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Thursday, June 2, 2011

What is the Efficient Frontier?

Source: FolioTechnologies


As a graduate student in economics, one of my fields was econometrics, which basically merges statistics and economics. Most econometricians spend considerable time doing regression analyses and mathematical economics. In fact, one great joke in graduate school was wearing a t-shirt that said "we are regressing - we are econometricians."

Understanding econometrics was important to me later when confronted by large-scale models of the economy. It provided the background to understand that most large-scale models of the macroeconomy - to put it politely - were pure bogus. Put in the data and solve the equations and the results were nonsense. Adjustments had to be made (called "fudge factors") and the output considerably massaged until anything resembling reasonable results emerged.

And this type of outcome, to a degree, is fairly common in a lot of areas. For example, not understanding the concept of the "efficient frontier" can lead to people being overly impressed with the concept. In the hands of a fast talker, with an expensive suit, it can be a great selling device to extract what I, and many others, view as excessive management fees.

After all, the efficient frontier indicates that considerable knowledge is necessary to structure a portfolio appropriately. You need to know expected returns and correlations to obtain the highest return portfolio. You need to carry out a (gasp!) mean - variance optimization.

Most people sitting through 20 minutes of this, with all the charts and correlation matrices etc., will gladly hand over their life savings and pay 1 to 2% to have it managed.

The problem is this: aside from being a broad conceptual guideline, the efficient frontier has not produced exceptional portfolios. William Bernstein, author of the widely regarded The Intelligent Asset Allocator, puts it like this:

"In other words, next year's efficient frontier will be nowhere near last year's." Anybody who tells you that their portfolio recommendations are "on the efficient frontier" also talks to Elvis and frolics with the Easter Bunny. (p.57)

In Bernstein's assessment, if someone tries to sell a portfolio based on the efficient frontier, run in the opposite direction. I agree.

So what is the problem? How is the efficient frontier generated?

How the Efficient Frontier is Generated

The efficient frontier shows the portfolios that have had the highest returns for a given amount of risk. Risk is measured by standard deviation. Returns are measured by averaging returns over a specified past period.

So, for example, we take 5 asset classes and calculate their respective average annualized returns over the past 10 years, say. Then we calculate the standard deviation of each asset classes returns over the same period.

We then combine the asset classes randomly and calculate portfolio returns and portfolio standard deviations. For example, one portfolio might be 20% of each asset class (small cap U.S. stocks, large cap U.S. stocks, 5-year U.S. Treasury note, small cap international stocks...). Do this randomization for 1,000 portfolios and plot the resulting outcomes on a graph with standard deviation on the horizontal axis and average annualized return on the vertical axis.

As you study the graph, you come to see that, for every given standard deviation, i.e. set risk, there is a portfolio that produced the highest return. In fact, the exercise produces a border, as shown above, that specifies the portfolio with the highest return for any given level of risk.

The Problem

What's the problem? The market doesn't cooperate. Past performance is not indicative of future performance. Asset classes become more risky and less risky over time. Top performing sectors, for example, Japanese stocks in the 1980s, later go through decades of subpar performance.

One really important result does emerge from the analysis. That is that even the most risk averse investor should have a small portion of assets in riskier assets. As shown on the diagram, expected return can be increased and risk reduced at the left hand side of the curve.


  1. That's the problem with all the studies that come out with results based on past performance. It's as if you can use a roulette table's past performance to come up with a strategy for the future!

    A set of economic/market variables molded past performance, is there any guarantee they will be fine tuned to deliver similar results in the future? I'm not so sure!

  2. Exactly! It is good to study past performance, but that's no guarantee of future returns!

  3. Actually if the roulette wheel is not balanced correctly (or being manipulated consistently) then you can determine future performance by past performance.....

  4. The virtue of historical prices is that they are objective, factual data of real market behavior in response to real market conditions. Do market conditions change? Yes, of course. Are future conditions known in an objective, factual manner? No, only in a subjective, speculative, best-guess manner.