoid excessive complexity. Our intent is to establish a sufficient foundation for this book that is reasonably clear, but this review is by no means comprehensive. We therefore include references to other sources that provide a more thorough and technical explanation of these topics.

DISCRETE AND CONTINUOUS RETURNS

We define the discrete return for an asset from time to as the change in price over some period plus any income generated, all divided by the price at the beginning of the period:

(18.1)

Next, we denote the log return of the asset using a lowercase :

(18.2)

Here is the natural logarithm ...