An Inequality for Detecting Financial Fraud, Derived from the Markowitz Optimal Portfolio Theory

摘要

The Markowitz Optimal Portfolio Theory, published in 1952, is well-known, and was often taught because it blends Lagrange Multipliers, matrices, statistics, and mathematical finance. However, the theory faded from prominence in American investing, as Business departments at US universities shifted from techniques based on mathematics, finance, and statistics, to focus instead on leadership, public speaking, interpersonal skills, advertising, etc... The author proposes a new application of Markowitz's Theory: the detection of a fairly broad category of financial fraud (called "Ponzi schemes" in American newspapers) by looking at a particular inequality derived from the Markowitz Optimal Portfolio Theory, relating volatility and expected rate of return. For example, one recent Ponzi scheme was that of Bernard Madoff, uncovered in December 2008, which comprised fraud totaling 64,800,000,000 US dollars [23]. The objective is to compare investments with the "efficient frontier" as predicted by Markowitz's theory. Violations of the inequality should be impossible in theory; therefore, in practice, violations might indicate fraud.