Articles - A Primer on Quantitative Risk Measures

  Ever since Harry Markowitz’s pioneering work on portfolio construction in 1952, the measurement of portfolio risk that has been a cornerstone of investment theory and practice is variance or its square root, standard deviation.[1] While Markowitz used variance as the measure of risk in his original model, over the past few decades, a number of researchers, including Markowitz himself, have proposed alternative risk measures. In this article, I explain these various risk measures, their motivation, and how some of them are used in measures of risk-adjusted performance.

   

  Variance and Expected Utility Theory

  The problem of constructing an investment portfolio is an example of a class of problems involving making decisions under uncertainty, i.e., problems in which someone has to make decisions today which effect outcomes that cannot be known until sometime in the future. In the 1940s, John von Neumann and Oskar Morgenstern developed a framework for developing models of decision making under certainty known as expected utility theory.[2] Expected utility theory had a major impact on Harry Markowitz’s approach to his theory of portfolio construction.[3]

   

  According to expected utility theory, a decision maker’s attitudes towards risk can be described by a utility function of some future quantity that the decision is concerned about such as consumption or wealth. As Figure 1 illustrates, the utility function is assumed to be increasing and concave; the former because the decision maker prefers more to less of the quantity in question; the latter because the decision maker is assumed to be risk averse.

  

    

  

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