Pairs Trading: Quantitative Methods and Analysis

CHAPTER 1

Introduction

We start at the very beginning (a very good place to start). We begin with the CAPM model.

THE CAPM MODEL

CAPM is an acronym for the Capital Asset Pricing Model. It was originally proposed by William T. Sharpe. The impact that the model has made in the area of finance is readily evident in the prevalent use of the word beta. In contemporary finance vernacular, beta is not just a nondescript Greek letter, but its use carries with it all the import and implications of its CAPM definition.

Along with the idea of beta, CAPM also served to formalize the notion of a market portfolio. A market portfolio in CAPM terms is a portfolio of assets that acts as a proxy for the market. Although practical versions of market portfolios in the form of market averages were already prevalent at the time the theory was proposed, CAPM definitely served to underscore the significance of these market averages.

Armed with the twin ideas of market portfolio and beta, CAPM attempts to explain asset returns as an aggregate sum of component returns. In other words, the return on an asset in the CAPM framework can be separated into two components. One is the market or systematic component, and the other is the residual or nonsystematic component. More precisely, if r_p is the return on the asset, r_m is the return on the market portfolio, and the beta of the asset is denoted as β, the formula showing the relationship that achieves the separation of the returns is given as

(1.1)

Equation ...