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Sound rational decision-making, in contrast, follows the laws of logic and probability theory. The best strategy: calculate the option with the highest mathematical expectation and steer away from intuition or heuristics.

Modern portfolio theory is said to have started with Harry Markowitz, whose mean-variance portfolio is taught to every finance graduate. When Markowitz did his own investments for retirement, one would have expected him to use his Nobel Prize-winning optimisation method. In fact, Markowitz instead relied on a simple heuristic, known as 1/N (See Markowitz’s method, below).

Those who claim that calculation is always superior to heuristics also miss an important point made by Frank Knight almost a century ago. There is a huge difference between situations of risk and situations of uncertainty. In a world of risk, all alternatives, consequences and probabilities are known, or can be reliably estimated. In a world of uncertainty, that is not the case.

Does this mean that the Nobel Prize-winning method is a sham? No. Markowitz’s mean-variance portfolio is optimal in a world of risk, as defined by his assumptions, but not necessarily in the uncertain world of the stock market, where so much is unknown. To use such a formula requires us to estimate a large number of parameters based on past data. Yet, as we have seen, 10 years is too short a time to get reliable estimates. Say you invested in 50 funds. How many years of stock data would be needed before the mean-variance method beats 1/N? A computer simulation provides the answer: about 500 years. That is, in the year 2500, investors can stop using the simple rule and do the calculations, provided the same stocks and the stock market itself are still around.

Simple rule

Some time ago, I gave a keynote at the Morningstar Investment Conference, explaining in some detail when and why simple rules have an advantage over complex strategies: if the situation is fairly unstable and unpredictable, if the number N of assets is fairly large and only small amounts of data (such as for 10 years) are available. In the audience was the head of investment of a large international insurance company, who afterwards came up to me and said he would check his company’s investments.

A few weeks later, he told me that he had checked the investments since 1969: “I compared 1/N to our actual investment strategies. We could have made more money if we had used this simple rule of thumb.” Then the real issue came up: “How do I explain this to my customers? They might say, I can do that myself.”

But customers still face plenty of open questions that professionals can help them with: how large N should be, what kind of stocks, when and how often to rebalance. And, most importantly, exactly when and where 1/N is a successful strategy.

The fact that simple heuristics can perform better than complex strategies is not a quirk or lucky event. There is a mathematical reason for that: it is called the bias-variance dilemma. Think of investment as throwing darts at a dartboard. You throw six darts and they all cluster tightly to the right of the bull’s eye, with an average distance of two inches. That is your systematic error, or “bias”. Your competitor’s darts, by contrast, show no bias; their average distance is smack in the middle, but the individual darts are all over the board. This second kind of error is called variance or instability.

An investment strategy must balance both kinds of errors, bias and variance. The mean-variance method has to estimate many parameters, and the result will depend on the specifics of the sample it uses, which may lead to instability. Different samples will produce different estimates, corresponding to the variability in dart throws. If the amount of data is large enough, such as in the course of 500 years, the instability is reduced so that complexity finally pays. 1/N, however, does not need to make any estimates and therefore produces no variance, only bias. In general, simple heuristics tend to have a larger bias but smaller variance; that is, they are less unstable and more robust. That makes it clearer why 1/N can have an edge over complex calculations. But 1/N is not the only simple investment strategy around. To answer the question of what stocks should be included in your portfolio, you might consider using the so-called recognition heuristic, which can be translated here as “buy what you know”. We asked passers-by in downtown Chicago, Munich and Berlin which stocks they recognised by name out of the Standard & Poor’s or similar lists, and then formed a portfolio out of those most frequently recognised. When comparing it to blue chip funds, indices, and professional analysts, it turned out that most of the time, the recognition portfolio made more money.

Lessons

What is the lesson of all this? Big data are not always the best. In an uncertain world, heuristics — often portrayed as a handicap — may actually be a strength. And the world of finance is as uncertain as it can be. Rather than incorporating as much data as possible into a fancy statistical software package, the true art is to know what to ignore and how to separate the noise from the signal.

Markowitz’s method

Allocate your money equally to each of N funds.

1/N is a heuristic. What is a heuristic? It is a rule that ignores part of the information to make better judgements. While mean-variance uses all past stock data available to estimate its many parameters, 1/N even ignores all previous stock data. If Markowitz had been a mere mortal, he would have been diagnosed with irrationality owing to his cognitive limitations that prevented him from calculating the optimal investments.

Yet ignoring all previous stock data, as 1/N does, is not necessarily an error, as some still believe. Heuristics have been able to outperform so-called rational strategies — from regression models to mean-variance — in uncertain worlds. For instance, in one study by DeMiguel and others, 1/N was compared to mean-variance. Seven situations were analysed, such as investing in 10 US industry funds.

The mean-variance portfolio made use of 10 years of stock data, while 1/N did not need any. The result? In six of the seven tests, 1/N scored better than mean-variance in common performance criteria.

Gerd Gigerenzer is author of Risk Savvy: How to Make Better Decisions