Recently Charles Schwab aired an advertisement that portrayed a couple in their fifties explaining why they hired an investment advisor. Their reasoning was simple. Although investing is important, it is also boring and confusing. Since life is already sufficiently hectic, there is no reason to spend precious time learning about this dismal topic when you can hire a professional to do it for you.

That large numbers of participants invest blindly and need help in determining their asset allocations is widely accepted. A recent EBRI study ¹ found that 45% of all workers have never determined their retirement income needs. John Hancock’s Fifth Defined Contribution Plan Survey ² showed just how little participants, even the college educated ones, know about investing. For example, 47% and 49% of the participants thought stocks and bonds could be found in money market funds respectively. Only 25% of the participants knew that the best time to transfer money into bond funds is when interest rates are expected to decrease.

Many plan sponsors believe that the vast majority of their 401(k) plan participants are unwilling to take the time to become knowledgeable about investing. This ignorance prevents participants from making informed asset allocation decisions and then monitoring their choices. These plan sponsors believe that participants want to be told how to invest their account balances. Companies that market asset allocation services to plan participants (with the endorsement of plan fiduciaries) have been formed to meet this perceived pent-up demand.

However, the fact that large institutional investors find value in hiring consultants to perform (and then explain) asset allocation studies does not necessarily mean participants will benefit from an apparently similar service. These services are based on mathematical models (portfolio optimizers), and, like any model, they have limitations. If participants don’t understand these limitations (and they probably are not even aware that these limitations exist), they can easily misinterpret the results and overestimate the model’s presumed predictive power.

The testimony to the limitations and uncertainties of optimizers came from Harry Markowitz himself when he discussed how he invests his retirement money:

Sophisticated institutional investors realize that optimizers are just another tool to be used in the process of developing an asset allocation. Unknowledgeable participants, on the other hand, will likely base their decisions solely on the recommendations without considering the very real possibility that the future will not be a rosy as the optimizer assumed it would be. This danger creates a fiduciary liability quagmire for the plan sponsor which appears to more than offset any benefit to the participants.

Plan sponsors want their employees to have financially secure retirements. However, plan sponsors cannot change the fact that there is no "one-minute" answer to the question: How should I invest my money? Achieving retirement security requires the development and implementation of a sound investment strategy that includes monitoring the asset allocation on an ongoing basis. Participants must accept responsibility for their own retirement security. The only alternative is to hope to get lucky.

Before providing or making available asset allocation services to participants, plan fiduciaries must develop an understanding of what portfolio optimization models can and cannot do. Only by undertaking this intellectual exercise will the fiduciary gain the knowledge that will not only allow him to make an informed judgement as to the merits of offering such services, but also enable him to articulate his decision in a judicious fashion. The purpose of this article is to outline the issues surrounding the advisability of offering asset allocation services to participants.

Scientists develop models for several reasons. Model building enables scientists to formalize their understanding of what they have observed. They review observations, both their own and those of others, in order to create a story (i.e., the hypothesis or model) that incorporates and explains known data and apparent relationships. It is essential that the data used as the foundation for a model be reproducible and predictable. If scientists cannot agree on the observations and measurements that form the basis of a model, it is highly unlikely that the model will be taken seriously.

Once a model is constructed, scientists have the opportunity to assess both its robustness and shortcomings. One measure of robustness is the degree to which new observations fit into the model’s framework. Another measure is the number of and type of exceptions to the model. The identification and analysis of exceptions is a valuable tool in the process of actually determining what is being observed and discovering if the model should be refined, drastically altered, or scraped altogether.

Another characteristic of a good model is its predictive value. If the system is disturbed or altered in a well-defined manner, a very specific outcome can often be foretold. Vaccinations are an example of this. Scientists, by understanding the immune response, have learned how to make effective vaccines to a wide variety of organisms. These vaccines protect practically all of us from everything from specific flu viruses to tetanus and polio.

Other models forecast a range of outcomes and assign, with a high degree of accuracy, specific probabilities to each of them. For example, if the genetic makeup of a couple is known, a geneticist can predict the likelihood that the couple’s next child will be a boy with brown eyes and blond hair rather than a girl with green eyes and red hair.

Scientific models, then, attempt to describe physical and biological processes and structure from various perspectives--causal, static, and dynamic. Depending upon its degree of complexity, a model can attempt to explain what is there today, how it got there, and how it will evolve in the future. Models can also describe interrelationships with other objects or processes. Furthermore, the model can provide insights into how the subject under study can be modified so that its usefulness can be enhanced.

So what is portfolio optimization and how does it fit into the concept of scientific modeling just discussed? To begin with, portfolio optimization is a powerful tool for analyzing how the different asset classes can interact with each other. Given a specific set of input data (each utilized asset class’s expected mean return and standard deviation and correlations between the different asset classes) and constraints (limitations on amounts, if any, of each asset class) the optimizer will identify the most efficient portfolio among the universe of possible ones. "Most efficient portfolio" means the portfolio with the highest return for the level of risk specified or the portfolio with the lowest risk for the return specified.

Optimizers can generate a variety of reports including the likelihood that a portfolio will generate a specified minimum return, the magnitude of downside risk, the consequences of changing the constraints and/or adding or deleting asset classes. Portfolio optimization is an invaluable tool by which an investor can get an understanding of the investment process and the types of portfolios that may meet her needs. In fact, the mathematical nature of portfolio optimization appears to guarantee that all the requirements of a scientific model are met:

1. a very formal and thorough understanding of a set of relationships;
   
   
2. a tool for analyzing interrelationships;
   
   
3. the ability to ask and answer different questions;
   
   
4. the ability to make quantifiable predictions (as to portfolio returns and volatility).

A portfolio optimizer can indeed make detailed predictions. However, the optimizer’s predictive ability must be broken down into two components: the optimizer’s algorithms and the input data. For this section of the discussion, it is assumed that the algorithms (i.e., mathematical rules) underlying optimization models are sufficiently accurate to capture most real world situations. This statement simply means that the optimizer is an efficient number crunching machine--nothing more and nothing less.

(Scientific models are built so that they may be tested. If the model correctly describes a process, such as mixing chemicals A and B under a specified set of conditions, then the outcome of the reaction, chemical C, should be generated regardless of where in the world this process is done. In addition, chemists should be able to predict what products will be obtained if the conditions are changed and/or other chemical substances are mixed with A and B. Structuring models in this way allows the model itself to be tested. Unlike scientific models, however, portfolio optimizers have no predictive value in and of themselves. Their usefulness is their ability to manipulate data.)

A portfolio optimizer’s worth to the average participant in a self-directed retirement plan, then, is its predictive value, and that is a function of the data it is crunching. The key questions are:

1. Will the future behavior of the asset classes have any correlation to the data that is inputted into the optimizer?
   
   
2. How much error in the input data (i.e., the difference in values of the projected versus actual means, standard deviations, and correlations) can the optimizer tolerate before its predictions become meaningless from a decision making perspective?

Unfortunately a major weakness of optimization models can be summarized by the old adage, "garbage in, garbage out."

Tables 1 and 2 show just how unreliable historical data can be when used to make predictions about future asset class returns. For example, Table 1 shows that for the ten year period from 1949 through 1958 (row two in the table), the S&P 500 had an annualized compound return of 20.06%. In the succeeding ten years (1959 through 1968, row three), however, the S&P 500 had a return of only half that amount (10.00%) representing a change in return of 10.6%. The last row of Table 1 shows the average magnitude of the changes in returns from each ten year period to the next.

Because timing (the length of the holding periods as well as the starting and ending years) can have an impact on studies like the one shown in Table 1, several similar studies were also done using different time periods. Tables 2a and 2b are a summary of these studies and clearly shows that the variation in returns from one period to the next can be observed regardless of the time period used.

			Ibbotson	Ibbotson
		Ibbotson	Int.-term	One Year
Period	S&P 500	Small Stocks	Govt Bonds	Govt Bonds	T-bills
1939-1948	7.26%	18.57%	2.04%	0.69%	0.30%
1949-1958	20.06%	17.23%	1.61%	2.07%	1.68%
1959-1968	10.00%	20.73%	3.52%	4.49%	3.52%
1929-1978	3.16%	4.48%	6.47%	6.84%	5.94%
1979-1988	16.33%	18.93%	10.97%	10.40%	9.09%
1989-1998	19.19%	13.22%	8.74%	6.44%	5.29%
Average magnitude
of change in return from	9.15%	8.25%	2.40%	2.73%	2.52%
one period to the next

Source: Stocks, Bonds, Bills, and Inflation 1999 Yearbook. Ibbotson Associates, Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). Used with permission. All rights reserved.

For example, the results of the study shown in Table 1 can be seen in the first row in Table 2a. For the successive 10 year periods beginning in 1939 and ending in 1998 (1939-1948 followed by 1949-1958, etc.), the return of the S&P 500 changed an average of 9.15% from one period to the next. The second row of the table shows that for the successive 10 year periods beginning in 1938 and ending in 1997 (1938-1947 followed by 1948-1957, etc.), the return of the S&P 500 changed an average of 6.83% from one period to the next.

Table 2b shows that the effects seen for 10 year holding periods can also be observed for 5 year holding periods. The words of John Allen Paulos seems to adequately summarize the observations shown in Tables 1, 2a, and 2b: "Stock prices seem to obey the laws that govern random phenomena, so its fair to infer that maybe they’re random." ⁴

Plan fiduciaries must ask: Will the inputs the asset allocation service provider uses accurately reflect the investment environment of the future? If the portfolio optimizer’s inputs represent the output of a lousy crystal ball, is there any value to the average plan participant in the recommendations generated? After all, the average participant wants advice, not a tool whose use requires an informed and sophisticated investor and/or the help of a highly paid consultant.

Table 2a:
Summary of Studies of Changes in Return Between Consecutive Ten-Year Time Periods

		Average Magnitude of Change in Annualized
		Compound Returns from One Ten Year Period to the Next
	Number of			Ibbotson	Ibbotson
	Successive		Ibbotson	Int.-term	One Year
Period	Periods	S&P 500	Small Stocks	Govt Bonds	Govt Bonds	T-bills
1939-1998	Six	9.15%	8.25%	2.40%	2.73%	2.52%
1938-1997	Six	6.83%	11.28%	2.33%	2.69%	2.54%
1937-1996	Six	6.89%	5.94%	2.67%	2.63%	2.52%
1936-1995	Six	6.65%	12.58%	2.30%	2.57%	2.47%
1935-1994	Six	7.52%	11.99%	1.85%	2.43%	2.35%
1934-1993	Six	5.52%	10.01%	2.43%	1.98%	2.16%
1933-1992	Six	5.53%	6.13%	2.35%	1.77%	1.96%
1932-1991	Six	6.56%	8.14%	2.89%	1.86%	1.54%
1931-1990	Six	5.62%	9.03%	2.71%	2.11%	1.65%
1930-1989	Six	8.92%	6.57%	2.76%	2.21%	1.72%

Source: Stocks, Bonds, Bills, and Inflation 1999 Yearbook. Ibbotson Associates, Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). Used with permission. All rights reserved.

		Average Magnitude of Change in Annualized
		Compound Returns from One Five Year Period to the Next
	Number of			Ibbotson	Ibbotson
	Successive		Ibbotson	Int.-term	One Year
Period	Periods	S&P 500	Small Stocks	Govt Bonds	Govt Bonds	T-bills
1934-1998	Thirteen	6.17%	15.41%	1.86%	1.64%	1.43%
1933-1997	Thirteen	5.47%	14.18%	1.78%	1.48%	1.42%
1932-1996	Thirteen	8.37%	18.42%	3.14%	1.57%	1.28%
1931-1995	Thirteen	7.16%	20.24%	2.38%	1.89%	1.39%
1930-1994	Thirteen	8.42%	15.15%	2.54%	1.88%	1.50%

Ibbotson

Ibbotson

Int.-term

Period

S&P 500

Small Stocks

Govt Bonds

T-bills

1930-1939

5.34%

15.39%

4.64%

0.56%

-0.05%

1.38%

4.58%

0.55%

1940-1949

10.30%

25.30%

1.83%

0.41%

9.17%

20.69%

1.83%

0.41%

1950-1959

20.84%

19.51%

1.37%

1.87%

19.35%

16.90%

1.34%

1.87%

1960-1969

8.69%

19.32%

3.54%

3.89%

7.81%

15.53%

3.48%

3.88%

1970-1979

7.50%

15.52%

7.07%

6.32%

5.86%

11.49%

6.98%

6.31%

1980-1989

18.19%

17.00%

12.17%

8.92%

17.55%

15.83%

11.91%

8.89%

1990-1998

18.75%

15.34%

8.44%

4.96%

17.89%

13.56%

8.25%

4.95%