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Above and Beyond The Efficient Frontier?

Dec 14, 2011 Marc Odo

A frequent question we receive at Zephyr is, “I’m using AllocationADVISOR, and the portfolios I entered appear above the efficient frontier. How is that even possible?”

I’d like to tell you that your portfolios have defied gravity and you’ve beaten the efficient frontier. Unfortunately, that isn’t true, or even possible. By definition the efficient frontier are those portfolios with the maximum amount of return per unit of risk, or conversely the lowest amount of risk per unit of return. If you’ve typed in a portfolio and you see it above the efficient frontier, the situation you’re seeing is driven by the constraints you have placed on the efficient frontier.

It is important to keep in mind that the efficient frontier is purely a mathematical construct. It’s 100% science, 0% art in its base form. The goal is to maximize return and minimize risk, based purely and only on the three inputs- return, risk and correlation. The problem with such a mathematical approach, however, is that the efficient frontier can be comprised of portfolios which don’t always make a lot of sense. The mathematically optimal portfolio might be a 30%/70% combination of cash and emerging markets, completely ignoring allocations to all other asset classes. Or the best risk-return combination might be 100% hedge funds. Obviously no one in their right mind would blindly follow these purely mathematical recommendations.

So what do people do? They constrain the portfolio. This is the human element, this is where the “art” comes in to play with the science. Limits are placed on the optimization to get realistic portfolios. Obviously it is a good idea to do something like this, but you’ll see the efficient frontier start to change. By capping exposure to certain asset classes, the highest possible potential return gets lowered. The efficient frontier gets shorter. The whole frontier starts to move in a southeasterly direction as limitations are placed upon it. Again, it probably makes sense to do this if you want to have realistic portfolios, but recognize the impact those discretionary decisions are having on the math piece of the puzzle.

What about those hard-coded portfolios that were typed in? Well, their allocations were typed in manually and their returns and risks were calculated accordingly. Those are locked in to the graph, constraints don’t impact them at all. However, as the efficient frontier gets shorter and moves downwards, it could be that those portfolios appear above the efficient frontier. It’s not that the portfolios have moved above the efficient frontier; it’s because the constraints have moved the efficient frontier itself.

As a matter of fact, if you see your hard-coded portfolios above the efficient frontier, what I can surmise is that those portfolios actually violate the constraints you have applied.

Hopefully this makes sense. If you need any further clarification, you are always welcome to reach out to us. 

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