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Markowitz 2.0

How Markowitz's portfolio-construction tool can be enhanced for the 21st century.

Paul D. Kaplan and Sam Savage, 04/13/2010

When the Wright Brothers pioneered powered flight in 1903, their genius lay in conquering the three axes of control: pitch, yaw, and roll. Over the years, technologies advanced, planes crashed, and aviation evolved to compensate. By 1952, the Wrights' original airplane was barely recognizable in a world of jets and supersonic aircraft, which nonetheless were still governed by the same three principles of control.

In 1952, another pioneer, Harry Markowitz, invented portfolio optimization. His genius was also based on three principles: risk, reward, and the correlation of assets in a portfolio. Over the years, technologies advanced and markets crashed, but portfolio-optimization models did not evolve to compensate. This is surprising. Markowitz himself was a pioneer of technological advancement in the field of computational computer science. Furthermore, he did not stand idly by in the area of portfolio modeling; he continued to improve his models and to influence the models of others. Few of these improvements, however, were broadly picked up in practice.

Going Supersonic
Because Markowitz's first effort was so simple and powerful, it attracted a great number of followers. The greater the following became, the fewer questioners debated its merits. Markowitz's original work is synonymous with Modern Portfolio Theory; it has been taught in business schools for generations and, not surprisingly, is still widely used today.

Then came the crash of 2008, and people are starting to ask questions. The confluence of the recent economic trauma and the technological advances of the past few decades make today the perfect time to describe the supersonic models that can be built around Markowitz's fundamental principles of risk, reward, and correlation. We assert that Markowitz's original work remains the perfect framework for applying the latest in economic thought and technology. We dub our updated model Markowitz 2.0.

The Flaw of Averages
The 1952 mean-variance model of Markowitz was the first systematic attempt to cure what Savage (2009) calls the "flaw of averages." In general, the flaw of averages is a set of systematic errors that occurs when people use single numbers (usually averages) to describe uncertain future quantities. For example, if you plan to rob a bank of $10 million and have one chance in 100 of getting away with it, your average take is $100,000. If you described your activity beforehand as "making $100,000," you would be correct, on average. But this is a terrible characterization of a bank heist. Yet, as Savage writes, this very mistake is made all the time in business practice. It helps explain why everything is behind schedule, beyond budget, and below projections, and it was an accessory to the economic catastrophe that culminated in 2008.

Markowitz's mean-variance model attempted to fix the flaw of averages by distinguishing between different investments with the same average (expected) return, but with different risks, measured as variance or its square root, standard deviation. It was a breakthrough that ultimately garnered a Nobel Prize for its inventor. The use of standard deviation and covariance, however, introduces a higher-order version of the flaw of averages, in that these concepts are themselves versions of averages.

Adding Afterburners
By taking advantage of the very latest in economic thought and computer technology, we can, in effect, add afterburners (more thrust) to the original framework of the Markowitz portfolio-optimization model. The result is a dramatically more powerful model that is more aligned with 21st-century investor concerns, markets, and financial instruments (such as options).

Traditional portfolio optimization, commonly referred to as mean-variance optimization, or MVO, suffers from several limitations that can easily be addressed with today's technology. Our discussion here will focus on five practical enhancements:

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