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Alternative Investments: CAIA Level I, 3rd Edition by CAIA Association, Hossein Kazemi, Keith H. Black, Mark J. P. Anson, Donald R. Chambers

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CHAPTER 9 Regression, Multivariate, and Nonlinear Methods

Previous chapters generally focused on single-factor linear models for simplicity. This chapter builds on those chapters with an emphasis on the multifactor and nonlinear techniques that are essential to the management of alternative investments. 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 in determining the relative weights within the alternative asset portion of the portfolio.

9.1 Single-Factor Models and Regression

Chapter 6 discussed 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 market 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. This section begins by detailing the application of simple linear regression to the ex post version of the single-factor market model.

9.1.1 Simple Linear Regression and the Single-Factor Market Model

A regression is a statistical analysis of the relationship that explains the values of a dependent variable as a function of the values of one or more independent variables based on a specified model. The dependent variable is the variable supplied by the researcher that is the focus of the analysis and is determined at least ...

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