How Markowitz’s Portfolio-Construction Tool Can Be Enhanced for the 21st Century

In 1952, Harry Markowitz invented portfolio optimisation – the original idea behind today’s Modern Portfolio Theory.

Because Markowitz’s first effort was so simple and powerful, it attracted a great number of followers. But the greater that following became, the less his work was debated. Modern Portfolio Theory became a regular class in business schools for generations and is still widely used today.

Then came the crash of 2008, and people started 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 new, powerful models that can be built around Markowitz’s fundamental principles of risk, reward, and correlation. 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 characterisation of a bank heist! Yet, as Savage writes, this very mistake is made all the time in business practice, 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 by 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 types of averages.

Adding Afterburners

By taking advantage of the very latest in economic thought and computer technology, we can, in effect, add afterburners to the original framework of the Markowitz portfolio-optimisation 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 optimisation, commonly referred to as mean-variance optimisation, or MVO, suffers from several limitations that can easily be addressed with today’s technology. Our discussion here will focus on five practical enhancements:

First, we use a scenario-based approach to allow for “fat-tailed” distributions. Fat-tailed return distributions are not possible within the context of traditional mean-variance optimisation, where return distributions are assumed to be adequately described by mean and variance.

Second, we replace the single-period expected return with the long-term forward-looking geometric mean; this takes into account accumulation of wealth.

Third, we substitute conditional value at risk, which only looks at tail risk, for standard deviation, which looks at average variation.

Fourth, we replace the covariance matrix of returns on asset classes; with a scenario-based model that can be generated with Monte Carlo simulation and can incorporate any number of interrelationships between assets.

Finally, we exploit new statistical technologies pioneered by Savage in the field of probability management. Savage invented the Distribution String, or DIST, which encapsulates thousands of trials as a single data element or cell. It eliminates the main disadvantage of the scenario-based approach-the need to store and process large amounts of data.


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