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A Pragmatic Approach to the Efficient Frontier

Sep 26, 2012 Marc Odo

Harry Markowitz’s idea of creating “optimal” portfolios that maximize return and minimize risk has been with us for a very long time. For many people, the manifestation of the idea of “optimal” portfolios is the efficient frontier- those portfolios that by mathematical definition have the most return per level of risk or conversely the least amount of risk per level of return.

However, focusing only on the efficient frontier sometimes leads to portfolios that are poorly diversified, too heavily weighted in obscure asset classes, or in some other way not intuitive. There are a number of very sophisticated solutions to these problems, like the Black-Litterman model or Michaud’s resampling process. With this article, I’d like to take a step back and propose a very simple, pragmatic alternative perspective on how to use the efficient frontier effectively.

When Markowitz originally developed the idea of mean-variance optimization, the idea was that if you have an opportunity set of investments and estimates for their returns, risks, and correlations, there would be an infinite number of ways you could potentially combine those investments. Each unique combination will produce the portfolio’s return and risk, which typically gets plotted in X-Y space. These portfolios will form a “cloud” of possible portfolios, seen in blue below.

Those portfolios with the most return per unit of risk or least amount of risk per level of return define the border of this cloud. In the image below these optimal portfolios are highlighted in green. The border of the cloud is known as the efficient frontier.  It would be mathematically impossible to be above this border. So far, so good. The problem, however, is that some practitioners became fixated solely on the efficient frontier, and some of the portfolios on the efficient frontier might not be intuitive.
It is useful to take a step back and remember that there are many other portfolios that exist just below the efficient frontier that have return/risk characteristics that, while not optimal, are almost as good as the green portfolios seen on the efficient frontier. These portfolios we see highlighted in red below.
In this use case, you might have some portfolios you have built using the “Custom Portfolios” section in AllocationADVISOR. Here you’re using the efficient frontier not as the be-all, end-all answer, but rather as a cross check or a sounding board to see if the custom portfolios are for all intents and purposes just as good as those on the efficient frontier. If the custom portfolios are close to the efficient frontier, you’re probably fine.

Alternatively, if there is a big gap between the custom portfolio and the efficient frontier that tells you one of two things. Either 1) you did a poor job building that custom portfolio and should go back to the drawing board, or 2) there is something really weird about the efficient frontier that you would probably never do in reality, like put 90% of your money with hedge funds. It would be up to you as the investment professional to identify why that gap exists and what needs to be done to narrow it.

I hope this alternative way of viewing the efficient frontier is useful. Feel free to drop us a line if you have any questions.

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