Is MPT the Solution -- or the Problem?
Malcolm Mitchell - July 2002

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The proper choice among efficient portfolios depends on the willingness and ability of the investor to assume risk. . . . If a greater degree of uncertainty can be borne, a greater level of likely return can be obtained.
   Harry Markowitz, 1959, p. 6.

To help investors determine the level of risk they're most comfortable with, here's a statistically based risk-tolerance quiz.
   Wall Street Journal, July 14, 2000

Bonds have a risk. Stocks have a risk. But their combined risk, when put together in a portfolio, tends to be less than when they stand on their own.
   Lebenthal & Co. radio ad, March 2002

Happiness is not a destination, it's a way of traveling.
   Church display, New York, March 2002


Modern Portfolio Theory bestrides the investment world today like the legendary Colossus. Its precepts dominate the education and training of every professional investment manager; its key terms -- risk-return tradeoff, diversification, expected stock returns -- frame virtually all advice offered to non-professional investors. Indeed, so complete is MPT's domination that we may forget how recent it is. While the set of concepts itself is a product of many years' labor by many individuals -- the seminal paper by Harry Markowitz was published exactly 50 years ago -- widespread adoption of MPT principles by the professional investment community is barely 20 years old.

Our thesis is that exclusive and uncritical devotion to investment ideas that can hardly be said to have stood the test of time is dangerous in itself -- but especially so today. For the first time in more than 20 years, the stock market has clearly stopped rising; broad indices are lower than they were in 1998. MPT purists react to the investment wreckage of the past four years by insisting that the theory itself remains valid, but that some managers have misused it, out of either ignorance or greed, and that the misuse has led many investors to form unattainable hopes. The accusation may be true; many investors have certainly been misled. Yet the problem of the future remains: correctly-applied MPT or no, investors may lose money over the next four years as well -- or longer.

What's more, the potential losers now include a large and growing number of working Americans with self-directed retirement accounts. At least 40 million men and women participate in 401k plans, a legal entity that didn't exist before 1980; their assets total over $1.5 trillion, even after recent losses. The retirement benefits of these 401k-ers are not guaranteed; their future is still at the mercy of the market. Yet MPT advocates offer no help except to point out that most non-professionals ignore the precepts of MPT and consequently miss the opportunity to improve the long-term growth rate of their assets. Professionals seem to be saying, "If only 401k-ers would behave more like us." On the professional investment side itself, however, there are some neglected questions that in our view undermine the continued reverence paid to MPT:

First, has MPT actually worked for professionals? The theory's ascendancy began in the late 1970s and was capped by the awarding of Nobel prizes to its brightest lights in the 1990s. Coincidentally, this was just the period of unprecedented gains in U.S. equities; the Dow Jones Industrials average rose 10-fold. Has it been proven that the adoption of MPT contributed anything to institutions' increased wealth over and above what equity markets contributed?

Second, why have institutions -- pension, endowment, and foundation funds -- paid virtually no attention to their own risk-adjusted returns at the total fund level? Institutions judge their external managers by the cornerstone of MPT, that is risk-adjusted measures, yet their own CIOs' financial and career advancement is determined primarily by the fund's total asset growth relative to comparable funds, not by the risk-adjusted growth.

And finally, most to the point, why have we seen a universal rush by corporations and public employers alike to switch employees from guaranteed to non-guaranteed retirement plans? Doesn't that switch at the very least cast some doubt on employers' confidence in their own and their managers' MPT-based investment skills? (Portability and a guaranteed benefit are not mutually exclusive, so claiming portability as the impetus for the switch is no answer.)

The critical reality today is that no one has certain knowledge of what investment markets will do in the future. But neither did anyone have certain knowledge in 1928, or 1945, or 1972. So what is it that MPT has changed? Do investors today really have a set of guidelines that, as MPT advocates believe, for the first time tell us "how to manage our affairs so that the uncertainties of human existence do not defeat us?"(1) In this article we offer a contrarian answer to that question, hoping thereby to provoke fresh discussion of the foundations of MPT. (Note (2) is for professional investors.)

Here is a brief summary of the article:

Section I -- Is Volatility Risky? -- looks at the "risk" that Harry Markowitz found a means to measure and by so doing laid the groundwork for all of MPT. We will argue that what professionals agree is the "extraordinary intellectual density and originality"(3) of Markowitz's Nobel prize-winning writings rests after all on his redefining risk as volatility. That unsupported and unexplained redefinition confounds what all investors previously thought of as risk -- and what non-professionals still think it is -- that is, the possibility of losing money.

Section II -- Diversification Is for Defense, Not Offense -- deals with diversification, the second concept, after risk, whose importance professionals claim was discovered by Markowitz. We will argue that a) investors have always understood the reason for the warning, "Don't put all your eggs in one basket," b) buying large numbers of equities is neither the only nor necessarily the best method of diversifying, and c) in any case, the MPT use of the term obscures the fundamental truth: "While there are many valid reasons to invest in diversifying assets . . . increasing the return of the portfolio is not one of them."(4)

Section III -- The Long Run: A Destination? Or a Receding Horizon? -- argues that the application of MPT creates a bias toward the expectation of rising stock prices. That bias was supported by the unprecedented rise in stock prices from 1980 to 1999. It is also encouraged by academic studies that proclaim the wisdom of owning "stocks for the long run" -- even though in those studies the tough job of defining the long run in practical terms is always fudged. We argue that statements such as, "One dollar invested and reinvested in stocks since 1802 would have accumulated to $11 million by the end of 1999,"(5) are dangerously misleading to investors making decisions today.

Section IV -- Risk Is Not in Our Markets, but in Ourselves -- argues that true risk, for professional investors and non-professionals alike, is defined by the impact that a loss would have on their overall financial health. Any advice that professionals offer to non-professionals, therefore, ought to begin with the question: How much money can you afford to lose? MPT-inspired studies of investor psychology and similar studies in "Behavioral Finance" can't explain when an investor is making a "right" decision or a "wrong" decision, because they ignore the varying impacts that the same loss has on different investors. We argue that investors' total wealth should influence their investment decisions far more than their age or profession, or aggressiveness or timidity.

In our Conclusion, we return to some time-honored advice for investors that MPT claims to have superseded, and we offer some new suggestions. We argue that for most investors happiness is a destination -- ending up with more money than they started out with -- and that reaching their goals depends more on making appropriate asset class choices than on correctly applying MPT. Indeed, the developers of MPT may have had a different destination in mind all along. A now-famous review of "What Practitioners Need to Know" in the Financial Analysts Journal seems to suggest just that: "The value of the contributions of these Nobel laureates [Markowitz, Sharpe, Modigliani, and Miller] does not depend on the degree to which their theories hold in an imperfect market environment. It depends, rather, on the degree to which they changed the financial community's understanding of the capital markets."(6)

Section I. Is Volatility Risky?

Risk: the possibility of loss, injury, disadvantage, or destruction.
Uncertainty: the state of being uncertain . . . something doubtful or unknown.
Variability: the fact of being variable, [being] able or apt to vary or change.
   Webster's Third New International Dictionary

In 1970, John O'Brien, later of Leland O'Brien Rubinstein fame, published an article in the Financial Analysts Journal that is recognized as the first general exposition of the new "market theory." In a section in which he explained the terminology of the new theory as applied to performance measurement, O'Brien made a parenthetical comment:
    In looking back at performance the term "uncertainty" seems better replaced by "variability", however for consistency with the market theory we will continue to use the term "uncertainty". [punctuation as in original](7)
With his timid suggestion, O'Brien in fact spotted the obvious difference in meaning between two words that Harry Markowitz had used interchangeably in the 1950s. When we look at past performance, there is no uncertainty; we know precisely what happened and how much variability there was. When we look forward, there is, by definition, uncertainty. Yet Markowitz used both words as synonyms for "risk." In the index to his 1959 book, the entry under Variability is, "see Risk." The entry under Uncertainty is, "see Risk."(8)

Needless to say, O'Brien's suggestion was never taken up by later developers of MPT, and Markowitz's equation of risk with variability and uncertainty has never been challenged. It needs to be.

The fact is that Markowitz did not find a way to measure the risk that investors care about: the risk that arises from an uncertain future, the risk that things will turn out to be worse than we expect. He simply ignored that kind of risk and focused instead on variability -- or, to take the term more commonly used today, volatility. Instead of measuring risk, Markowitz demonstrated how to measure volatility in a portfolio. Why volatility? One obvious reason is that volatility is measurable, whereas uncertainty is not.

Another possible reason for calling risk volatility is that it does share one characteristic with uncertainty: both terms refer to a spread of results around a median. What concerns investors, however, is not the spread of results that occurred in the past, but the expected spread in an uncertain future. Interestingly, the word "uncertainty" did not appear at all in Markowitz's 1952 article, but by 1959 he apparently realized the importance of trying to make volatility seem more like uncertainty.

Despite the obviousness (in our view) of the preceding argument, the triumph of MPT has had this result: whenever the word "risk" appears in investment literature or discussion, it means "volatility" -- whether the writer or speaker is fully conscious of that meaning or, more likely, isn't. Among the many millions of investors today, whether professional or non-professional, there is probably a minuscule number who both understand that MPT risk is volatility and agree that volatility is what concerns them.

The following passage, written by a professional who certainly does understand, perfectly illustrates the MPT meaning of risk. The passage appears in a fine explanation of how the discoverers of option pricing theory arrived at their insight, but that doesn't diminish its relevance for our purposes. We cite the passage as evidence that the volatility that MPT calls risk isn't risky for investors.

    Consider two stocks, one much riskier than the other, but each selling for $20 a share. To simplify matters, assume that neither pays a dividend. The market believes that the less risky stock will be selling for $32 five years from now, or within a range of, say, $30 to $34, for an average expected return of 10 percent a year. The market believes that the riskier stock will be selling for $40, within a much wider range of $32 to $48, for an average expected return of 15 percent a year.

    But the two stocks are selling at the same price of $20 today because investors have taken into consideration the differences in risk, even though the expected future prices of the stocks differ widely. The higher risk cancels out the higher expected return and leads to the same price today for the risky stock as for the less risky stock.(9)

We would argue that on the given assumptions the conditions described in this passage could not hold -- at least not for more than an instant. What possible problem could the greater volatility of the more "risky" stock pose for an investor, when the least of its expected spread of results over five years is $32, and the least of the less risky stock's results is $30? Would any investor refuse the chance to more than double his or her money, simply because that chance exists? Given the choice between the two stocks in this passage, investors would always choose the "risky" stock, and thus push the price of that stock above the price of the other.

In the real world, the risk that investors face with either stock is the possibility that an early move of their $20 investment might be to $15, instead of toward "expected [higher] future prices." If that were to happen, what investors would begin to fear is not volatility but the possibility that they were wrong about the direction of their expectations. In deciding between the two stocks, investors might indeed consider the stock with a wider range of expected future prices more risky than the one with a narrower range because the wider range includes a greater possibility of the stock going to $15 at some point. But that isn't a scenario the passage considers; nor is that the MPT definition of "risky."

There is actually one kind of risk that may result from volatility. If the more volatile of the two stocks described does rise quickly to $35 or $40, investors might push their expectations still higher and believe they will have even more money to spend than they originally planned -- for example, on the proverbial daughter's wedding. If the investment then reverts to $32 on the week of the wedding, they might find themselves short, despite having a 60% profit on their $20 investment. That risk, however, arises not from the range of expected future prices but from the way some investors respond to paper wealth. And again, MPT has nothing to say about that kind of risk.

In sum, we believe that defining risk as volatility is irrelevant to investors' real experiences, and worse, that it obscures the true definition of investment risk as the possibility of losing money. (In Section III we'll return to the reasons why MPT discussions typically ignore the risk of losing money.)

Section II. Diversification Is for Defense, Not Offense.

Until 1952 . . . the relation between the risk and return of a portfolio had not been considered at all. Economist John Maynard Keynes, an astute individual by any standards, viewed the best investment strategy as one where you put all your money in the few stocks about which you felt favourably, without any regard to diversification.
   Raman Uppal, Associate Professor of Finance, London Business School, in the Financial Times, June 4, 2001.

The well-known investor Gerald Loeb railed against diversification in 1935. . . . "Once you obtain confidence, diversification is undesirable," Loeb declared. Diversification "is an admission of not knowing what to do in an effort to strike the average."
   S.L. Mintz et al., Beyond Wall Street, p. 160.

Diversification does not ensure a profit or guarantee against loss.    Stages magazine, 2002

For some obscure reason, John Maynard Keynes and Gerald Loeb are singled out by MPT advocates as proof that pre-Markowitz investors did not understand the importance of diversification. We'll show below that both men in fact held sensible and useful ideas on diversification, but our first job is to try to explain the silly argument that MPT discovered diversification. Clearly, intelligent people have long understood the intended benefits of diversification. The danger of risking everything in a single investment or on a single roll of the dice -- of putting all your eggs in one basket -- is as familiar as children's fables and has appeared in world literature for at least 500 years. What, then, could MPT advocates mean?

We believe that MPT confounds the age-old purpose of diversification, just as it confounds the true meaning of investment risk. Diversification has always implied -- and still does for most investors -- spreading your investments among several securities (or asset classes) so that if one of them goes unexpectedly down a profit in the others may offset the loss. In other words, diversification is a response to investors' uncertainty about the future, to the unavoidable risk that any expected profit may turn out to be a loss.

Since risk is redefined in MPT to mean not the possibility of loss but simply volatility, we might expect that the role played by diversification is also redefined. Indeed, it turns out that the crucial purpose of diversification in MPT is to fine-tune the balance between a portfolio's expected return and its expected volatility. The goal is to create "efficient" portfolios that both maximize expected return and minimize expected volatility. We have argued that volatility doesn't concern investors. Markowitz not only said it should, but that it should be equally as important to investors as the hoped-for return. "The investor," he wrote in 1952, "does (or should) consider expected return a desirable thing and variance of return an undesirable thing [italics in original]." (10)

The main thrust of Markowitz's writings in the 1950s, after defining risk as volatility, was to develop the mathematics of diversifying into appropriate securities in order to produce "efficient" portfolios, that is portfolios with the highest expected return at any given level of expected volatility. Structuring these efficient portfolios has become the holy grail of MPT, and diversification, properly used, is the principal tool in the quest. No wonder MPT advocates claim that pre-Markowitz investors didn't understand diversification; not having the benefit of learning that risk is volatility, they could hardly have understood how diversification is meant to adjust a portfolio's risk-return profile.

A disturbing, albeit unintended effect of MPT's re-conception of diversification is that it appears to be used to enhance return. In MPT practice, portfolios are diversified into selected securities because of the way the securities' expected returns and volatility combine with each other (through their correlations) to produce efficient portfolios. Yet because the goal is maximum expected return at a fixed level of volatility, it can seem that, with volatility fixed, diversification enhances expected return.

In reality, sensible investors, including Keynes and Loeb, have always understood that diversification reduces their expected return as a condition of its protecting them against unexpected loss. The reason we don't put all our assets into the one "best" security or asset class, that is the one with the highest expected return, is not that we believe we can make more money with several. Quite the opposite; we invest some assets in a second-best security because we're willing to accept less money than we would make if we are right about the best, in order to protect against our being wrong. It isn't that we change our belief about the investment we are most certain of; we simply act on the possibility that in an uncertain world even that one may disappoint us.

Keynes and Loeb took very different approaches to solving this dilemma of uncertainty, but they agreed on one important truth: investors are better off acting on full and good knowledge than on scant knowledge. For Keynes, who advised insurance funds and other asset pools that remained fully invested, the solution was to buy only those investments about which his knowledge was "adequate" -- even if that meant the amounts invested in each one were large. In the passage usually quoted to prove he didn't understand diversification, he explains:
    I am quite incapable of having adequate knowledge of more than a very limited range of investments. Time and opportunity do not allow more. Therefore, as the investable sums increase, the size of the unit must increase [i.e., the amount invested in a single stock must grow]. I am in favour of having as large a unit as market conditions will allow. . . . My objection [to "good examples" of potential capital profits] is that I have no information on which to reach a good judgment, and the risks are clearly enormous. To suppose that safety-first consists in having a small gamble in a large number of different directions of the above kind, as compared with a substantial stake in a company where one's information is adequate, strikes me as a travesty of investment policy.(11)
That seems to us advice that displays a thorough understanding of diversification and is eminently sensible besides. Warren Buffett could hardly have said it better.

Gerald Loeb acted as a stock broker for individuals and therefore took a different approach to the dilemma of uncertainty. He advised investors to diversify by holding back cash (in short-term Treasury bills) and investing only on "convincing" knowledge. In the same passage in which he dismissed diversification as "an effort to strike an average" -- which, by the way, is precisely what broad diversification is -- he explains that his policy includes "holding one's capital uninvested [in stocks] for long periods of time," since "bargains . . . are not available except occasionally." Here is his explanation of why he prefers a few large stock investments to many small ones:
    [A] few large holdings may total only 30% of funds available at the moment. . . . Confining oneself to situations convincing enough to be entered on a relatively large scale is a great help to safety and profit. One must know far more about it to enter the position in the first place. . . . A large number of small holdings will be purchased with less care and ordinarily allowed to run into a variety of small losses without full realization of the eventual total sum lost. Thus over-diversification acts as a poor protection against lack of knowledge.(12)
Again, eminently sensible advice from a pre-MPT investor. It suggests to us that MPT adds to an investor's understanding of diversification only in the context of the theory itself, that is, only if the investor's primary goal is to hold an efficient stock portfolio, rather than to make money.

We'd like to give the last word on pre-MPT understanding of diversification to Benjamin Graham and David Dodd, whose 1934 book, Security Analysis, quickly became, and remains, the bible of non-MPT investing. Not the least impressive feature of their book is that it appeared in the depths of the Great Depression that followed the 1929 stock market crash, and yet the authors advised investors not to give up on America's corporations:
    On the assumption that . . . our national wealth and earning power will increase [and be reflected in] the increased resources and profits of our important corporations . . . common stock [properly selected] should on the whole present the same favorable opportunities in the future as they have for generations past.(13)
For Graham and Dodd, the investor's method of selecting stocks is critical, since the method determines whether the purchase is an "investment" or merely a "speculation." A stock purchase can qualify as an investment when the investor has carefully analyzed the price of the stock versus the value of the company. Yet it is still not an investment if only that one stock is bought:
    While [diversification] had always been regarded as a desirable element in investment, our formulation goes much farther in that it holds diversification to be an integral part of all standard common-stock-investment operations. In our view, the purchase of a single common stock can no more constitute an investment than the issuance of a single policy on a life or a building can properly constitute an insurance underwriting.(14)

Section III. The Long Run: A Destination?
Or a Receding Horizon?

If you've set aside adequate funds for your short-term needs, time is on your side and the stock market has historically been the place to be. And when I say long term, I don't mean three weeks from Wednesday. I mean a minimum of five, 10, or 20 years.
   Peter Lynch, in Stages magazine, Spring 2002, p. 24.

History backs me up here: The long-term trend of the stock market in the United States has always been up. . . . "One dollar invested and reinvested in stocks since 1802 would have accumulated to $11 million by the end of 1999," [Jeremy Siegel] says.
   Charles Schwab, You're Fifty -- Now What?, p. 14.

Investing in stocks seems to be a game in which all the players are on one side. Everyone wants prices to rise; short-sellers are a rare species. Even the old bear raids that drove stocks down became impossible after 1933, when short sales were required to be on an uptick -- that is, at a higher price than the stock's previous trade. Yet bull raids that inflate stock prices are with us still, as revelations about analysts' recommendations are making painfully clear.

All in all, it's a wonder that the stock market ever goes down. Indeed, according to most MPT advocates, in the long run it doesn't. The belief that stocks produce a positive return to investors over time is so deeply ingrained in investment thought today that it's nearly impossible to consider the belief objectively. Nonetheless we're going to try. We'll first point out that both MPT practice and the 20-year super-bull market encourage the expectation of future stock profits. Then we'll look at the claim that stocks increase investors' wealth over time, and we'll ask: What stocks, what investors, and what time?

The fundamental MPT activity is the attempt to structure efficient portfolios by choosing securities or asset classes with specific expected returns, volatility, and correlations. As no investor considers adding to his or her portfolio an investment that is expected to lose money, MPT research is based on investments with only positive expected returns. This was true for the studies that Markowitz produced in the 1950s, and it continues to be true today. As we showed in Section I, the uncertainty that MPT claims to have overcome is investor uncertainty about a range of positive expected returns, not investor uncertainty about making or losing money.

It happened that during the 20 years of MPT's ascendancy throughout the investment world, assumptions of positive returns from stocks were fully justified. From 1980 to 1999, the S&P 500 grew more than 12-fold; in only three of the 20 years did the index record small losses, and in each case the losses were more than made up the very next year.

In historical terms it was a unique 20-year run, and its coincidence with the adoption of MPT is striking. Most reasons given for the surge in stock prices are independent of MPT: new technologies, new corporate behavior, improved inflation-fighting techniques -- in short, a new economy. Yet some MPT advocates argue that the new investment ideas themselves, by generating greater confidence in building portfolios, improved capital allocation, more investor patience in down periods, etc., also had a role in sustaining stock prices.

Whatever was pushing stock prices higher for so many years, it seems to have run out of steam. The S&P 500 is lower now than at the end of 1998. There has been enough damage to stock values to make continued confidence at least suspect, and the possibility cannot be dismissed that the stock market has reverted to one of its recurrent long periods -- 10 years or more -- of moving sideways. In short, compared to the full historical record that we now have on economies and markets, the past 20 years are too brief a period, in our view, to prove the lasting validity of either MPT or a new economic paradigm.

When we turn to that long historical record, however, stock enthusiasts seem to be on firmer ground. Leaving aside the patchwork involved in creating centuries-long statistics, there are now accurate and consistent measures of over 75 years of stock market history, and it does seem to be true that over all that time stocks have provided an average annual return to investors of some positive percentage (the precise number is irrelevant to our discussion). Surely, investors can be confident of the future on the basis of such a long history. Or can they?

Consider, first, what the history is of -- namely, indices of stock prices. The best the record can show, therefore, is that an investor who owned the index over the whole period made money. Unfortunately, investors weren't able to buy an index -- indeed didn't conceive of buying an index -- until almost 1980. Forgetting that fact can lead to some questionable arguments, for example the following defense of John J. Raskob, whose infamous advice to buy stocks appeared just months before the 1929 crash, in an article entitled, "Everybody Ought to Be Rich:"
    The conventional wisdom is that Raskob's foolhardy advice epitomizes the mania that periodically overruns Wall Street. But is that verdict fair? The answer is decidedly no. If you calculate the value of the portfolio of an investor who followed Raskob's advice, patiently putting $15 a month into stocks, you find that his accumulation exceeded that of someone who placed the same money in Treasury bills after less than four years! After 20 years [that is, by 1949], his stock portfolio would have accumulated to almost $9,000, and after 30 years [by 1959], to over $60,000. Although not as high as Raskob had projected, $60,000 still represents a fantastic 13 percent return on invested capital [our italics], far exceeding the returns earned by conservative investors who switched their money to Treasury bonds or bills at the market peak.(15)
Here's the problem with this history. Since no index funds were available at the time, the only way a $15-a-month stock investor starting in 1929 could have accumulated $60,000 by 1959 was to make one stock pick every month for 30 years, then to decide whether to hold each purchase through its ups and downs over all the remaining years or to switch it at some time to another stock, and in all those thousands of decisions to be right often enough and wrong seldom enough to emerge with a "fantastic" return that professionals would have envied. Such a "patient" 30-year feat can't be proven impossible, just as you can't prove that an infinite number of monkeys using infinite typewriters over infinite years wouldn't produce Hamlet. It just seems to us quite unlikely.

The reality is that, looking back from today to 1926 (the initial year of the most authoritative return series), we have no idea whether investors made money or didn't for over two-thirds of the period studied. Nor do we have any idea of what would have happened if investors had been able to buy an index in those years, instead of only individual stocks. In our view, the record for the years prior to 1980 can make for interesting academic analyses but is hardly the stuff of safe advice for investing real money today.

On the other hand, we do have a good idea of the investor base and the nature of their activities over the long history. And again, profound changes during the past 15 to 20 years give reason to wonder whether the full record can still be relevant. The changes are easily recited: huge numbers of new investors, not just absolutely but relative to the total population; an explosion in the number and variety of mutual funds and other available investment vehicles; new sources of investable assets, changed investor goals, and a revolutionary social context for investing -- that is, an unprecedented relationship between stock market expectations and retirement planning on a society-wide scale. What's more, all of these changes have coincided with huge growth in total stock market capitalization as a percentage of U.S. GDP -- that is, a huge increase in the impact of stock market movements on the health of the overall U.S. economy.

In short, the investment world has become a vastly different place in the last 25 years from what it had been in the previous 50 years. The ability to look through all of the changes and see only an average annual rise in stock prices over the 75 years is a symptom, in our view, of an advanced and dangerous case of tunnel vision.

Nonetheless, let's grant that 75 years of stock market history may be reasonable evidence of what lies ahead. Let's further grant that the recent creation of index funds means that now "matching the market is sufficient to achieve the superior returns that have been achieved through stocks over time."(16) There still remains a crucial question: Over what time? And the answer to this question is one that stock enthusiasts always fudge. Consider Peter Lynch's definition of the long term as "a minimum of five, 10, or 20 years." We want to ask, Well, which is it? If the long-term investor can expect to be rewarded in five years, what do the 10 or 20 years imply? On the other hand, if the investor may have to wait "a minimum of 20 years," why not say just that? It seems redundant to add the "minimum of five or 10 years."

The explanation is that proponents of long-term investing claim to know what will happen in the future, but they say they can't be sure of the timing. In our view, however, stock enthusiasts, like messianists, purposely fudge the "when" in order to deflect doubts about the occurrence itself. We would argue that, at least for investors, there is no such thing as a sure occurrence at an unspecified time in the future, because the basic goal of every investor is to enjoy an increase in assets in time. Sensible stock investors, professionals or non-professionals, don't expect their reward next week or next quarter, but no one is content with the idea of waiting 20 years. The common reaction of all investors, if their expectations aren't realized in five or ten years, is to begin questioning the validity of those expectations, whether for a single security or for an asset class.

There's a simple truth: neither Peter Lynch nor anyone else knows that investors will enjoy a positive return from the stock market, not over the next five years or the next 10 years or the next 20 years, just as no one knows what the market will do next month. In the face of uncertainty about future stock prices, the best that stock enthusiasts can offer is to assign a measure of probability to various potential scenarios, based on statistical analyses of 75 or more years of stock market history. But there's a better approach for investors than playing probabilities, and that is to look at stock market prices versus stock market value. We'll refer to that approach in our Conclusion.

Even if higher probabilities for certain stock market outcomes can be proven, however, such proofs, as we will argue in the next section, are not equally helpful to all investors -- not even, as MPT-inspired advisors would have it, to all investors of the same age, income level, and emotional stability. The risk posed to investors by any chance that their assets will shrink rather than grow, over any time frame, is not determined by the probabilities of market results, but by the ability of individual investors to remain financially healthy despite the shrinkage.

Section IV. Risk Is Not in Our Markets, but in Ourselves

Markowitz once pointed out to me how someone with "pathological risk aversion" would behave. . . . Offered a choice between a certain gain of 5 percent and a 50-50 gamble of coming out with either nothing or infinite wealth, the pathologically risk-averse person would choose the 5 percent.
   Peter Bernstein, Capital Ideas, p. 59

Studies in behavioural finance have shown that investors are far more distressed by prospective losses than they are made happy by equivalent gains.
   Greg Elmiger, in the Financial Times, June 11, 2001

401k and similar plans are designed to give ordinary people economic security in retirement by encouraging them to mimic the portfolio strategies long pursued by the wealthy. But little attention is usually paid to the fact that the wealthy, because of the overall level of their assets, have less reason to worry about losing substantial amounts in a market decline.
   Robert J. Shiller, Irrational Exuberance, p. 217

We have argued so far that MPT shifted the focus of investment risk from potential losses to volatility, and that with a little help from academics and from 20 years of unprecedented stock profits, it encourages investors to entirely ignore the risk of losing money.

Nonetheless, despite MPT's monopoly of the advice offered to non-professionals, many investors still view stock market investing with some skepticism. This has become a gnawing puzzle to MPT advocates, who take any investor's failure to properly balance return and volatility very seriously. Markowitz's charge of "pathological risk aversion" is only an extreme example of how MPT commonly ignores an investor's overall financial situation and the potential impact on that situation of any particular choice -- whether it's avoiding a loss or taking "a certain gain." Most of us would consider a man on the verge of starving to death quite sane to eat a single ham sandwich rather than take a 50-50 gamble on a week of steak dinners, or nothing.

Attempts to address the supposed puzzle of investors' risk aversion led to the development of a new academic discipline called Behavioral Finance, in which risk aversion is more realistically called "loss aversion." We're going to quote at length from one discussion, because it is so revealing of how the discipline -- whatever its contributions to economics and finance studies may be -- has been misapplied in the investment world:
      Much of the credit for articulating the concept of loss aversion and exploring its implications goes to Richard Thaler [Professor of Economics and Behavioral Science at the University of Chicago's Graduate School of Business]. Thaler first observed the phenomenon of loss aversion as an unintended consequence of his dissertation on the value of human life. "I was trying to estimate how much you had to pay people to get them to take risky jobs," Thaler says. "The economist's approach is to study a lot of statistics and estimate how much more people get paid in risky jobs." Instead of building a model based on voluminous statistics, Thaler started asking people questions -- an approach his thesis adviser had frowned on.

      According to statistical estimates, the value of saving one life would be somewhere in the range of one million to two million dollars. But Thaler asked two questions, not one. First he asked, "Suppose you were exposed to some risk, a one-in-a-thousand chance of dying next week. How much would you pay to avoid that risk?" A typical person gave one thousand dollars as the answer.

      Then Thaler turned the question around. "How much would you require to accept a risk with a one-in-a-thousand chance of dying?" he asked. "According to economics," Thaler explains, "those two questions should be more or less the same." Both ask the value of a life in the face of one chance in a thousand of dying. "But people don't think of those questions as the same," he says. "The very same persons who would say they'd only be willing to pay a thousand dollars to get rid of a risk would have to be paid fifty thousand or two hundred thousand to take a little bit more risk."

      These inconsistent responses puzzled Thaler. . . . In the stock market, loss aversion tends to cloud investment decisions. "When people are thinking about investing . . . ," Thaler says, "they think more about losses than they do about potential gains. So whenever I talk to investors about how they should be investing, say, for retirement, if they take a very cautious attitude and say, 'This is my retirement savings, I can't afford to lose,' " Thaler then asks, "Have you thought about how much you are losing by not investing that money in the stock market?" [italics in original](17)
One hardly knows where to start in pointing out what's wrong here. There is, first, a startling absence of human understanding and compassion in any suggestion that the two value-of-life questions "should be more or less the same." On the one hand, most people live on a limited budget and are therefore limited in what they can pay for anything, including the chance to survive an unavoidable life-threatening risk. On the other hand, most people, at least among the subjects of Behavioral Finance studies, manage to live decently on their limited budgets, and while some may be willing to change jobs in order to improve their lifestyle, it would take a whole lot more than just increased income to make them willingly put their lives at risk. Indeed, it is hard to imagine a circumstance in which any normal person would treat the two questions equally.

Even more startling, however, and also more relevant to our investment discussion, is the failure of both Professor and commentator to realize that there is no such thing as "a typical person" when it comes to placing a value on avoiding a life-threatening risk or taking one on. Everyone will evaluate the situation in the context of his total wealth and financial options. In the real world there is always a wide spectrum of responses to the same risk. Even kidnappers have figured that out.

Similarly, there is no typical investor, not even a typical 40-year-old, moderately aggressive investor. There are only investors of varying financial means -- varying in terms of family wealth, income, net fixed assets (home value, car, etc., minus debts), and secure investments (Government bonds, bank accounts, etc.). The total of these forms of wealth determines what kind of investor an individual can be; it determines his or her answer to the classic pre-MPT question, How much can you afford to lose?

We would argue that neither MPT nor the new business of investing retirement assets has diminished the importance of that question. Quite to the contrary, the attempt to secure critical retirement benefits through long-term investments ought to generate even greater attention to what will happen if those investments don't perform as expected -- if investors don't just make less over time than they hoped but actually lose some of their own accumulated savings. Every investor's first job is to determine how that possible scenario would impact his or her overall financial condition.

As for Thaler's final question -- "Have you thought about how much you are losing by not investing that money in the stock market?" -- we would point out that hucksters always try to deflect attention from potential loss by emphasizing potential gain: Think what you can do with all that money; Think what you are giving up by not playing. The gambler's sickness is to picture so clearly what he might win that he comes to believe that he will win. He imagines that he is actually losing money when he doesn't play. That's a true psychological illness that should hardly be encouraged among investors.


Simply put, Wall Street shapes Main Street.
   Peter Bernstein, Capital Ideas, p. 6.

Uncertainty is a salient feature of security investment.
   Markowitz, 1959, p. 4.

Samuel J. Palmisano, chief of I.B.M., says investor uncertainty is holding back the stock market and business investment.
   New York Times photo caption, June 2, 2002.

In times of crisis, money moves from weak hands to strong hands.
   Wall Street maxim.

We've shown that MPT's claim to have solved the dilemma of investor uncertainty doesn't hold water; we've also shown that investors can't expect to make money from stocks merely, as it were, by being there. On what basis, then, can sensible people make reasonable and reasonably promising investment decisions at all?

In this concluding section, we'll first reemphasize the goals that investors should be trying to reach. We'll also consider the assumptions investors make, either implicitly or explicitly, that lead them to believe a goal is achievable. Finally, we'll list some initial steps for non-professionals to follow, given the arguments we've made in this article.

It may seem obvious that investors' goals should be to make money, but for several reasons we need to dwell a bit on the point. In the first place, one of the central MPT concepts dominating the investment world, both professional and non-professional, is that a return, that is, the amount of money made, is only as good as the (low) volatility that accompanies it. We've argued that this is a misleading concept and that investors should focus on making money. Indeed, Chief Investment Officers of pension, endowment, and foundation funds compete among themselves not on the basis of "risk-adjusted" returns but on the amount of money they make for their funds. The reason, of course, is that the more money the fund's investments return, the more secure is the fund's ability to pay out. In the case of a defined benefit pension fund, the higher the return the less the fund's corporate sponsor will have to contribute.

There are additional aspects of the institutional focus on making money that non-professionals also need to understand if they hope to make sense of the MPT-based advice they hear. The rewards that professionals receive are based not on the absolute return of their fund but on its comparative return. As long as the CIO is doing better than his counterparts in other funds, his career and earnings are safe. This is true also for managers of the mutual funds that invest non-professionals' assets. If a mutual fund actually loses money, but loses less than competitive funds, the fund manager is rewarded, and the fund company boasts of the fund's success to its holders and prospects.

This seeming anomaly of managers being rewarded for losing money arises naturally from the fact that managers must invest their funds' assets; they can't, like Gerald Loeb, remain uninvested until the right security comes along. Furthermore, every manager is given a benchmark, that is an index of a specific group of securities, and is expected to produce the best return he can through investing in those securities -- best, that is, compared to both the benchmark and to other managers.

All of these features of institutional investing have both affected, and in turn reflect, the development of MPT. It's not surprising, therefore, since we have questioned the foundations of MPT, that the practical lessons we believe non-professionals should draw from the institutional world regarding the goal of making money are mostly negative lessons. When you move from the business of investing other people's money to the problem of investing your own money, most rules change.

Principal among the lessons is that individuals, who can choose to invest or not invest, should not be happy to lose money; nor should losing less than their neighbors ease their unhappiness. It follows, however, that individuals should be happy if they make money, even though they make less than their neighbors.

What we have said so far suggests that the proper goal for non-professionals is a positive absolute return, taking into consideration the investor's total financial situation -- that is, how much the investor can afford to lose. We now have to explain how the goal should be derived, not from promises or dreams, but from realistic assumptions about the investor's own investment skills and the returns that are achievable with those skills.

The fundamental, mostly unrecognized assumption that investors make is that by putting their money out -- which is what investing simply is -- they should receive more back. When applied to bond investing, the assumption can make sense. A corporation (or a government entity) presumably puts investors' money to work and thereby earns more money (or generates more tax revenue), some of which it returns as promised to its bond investors. The U.S. government always has the taxing power to pay positive returns to investors, so at least in the case of Treasury bonds, the assumption of making money is fully justified.

When we turn to stocks, however, investors' assumptions become more complicated, especially since corporate dividends are now so inconsequential a part of what investors expect to earn. This downgrading of the importance of dividends is a relatively new phenomenon. In fact, until the late 1950s stock investors had always expected a higher return from dividends alone than was available from the interest on bonds. (In another article, we'll deal with the profound implications of the disappearance of stock dividends.)

If not for dividends, then, why do investors today assume that a stock purchase will produce more money than they put in? In the case of a company's first sale of stock -- its initial public offering (IPO) -- there is a presumption that, as with a sale of bonds, the company will use the money received to grow and become more valuable, and thus the price of the stock will rise. There are a number of real problems with this assumption, as the last five years of NASDAQ history shows, but IPOs are so small a percentage of total stock investments that they aren't worth dwelling on.

There can be only two reasons why an investor today assumes he will make money on a stock purchase: either 1) he believes that regardless of the price he pays, another investor will be willing to pay a higher price; or 2) he believes that he has deeper understanding of the value of the company than the investor who sold him the stock, and that the seller and others will realize later what they missed and want to buy the stock then at a higher price. The first assumption -- which Wall Streeters call "the greater fool theory" -- is clearly not one that a reasonable investor wants to make. The second, we would argue, is a valid approach (Warren Buffett showed it works), but only for investors who will devote the time and resources necessary to study each company and try to develop the deeper understanding.

Turning to index fund investing, what are the assumptions that investors make? Let's consider first a new category of index funds that represent subsets of the full stock universe: large capitalization funds, small capitalization funds, value stock funds, growth stock funds, etc. These funds exist in order to allow investors to make choices among groups of stocks. Thus they are bought and sold on the same assumptions as are single securities: in order to expect to succeed, sensible investors have to assume they have the same deeper understanding of the group of stocks as they had of a single security.

Let's consider now a broad index fund that does capture the movement of the universe of stocks. We argued in Section III above that an investor cannot be assured of making money in such a fund over any reasonable time frame merely by being there. We can now point out that since the level of an index fund is merely an aggregate of the prices of all individual securities, there are the same two reasons for investors to expect to make money in an index fund as in one or more securities. They either believe in the greater fool theory or believe they understand something that is being missed by sellers of individual stocks at current stock prices.

Their deeper understanding in this case may be about the new economy, or changing valuations, or other factors. Nonetheless, we would argue that making a reasonable decision on the assumption of deeper understanding of any of those factors requires at least the same devotion of time and resources as is necessary for a single stock purchase. (We will explain the application of the price-earnings ratio to index fund investing in another article; we'll show that taking a p/e approach to investing in the whole economy is not difficult, yet it greatly increases investors' chances of success.)

We'll now sum up what we have argued in this article by suggesting some initial steps that non-professional investors ought to take. This is not at all a full program of investment advice, but our suggestions will at least save investors from losing more money than they can afford to.

1. Recognize that a positive return is always possible. U.S. Treasury bonds, for example 10-year bonds, offer good returns with no risk. The argument that buying bonds leaves you open to the risk of loss through inflation -- an argument that comes mostly from stock enthusiasts -- has two answers. First, inflation is not endemic to human life, not even to a growing economy. The hyper-inflation suffered in some countries in the 20th century, and to a lesser extent in the U.S., was historically an aberration. Indeed, stock enthusiasts themselves base their optimism importantly on their belief that the new economy has conquered inflation.
   Second, there are simple methods of buying Treasury bonds periodically -- and holding them to maturity -- that offer some protection against any future inflation by generating higher interest if inflation rises. (In another article we will describe one study that shows the results of this "laddering" investment method.)

2. Treat all investments, whether in a 401k account or elsewhere, as part of your total financial situation. There is nothing special about your 401k, except that it enables you to save money pre-tax. But there should be no difference in your mind between your 401k savings and your other assets, including the net value of your home, life insurance, and other property. To the extent that you will depend on your savings for retirement benefits or other necessary expenditures, consider them savings that you cannot afford to lose, and keep them in "laddered" Treasury bonds.

3. In contemplating potential returns from any stock investments, over any time frame, include the possibility of losing money. Feel confident only to the extent that you can lose some of your savings without a significant impact on your lifestyle or your retirement benefits.

4. If you cannot, or will not, spend several hours every day studying stock investments, buy only a broad index fund, not individual stocks, and not a "value stock" fund or any other subset fund.

5. Recognize that with any stock investment today, including a stock index fund, you cannot make money unless someone else will find a reason to buy the investment later at a price higher than you paid. Ask yourself why someone should pay the higher price. (We'll have much more to say about the Graham and Dodd concept of "investing" versus "speculating" in our future article on the price/earnings ratio.)

6. Finally, keep a record of the total value of your 401k fund (or any other investment assets) on a regular basis. If you haven't done that so far, start today. By consistently maintaining the record over the years, you will be able to test your progress on the two questions that matter to you: whether you are on track to achieve the goals you have set, and how much your investments have added to your fund over and above your own and your employer's contributions.


Peter L. Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street, The Free Press, New York, 1992.
This is an indispensable book for understanding the origins and development of MPT.

Benjamin Graham and David L. Dodd, Security Analysis: Principles and Technique, McGraw-Hill Book Company, Inc., New York, 1934.

John Maynard Keynes, Letter to F.C. Scott, February 6, 1942, in Charles D. Ellis and James R. Vertin, Eds., Classics: An Investor's Anthology, Business One Irwin, Homewood, Illinois, 1989.

Mark P. Kritzman, "What Practitioners Need to Know," Financial Analysts Journal, January-February 1991.

G.M. Loeb, The Battle for Investment Survival, Barron's Publishing Company, Inc., Boston, 1952.

Harry Markowitz, "Portfolio Selection," The Journal of Finance, Vol. VII, No. 1, March 1952.

Harry M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons, Inc., New York, 1959.

S.L. Mintz, Dana Dakin, and Thomas Willison, Beyond Wall Street: The Art of Investing, John Wiley & Sons, Inc., New York, 1998.
This book is based on an eight-part PBS documentary hosted by Andrew Tobias and Jane Bryant Quinn and is thus a fair representation of the public understanding of modern portfolio theory.

John W. O'Brien, "How market theory can help investors set goals, select investment managers and appraise investment performance," Financial Analysts Journal, July-August 1970.

Thomas K. Philips, "An Opportunistic Approach to Alternative Investing," Investment Policy, Vol. 1, No. 2, September/October 1997.

Charles R. Schwab, You're Fifty -- Now What? Investing for the Second Half of Your Life, Crown Business, New York, 2001.

Robert J. Shiller, Irrational Exuberance, Princeton University Press, Princeton, 2000.

Jeremy J. Siegel, Stocks for the Long Run, Richard D. Irwin, Inc., Chicago, 1994.

Stages, Fidelity Investments magazine for 401k-ers, Spring 2002.


1. Peter L. Bernstein, Capital Ideas, p. 306.
2. A note to professional investors:
   This article is clearly not intended to encompass every aspect of MPT, but to refocus some discussion on the core concepts. This is necessary, in our view, for two reasons. First, we believe that MPT's core concepts can't speak to the needs of non-professionals who are making their own retirement fund decisions (even if we clarify the concepts for them).
   Second, we believe that, viewed from the perspective of commonsense investors risking (in the old sense of the word) their own or their clients' assets, the foundations of MPT are shaky. We're prepared to be enlightened, of course, and would welcome comment. We'd insist, however, that the foundations of any theory need to stand on their own, without drawing strength from the theory's additional building blocks.
   For example, our contention that volatility is not risky would lead us to argue that neither efficiency nor any measure of risk-adjusted return are important goals for a portfolio. We would be making that argument in the context of expected positive stock returns, and one might respond that a further MPT purpose in controlling portfolio beta is to position the portfolio for a falling market. That may be true as a description of further MPT concepts; nonetheless, we would argue that it remains valid to reassess the core MPT concepts on the same basis as that on which Markowitz made his original assertions in the 1950s.
   For the record, we would also question the value of seeking efficiency, or of measuring risk-adjusted returns, in a falling market. Asset owners who are losing money long-term, either absolutely or relative to other owners, are not likely to be consoled by the ability of their managers to show that they are losing it efficiently.
3. Peter L. Bernstein, Capital Ideas, p. 41.
4. Thomas K. Phillips, 1997, p. 44.
5. Charles R. Schwab, You're Fifty -- Now What? p. 14 (attributed to Jeremy Siegel).
6. Mark P. Kritzman, 1991, p. 12.
7. John W. O'Brien, 1970, pp. 91-103.
8. Harry M. Markowitz, 1959, pp. 343-344.
9. Peter L. Bernstein, Capital Ideas, p. 213.
10. Harry M. Markowitz, 1952, p. 77.
11. John Maynard Keynes, 1942, in Classics: An Investor's Anthology, pp. 85-86.
12. Gerald Loeb, The Battle for Investment Survival, p. 45.
13. Graham and Dodd, Security Analysis, p. 318.
14. Ibid., p. 320.
15. Jeremy J. Siegel, Stocks for the Long Run, p. 4.
16. Ibid., p. 304.
17. S. L. Mintz, Dana Dakin, and Thomas Willison, Beyond Wall Street, pp. 197-198.

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