In Pursuit of the Perfect Portfolio: a review

A new book by Andrew W Lo and Stephen R Foerster profiling key figures in the development of modern portfolio theory offers a fresh perspective on the active versus passive debate

Justin Reynolds
The Patient Investor
15 min readOct 8, 2021


Investment is at least as old as the stone tablets of ancient Mesopotamia, the art and science of making money work for itself evolving from the commerce of the ancient world, the development of the banking system in the Italian city states of the late Middle Ages, the emergence of stock trading in the Netherlands, through to today’s digitally connected global marketplace.

But modern investment theory, based on the principle that a portfolio should be a consciously designed set of assets that work together to maximise return rather than a haphazard collection of individually promising investments, only emerged in the second half of the last century.

In Pursuit of the Perfect Portfolio (2021) by Andrew W Lo and Stephen R Foerster, professors at the MIT Sloan School of Management and Ivey Business School, is a useful popular history of the genesis and evolution of that theory, compiling profiles and interviews gathered since the turn of the millennium with ten academics, fund managers and writers who laid the foundation for modern portfolio management.

Their subjects — Jack Bogle, Charles Ellis, Eugene Fama, Martin Leibowitz, Harry Markowitz, Robert Merton, Myron Scholes, William Sharpe, Robert Shiller, and Jeremy Siegel — are not so representative of the industry today. There is a strong showing from the Chicago School associated with theories of efficient markets and passive investment, but with the exception of Robert Shiller, not so much from the behaviourist perspectives that have asserted themselves in more recent years.

But with six Nobel Laureates among them, Lo and Foerster’s line-up is indicative of the industry as it was during the post-war years when modern portfolio theory developed, and allows for extensive discussion of some of the issues at the heart of contemporary portfolio management, including diversification, market timing, the passive versus active debate, and the appropriate balance between equities, bonds and alternative assets.

Lo and Foerster’s profiles seek to introduce the technical elements of their subjects’ thought, interweaving the text with diagrams and formulas indicating the conceptual frameworks they developed. But it’s possible to skip most of these: by and large the authors do a pretty good job of translating the language of mathematical economics into accessible prose.

The opening chapter is somewhat anomalous, offering a brief history of investing from classical antiquity to the present day, but it serves to highlight Lo and Foerster’s premise that ‘while the art of investing has been practiced for centuries, the science of investing is a thoroughly modern invention’. The first significant efforts to formalise investment principles emerged during the Renaissance in tracts like Girolamo Cardano’s The Book on Games of Chance (1565), which applied mathematical models to gambling. The investment classics still widely read today began to appear in the first half of the 20th century, notably Reminiscences of a Stock Operator (1923), Edwin Lefèvre’s tragicomic observation on investor psychology, and Security Analysis (1934) by Benjamin Graham, the first articulation of the principles of value investing that were to find a huge and lasting audience through his later The Intelligent Investor (1949).

Markowitz’s insight

But the principles that guide contemporary portfolio management only began to evolve in the post-war years with the pioneering work of economist Harry Markowitz. In a sense modern investment theory is one long commentary on Markowitz’s insight — which came to him one afternoon as a graduate student while working on a paper in the University of Chicago library — that investors should select securities with regard to the role they will play within the context of a portfolio rather than their merits as independent investments. As Lo and Foerster put it:

It struck Markowitz that if an investor was only concerned with the expected value of a stock, then by extension such an investor should only be concerned with the expected value of the entire portfolio of stocks. But Markowitz quickly saw that the logical conclusion of such an approach would be that investors would only include one stock in their portfolios: the one with the highest expected return.

What matters is less the performance of individual securities within a portfolio than their movements relative to one another: the assurance that when the value of one falls that of another rises to compensate. A robust diversified portfolio moves forward as a tightly connected unit, with minimal collective risk, maximised to earn a collective return.

In a series of articles, beginning with the seminal Portfolio Selection, published in 1952, Markowitz argued that well diversified portfolios tend towards an ‘efficient frontier’, the highest level of expected return for a given level of risk. Investors should begin the process of portfolio construction by considering the blend of asset classes — stocks, bonds, and alternative holdings like infrastructure funds, currencies, and commodities — appropriate for the level of return they seek and the degree of risk they are willing to tolerate. Only when such a framework is established should they move on to choosing the particular stocks, funds, trusts or index funds of which it will be comprised. Markowitz himself, like most of Lo and Foerster’s subjects, favours simple building blocks, a blend of low-cost index funds for equities and bonds for fixed income.

Lo and Foerster go on to give a similarly useful overview of the work of William Sharpe, who built upon Markowitz’s work with his capital asset pricing model (CAPM), a formula for constructing portfolios that move towards Markowitz’s efficient frontier, a blend of securities that minimises the risk that needs to be borne to pursue a projected return. Although subject to much critique and many revisions since it was first published in the early 1960s, the formula continues to offer a useful metric — accessible to private investors — to calculate risk/return ratios.

The CAPM indicated that the optimal portfolio tends towards the market portfolio, the blend of securities that constitutes the aggregate portfolio of all investors, equivalent to the entire market. The core holding within Sharpe’s ideal portfolio, therefore, would be what he calls a ‘World Bond-Stock Fund’, a theoretical fund representing the world’s tradable securities in market proportions. He suggests investors can approximate that through a simple portfolio consisting of a US total stock market fund, a non-US total stock market fund, a US total bond market fund, and a non-US total bond market fund.

The efficient market hypothesis

Aside from Markowitz, the central figure in the book, perhaps, is Eugene Fama, another Chicago School luminary, whose work continues to provoke some of the sharpest disagreements in the investment world. Fama’s efficient market hypothesis (EMH) pushed Markowitz’s thought on the virtues of diversification to its logical conclusion, maintaining that if information in a market is open to all participants, and participants process that information rationally, then the price of a security will always accurately reflect its value.

In a modern market accessible through low cost digital platforms awash with information, scrutinised by a vast pool of professional analysts, it should be almost impossible to find stocks that have flown under the market’s radar. The considerations used to price a share — such as assessment of fundamentals, industry trends, and prevailing macroeconomic conditions — are quickly and efficiently processed and priced into a security by tens of thousands market participants, certainly by the time they come to the notice of the average private investor. In today’s transparent markets it simply isn’t possible to consistently select stocks in the confident expectation that they move one way or another: today’s price offers no indication of tomorrow’s.

In evolving this argument Fama built on the concept of the ‘random walk’ formulated by the early 20th century mathematician Louis Bachelier, who suggested that prices in an efficient market move rather like the random motion of particles suspended in a medium, rising or falling with equal probability in accordance with a stochastic process now called Brownian motion. The implication of Fama’s hypothesis, at once both sobering and liberating, is that private investors should not attempt to beat the market but be content simply to follow it.

Even fund managers with access to far more information than private investors cannot consistently beat the market over the longer term. Citing the well known guidance given by Warren Buffet to his trustees that 90pc of his fortune should be invested in a low-cost S&P 500 index fund, Fama suggests private investors should hold a global tracker as their core holding, and allocate the rest to simple fixed income securities such as short-term government bonds. Speaking to Lo and Foerster, Fama does concede that portfolios can be tilted in certain directions, perhaps towards value, growth, small cap, domestic or international securities, so long as it is recognised that efforts to secure a higher return than the market come with additional risk:

I think, at least, in my current view of the world, you have a multidimensional surface that’s characterised by a continuum of portfolios with different sorts of tilts, and the market portfolio is the centre of that universe. In aggregate, people have to hold the market portfolio. That’s it, and that’s an efficient portfolio in any model you want to think of. And you can decide to tilt away from that, towards other dimensions that we think capture different kinds of risk, and that’s a personal decision.

He insists, however, that capacity to beat the market diminishes over time, and is impossible in the longer term. Outriders like Warren Buffet are the inevitable big winners that emerge in any statistical sample, in which winners are always balanced by losers. The short term successes that good fund managers are undoubtedly capable of securing must be put into perspective by viewing them against a longer term horizon: ‘Institutional people, especially, tend to change their portfolios based on three to five years of past returns, and I show them simulations in which that’s basically noise. … There is almost no information in there about expected returns. … The higher expected returns on stocks comes about with a large amount of risk.’

The smooth, stylised environments that serve as the theoretical ground for Markowitz, Sharpe and Fama’s work seem to bear little resemblance the emotional markets that investors encounter in their day-to-day experience. But their fundamental argument, that a diversified portfolio that tends towards the market portfolio offers the best chance private investors have to secure a decent long term return, continues to drive the long term industry trend towards passive investment, with has been charged in more recent years with the rise of exchange traded funds (ETFs).

Popularising passive principles

Lo and Foerster profile three well known figures who have popularised the Chicago philosophy through best selling books and passive investment products. In his best selling Winning the Loser’s Game (1998) investment consultant Charles Ellis helped foster increasing investor scepticism regarding the value of active funds, insisting that few fund managers beat the market for any length of time and that it is impossible to identify in advance those who will do so. Investors with the patience sit tight and track market over a 15 to 20 year period are guaranteed to secure better returns than 80% of their peers.

Ellis also cautioned against trying to time the markets by attempting to hitch a ride on a surging market and getting out just before it peaks. Investors are prone to attach themselves to a bull market towards the end of a surge, and sell just as it starts to rise again. Ellis argues it is better simply to tough it out through good and bad times. Successful investing is essentially a matter of emotional discipline. Investors can try to succeed intellectually, physically or emotionally: by being smarter than other investors by intuiting opportunities others miss; by working harder to accumulate research; or by having the discipline to stick with a core set of simple investments that gradually rise with the market. For Ellis ‘You have to control your emotions, and most of the time that means the best thing to do is nothing.’

Another best-selling writer, Jeremy Siegel, argued in his Stocks for the Long Run (1994) that investors prepared to let wealth accumulate through index funds can secure higher returns by weighting their portfolios towards equities, which history shows tend to rise by an annual average rate of 6 to 7%. It’s a strategy that requires forbearance, but cold hard data shows it works.

Lo and Foerster’s chapter on Jack Bogle, founder of the hugely successful range of Vanguard index funds, presents the passive philosophy in perhaps its purest form. In the course of marketing Vanguard’s products Bogle condensed passive principles into a set of pithy, folksy expressions. Investors should stop ‘trying to find the needle’ and instead ‘invest in the haystack.’ Those concerned about market volatility should ‘close their eyes.’ If they are worried that market downturns are cutting into their gains, they will ‘just have to save more’ and keep faith in the market’s capacity to generate returns over time. Bogle urged investors to ignore ‘the short-term noise of emotions reflected in our financial markets and focus on the productive long-term economics of our corporate businesses.’

Lo and Foerster’s conversations with Bogle indicate that his scepticism extended even to the booming market for thematic ETFs, which he argued are too dependent on the capacity of their managers to select a basket of securities that is likely to rise over the long term, a judgement made in the face of the same market uncertainties as those made day-to-day by active managers. Rather than following a hot new theme, be it automation, biotech, cryptocurrency, or the emerging space economy, investors should rest content with broad-market, low-cost index funds designed to be bought and held — forever. These have much less volatile cash flows, and the element of fallible judgement is removed, guaranteeing investors exposure to the best performing securities.

Unsurprisingly Bogle advocated radical simplicity in terms of holdings. He suggested investors make a cheap S&P 500 tracker their core holding, arguing that the US market has an unmatched long term record, offers the best investor protections and legal institutions, and secures indirect international exposure through the inclusion of leading multinational firms — Bogle suggests a 20% exposure to global securities is sufficient, the data indicating minimal marginal benefit in investing a greater proportion of equities internationally. Investors should also keep their fixed income holdings simple. There is no need to investigate alternative assets when bonds are perfectly capable of providing steady fixed income. For Bogle:

The secret to investing is that there is no secret … There is only the majesty of simplicity … When you own the entire stock market through a broad stock index fund, all the while balancing your portfolio with an allocation to an all-bond-market index fund, you create the optimal investment strategy.

Bogle was a passive evangelist, a businessman with a product to sell. But whatever one makes of his corrosive scepticism about any and all forms of active management, the case he makes for the importance of managing a portfolio’s compounding cost, well presented by Lo and Foerster, has undeniable force. Bogle’s cost matters hypothesis, abbreviated to CMH with wry reference to the EMH, highlights the hidden cumulative costs that can cruelly erode gains. Some, like maintenance charges and performance fees, are clear, others less so, notably the ‘turnover cost’ incurred by managers in the course of buying and selling the holdings within a fund or trust. It is worth quoting Bogle at length:

[A]ny fund that turns its portfolio over at that rate is costing you an extra 1% a year: a half percent to buy all those securities, including market impact costs, and a half percent to sell them … Actively managed funds … had an average expense ratio of 1.12%, transaction costs of 0.5%, a ‘cash drag’ (since funds typically hold cash reserves) of 0.15%, and sales charges and fees of 0.5%, totalling 2.27%. Furthermore, actively managed funds had a tax inefficiency differential (resulting from realised capital gains that are taxed, compared with untaxed unrealised gains) of 0.45% compared to the index fund, resulting in a 2.66% differential.

An investor with a 40 year horizon securing the annual market return of 7% though low-cost index funds would bank two-thirds more of their accumulated gain than investors holding more expensive active funds.

Alternative views

Lo and Foerster round off the book with a set of profiles that serve as something of a counterweight to the prevailing balance towards passive investment. Myron Scholes has close affinities with the Chicago School and the wider world of passive investment, having studied and worked with Eugene Fama and contributing to the development of Jack Bogle’s first Vanguard index fund. But for him those experiences highlighted the compromises inherent in the passive approach.

Scholes notes that the dependence of index funds on stocks with large market caps is a weakness as well as a strength. Indices heavily weighted towards big name companies allows investors to ride market upturns effectively, stock market history showing that a small proportion of stellar stocks have driven most of its gains. Fascinating research conducted by Hendrik Bessembinder, an academic at Arizona State University, on historic stock market returns in the US, shows that the entire gain of the market since 1926 is attributable to the best performing 4% of listed companies. The only way to guarantee access to those gains is to buy the entire market through a tracker.

But investors are left exposed when blue chip companies fall, as was vividly illustrated by the crash in tech stocks at turn of the millennium. By the late 1990s the S&P 500 was precipitously overbalanced towards stocks at the frontier of the emerging online economy. The markets of certain countries were dominated by them, Nokia, for example, accounting for 70pc of Finland’s entire stock market capitalisation. When the tech bubble burst the lack of diversification offered by US and European markets was cruelly exposed.

Scholes also offers a counterargument to the foregoing advice that investors should simply buy and hold, arguing that the information and platforms available today make it possible to avoid the most severe market downturns. Indicators such as the Cboe Volatility Index — better known as the VIX index — offer insights into the likelihood of future volatility. When the VIX is above its historical average investors should consider rebalancing their portfolio towards fixed income, which today can be done without too much time and cost by fine turning the balance of index funds towards equities or bonds as appropriate.

Robert Merton enters the discussion from a position somewhat perpendicular to the active versus passive debate running through the book. He agrees that private investors may not be able to beat market, but rather than suggesting they rest content with a simple DIY approach of purchasing a set of passive funds, he suggests they consider entrusting their finances to professional managers. Investors unconvinced by passive evangelism, but sceptical about their capacity to beat the market themselves, might simply want to entrust the task of designing and managing an appropriate investment strategy to professional advisers. Equipped with the relevant information provided by their clients, good managers can develop glide-path funds that adjust asset allocation over time toward less risky assets, smoothing the passage towards retirement.

Beyond the EMH

As Lo and Foerster note in the book’s concluding chapter, the only points on which all of their subjects are in agreement are the fundamental importance of Markowitz’s insight into the value of a diversified portfolio, and the usefulness of a market portfolio, representative of all assets in the global market, as a starting point for portfolio construction.

Though they give its advocates plenty of space Lo and Foerster are themselves unconvinced by the classic version of the EMH, and sketch an alternative in the form of an Adaptive Market Hypothesis (AMH) that seeks to augment Fama’s framework with the collective critique to which it has been subject over the past few decades. Detailed in Lo’s recent book Adaptive Markets (2019), the AMH suggests the EMH ‘isn’t wrong so much as incomplete’. The classic formulation of Fama’s hypothesis can’t acknowledge what all participating in the daily cut and thrust of the markets can plainly see: they are emotional places where securities rise and fall with the tide of human sentiment. Adopting elements from behavioural economics the AMH ‘applies the principles of ecology and evolutionary biology to show that investors may not always act in the ways that economic theory predicts but that they do adapt to their environments and respond to economic incentives in ways that can be modelled and, in some cases, anticipated.’

Although not summarised in the present book in any detail, it is clear the AMH has affinities with influential theories of market turbulence associated with George Soros and Hyman Minsky. Soros’s theory of reflexivity pictures the market as a self-referential system in which observers participate in what they observe. In Soros’s words ‘human beings are not merely scientific observers but also active participants in the system’. Individual stocks are not priced in insolation but with relation to each other. And prices do not simply reflect fundamentals but influence them, in a ceaseless feedback loop. Markets not only anticipate economic developments but drive them and are in turn driven by them, a phenomena best illustrated by the phenomenon of contagion, the power of markets to destabilise confidence in an entire economy as powerful investors bet against governments’ capacities to shore up confidence.

Hyman Minsky noted the tendency of markets to destabilise themselves. Long periods of financial stability can encourage excessive leverage and risk-taking, cumulating in financial crises. In time the cycle repeats itself, a crisis followed by a period of calm after which storm clouds again emerge on the horizon, driven by the same factors that generated the previous crisis. Commenting on Minksy’s observations, hedge fund manager Paul Marshall in 10 1/2 Lessons from Experience (2019), writes that markets are ‘highly complex non-linear systems created by a myriad of half-informed or uninformed decisions made by fallible (human) agents with multiple cognitive biases’.

So long, therefore, as markets are imperfect, they will always offer opportunities for shrewd investors, undervalued stocks to be bought and sold on, overvalued stocks to be shorted, and emerging sectors and markets that have hitherto escaped notice. The bass note of Lo and Foerster’s survey, however, is that private investors confident they can beat the markets should tread with great caution. Investment theory has moved on from strong forms of the EMH, Soros, Minsky and others noting the systematic tendency of markets to instability. Openings can be found, as better investors prove from day-to-day. How long they can consistently beaten them is unclear. And whether private investors with limited resources should attempt to do so over the longer term even less so. In Pursuit of the Perfect Portfolio offers a most useful resource for taking that lesson seriously.

In Pursuit of the Perfect Portfolio by Andrew W Lo and Stephen R Foerster is published by Princeton University Press. Photo by Joseph Andrews on Unsplash.



Justin Reynolds
The Patient Investor

A London-based financial writer and essayist. Edits The Patient Investor. Twitter @_justinwriter.