Regression, Multivariate, and Nonlinear Methods
This chapter builds on the quantitative and statistical tools introduced in Part One, with an emphasis on the multifactor and nonlinear techniques that are essential to the portfolio management of alternative investments. Much of this material is fundamental to the challenges faced by an asset allocator in determining the mix between traditional assets and alternative assets in a portfolio, as well as determining the relative weights within the alternative asset portion of the portfolio.
29.1 SINGLE-FACTOR MODELS AND REGRESSION
Chapter 4 introduced the concept of factor models in which asset returns are described as being determined by the product of asset-specific sensitivities and marketwide variables. The best-known single-factor model is the capital asset pricing model (CAPM), which states that the expected return and realized return of an asset are linearly related to its market beta. The section begins by detailing the application of simple linear regression to the ex post version of the CAPM.
29.1.1 Simple Linear Regression and the CAPM
A regression is a statistical analysis of the relationship that explains changes in a dependent variable as a function of changes in one or more independent variables. The dependent variable is the variable that is determined at least in part by other (independent or explanatory) variables. In a linear regression, the relationship between the dependent variable and the independent ...