Is Portfolio Theory Harming Your Portfolio?

Modern Portfolio Theory (MPT) teaches us that active equity managers who use judgment to make investment decisions won’t be able to match the returns (after fees and expenses) of blindly-invested, passively-managed index funds.  Data on returns supports the theory, so it’s no surprise that investors are leaving actively managed funds in droves for the better average returns of super-diversified index strategies.  Yet the reality is much murkier than we’ve been led to believe. 

It turns out that the portfolio theories which inspired the creation and popularity of index funds and top-down, quantitatively-driven index-like strategies, are both flawed and impractical.  There’s compelling evidence, moreover, that a subset of active managers do persistently outperform indexes.  However, this important fact has been lost because we allow MPT to define the debate in its own misleading terms, tilting the field in its favour and hiding the reality about active manager performance in a complex game of circular arguments.

MPT relies on a number of unrealistic assumptions including an inaccurate definition of risk.  Yet this characterization of risk sets the rules for comparing active vs. passive strategies, often causing active strategies to appear more risky and less efficient than their index counterparts.  The same flawed logic is used to risk-adjust returns, biasing them downward for more active, concentrated managers, and rendering this highly important measure highly suspect.  Furthermore, reliance on MPT’s measure of risk pressures active managers to super-diversify.  The average active fund is thus disfigured to the point where the typical “active” manager is not very active at all, casting the fund in an unfavorable light in a beauty contest versus super-efficient index funds.

Stripping away the influence of portfolio theory involves isolating and evaluating the relatively small group of equity managers who rely heavily on judgment to build concentrated equity portfolios.  Empirical data from multiple studies show that these concentrated managers, in fact, persistently outperform indexes.  The implications of this statement are enormous.  Concentrated manager returns present the best test of whether human judgment can add value in allocating capital, and they win, convincingly.  Yet while judgment has prevailed over passive investing, few have taken notice.   Most investors continue to look at average active manager returns, not recognising that these returns are minimally influenced by judgment. 
Regardless of MPT’s shortcomings on both a theoretical and empirical level, its dominating influence will not easily be dislodged.  MPT is deeply woven into the fabric of our financial system, its mathematical grounding and precise answers inspire confidence.  Further, its application is crucial in bringing increased scale and profitability to the financial services industry.  Few want to see change.  As such, common sense and judgment will continue to diminish in importance as top-down, quantitative strategies and blind diversification gain investment dollars. 

An informed investor should welcome this shift.  As highly-diversified strategies gain assets, inefficiencies become more prevalent because share prices are increasingly driven by factors other than fundamentals.  Individual investors, seeking to exploit these inefficiencies and outperform indexes, should invest in several concentrated funds with strong track records.  Managers of these funds have proven themselves adept at turning inefficiencies into strong returns for their investors, and persistence data demonstrates that past performance can indicate which managers are likely to continue to outperform.  Concentrated fund returns may exhibit more volatility than indexes, but we now have proof that over the long-term, good judgment will be rewarded.

Paul Samuelson was a giant in the field of economics.  He taught the subject at M.I.T. for over 50 years, rewrote large portions of economic theory, and was the first American awarded the Nobel Prize in Economics.   Samuelson’s work was usually at the vanguard of economic theory.  He was instrumental in bringing mathematical rigour to the soft science of economics and it wasn’t surprising that he would attempt to engender the same metamorphosis in economics’ close cousin, finance.  So it was in the early 1970’s that, based on both his own work and that of a few other important scholars, he became convinced that human judgment could be proven useless in making investment decisions in the stock market.  Moreover, the behaviour of financial instruments could better be described and predicted using mathematics and statistics. 

In 1974 he penned an article entitled, “Challenge to Judgment.”  In it, Professor Samuelson, who represented “the new world of the academics with their stochastic processes”, challenged the old, practical world of money managers to show that any group of them could consistently beat the market averages.  Absent that proof, Samuelson argued that portfolio managers should “go out of business – take up plumbing, teach Greek, or help produce the annual GNP by serving as corporate executives.”   Investors were better off investing in a highly diversified, passively-managed portfolio that mimicked an index than using judgment to pick stocks. 

The Challenge marked the start of a dramatic shift in our approach to finance.  Up to this point we had mostly evaluated investments one at a time, carefully trying to understand the specific circumstances around each to derive its chances of success or failure and determine its value.  However, the compelling new theories and mathematical formulae from the world of academia suggested we could do better by building large portfolios based on top-down mathematical models which replaced or minimized the need for judgment. 

Samuelson’s Challenge was never adequately addressed by the active fund management community.  Perhaps awed by the brilliance of the theories, the credentials of the academicians behind them, and the unassailable mathematical “proof,” practitioners in the fund industry seemed to opt for the “if you can’t beat ’em, join ’em” strategy.  Samuelson presciently forecasted this in his piece as well, noting that the two worlds – the practicing active managers and the academic quantitative-economists – would begin to converge.   The two are now so intertwined that it is often difficult to tell where one stops and the other starts.  

Unable to meet Samuelson’s Challenge, active managers have steadily ceded share to passive-style vehicles.  Passively managed funds now control 20% of all domestic equity fund assets, according to Morningstar, from almost nothing 30 years ago .  It is likely this figure dramatically understates the case since many actively managed funds are so highly diversified they should be reclassified “quasi-passive.”  Passively managed equity funds have recorded positive flows for over a decade while active equity funds are on track for three straight years of outflows .  And though the outflows from actively managed funds are small relative to the massive size of the industry, the directional signal is telling. 

The reason for the outflows is no mystery, Samuelson and his cadre appear to be correct.  Active managers in general have been shown to underperform passive funds, especially when taking into account their higher management fees, taxes, sales charges, and trading costs.  If you can make more money in index funds then why bother with the hassle of trying to find a good manager?  According to Samuelson, there’s no such thing. 

The equation is not as simple as it seems, however, and individual investors may serve themselves well by digging deeper into the active versus passive debate before making the switch.  There’s compelling evidence that the core theories behind the push to passive management do not work and they distort the facts around the passive versus active debate, giving passive management the false appearance of having an edge.  Most importantly, there is compelling empirical research that shows active managers who are truly “active,” do persistently outperform indexes.  The astute individual investor can seize the opportunity that blind, passive index investing provides in the form of increased market inefficiencies by hiring active managers who have shown the ability to exploit and profit from these inefficiencies.

We can trace the beginning of our fascination with the idea of passively managed funds back to 1952.  That year, a student of linear programming, Harry Markowitz, first applied his craft to the world of finance in a paper entitled “Portfolio Selection.”  In it, Markowitz provided mathematical proof that proper diversification could minimize a portfolio’s variance for a given level of return.  Mean-variance was used as a proxy for risk because assets whose prices were more volatile were seen as more likely to produce losses.  It was the first time anyone had formally quantified this tradeoff between risk and return.  Paying special attention to how an asset’s returns correlated with other assets allowed mathematicians to create groups of portfolios which minimized risk for a given level of return, or that maximized return for a given level of risk.  These large, mathematically optimised portfolios formed the “efficient frontier” and helped inspire today’s highly diversified, passively managed funds. 

“Portfolio Selection” spawned William Sharpe’s “Capital Asset Pricing Model” (CAPM),  which made Markowitz’s work more user-friendly.  CAPM introduced “beta,” a measure that incorporated a security’s variance versus an underlying index (rather than vs. every other security in a portfolio), and that represented systematic risk.  The name of the game according to CAPM was to diversify away stock-specific or idiosyncratic risk leaving only market (systematic) risk, which was defined by beta.  According to the theory, investors are foolish to hold a small number of stocks because they’re taking stock-specific risk when they don’t have to.  Since other investors are buying the same securities in diversified portfolios, the non-diversified investor will bear more risk for equal return and therefore pay too much for a given stock which is priced for inclusion in a diversified portfolio.  A portfolio should be optimised in a manner such that it has the lowest possible risk (beta) for a given level of expected return which in practice means holding the market portfolio and lending or borrowing to adjust risk. 

Finally, the “Efficient Market Hypothesis” (EMH) was introduced in 1970, by Eugene Fama, in the form we’ve come to recognise.   Providing what some call the capstone to modern portfolio theory, the efficient-market hypothesis asserted that because the stock market is such a successful mechanism for pricing securities it is difficult or impossible for an investor to achieve returns above the market average in any consistent fashion.  Prices reflect all relevant information, and changes in securities prices are mostly unpredictable, so using judgment to pick stocks may be ineffective in the long-run. 

Fama named three versions of EMH – weak, semi-strong, and strong.  The weak version holds that past prices don’t predict future prices, so technical analysis (which is based on past trading information) is irrelevant.  In the semi-strong version all publicly available information (not just price information) is instantly discounted in stock prices.  And in the strong version, even non-public information is discounted such that insiders wouldn’t be able to profit consistently from trading around their knowledge. 

The three theories — EMH, CAPM, and Portfolio Selection –were classified together as “Modern Portfolio Theory” (MPT). They were so compelling and useful that they came to provide the backbone for much of modern financial economics and earned both Markowitz and Sharpe Nobel prizes.  They were identified together, built on one another, and became joined in practical expressions.  And although they each got there taking different avenues, their conclusions were much the same – buy the market basket.   

Practical Adaptation
The practical application of MPT was an enormous success.  The MPT thought process is now so ingrained in our capital markets that the theories are taken for gospel and their results viewed as “the truth”– whether allocating assets in a diversified portfolio, making corporate finance decisions, developing a risk management strategy, or valuing companies and securities such as mortgage derivatives or just about any financial instrument.  Furthermore, by allowing market participants to make assessments quickly and confidently as to the allocation of capital, MPT has allowed the markets to become much deeper, more liquid, and more efficient.  Efficient capital markets add to the value of the overall economy by allowing enterprises (whether farmers, households, small businesses or large businesses) to attract the right capital and capital structure and accept the kinds of risks for which they are best suited — while protecting themselves from risks they don’t wish to take.  In short, these theories of financial economics play a key role in providing a fundamental framework for our capital markets.

The mutual fund industry eagerly adopted these quantitative methodologies.  At the end of 1975, John Bogle launched the First Index Investment Trust (later renamed Vanguard 500), the first stock index fund for individual investors, which is now one of the largest mutual funds in the world.  And despite the fact that the majority of financial economic work implicitly, and in some cases explicitly, questioned the value of active fund management, active fund companies and their portfolio managers came to embrace many of MPT’s key concepts. 

While diversification has always been a selling point for actively managed mutual funds, the average number of holdings in a fund have increased dramatically since MPT made the scene.  The average number of stocks held in actively managed funds is up roughly one hundred per cent since 1980, according to data from the centre for Research in Security Prices.   Some might call it “super-diversification” while others apply the label “over-diversification,” but the average fund holdings had risen to approximately 140 positions by 2000.   The actual number of holdings in a given year could easily surpass 200 because portfolio turnover exceeds 100 per cent per year on average.  

Funds have become more quantitatively-driven in other respects as well.  The industry has seen an explosion of “quant” funds, many of which were founded on MPT’s core premises.  Other actively managed funds come very close to being index funds in an effort to find the “efficient frontier.”  Some of these funds are known as enhanced index funds.  Some of them are “closet index funds” – funds whose managers masquerade as “active” managers but hug an index so tightly their returns will never stray far from it.  A recent study showed that these “closet” index funds have increased from one per cent of assets under management in 1980 to more than 20-seven per cent in 2003 .  Recently we’ve even seen active fund complexes offering “active ETFs” so that they can cash in on the hottest investment vehicle of the moment.   

Not only have funds become more index-like, the methods for measuring portfolios and managing fund complexes have also been adapted for a quantitatively driven industry.  Active portfolio returns are benchmarked against indexes.  Portfolio managers are often measured and compensated based on their beta-adjusted results.  In addition, managers who oversee fund complexes typically use top-down statistical measures to monitor portfolio managers since doing so on a position-by-position basis has become impractical.  They may take into account beta, tracking error (how much performance varies vs. a particular index), alpha, risk-adjusted returns, and value-at- risk, to mention a few. 

So, What’s the Problem?
By marrying itself to quantitative theories, the actively managed equity fund industry has warped itself into something that closely resembles what it ought to be fighting against – the efficient, passive index fund.  In so doing it has doomed itself to an inescapably unfavorable comparison with these highly efficient index funds by minimising the role of the “active” manager.   Investors in actively managed funds suffer – they receive quasi-active management at full active management prices. 

Not only was it a strategic error to minimize the comparative advantage afforded through true “active” management, but it turns out that these quantitative theories weren’t worth marrying in the first place.  Here we make a distinction.  By quantitative theories we mean Portfolio Selection and CAPM but not the Efficient Market Hypothesis.  EMH isn’t problematic as it doesn’t attempt to define relationships in capital markets through quantitative equations, as do the other two theories.  At a certain level, EMH makes common sense and is validated by empirical data.  Although it has been disputed constantly since it was first introduced, this controversy is probably overstated.  The attention is driven by those at the extremes – those who believe markets are perfectly efficient at all times and those at the other end of the spectrum who think the idea of efficient markets is ridiculous.  In reality, there is an abundance of evidence that markets are less than perfectly efficient, yet most practitioners and academics find that exploiting these inefficiencies is, at minimum, very difficult.  It is not easy to consistently outperform the market, but talented managers can and empirical data supports this fact as we will see later. 

Portfolio Selection and CAPM are at the heart of the controversy.  Both represent brilliant theoretical work accompanied by sound mathematical proof and practical formulas.  However, they were science experiments.  They worked well in a laboratory where the environment around them could be perfectly controlled, but when put into practice the theories’ underlying assumptions and logic didn’t translate. 
One of the most basic, pervasive, and troubling issues with quantitative finance is that it relies so deeply on the idea that risk is embodied in variance from the mean, or some derivative of that measure. 


When Harry Markowitz first theorized that there was a tradeoff between returns and variance he didn’t directly associate variance with risk, but noted instead that, in financial writings, if risk were replaced by variance of return, “little change of apparent meaning would result.”   Amazingly enough, there’s not  much empirical “proof” as to why we should use variance as a measure of risk, yet it plays a critical role in almost all large financial transactions.  It seems that academicians needed a way to quantify risk to fit mathematical models and they grabbed variance, not because it described risk very well, but because it was the best quantitative option available.   But just because it is convenient, and it carries a certain intuitive appeal, doesn’t make it right. 

Risk is a complex notion.  We’ve been studying it for centuries.  Whole books have been devoted to the subject, yet it’s still difficult to define precisely.  While not many people would dispute Markowitz’s premise that we demand higher returns for riskier assets, the idea that assets whose prices have varied significantly warrant higher expected returns doesn’t hold up in empirical tests.  In other words, there’s more to risk than variance alone.   

Risk is often in the eye of the beholder.  While “quants” (who rely heavily on MPT) might view a stock that has fallen in value by 50 per cent over a short period of time as quite risky (i.e. it has a high beta), others might view the investment as extremely safe, offering an almost guaranteed return.  Perhaps the stock trades well below the cash on its books and the company is likely to generate cash going forward.  This latter group of investors might even view volatility as a positive; not something that they need to be paid more to accept.  On the other hand, a stock that has climbed slowly and steadily for years and accordingly has a relatively low beta might sell at an astronomical multiple to revenue or earnings. 

A risk-averse, beta-focused investor is happy to add the stock to his diversified portfolio, while demanding relatively small expected upside, because of the stock’s consistent track record and low volatility.  But a fundamentally-inclined investor might consider the stock a high risk investment, even in a diversified portfolio, due to its valuation.  There’s a tradeoff between risk and return, but volatility and return shouldn’t necessarily have this same relationship.

Another issue with the use of variance in practice is that it is backward-looking, coming from historical samples of returns.  So a key question is, “can we rely on measures from the past to see the risks of the future?”  Think about how you make decisions that involve risk in your everyday life.  You probably rely fairly heavily on past experience.  But is that all you rely on or do you factor in current circumstances?  The fact is that no two decisions are ever precisely the same because the world is not static and circumstances change, even if the change is difficult to detect.  Often circumstances have changed sufficiently since you were last faced with a like decision that you think the probabilities of different outcomes have changed as well.  When we use historic volatility as the sole measure of risk (or for that matter, any historic quantitative measure) we’re relying 100 per cent on the past to predict the future.   But volatilities are volatile (sorry) and historic volatility has proven unreliable at predicting future volatility. 

Constantly changing volatilities create a great practical difficulty.  Over what time frame should we measure historic variance?  Is it one year, 90 days, nine days, or 10 minutes?  We’ll get different values for each (often dramatically different) and because models are highly sensitive to this value, the output will vary considerably depending on which time period we use.   Another troubling assumption that must hold to make Markowitz’s theory valid is that asset returns abide by the rules of stable normal distributions – otherwise the maths behind the theories won’t hold up.  In reality, return distributions are frequently neither stable (meaning they change over time) nor normal (for instance, they may be nonsymmetrical or wider than a normal distribution), which means formulas derived from Portfolio Selection generate highly unreliable results. 

Even though the assumptions behind Portfolio Theory are often out of touch with reality, the model may still be useful if it produces valid results.  Unfortunately, it doesn’t.  Numerous empirical studies have shown that taking on more risk (as represented by volatility) doesn’t reliably deliver additional reward.   So, the quantitative cooks continue to tinker with recipes to fit variables to an equation that can make sense of financial markets.  New multi-variable regression models are introduced to describe alternative factors that influence returns most, but these efforts amount to data mining.  Just because these new and improved formulas generate more respectable correlations doesn’t mean there’s a causal link between their variables and the returns they predict – as such, observed relationships can be fleeting.  While the multi-variable models can solve some of the problems in certain instances, these reworked formulas still suffer from many obstacles to successful, practical implementation. 

It’s an uncomfortable fact for financial economists, but returns and return expectations are influenced in a highly dynamic fashion by many variables which largely defy quantification.  Why should we believe we can build formulas that capture the behaviour of management, employees, and customers of a business, as well as investors? Even if there were a magical formula we could use to describe human behaviours, it would likely change from asset to asset and over time. 

While Markowitz’s theory has serious issues when applied to real life, Sharpe’s CAPM is in even worse shape.  CAPM is built on the back of Markowitz’s theory so it starts with all of the baggage and incorrect assumptions and then adds more.  Some of the doozies include an assumption that all investors could borrow and lend at the riskless rate and an assumption that investors all have identical views of expected correlations, returns, and risks. 

That these quantitative financial models don’t work in practice isn’t controversial.  The theories have been losing the battle in scholarly articles for the last three decades.  Even many of the influential researchers behind modern portfolio theory admit to their shortcomings.  Markowitz is quoted as describing his book on Portfolio Theory as “really a closed logical piece” – i.e., something that only works in the lab.   Eugene Fama called CAPM “atrocious as an empirical model” and said “CAPM’s empirical problems probably invalidate its use in applications”  Fama & French (2004).   Even the ardent supporter of EMH, Paul Samuelson, noted “… few not-very-significant apparent exceptions” to micro-efficient markets, and admitted the existence of some exceptionally talented people who can probably garner superior risk-corrected returns.


The real controversy is that, even though its chief architects admit the quantitative theories are ill-suited for practical use, and empirical data confirms it, they are still embraced,(indeed some might say “worshipped”) by operators in our capital markets, and heavily relied on to make important financial decisions.  The theories have become so deeply ingrained in our financial system that we can’t see their folly.  Their mathematics, as well as the precise nature of their output, gives us a sense of comfort which is critical in deploying large sums of money.  They also lead to a misallocation of resources, however, causing giant distortions.     

Diversification and Quantitative Finance
Equity markets are where the blood, sweat, tears, and raw emotion of human enterprise meet the hard facts of price realisation.  Like a cold front passing through on a humid August afternoon, it’s a transition often full of energy and surprise.  Providing theories that translated to precise formulas, quantitative finance promised to take some of the emotion out of this transition – to quantify it, to provide the “right” answers, to at least make the hail storms more predictable.  The quantitative certainty appealed to us and we latched on.  Even though we understand that the forecasts the theories provide aren’t right much of the time, we keep listening to them because doing so is comforting. 

Diversification is a case in point.  Prior to MPT our take on diversification was rudimentary.  In fact, it probably hadn’t changed much since early humans hid their food stores in numerous places to avoid total loss from scavengers.  Don’t put all of your eggs in one basket – our modus operandi.  Markowitz and Sharpe put meat around the bones of this naïve view, delivering a formula that helped us quantify the benefits of adding baskets, while describing the most promising arrangements. 

While we had always found diversification appealing, MPT ignited an all-out love affair with the concept.  Not only did diversifying feel “safe” we now knew it was “smart” because its benefits had been quantified and real mathematical proofs supplied.  Professional money managers who applied MPT in practice built large, volatility-minimising portfolios to gain the efficient frontier, and a conventional wisdom took hold that the more diversified a portfolio the better.  Like baseball and apple pie, super-diversification became universally accepted.  That the concept underlying this aggressive diversification didn’t work wasn’t a point of discussion. 

Part of what solidified the push for more aggressive diversification was the strategy’s warm embrace from the financial services community at large.  Diversification has become the Holy Grail for financial advisors and planners who preach its virtues with an unquestioning, cult-like enthusiasm.  Almost every piece of marketing literature generated by these outlets extoll its benefits.  The mutual fund industry played an important role, too.  The idea that investors could dine from Markowitz’s risk-minimising, free lunch buffet by diversifying their portfolios was music to the fund companies’ ears.  After all, a key selling point for mutual funds was their ability to offer investors an inexpensive way to diversify holdings while letting a professional manager invest their money. 

The concept fed on itself — as more assets poured into the funds the portfolios needed to become more diversified due to liquidity constraints.  It appeared to be a win-win.  The larger a fund became, the more diversified, and not only were investors happy but so were the fund companies.  But fund companies and planners had everything to gain from pushing diversification, it made them more vital to their clients and more profitable. 

The concept was not only difficult for the average investor to implement and understand, but it also gave an implicit “OK” to super-large, super-diversified, super-profitable funds. Though the fund companies undoubtedly win by managing more assets, are investors in active funds best served owning highly diversified portfolios? 

The appeal to diversification, according to quantitative finance, is the idea that it allows us to enjoy the average of all the returns from the assets in a portfolio, while lowering our risk to a level below the average of the combined volatilities.  But since we can’t call volatility risk and we can’t reliably predict volatilities or correlations, then how can we compile diversified portfolios and claim they are on some sort of efficient frontier?   These super-diversified portfolios may be inefficient — it may be possible to earn higher rates of return with less risk.  It may be that by combining a group of securities hand-selected for their limited downside and high potential return, the skilled active manager with a relatively concentrated portfolio has greater potential to offer lower risk and higher returns than a fully diversified portfolio. 


Not only are we unlikely to find an “efficient frontier” by super-diversifying an actively managed portfolio, but diversification adds a cost that is rarely acknowledged.   A fund manager’s job is to identify assets that are priced “inefficiently,” where the market has ostensibly made an error and a stock is available at a level that allows for relatively little risk versus expected return.   But finding inefficiencies and maintaining a portfolio is difficult work and requires resources (a manager’s time and brain power, among the most important of these).  Resources are not unlimited (most importantly a manager’s time). 

Therefore, the amount of resources devoted to each specific investment varies inversely with the amount of investments owned in the portfolio.  The more positions added to the portfolio, the less likely a manager is to capture these difficult-to-find inefficiencies because he/she has less time and other resources available to do so. 

Over-diversification not only decreases a manager’s ability to find inefficiencies but it may, in fact, increase risk.  Warren Buffett expressed the idea more eloquently, “We believe that a policy of portfolio concentration may well decrease risk if it raises, as it should, both the intensity with which an investor thinks about a business and the comfort-level he must feel with its economic characteristics before buying into it.”   

Over-diversification inhibits a manager’s ability to understand the risks taken with each security, potentially creating greater risk.  This argument turns CAPM on its head.  A highly diversified, active manager cannot fully understand the risks he is taking on his positions so he may be paying too much for them, thus operating below the efficient frontier.  While the concentrated manager is able to pick securities with an intimate understanding of their risk which helps him uncover assets whose prospective return more than compensates for the risk taken.  The concentrated manager aims to buy assets that are beyond the efficient frontier. 

Diversification is a helpful tool, but it should only be employed to the point where its costs equal its benefits.  Adding positions beyond that point is watering down a portfolio – the benefits are minimal, but the costs detract from a manager’s ability to add value.  The average actively managed equity mutual fund today is diversifying far beyond the point where costs exceed benefits.  These funds cease to be actively managed in the traditional sense but their active management fees and other expenses continue to be real.  Thus, passive funds with their low fees and turnover, easily outperform the average actively managed fund. 
The individual investor can achieve greater success spreading money among talented managers who have each limited diversification to the point where its costs are equal to its benefits.  An individual investor’s tolerance for risk can be expressed by choice of manager as some concentrated funds are run conservatively while others accept more risk. 

Is a relatively concentrated strategy really more risky for the investor?  There’s no doubt that the concentrated portfolio will exhibit more volatility on average than a highly diversified one, but as discussed earlier, volatility isn’t a very useful descriptor of risk (all bets are off if you’re talking about short-term money).  Without an accurate way to quantify risk we can’t make the generalization.  But just because we don’t have a good top-down, historically-based mechanism for understanding risk doesn’t mean that we can’t tell how risky an asset is.  If we think that risk is roughly equivalent to the probability of losing money on an investment, then perhaps we should ask, “are you more likely to lose money owning a concentrated portfolio or a highly diversified portfolio?”  The common sense answer is that it depends on what’s in each portfolio!  Perhaps then the risk in a portfolio is better described by taking a bottoms-up view of the fundamentals of the businesses owned, and how those fundamentals manifest themselves in stock prices, rather than computing the portfolio’s historic variability with respect to the market?  

Running a concentrated portfolio means taking stock-specific risk but that doesn’t necessarily mean taking more overall risk than a diversified portfolio.  Finding appropriate stock specific risk is how active managers (should) make their living.  If a manager is successful in finding these inefficiencies, he is more than compensated to take those risks.  Thus taking stock specific risk should be a net positive for a talented active manager.  This is reflected in the empirical data as we will see later.     

Practical Implications
So how much is the correct amount of diversification?   Unfortunately there isn’t a “right” answer.  The correct amount of diversification will vary from manager to manager depending on style and resources available, among other factors.  More important than pegging an optimal absolute number is making the conceptual leap from thinking that unbounded diversification is good, to understanding that diversification carries costs for fundamental active managers and acknowledging that diversification’s benefits, in terms of risk-minimization, are not fully understood.  “Diversification is a protection against ignorance.  It makes very little sense for those who know what they’re doing” sums up Warren Buffett.  

When managers adopt a framework whereby each position added carries an important cost that can dilute the value of their work, and come to accept that taking stock-specific risk in less than perfectly efficient markets can be a net positive, concentration will increase.  The degree of concentration in a fund should reflect the confidence a manager has in the inefficiencies found, and the weight of those investments should reflect the probability of success as well as the level of asymmetry present in the prospective return profiles of the assets.

Those who crave more concrete numbers can look at empirical work built around the MPT framework.  Research has shown that much stock specific risk (non-market related volatility) can be eliminated by owning portfolios of relatively few stocks.  Some say as few as 10, others say 60.  Yet these studies often assume randomly chosen portfolios, while most portfolio managers pick and choose stocks in a manner that attempts to limit volatility—thus the actual number of stocks required to get most of the volatility-lowering benefits of diversification may be lower.  We should also question the assumption that reducing volatility is paramount, as it throws us off the more appropriate fundamental scent of risk and return. 


The idea of limiting diversification is an uncomfortable one for the mutual fund industry, but coming to terms with it is necessary to end share losses to passive strategies.  The push for diversification has attracted a mountain of assets to active strategies and created individual funds that are mind-bogglingly large.  Fund companies certainly won’t shut down these giant, over-diversified funds; they make too much money operating them.  You, the investor, however, can pull your assets from these super-sized mutual funds and reallocate them to smaller, more concentrated portfolios. 

Shifting emphasis to small, concentrated portfolios would hurt fund companies in the short-run.  Economies of scale would be reduced so the funds would be less profitable for the fund complexes and slightly more expensive for individual investors (fund complexes have taken most of the benefits from economies of scale).  But it would enable fund managers the opportunity to better display their talent.  Instead of having few large portfolios, fund complexes could have many small portfolios.  While additional choices might create more confusion for individual investors, the rewards could be significant for finding a talented manager.  Investors could still diversify by owning a portfolio of concentrated portfolios but they would want to adhere to the same rules as far as paying attention to the costs of diversifying when they chose managers.    

The Triumph of Judgment?
Ironically, it turns out that Samuelson’s claim that “it is virtually impossible for academic researchers … to identify any member of the subset with flair” was too weak, it should have been re-worded “totally impossible.”    His Challenge to Judgment was flawed from the start.  Measuring persistent “risk-corrected” returns is akin to measuring all the love in the world.  We simply don’t have a yardstick.  If we don’t have a reliable measurement for risk, how can we measure performance in any relative sense?  Performance must always be adjusted for risk bias if we assume that there’s a tradeoff between the two.  Portfolios which contain dramatically less risk than an index should return less than the index, on average.  However, we can’t measure or correct for this disparity in a reliable manner.  Likewise, measuring a fund’s ability to persistently perform versus an index is futile because this is also a relative measure and needs to be adjusted for changes in risk over time. 

But let’s put aside this thorny issue for a bit and look at the empirical studies.  You may be asking, “why are we looking for persistence in actively managed returns in the first place?  Don’t we just want to know if active managers in general outperform the market?”  Because there are so many funds managing so many assets, it’s mathematically impossible for the group to perform in a manner much different than the market as a whole.  So we don’t expect to see outperformance from active managers as a class.  Persistent returns, however, whether above or below the market, are a marker for active talent or lack thereof.  If the market is completely efficient then returns will be random and we wouldn’t see managers consistently outperforming or underperforming the market over time.   

Remarkably, the evidence shows plenty of support for the notion that persistence exists (and also support for the opposite).  This is remarkable because the data is heavily biased in favour of the quantitative non-believers (though the academic community would often lead us to believe the opposite.)  As we’ve already noted, the sample set of “active” managers is heavily influenced by funds that are not really active.  In a 2007 study, K.J. Martijn Cremers and Antti Petajisto found evidence that as of 2003, close to 30 per cent of assets under “active” management were in fact managed by closet indexers.  In addition, it seems very reasonable to assume that, of the remaining 70%, significant portions are not the stock picking fundamental managers Samuelson challenged.  Rather, they are often top-down, quantitatively driven, efficient frontier-hunting managers who might be mistaken for machines.  These funds make bets and have some tracking error so in that sense they’re active, but their inclusion in the data only serves to muddy the impact of true “fundamental” active managers. 

Researchers often make a big deal about “survivorship bias” – the idea that only the better active funds survive so the databases are skewed in a positive fashion.  This is corrected by including all of the poor returns from “dead” funds in the data.  However, no one corrects for the fact that as a fund has success and grows larger, it will naturally migrate toward average returns while becoming more diversified.  The more diversified, the harder it is to show outsized performance or persistence.   


Finally, sometimes studies find persistence but then dismiss it as statistically insignificant and declare that there’s a lack of evidence.  Achieving statistical significance, however, is an especially high hurdle when the sample sets are not very large and the data are skewed by funds that are not truly “active.” Thus, it’s not surprising that we wouldn’t see strong evidence for persistence. 

While the empirical data on persistence is mildly supportive of the argument for active management, we still question it because of its inherent biases.  Notably, however, there is a growing body of research that shows strong persistence in funds that are not highly diversified.  This is noteworthy, of course, because these are precisely the funds we would expect to display persistence if managers are capable of adding value.  These are the active managers who make a living on their judgment; their track records represent the true test of Samuelson’s Challenge. 

Multiple studies indicate that funds which are more actively managed, or more concentrated, outperform indexes and do so with persistence (Kacperczyk, Sialm and Zheng (2005), Cohen, Polk, Silli (2010), Bakks, Busse, and Greene (2006), Wermers (2003), and Brands, Brown, Gallagher (2003), Cremers and Petajisto (2007)). 

Funds with the highest Active Share [most active management] outperform their benchmarks both before and after expenses, while funds with the lowest Active Share underperform after expenses …. The best performers are concentrated stock pickers ….We also find strong evidence for performance persistence for the funds with the highest Active Share, even after controlling for momentum.  From an investor’s point of view, funds with the highest Active Share, smallest assets, and best one-year performance seem very attractive, outperforming their benchmarks by 6.5% per year net of fees and expenses. 

While we need to acknowledge that because we can’t measure risk, these studies, like any empirical work, need to be taken with a grain of salt.  It is nonetheless interesting that if we compare the studies that focus on teasing apart the influence of more active, concentrated management, to the broad all-inclusive studies, there’s a large change in the signal received.

Not Quite a Triumph, but an Opportunity
It is ironic that while the financial services industry and investors have spent the last 30 years rushing after the quantitatively inspired ideas of Samuelson, Markowitz, Sharpe, Fama, and others, academics, on balance, have been running in the opposite direction — relentlessly throwing into doubt the underlying tenets of quantitative finance.  Moreover, Samuelson’s flawed Challenge was met and returned with the brute force of empirical results from the practitioners most reliant on judgment –concentrated active fund managers.  Judgment pulled-off the big upset, rallied from behind to win the game, but almost no one has taken notice. 

The triumph of judgment has been overlooked by most investors due to the confusion created by MPT.  We’ve allowed one of the players in the match (MPT) to dictate the rules of the game.  MPT’s rules not only insure its own victory, but they also create a complex web of circular arguments that inhibit our ability to discern the truth.  MPT’s characterization of risk is the ruler we use for comparing active vs. passive strategies, often causing active strategies to appear more risky and less efficient than their index counterparts.  The same flawed logic is used to risk-adjust returns, biasing them downward for more active, concentrated managers, and rendering this highly important measure highly suspect.  Furthermore, reliance on MPT’s measure of risk pressures active managers to super-diversify.  The average active fund is thus disfigured to the point where the typical “active” manager is not very active at all, casting the fund in an unfavorable light in a beauty contest versus super-efficient index funds.

Even when investors recognise judgment’s triumph, we should not hold our breath for an industry-wide demotion of quantitative theory and practice.  MPT is too deeply woven into the fabric of our financial system.  It is difficult for investors to see past the very real performance numbers that show the average active manager underperforms corresponding passive index funds.  There’s a feeling of safety that accompanies index investing; neither the advisor nor the investor risks losing face or losing a job over putting money to work in a broad index.  We enjoy the mathematical certainty of MPT, it’s reassuring that we can fix a value to assets, and that we can quantify risk in a non-subjective manner – free from human error. 

Further, moving to judgment-based finance isn’t good business for the financial services industry.  The industry depends on quantitative finance to bring it scale and profitability.  None of the above are valid arguments, but that’s not the point.  When defending an entrenched system that furthers the economic interests of powerful entities, the rationale doesn’t need to be sound, it just has to be somewhat convincing. 

The fact of the matter is that quantitative finance is close enough to being “right” most of the time, so we put up with it.  History repeats itself often enough that the patterns from the past lull us into the belief that they can reliably predict the future.   Yet our investing lives, much like our non-investing lives, are defined at the extremes.  Just as we may get the best measure of ourselves in the worst of times, so to a devastatingly ugly market painfully exposes which investment strategies are not meant to last.  The issue with statistical finance is that while it may adequately predict the future the majority of the time, it is at the extremes, when we most need an accurate picture of the future, that historic relationships break-down and statistical methodologies fail us.  While some argue that a system which works 99 per cent of the time is good enough, these are the same people who would sell you a burglar alarm that works perfectly well until a would-be-criminal approaches your home.  What good is a system that breaks down only when you most need it?  See the financial crisis of 2008 or Long-Term Capital Management for a compelling answer. 

What would a return to judgment mean on an everyday, practical level?  Of course it would entail relying a lot less on top-down statistical measures and methodologies.  It wouldn’t mean, however, we forsake the use of all quantitative theories, mathematics, and statistics, and instead rely solely on gut instincts.   Rather, it would involve taking a bottoms-up, fundamental approach to understanding the nature of the entity behind a financial instrument.  Taking a holistic view of that entity – understanding basics such as its balance sheet and off-balance sheet arrangements, competitive positioning, growth strategy, and its principals, among other things is key.  That fundamental analysis is crucial in projecting the entity’s cashflow and in arriving at an appropriate assessment of risk, which helps determine intrinsic value.  The result isn’t precise, but the point is that it’s far better to be approximately right than precisely wrong.  Quantitative measures like risk-adjusted returns and value-at-risk may still play a role, but it is greatly diminished (as is the automated system for processing and investing that MPT fostered.)  In a judgment-based world, financial services firms understand that scaling and automating their businesses will maximise profits in the short term, but can be disastrous over the long-term.  

Where does all of this leave you the investor?  A system that is increasingly dominated by mechanistic, top-down focused, quantitatively-oriented investors, creates an exciting opportunity for informed individual investors with a fundamental bent.  Never before has so much money sloshed around our capital markets without the benefit of judgment. 

If everyone eschews judgment, who will make market prices even approximately right, or ferret out the offerings of thieves and promoters of worthless securities?  Paradoxically, the efficiency of securities markets is a public good that can be destroyed by the unqualified faith of its believers.  
We’ll never get to a point where all investors eschew judgment – there are too many individuals ready to apply common sense to make a profit.  However, as more money flows from truly active managers to investment vehicles that deploy money “blindly,” inefficiencies become more prevalent creating opportunities for those whose eyes are open to them.   

Do your homework and uncover mispriced assets on your own or look for concentrated, fundamentally-driven, relatively small funds with talented managers. Since persistence has been demonstrated in this subset, it turns out that a good manager may be identified from past performance among other considerations.  Find managers who fit your style and risk tolerance, and invest for long term returns.  Take advantage of the fact that your neighbours are leaving for passive funds, as their passive investments could provide the inefficiency your manager seeks to exploit.  But, by all means, avoid investing in highly diversified active funds whose returns closely match an index.  If index returns are what you seek, then pull your money and invest in efficient passive index funds or ETFs.

Most of the wealth in the world has resulted from individual entrepreneurs using their judgment to invest in opportunities (inefficiencies) in a highly concentrated, even exclusive, fashion.  Think about that for a moment, because it’s a big statement.  Sure, wealth has been lost using this formula, but the good has dramatically outweighed the bad.  Although far from perfect, human judgment has advanced us a very long way.  While public markets are much more efficient than the entrepreneurs’ private markets, they still contain inefficiencies.  Accordingly, good judgment will reward investors over time.  Demoting a time-tested, highly successful system that favours judgment in preference for one supported by an unsound infrastructure of quantitative theories and formulas, doesn’t make a lot of sense.   Make this flaw your opportunity.