The Efficient Frontier (EF) is one of the pillars of current investment practice. First defined in 1952 by Harry Markowitz, it shifted the investment focus from individual securities to the entire portfolio. Nowadays, it is used for everything from selling mutual funds to determining the “right” asset mix.
To refresh your memory on the concept of EF: The portfolio return and the risk –defined as the standard deviation of returns– of two securities are plotted on a chart (Figure 14.1).
The vertical axis indicates the return –growth–; the horizontal axis represents the risk.
The return and the risk of the portfolio consisting of these two securities (let’s call them
“A” and “B”), at different proportions are plotted on the same chart, as shown in the example below. These points are then connected. The top part of the line –the heavy line–
is called the efficient frontier.
Figure 14.1: A typical efficient frontier diagram
Efficient Frontier
Looking at this chart, we can reach the following conclusions:
• Investing all of the money in “B” produces the lowest return. Instead, if you invest 60% in “A” and 40% in “B”, you end up with a significantly higher return for the same level of risk.
• Investing 50% in each of “A” and “B” produces the highest return at the lowest risk.
• Investing all of the money in “A produces a higher return than investing 60% in
“A” and 40% in “B”, but at a significantly higher risk.
After observing this chart, an unsuspecting investor might conclude, “Gee, this is wonderful, let’s invest 60% of the money in A and 40% in B.” Actually, this is the generally accepted method33
What is the flaw of in the EF? There are a few:
of optimizing the asset allocation.
1. The look–back time:
The first one is the time frame. EF charts are based on historical performance of a limited time. Many use a 3–year or a 5–year history. Such a short time period mismatches the length of the two most prominent market cycles.
Secular trends can last up to 20 years. Even if you use a 20–year history for your EF, it may reflect one specific secular trend which may never repeat again in your lifetime.
Cyclical trends last 4 to 6 years. If you use a 5–year history, you may be applying the events of one cyclical trend to your EF analysis, which is usually irrelevant during the subsequent cycle.
2. Recent past will repeat itself:
The second flaw of the EF is that it inherently assumes that the risk and return profile of investments will remain essentially the same in the future as it was in the recent past. This is usually not the case.
3. Gaussian Mindset:
The third and the most important flaw of the EF is that it defines risk as the standard deviation of returns (volatility). This may be reasonable in a “normal”
Gaussian model, but it is incongruent with what happens in real life.
In distribution portfolios, the primary risk is the sequence of returns and not the volatility of returns. What makes or breaks the outcome of a portfolio is not what happens 95% of the time in “normal” markets, but what happens in 5% of the time in “extreme” markets, up or down (see Chapter 27). Therefore, 95% of the data included in the statistical analysis corrupts its conclusions to the point of uselessness.
Conventional EF analysis totally ignores the cash flows in and out of the portfolio. They start with a fixed portfolio value and vary only as a result of the growth of its underlying assets. To overcome this shortfall, here is what I did: I considered one accumulation and one distribution portfolio. In the accumulation portfolio, the investor saves $10,000 each year. In the distribution portfolio, the investor starts with $1 million and takes out
$50,000 each year, indexed to inflation. My objective is to find the “right” asset mix using the efficient frontier to establish an optimum mix of stocks and bonds for each portfolio.
Assume it is 1910. I draw the efficient frontier line using the preceding ten year history, i.e. 1900–1909 similar to Figure 14.1. From this EF curve, I optimize the asset mix using the annual returns and volatility of each asset class.
Next, I move on to 1911. I repeat the same process using the preceding 10 years of data.
Calculate the EF for 1911. I repeat the same process for all the years until the end of 2005. Now, I have an efficient frontier curve for each year since 1900. Based on each year’s EF curve, I figured out the optimum asset mix.
So, I was very happy to have created a model that can automatically draw the EF curve based on the client’s assets and included his cash flow.
However, my joy was short lived once I plotted these findings. A very interesting picture appeared. Observe Figure 14.2 for accumulation and Figure 14.3 for distribution portfolios. Notice that it took the efficient frontier four years to recognize the devastating 1929 crash and to go from 100% to 0% equity. Ironically, this happened just prior to the greatest cyclical bull market of the last century (1933–1936). In effect, what disappointed me was, this looked very much like a market–timing model. The equity percentage swings from 0% to 100% in short periods of time. This cannot be described in anything other than a complicated market–timing model, a very bad one, I might add.
Figure 14.2: Optimum asset mix for an accumulation portfolio
Figure 14.3: Optimum asset mix for a distribution portfolio
I tried the same procedure with a 20–year history instead of a 10–year history. This smoothened some of the jagged edges, but the general picture remained the same. The efficient frontier still worked like a bad market–timing model. It was then I realized that EF might be a great idea for randomly moving events 100% of the time, but it does not work well if that randomness prevails only 95% of the time.
Regretfully, that is what we have been selling to unsuspecting investors. No wonder only 15% of fund managers can randomly beat the index over the long term. No wonder less than 1% of fund managers can consistently beat the index over the long term. We all have been using the wrong tool.
Conclusion:
Here are my rules for the efficient frontier analysis:
Do not use EF:
• For optimizing the optimum asset allocation unless the historical data covers at least two secular trends, i.e. a minimum of forty years of look–back.
• For the purpose of market/sector/country timing by applying a shorter history. Analysis based on three or five years is useless for this purpose. Much better timing tools are available in the realm of technical and intermarket analysis.
• For distribution portfolios.
You can use EF:
• For comparing different mutual funds of the same asset class using a minimum of ten years of history, as long as each mutual fund maintains the same fund manager over that time period.
• For individual stocks within a portfolio with a shorter history.