ABSTRACT
This chapter considers the single-index model, which is a type of extension of the market model to a set of N assets. The single-index model leads to a simple model for the covariance matrix of an asset return vector. The property of the correlation between the returns of any two assets in a given time period may be described in terms of their partial correlation. The chapter applies the single-index model to the returns on the stocks of five companies, Cablevision Systems Corp. (symbol CVC), Edison International (EIX), Expedia, Inc. (EXPE), Humana, Inc. (HUM), and Wal-Mart Stores, Inc. (WMT). It considers the covariance matrix for portfolio theory. According to the assumptions used to derive the capital asset pricing model (CAPM), the market portfolio is the optimal choice for investors. The chapter also describes the Treynor–Black portfolio in terms of a portfolio constructed from the N assets combined with the market portfolio.
