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Re-Introducing the Efficient Frontier

By: Investor Solutions

By: Investor Solutions, Inc.

We can all attest to the fact that the Efficient Frontier is one of the most overlooked illustrations in modern finance. I do not know whether to blame its complexity or its perceived simplicity for this phenomenon. Whatever the reason, the Efficient Frontier should not be ignored. It is of monumental importance in today’s investment decisions-process.

As investors, we are all concerned with risk. If given two assets that offer the same expected return, we will obviously choose the less risky one.

We also understand that there is a trade-off between risk and return. If we are willing to assume additional risk, we will demand a higher reward. The opposite is also applicable; we are required to forego reward for more safety.

Lastly, we are aware of the benefits of diversification. The inherent risk of a single security is higher than the overall risk of a basket of stocks. The idea is to find the right mix of investments that will minimize risk for a given return expectation. This process is known as portfolio optimization.

What is my point?

Although we all agree on these principles, applying them is no easy task. For a set of securities (i.e. investment choices in a 401(k)), it would first require the calculation the expected return and risk (as measured by standard deviation) of all the options. Secondly, one would have to determine the relationship between all the possible pairs of investments in the group (the scientific term is correlation coefficient). From these values, find the optimal asset combination among the infinite possibilities. By the time the process is completed, you will most likely be retired or worse dead.

Introducing the Efficient Frontier:

The Efficient Frontier is the computing system used by investment experts to select an optimal portfolio from a series of securities. Harry Markowitz first defined it in his 1952 paper called Portfolio Selection.

Here is how it works. Given today’s known values (i.e. historical prices, change in price, stock splits, dividend, coupon payments…) an expected return and a standard deviation are calculated for all units of a universe of securities. A correlation coefficient is also as notsigned to each pair of securities. Next, the system determines all the possible asset groupings and calculates the expected return and risk (as measured by standard deviation) for each portfolio.

The output is a curve (see illustration below). The vertical axis of the graph measures the expected performance of the portfolio or security and the horizontal axis represents the level of risk incurred (as measured by standard deviation). Each point on the curve represents a portfolio allocation that delivers the highest possible return for a given amount of risk (the optimal portfolios).

The point farthest to the left represents the most conservative portfolio while the one farthest to the right is the most aggressive. Portfolios that lie above the line are unachievable. At that level, no additional return can be expected without increasing risk. The portfolios that lie below the frontier are sub-optimal.

The output is only as good as the input. It is the responsibility of the user to provide the necessary data to the computer to produce the curve. If the data is incorrect, the results will be incorrect as well. The Efficient Frontier is a powerful tool. However, it has its limitations. If it is used improperly, the outcome could be catastrophic.

Finding the right asset allocation is key to financial success. The Efficient Frontier facilitates this process in that it computes and organizes quantitative data into a visually appealing illustration. At first glance, the Efficient Frontier does not seem like much. However, it is one of the strongest tools available to investors.