In the early 18th century, Daniel Bernoulli proposed that individuals maximize expected utility when they make decisions under uncertainty. This reasoning launched the rationality model of human behavior that underpins many of today’s theories in economics and finance, including modern portfolio theory (MPT). The mathematical models that sprang from these theories provide a veneer of orderliness while obscuring the behavioral messiness of real-world financial markets.
The Rise of MPT
Pillar I
In 1952, Harry Markowitz published his article on portfolio selection, arguing that portfolios should optimize expected return relative to volatility, with volatility measured as the variance of return. He proposed the now ubiquitous efficient frontier. By the mid-1960s, this mean-variance model had become a mainstay within academic finance departments.
Pillar II
Combining Markowitz’s model with restrictive assumptions regarding investor rationality, information availability, and market trading structure, Bill Sharpe (and others) derived a model of capital market equilibrium in the mid-1960s. Soon the capital asset pricing model (CAPM) became a central tenet of MPT.
Pillar III
Eugene Fama erected the final MPT pillar in the mid-1960s, in perhaps the most famous finance doctoral dissertation of our generation. Extending the concept of rational investors to its logical conclusion, Fama proposed the efficient market hypothesis (EMH), that financial market prices reflect all relevant information and thus generating excess returns through active management is impossible.
MPT quickly became the ascendant paradigm. For the quantitative-based analysts who dominated the investment industry, a simple theory like MPT that explained messy financial markets was very attractive. Now they had a rigorous theory of markets and a rational approach to building investment portfolios.
But their conception could not have been further from the truth.
The Fall of MPT
The first shots were fired across MPT's bow in the late 1970s.
The initial CAPM empirical tests uncovered a negative return to beta relationship, the opposite of what was predicted. Rather than reject CAPM, however, the discipline responded by searching for statistical problems in these tests.
As EMH came under attack, Sanjay Basu’s research demonstrated that low P/E stocks outperformed high P/E stocks. In the early 1980s, Rolf Banz showed small-cap stocks outperformed large-cap stocks. The problem, of course, is that both P/E and firm size are public information and should not allow investors to earn excess returns.
In response, EMH proponents integrated these anomalies into a new “factor model,” though they admitted they did not know if the model captured either risk or opportunity. Ironically, these anomalies were then used by financial industry adjuncts — investment consultants, for example — to create that classic active management handcuff, the style box. In turn, the style box unintentionally led to additional active management restraints, such as style drift and tracking error.
These same proponents also argued that the EMH remained viable as long as active equity managers could not use anomalies to earn excess returns. But for the last 20 years, multiple studies have shown that many active equity managers are superior stock pickers and do indeed earn excess returns on these holdings. Russ Wermers demonstrated that the average stock held by active equity mutual funds earns a 1.3% alpha, and Randolph B. Cohen, Christopher Polk, and Bernhard Silli found that ex-ante best idea stocks earn a 6% alpha.
In the early 1980s, Robert Shiller argued that almost all volatility observed in the stock market, even on an annual basis, was noise rather than the result of changes in fundamentals. Since EMH held that prices fully reflect all relevant information, volatility driven by anything other than fundamentals strikes at the very heart of the theory.
Shiller’s noisy market model also created problems for Markowitz's portfolio optimization. If volatility is the result of emotional crowds, then . . . emotion has been placed in the middle of the portfolio construction process.
So rather than being a risk-return optimization, it is an emotion-return optimization.
In summary, all three pillars supporting EMH have been toppled.
Rejecting the World Rather Than the Paradigm
Much of finance pushes aside the mounting contrary evidence and soldiers on under the yoke of the MPT paradigm. This might seem surprising: Isn't finance a discipline based on empiricism, one that only accepts concepts supported by evidence? Unfortunately, as Thomas Kuhn argued years ago in his classic work, The Structure of Scientific Revolutions, scientific and professional organizations are human and are susceptible to the same cognitive errors that afflict individual decision making.
The concepts underlying MPT have not been rejected. Instead, they are widely used in studies and show up in textbooks all over the world. MPT's ubiquity confirms its legitimacy through social validation rather than empirical evidence. Emotional decision making is rampant in what is supposed to be a rational discipline.
Just because something is widely used doesn’t mean it's useful. The conventional wisdom is often wrong.
Let the Transition Begin
After decades, there is little evidence to support MPT. It is time to move on. There is an alternative way to view securities markets, their movements, and their participants: behavioral finance.
At some point, the industry will make the transition to something other than MPT. Behavioral finance is the leading candidate. Then the investment world as we have known it will be changed forever. As Kuhn observes, when paradigms change, everything changes, including basic concepts, facts, history, tools, and methodologies.
After the dust settles, virtually nothing of MPT will remain.
The ultimate irony of rationally based MPT is that it gives advisers and analysts the tools to enforce "The Cult of Emotion," including volatility as risk, efficient frontier, downside capture, downside risk, R-squared, and the Sharpe ratio.
The law of unintended consequences should not have the last word. As MPT fades into history, so will these tools. It's just another step on the road to the Active Equity Renaissance.
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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author's employer.
Image credit: ©Getty Images/mmac72
35 Comments
Hello Nathan,
Thanks for taking the time to comment and to append your thoughts to our article.
I do not think that someone who is critical of something is necessarily responsible for providing an alternative. There are several phases: one, identify the flaws of a broken paradigm; two, research new ways of viewing the world; three, test those new methods; and four, implement them widely. In the case of MPT, what is good about it is that it suggests that investors should be compensated for the risks that they take on. This is logical, and intelligent. However, it then goes on to propose a measure of risk that is merely mathematically convenient, rather than being mathematically useful. On this basis alone MPT and its calculations can be rejected. Another good thing about MPT that is logical and intelligent is its suggestion that not all diversification matters. Few people would reject these ideas, and none do, as far as I know.
Without MPT, how do you build a portfolio? I never used MPT in my investment management career and I bested my benchmark, the S&P 500 by 49.1%, with 2/3rds the volatility, and double the dividend yield. How did I do it? By applying my mind to the problem and developing something other than MPT. What that is remains proprietary to my former employer. But I will point out that physicists and mathematicians - the honest ones at least - believe that about 40% of natural phenomenon can be described with mathematics. Therein I have revealed a big clue about what you can do.
Another problem with MPT, in my mind, is that it does not get rid of the ex-ante/a priori problem. Namely, you still are left making predictions about the future. In the case of MPT you need to have return and risk estimates for every security in the portfolio. Most people stop short of making predictions about these things and use past data to inform their future view. If they do, in fact, make non-historical based predictions then, to my mind they have simply added another layer of predictions needed before investing. Why add another layer of abstraction and complexity to an already abstract and complex activity: investing?
I find your use of language to be a bit fast and loose; and here I am referring to what I believe is a conflation of 'things other than MPT' with irrationality, as evidenced in your series of sentences, "I’m not ignoring the flaws in MPT, just pointing out that there is no better alternative for process driven portfolio construction. Clearly rational decision making is preferable to irrational, and disciplined investing preferable to undisciplined." I do not think that comparison is appropriate and it awards MPT a distinction undeserved by its poor evidence in delivering alpha. While on the subject of 'rational;' is it rational to use a theory that you admit is flawed ("I'm not ignoring the flaws in MPT...")?
Last, as for what should we do? I would say roll up your sleeves, put on your thinking cap, and get busy.
In closing, the philosophy of MPT is better than the mathematics created for its implementation. And therein resides another clue.
Yours, in service,
Jason
Jason,
As a practitioner, the criticism of an investment approach has little value if an alternative is not proposed. I hate the idea of having to eat healthy and exercise to stay in shape, but I don't have a better solution so I am left with the best available advice as my only option. Additionally I congratulate you on your phenomenal track record, but my guess is that your skill cannot be replicated by the broad investment universe, otherwise it would be.
I do believe we are discussing different uses of MPT. You appear to be focused on a pure stock selection / equity portfolio, where I view MPT in the context of a diversified portfolio of asset classes. That may be the key to our disagreement.
I agree with the article's premise that human behavior is a factor that cannot be ignored. But how do we model it? And is it predictable? I would argue that we cannot model it, nor is it predictable. We can only observe it, and manage it with our own clients.
MPT provides the framework for a conversation around goals, objectives, risk tolerance, and managing expectations. Without a framework, discussing the tradeoffs between risk and return would lack substance. Most investors would choose to earn higher returns and lose less money in all cases. Without the ability to quantify a range of outcomes, an adviser is almost certain to disappoint their client at some point. Returns weren't as high as they wanted, or they lost more than they were comfortable with in challenging moments.
Until the holy grail of return without risk is discovered, educating clients about how their portfolios will act in different markets may be our best approach. If there is a better way to describe how portfolio decisions are made or to discuss the range of outcomes in different market environments, I would love to hear it.
Hello Nathan,
Again, thank you for the consideration you give to my points, and for taking the time to share your own.
Regarding 'something better than MPT' - your example of diet and exercise is too generalized, in my opinion. What I mean by that is that there are many ways to diet. For example, caloric restriction, vegetarianism, periodic fasting, paleo eating, Atkins/high protein, and so forth. It is the underlying principle that matters, not necessarily the means. The aforementioned 'diets' have at their heart something implicit: something that is being maximized/minimized. This is up to the one dieting. Likewise, there are many forms of exercise as well. Because your analogy was, in my opinion, too generic I think you miss the idea that how you construct portfolios to maximize returns per unit of risk is not constrained, but by seeing the world only through an MPT lens, you might think it is.
As for my track record...I made choices, in time, in response to the unique events that affected my securities, and as constrained by my investment charter. Those times and those events will never replicate, so you are correct, those returns are impossible to achieve again. However, to the degree that there are approximate times and approximate events, and as filtered through method, one could hope to improve one's results. I have shared nearly the entirety of what I did to earn my returns on Enterprising Investor, and in the publications that I have authored for CFA Institute. I believe if you review them you will see thinking not described elsewhere. Whereas, I consider my DNA to be entirely mundane. Put another way, my knowledge could be used to generate returns that are differentiated.
As for my thinking about MPT, my own portfolio that I managed had a flexible charter that I took advantage of to generate the returns of the portfolio. The Davis Appreciation and Income fund was long only; the charter was to deliver 80% or more of the upside of the S&P 500, while limiting the downside to 50% or less of the S&P 500; and the vehicles for this were equities, fixed income, preferred stocks, convertible bonds, convertible preferred stocks, warrants, options, and very importantly, cash. On occasion I would be long both the equity and fixed income of the same underlying business/credit, yet, in a proportion designed to deliver the 80:50 strategy. In this instance, if I used MPT, I would have been unable to deliver on my charter. Notice though, that the charter/prospectus is the contract with the investor and it provides many means of discussing goals, objectives, risk tolerance, and managing expectations. Just as there are many diets, and many forms of exercises, there are many ways of having these types of conversations, too; if only the underlying principle is understood and one is willing to temporarily avert one's eyes from form, and direct it instead to substance.
As for human behavior being predictable...yes, it is true we have a profession that is better described by soft sciences, than hard sciences. However, that human behavior is not perfectly preditable in the way that F = MA implies does not mean that human behavior is not predictable. If human behavior were not predictable then there would not be consumer products companies, there would not be 'impulse items' at the cashier, there would not be behavioral finance, and so on. As an out of context example, I am currently reading a book about personal development that was authored around 300 C.E. It admonishes against bad human behavior that is easily recognizable to someone living almost 1,800 years after the text was authored.
Last, in my opinion you have set up a straw man in your final paragraph that seems unnecessarily absolute. Here I am referring to your sentence, "Until the holy grail of return without risk is discovered..." I know that neither Tom, nor I believe in that. However, how we go about seeking return and evaluating risk, and hence how we conduct securities analysis and portfolio construction, is not limited or constrained by MPT. Our point is that MPT is a poor way of conducting these goals, and that there are other ways to do this. The point of our series is to discuss just that. Again, I refer back to my previous comment when I highlighted that the philosophy of MPT makes sense, whereas its implementation does not. Philosophy also has the luxury of not being constrained by, or hiding behind, poor mathematics.
Yours, in service,
Jason
If expected return and risk are not used as inputs into rational decision making then what do you propose we use to make investment decisions? Isn't ex-ante vol just a level of uncertainty about your estimated returns? Seems right to me to discount your expectations by the level of confidence you have in them.
Mathew-
We agree with you that expected return and risk should be inputs into a rational decision process. We just don't think volatility is a good measure of risk.
The next post discusses our ideas regarding measures of true risk, which is the chance of permanent loss, not how bumpy is the ride.
Volatility most often reduces compound returns and so using compound returns is the best way to capture the impact of volatility.
I agree that volatility compared to permanent impairment of capital is not a good measure of risk but it is nonetheless a hugely important in client comfort along the way to their investing goals. We do a huge amount of work with our clients regarding emotional reactions to market movements etc and yet at points of significant volatility some will still let their emotions rule. The 'bucket' approach to managing client assets has merit but may also complicate things unnecessarily from a client point of view and may risk heightening emotional reactions to market movements if the different buckets are not viewed together as part of one overall portfolio.
Richard-
You bring up some very good points. Clients, no matter how much we work with them, will at times succumb to their emotions and make poor choices.
Effective client dialog is critical in helping clients through highly emotional events. A needs based planning model is only one part of creating this narrative.
It sounds like you are doing a lot to avoid this type of situation and so you are to be commended.
Nathan-
Let me take a first crack at responding.
My comments apply to the long-horizon growth portion of a client's portfolio, not the emergency/liquidity or income portions.
Neither correlation nor volatility are very important in building long horizon wealth. Expected and excess returns (earned by truly active equity managers) dominate all other portfolio considerations. This being the case, why invest in anything other than equities since there is no other asset class of which I am aware (with the maybe the exception of real estate and manged futures) that has an expected return anywhere close to equities.
So if maximizing long horizon wealth is your goal, there is no need for an alternate portfolio construction methodology. Just invest in equities and any other asset class with comparable expected returns, if you can find them. Equal weighting will work fine in this situation.
This is quite a change of heart for me as I began my academic career nearly 40 years ago, being skilled in and enjoying estimating variance-covariance matrices, the foundation of mean-variance portfolio construction. But alas, that is now all a distant memory.
Tom,
In the long-run, correlation and volatility are important in building long-horizon wealth due to the impact of compounding. We know this from a simple two asset portfolio. If two portfolios have the same return but one has less volatility, the portfolio with less volatility will compound to a higher level of wealth over the long-term. Therefore if I can accomplish the same level of return of equities with less risk by owning something else alongside, I'm better off.
In addition, while segregating assets into emergency/cash reserve, income, and growth, may make sense initially, we know that all investors suffer from loss aversion. They feel the pain of losing twice as much as the joy of winning. Most investors would happily trade some upside to limit the downside in the worst moments.
Nathan-
You are technically correct that lower correlations and volatility lead to higher compound returns, assuming the same expected return. But the problem is that the expected returns on other asset classes are so much lower than they are for stocks. So these differences swamp any advantage of low correlations and volatility.
For example, given the current low expected returns on bonds, it makes no sense to invest in bonds for building long horizon wealth, even with their lower correlations and volatility.
Correlation and volatility are a third order effect at best and should receive very little consideration in building growth portfolios.
Yes, myopic loss aversion is by far the most common cognitive error made by investors. And for those clients who do not respond to emotional coaching, the answer might be a trade off between short term emotional comfort and long horizon wealth.
But the cost of such trades off is huge and so as investment professionals we need to do everything we can to help our clients avoid such monumental mistakes.
In the case of the income portfolio, we can emphasize the growth in dividend income versus short-term draw downs. In the growth portfolio, we can emphasize the long investment horizons we all face, and thus the need for patience in tough market environments.
Not saying this will be easy, but the best advisors do everything they can to help clients build as much long horizon wealth as possible.
Remember, we are the adults in the relationship.