Markowitz and the Expanding Definition of Risk: Applications of Multi-factor Risk Models

Abstract

In Chap. 1, we introduced the reader to Markowitz mean–variance analysis. Markowitz created a portfolio construction theory in which investors should be compensated with higher returns for bearing higher risk. TheMarkowitz framework measured risk as the portfolio standard deviation, its measure of dispersion, or total risk. The Sharpe (1964), Lintner (1965), and Mossin (1966) development of the Capital Asset Pricing Model (CAPM) held that investors are compensated for bearing not only total risk, but also rather market risk, or systematic risk, as measured by a stock’s beta. Investors are not compensated for bearing stock-specific risk, which can be diversified away in a portfolio context. A stock’s beta is the slope of the stock’s return regressed against the market’s return. Modern capital theory has evolved from one beta, representing market risk, to multi-factor risk models (MFMs) with 4 or more betas. Investment managers seeking the maximum return for a given level of risk create portfolios using many sets of models, based both on historical and expectation data. In this chapter, we briefly trace the evolution of the estimated models of risk and show how risk models enhance portfolio construction, management, and evaluation. Starting from the path-breaking risk estimations of Bill Sharpe (1963, 1964, 1966), and going on to the MFMs of Cohen and Pogue (1967), Barr Rosenberg (1974, 1982), Farrell (1974, 1998), Blin and Bender (1998), and Stone (1974, 2008), estimations of risk have complemented the risk and return analysis of Markowitz. Several of these MFMs are commercially available and well known by institutional investment advisors.