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Chapter 5: Travels on the Efficient Frontier

By: Investor Solutions

When Harry Markowitz defended his dissertation on Modern Portfolio Theory in the early 1950s, it’s doubtful that anyone present had any inkling of the tremendous impact it would have on modern finance. But the revolution didn’t exactly spread like wildfire; it took a long time for the impact to be felt. Academics labored away in obscurity, steadily building a wealth of knowledge until the world was ready for it.

For the most part, Wall Street ignored the academics. The old ways were good enough, and change would have imperiled many of the Street’s most sacred myths. During the early eighties, a few academics infiltrated the large houses and institutions, but they were considered slightly unusual. More than any other event, the crash of 1987 focused Wall Street’s attention on the need for better understanding of the world’s markets. Wall Street was ready to listen, at least at the institutional level. Today, financial economics is in vogue, and academics are widely consulted and sought after by large money managers.

Even the law is rapidly changing to incorporate elements of the new financial theory and practice. Fiduciaries run substantial personal risk if they fail to follow MPT basics. The old “legal list” of approved investments is long gone, replaced by an “expanded federal prudent man rule” for fiduciaries. Risk is required to be measured at the portfolio level, and no single asset is deemed too risky for a prudent portfolio. Rather the impact of the asset on the portfolio as a whole is deemed the appropriate test. Pension trustees and other fiduciaries are now required to properly diversify, follow a written investment policy, consider possibilities for profit as well as risk of loss, and build asset allocation plans with appropriate attention to expected rate of return, risk, and correlation of investments.

What practical benefits does Modern Portfolio Theory (MPT) have for investors? How can you apply this to your needs? Let’s look at a couple of real-world, but simple applications.

Improving an All Bond Portfolio

First, let’s look at the case of a retiree living on his portfolio income. His primary concern is the safety of his principal and income. He presently holds a portfolio comprised exclusively of government bonds. Recently he has noticed that his income isn’t going as far as it used to, and the gyrations of his principal value have been disconcerting. He doesn’t want to do anything risky, but he is curious about how he might improve his situation.

Our retiree finds himself stuck on the old risk-reward line. Let’s examine his portfolio of 100% long-term government bonds (Portfolio A). By itself, it isn’t a very efficient portfolio: risk is high compared to the meager total return. The expected return is 5% with a standard deviation (risk measurement) of 11.7%*.

Portfolio A

Before the advent of MPT, the traditional answer to increasing his yield would have been to creep ever further out into the risk spectrum with bonds – first to high-grade corporate bonds, then junk bonds, each with a growing risk. But MPT expands the list of options.

From his start position on the risk-reward line, any movement either upward (more return) or to the left (reduced risk) improves his position. (Every investment manager longs to be in the Northwest Quadrant of the risk-reward chart.)


If we add different combinations of cash and stocks, it is possible either to substantially improve returns without increasing risk (Portfolio B), or to dramatically reduce risk without sacrificing returns (Portfolio C). Paradoxically, addition of a more risky asset can actually reduce the risk in the total portfolio! This occurs because cash, bonds and stocks often move in different directions during market cycles (low correlation). MPT proves that the risk level of the portfolio as a whole should be considered paramount rather than any separate component.

Portfolio B contains 50% stocks, 35% bonds, and 15% cash. The expected rate of return has increased to 8.4%, while standard deviation has remained 11.7%.* (Much higher return, no more risk.)

Portfolio B

Portfolio C contains 20% stocks, 5% bonds, and 75% cash. This combination achieves the original 5% expected return, while lowering the risk to 4.9% standard deviation. (Same return, less than half the risk.)

Portfolio C

Historical returns from 1926 to 1992, courtesy Ibbottson and Associates. Cash based on 30-day Treasury Bills, bonds based on long-term government bonds, and stocks based on the S&P 500 index. Historical returns are no guarantee of future performance.


International Investing and Modern Portfolio Theory

Here’s another example: An investor holding a portfolio of large domestic stocks would like to see if international investing would improve his position. He is comfortable with equity risk, but would like to improve his returns, or lower his risk.

Here are various mixes of domestic large stocks, represented by our S&P 500 index, and foreign large stocks of developed nations, represented by Morgan Stanley’s Europe, Australia, Far East (EAFE) index. The foreign stocks have both a higher return and risk than our domestic market. You might expect that as we mixed the two together the resulting portfolio combinations would fall on a line connecting them. But you can see that as we add foreign stocks to a domestic portfolio, return increases (moves up) and risk decreases (moves left) until we reach an optimum position at about 60/40 domestic to foreign. The combination of lower risk and higher returns is why we feel so strongly that global diversification is essential for all investment portfolios.


International Investments (click on image for full-size chart)

International investing has two key benefits for American investors: higher returns and a strong diversification effect. International markets have a very low correlation with our domestic markets. This diversification effect will lower risk at the portfolio level, which is one of the chief advantages offered by Modern Portfolio Theory. (This is a very simple two-asset-class illustration. Our investor should also consider the impact of small cap stocks, emerging markets, value investing, real estate, hard assets and other asset classes on his program.)

Modern Portfolio Theory is certainly a great leap forward in our ability to construct rational investment plans. But like any good tool, it must be used with judgment. And, like any good idea, there will always be someone who will take it to an illogical extreme.

First, we must understand that MPT is not a risk elimination process; it is a risk management tool. It allows us to build more rational investment plans, control risk, and get “the most bang for the buck” of risk. It is not a substitute for judgment, and in fact requires great judgment for its proper application. There are severe limitations which, if not properly understood, can lead to very strange and counterproductive results. When dealing with investment tools we must always remember that none of them work every day, every quarter, or every year. So an optimized portfolio is not a substitute for CDs. Patience and discipline are still required if the process is to bear fruit.

MPT is based on an examination of past results. We can say that some things happen more often than not, but there is no guarantee that tomorrow will always be just like today. Short-term returns will always remain random and variable.

We can take a great deal of comfort in the fact that none of the three variables appears to be changing in any fundamental way. In particular, there doesn’t seem to be any fundamental change in the correlations between the world’s markets. While we may be moving toward a global economy, individual economies and markets still respond to local conditions and politics.

There are a number of “optimization” programs readily available to financial planners and portfolio managers that will quickly and easily solve the math problems associated with MPT. However, like any computer program, if we put garbage in we will get garbage out. Many of us put far too much value on the output of a computer program without considering the input and programming problems. If it’s from a computer, we believe, it must be right! Beware the black-box approach to solving life’s little problems.

The MPT process and math is particularly vulnerable to data input distortions. For each asset or asset class, we must enter the expected rate of return, risk, and correlation to every other asset class. This leads to two problems. First, the data changes every day. Next, a tiny change in an input of any of the three factors will have a giant impact on the suggested allocation. Even if we assume that all the data going in is totally accurate, we still have problems.

Left to its own devices, the optimizer will identify the one most efficient asset and suggest that you put all your resources in that asset. Of course, this leads to a gross violation of the diversification principal. In practice, most advisors restrain the program to reasonable asset allocations. Blindly following the black box will lead to putting all your assets into one stock or one market.

I attended a meeting in 1994 where Bill Sharpe spoke on the problem of optimizers. According to Dr. Sharpe, optimizers will readily identify input errors and recommend that you put 100% of your assets in the wrong asset. Sharpe shared the Nobel Prize for Economics in 1990 with Harry Markowitz for his work on MPT. He developed the Capital Asset Pricing Model and other refinements to MPT. I believe he speaks with some authority on the problem.

If the inputs are updated frequently, another strange abnormality creeps into the process. Because assets which are under-performing recently will show lower rates of return and higher risk, the program will decide that they are no longer efficient. Then the program recommends sale of the asset. Blindly following the black box then leads to buying high and selling low. In the real world, tax and transaction costs are high. Frequent updates, and the resulting frequent trading, will increase transaction costs far beyond the benefits that MPT can offer. Most of us don’t need that kind of advice. How often to update the data, and what time frames to use, becomes a matter of judgment. The computer can’t solve that for you.

In the case of foreign investing, if we examine monthly or quarterly data, we will get different results than if we use annual data in our series. In a like manner, if we look at 10-year time periods, we will get different results than if we use three- or five-year time periods. There is always an effect, and it is almost always better to have a diversified portfolio, but the optimum ratio of foreign to domestic will change with each different set of data observations.

Two very clear examples come to mind to illustrate the problem of the black box. During the preparation for Desert Storm, foreign markets performed miserably. All the optimization software I saw recommended selling foreign stocks. Those investors and advisors who sold locked in their losses, and were not invested when the inevitable turn came.

During 1993, emerging markets exploded upward. Mutual fund companies rushed new emerging market funds through registration. Their representatives touted an asset allocation of up to 40% in emerging markets and used optimization results to add to the hype. Of course, they downplayed the very short-term data that they were using as input to the process. The very short-term data indicated that emerging markets had high expected rates of return and almost no risk! Investors who rushed out to load up on emerging markets were left with egg on their faces, and have had all of 1994 to wonder what went wrong. Longer-term data would have showed a very high rate of return, very high risk, very low correlation, and an optimum portfolio with a low percentage of assets in emerging markets.

Most advisors use past data for expected rates of return and risk inputs. However, some may forecast based on their research or feelings. In my not very humble opinion, this adds another layer of risk and complication to the process.

A better approach, and one that I have used successfully in my practice for years, is to use long-term data to structure a portfolio that makes sense, and then test the results with the optimizer. Rather than sell assets that are under performing in the short term, as the optimizer programs might suggest, we use re-allocation to increase positions in down markets and decrease positions in markets that have had strong short-term results. This can be emotionally painful and requires discipline. I can’t honestly say that I enjoy selling winners to buy losers, and I get to explain it all too often to concerned clients. But while it goes against the grain, this discipline will lead to more consistent results, lower risk, and reverses the buy-high, sell-low problem.

The terrible truth is that financial management remains an art much more than a science. Forecasts are notoriously difficult and unreliable, and judgment is always required. We must recognize that nothing works every day, quarter, or year. Discipline is difficult in the face of intense media speculation and hype, but discipline leads to acceptable long-term investment results. As long as the world economy continues to grow, patient investors will profit.

For all its limitations, MPT offers one of the strongest tools available to the rational investor. Used properly — that is, with judgment, patience, and understanding — it will go a long way toward smoothing out the often-bumpy investment process.

In the next chapter, I will discuss a closely related area: the impact of asset allocation on investment results.