Though literally everyone talks about diversification for an investment portfolio, very few understand the true statistical data underlying the definition. As a result, few portfolios are properly diversified and an extended risk is being taken- unquestionably unwittingly, but nonetheless evident- by most consumers.

In order to properly explain the problem, certain other definitions are required:

Systematic Risk- this is risk due to the movement of the market itself. The benchmark could be the Dow (normally used by consumers and brokers alike), the S&P 500, Wilshire index, etc., but the index may also be that of select or special uses such as gold, real estate, biotech and other sector funds. If one had one or a few investments in a given area, they could compare its return to that of the benchmark index to determine how well it is doing.

Unsystematic Risk- This is the risk of ONE company causing a significant move- either up or down- in a portfolio. This is usually the risk that most consumers would want to eliminate- unless they are TRUE risk takers (few are). It may be tempered- and in fact virtually eliminated- by the purchase of a certain number of stocks or bonds. The graph below shows the statistical reference.


As is easily identified, the number of stocks necessary to insulate a given portfolio from unsystematic (firm- specific) risk is around 10 to 15. Slight variations are possible depending on the volatility (beta is one of these elements) of the portfolio and correlation of the individual stock and some texts have suggested 20 stocks should be purchased. Overall however, the use of 13 stocks may be used an "acceptable" average/compromise for proper diversification- ASSUMING ADEQUATE CORRELATION described more fully below.

Below is a table from Investments by Bodie, Kane and Marcus (standard text for CFA's)

Number of stock Standard Deviation

1 50.00

2 41.83

5 36.06

10 33.91

20 32.79

100 31.86

The minimum, or nondiversifiable risk for this scenario would be 31.62 so you can see that once you get past 10 stocks, each additional stock does not reduce the volatility that much. And that's the problem if the stocks tend to move in the same direction as the above chart reflects. In such a scenario, the use of just the 13 or so stocks would not decrease the risk appreciably. Hence the next important issue is called correlation. This means that all the stocks selected all move in the same direction when something happens in the marketplace- either all up or all down. Most portfolios would prefer some negative correlation- that is some stocks/investments would go up when other investments in the portfolio were going down. If we take the same number of stocks and gave them a complete correlation, look at how the volatility (standard deviation) is reduced.

Number of Stock Standard Deviation

1 50.00

2 35.36

5 22.36

10 15.81

20 11.81

100 5.00

As you can see in the top chart, 20 stocks have a standard deviation of 32.79 versus the much lower 11.81 directly above. The first portfolio- which, I submit, would might be used by unknowledgeable and/or untrained brokers and investors- is 64% more volatile (linear). But all this is a rather moot point since investors aren't diversified to begin with. A study by the New York stock exchange shows that 49% of stockholders held only one common stock, 20% held two, 22% held between three and seven issues and only 9% held 9 or more. Thus 91% of all individual investors had portfolios of eight or less issues making the portfolios substantially more risky than acknowledged by their attitudes. That report was from the early 90's and is unquestionably tempered by the significant use of mutual funds from about 1990 onward. However, the risk is still apparent since a significant number of 401(k) plans show a large use of employer stock as identified next.

An excellent example of the problem of unsystematic risk that is endemic in society is through company incentives to employees to purchase company stock through discounts, stock options and profit sharing plans. Employees invariably end up with highly non diversified portfolios since most people do not buy other securities to offset such risk. Digital stock defines such a problem. It reached a high of 200 but subsequently dropped to about $33 (12/92). Employees did maintain large undiversified holdings and will probably never see their investment return to even half the value in their remaining lifetime. As a question therefore, are such companies liable for not making employees aware of such risk? The answer is clearly yes under the rule 404(c) which requires that employers give employees education on risk. (In such cases, one would use a weighted portfolio to ascertain the overall risk.) It would appear that the continued use of employer stock will be cause for significant employer liability in the future.

One type of guide to diversification, though one not normally monitored except by certain portfolio managers and sophisticated investors who statistically monitor various funds, is called R squared. It's an indication of a fund's overall diversification and measures the percentage of the funds performance as compared to the overall market. A R2 squared of 75 means that the fund is 75% as diversified as the S&P 500- though other indexes may be used. This means that 75% of the fund's performance is due to the overall market movement while the other 25% is unique to the fund's characteristics.

CAUTION: Though diversification has been properly defined with around 13 stocks in a SINGULAR portfolio, that is NOT to say that the ENTIRE portfolio for the investor, in and of itself, is diversified. For example, a diversified mutual fund portfolio in totally small capitalization stocks or junk bonds (under BBB rating) will unquestionably have 20 or more issues in the portfolio, but the underlying risk of owning ONLY this ONE fund is unacceptable for almost all purposes. The entire investors portfolio should contain other "diversified" investments of, say, growth stocks, bonds, municipals, etc. in order to maintain proper diversification of all the holdings. This is better known as asset allocation.

TIME DIVERSIFICATION?: It has been usually held in the industry that the longer one holds an investment, the less the overall risk. It's based on standard deviation (volatility around a norm) and it means that if you have a risky fund, risk would lower the longer the fund was held. For example, if the standard deviation for one year was 20% (about equal to the S&P overall) and you held the fund for 5 years, you would divide 20% by the square root of five for a standard deviation of 8.94%- an apparent decrease over 55%. But the standard deviation of the dollar RETURN (that's your money folks) is INCREASED by the formula (1- .0894)5th or .626. This means that the final five year wealth may be only 63% of projected. That represents a 37% loss- far greater than a one year 20% swing. Per Investments by Bodie, Kahn and Marcus, Richard Irwin Inc. 1989, page 224, ".....time diversification does not reduce risk. Although it is true that per year average rate of return has a smaller standard deviation for a longer time horizon, it is also true that the uncertainty compounds over a greater period of years. Unfortunately, this latter effect dominates in the sense that the total return becomes more UNCERTAIN the longer the investment horizon". "Investing for more than one holding period means that the amount at risk is growing. This is analogous to an insurer taking on more insurance policies. The fact that these policies are independent does not offset the effect of placing more funds at risk."

That is the major reason why I feel it is necessary to monitor investments. Maybe nothing would wrong, but are you willing to trust your entire life's savings to MAYBE'S????? The validity of that point is (allow some latitude) by the significant risks absorbed by the property casualty insurers during the last few years. They use the same type risk scenario- over time the odds of risks can actually decrease. But in just a short time, there were the hurricanes in Florida and Hawaii, flooding over two years in the mid west, an earthquake in California and the numerous major fires as well. The point is that these major insurers used all the tables to develop risk analyses and profit return. But they obviously did not properly account for what could and did happen- major catastrophes all at one time. Investors must weigh this risk and stay vigilant.

EFFICIENT FRONTIER: The chart shows the Markowitz Efficient Frontier Graph. For each level of risk and return, you can plot different curves. The essence of the graph is that point M represents the highest expected return relative to all other portfolios of comparable risk.

My point to this discussion however is to quote on aspects of diversification: (Stalla CFA Manual) "In the illustration, single asset portfolios will be well located within (below) the efficient frontier (solid line) because these portfolios have high levels of market and specific risk. Multi- asset portfolios lie closer to the efficient frontier because diversification causes their specific risk to be reduced by the law of large numbers. Ultimately, portfolios lying on the efficient frontier will be those whose specific risks have been eliminated by diversification; they are efficiently diversified portfolios."

Unfortunately, the above definitions have been lost on the brokerage community (and attorneys, expert witnesses and consumers as well). This is also evident in the initial license preparation for literally all new security licensees. As an instructor in securities licensing training for the two largest firms in the United States, I have been involved with literally all the major licenses/exams- Series 7 for stockbrokers; Series 6 for mutual funds; Series 24 and 8 for supervision and a host of others. In perhaps 10 to 15 minutes over a period of two to four days, there might be some superficial commentary regarding systematic and unsystematic risk, but in NO cases is the statistical information given- since it is not required for passing the exam.

Further, and most importantly, there has been NO continuing educational training OF ANY TYPE required for brokers, supervisors, compliance representatives, etc. once they attained a securities license- until 1995. And a good portion of this new training is still sophomoric and redundant. As a result, a goodly number of brokers and firms are designing portfolios exhibiting substantially greater risk than consumers want or should accept. Confirmation of that point is offered by a study from the New York Stock Exchange which found that 49% of all stockholders held only one common stock, 20% held two, 22% held between three and seven issues and only 9% held nine or more. Thus 91% of all individual investors had portfolios of eight or less issues making the portfolios substantially more risky than that undoubtedly acknowledged or desired by their attitudes.

And as stated, securities attorneys are ignorant of this issue as well- though not necessarily surprising since there is nothing inherent in a law degree that covers such technicalities. Additionally, none of the SEC or NASD texts address the issue either. As a result, in literally all the cases I have reviewed and in all cases where I have acted as arbitrator, there has never been one argument on improper diversification. Yet it is has been quite apparent that it should have been raised in at least 85% of such cases. A key aspect is not even addressed. Risk is the key investment factor that must be developed for all clients.

Expert witnesses have also not addressed the issue. But since most witnesses come from retired members of the brokerage community, it is not surprising that the knowledge is not there. Unless one has advanced education in investments or is a CFA (Chartered Financial Analyst), it is rarely noted. As far as consumers are concerned, unless they have attended some obscure seminar by the likes of AAII (American Association of Individual Investors), none of the investing public has any comprehension of the numbers as well. It is also apparent by the non diversified portfolios they hold/are sold.

And since the members of the arbitration panel all come from the ranks of the above, the arbitrators are therefore woefully ignorant of a material issue as well.

NYSE Rule 405 demands that brokers "know thy client". The NASD rules demand suitability. I submit it is literally impossible to discuss the singular merits of a bond, stock or the like if the portfolio consists of only two, three, four or only six stock. Regardless of a low beta and/or limited volatility of one (or just a few) purchase(s), the unsystematic risk suggests an unsuitable portfolio in and of itself.

This lack of education regarding proper diversification is the foremost issue in literally all cases- especially where individual stocks are purchased. It is IMPOSSIBLE to properly judge the correctness of an account if the material benchmark is missing- that of RISK of the entire portfolio. And even if the broker is addressing only a small part of an investors holdings, it is mandatory that they "know thy client" and therefore must require detailed knowledge about the rest of the investment assets to determine proper diversification and risk throughout.

Commentary 2000: The above was written prior to the release of Malkeil's later research on volatility. Due to the closer correlation of individual issues, the number of securities now needed is 50 instead of the 15. This clearly increases the risk for each consumer with stocks and makes it literally impossible for almost anyone to determine a portfolio of individual issues.