Efficient Frontier Surfing

WATS provides a new method of portfolio validation that enhances the established methodology of Efficient Frontiers. We'd like to invite you into the water.

Efficient Frontiers

The Efficient Frontier represents portfolios that achieve the highest level of return for their level of risk, or, conversely, the lowest level of risk for their level of return.

Consider the following graph:

The red dot (bottom left) represents a conservative investment such as a bond. The blue dot (top right) represents an aggressive investment such as stock. The higher the potential return, the higher the risk. The yellow line between the two dots represents the feasible region, which is every potential mix that can be made using these two investments (like 90% bond/10% stock, 50% bond/50% stock, etc.).

In this simple example, with only two investments to consider, the feasible region is not a region (geometrically speaking) at all, but rather a curved line between the two end points.

If we add another candidate for the portfolio (say, an investment in international securities represented by the green dot), and then consider all possible portfolio mixes (like 30% bond/40% stock/30% international) the feasible region becomes a true geometric region (with an area, not simply a line). A depiction of this is as follows:

The Efficient Frontier is defined relative to the feasible region--it is the part of the feasible region with the highest level of return for a given level of risk (or conversely, the lowest level of risk  for a given level of return).

In the graph above, the yellow region is the feasible region (every possible asset allocation that can be created using these three investments). The purple line in the graph is the Efficient Frontier, a subset of the feasible region, holding only the optimal mixes.

Choosing a Portfolio that is On the Efficient Frontier

Something every investor would like to do is to be as efficient as possible, taking only as much risk as is necessary to achieve a given level of return. If our portfolio remains near the efficient frontier, we can rest comfortably at night knowing our investments are allocated about as well as they can be.

The questions are:

Those are important questions. WATS cannot directly answer these question, probably no one can. What WATS does do is to show you, historically, how closely your portfolios track to the Efficient Frontier. This is done with a technique called Efficient Frontier Surfing (EFS).

The prior graphs made no mention of time. To understand EFS, you need to set things in motion.

Continuing the example, suppose the graphs we have looked at both represent the 10-year period from January 1991 to December 2000. Also suppose that we have chosen our portfolio to be 50% bond, 30% stock and 20% international. An updated version of the graph is as follows:

Our portfolio is represented by the black dot. With WATS, we can measure the portfolio's efficiency, which is the relative distance from the Efficient Frontier. WATS measures efficiency by checking two things: 1) How many portfolios whose risk is equal to our own have higher returns, and 2) How many portfolios whose return is equal to our own have lower risk?

By averaging these two numbers we can determine how close our portfolio is to the Efficient Frontier. The lower the rating, the better the portfolio. In the example, 67% of portfolios with the same level of risk as our portfolio have higher returns. Going the other way, 50% of portfolios with the same level of return have lower risk. We can combine these two rankings into a single number, called the Efficiency Rating, by simply averaging to get 58.5%, meaning about 58.5% of all portfolios with comparable risk/reward characteristics are more efficient than our mix.

This portfolio is not terribly efficient, at least, not in this particular 10-year period. What would be great is if someone could show us a strategy that would be efficient over the next 10-year period, or 20-year period, or whatever horizon. To our way of thinking, that someone doesn't exist. No one can predict the future. As an alternative to predication, we take a hard look at the past.

Time To Surf

WATS tests portfolio efficiency for every historical time period. You can step through history, seeing how the shape of the Efficient Frontier changes over time, and measuring how far your portfolio falls off the Efficient Frontier.

We liken this process to surfing: The feasible region is the ocean. The Efficient Frontier is the surf where the best waves are. Your portfolio is the surfboard. Your goal, as the surfer, is to remain as close as possible to all the biggest waves, and maybe even catch a few if you can.

Using WATS, you can test how efficient your portfolio has been in the past, which will help you choose your investment strategy going forward.

C'mon dude, surf's up.

Note: Efficient Frontier Modeling is available in the Advisor Edition of WATS. It is not available in the Personal Edition.

Copyright © 2000, 2004  Zunna, Inc.

Last updated on 02/12/2004