Experiments show that cats, monkeys, and deer can often ‘compose’ more profitable investment portfolios than those of professional investors. However, one should not rely on luck when investing.
January 25, 2021   |   Mikhail Tishchenko

Burton Malkiel, a professor of economics at Princeton University, once conducted an experiment. He asked his students to flip coins and draw imaginary charts of stocks based on the way the coins fell (heads- or tails-up). Heads meant that the price increased by 0.5 percentage points during the trading day; tails meant that it fell by the same amount.

The results looked like real stock price charts, showing seemingly obvious trends, although this was a mere statistical illusion. When Malkiel showed one chart to a stock analyst he knew, the analyst could not hide his excitement, ‘What company is this? We should buy it right now. This is a classic pattern. It will definitely go up 15 points next week.’

Malkiel, a former president of the American Finance Association and ex-head of Vanguard, one of the world's largest investment firms and a pioneer of index investing, conducted the experiment to prove his random walk hypothesis, i.e. the idea that stock prices change unpredictably and do not correlate with one another. Moreover, past fluctuations cannot predict future ones, the trends discovered can be random, and the flow of information constantly affecting prices makes forecasts based on technical and fundamental analysis futile.

In his book A Random Walk Down Wall Street, Malkiel acknowledged that, unlike the mathematical notion of a random walk (a sequence of completely random movements), prices can still be subject to some impulses, but he insisted that it was still impossible to develop an investment strategy outperforming the market in the long run.

Malkiel's idea is based on the efficient market hypothesis, put forward in 1965 by the economist Eugene Fama (awarded the Nobel Prize in 2013 for his asset pricing analysis) and introducing the notion that assets are always traded at their fair value, reflecting all available information; since the information is available to everyone, any opportunity to profit from predictable price movements will be used immediately, and one can ‘outperform the market’ only by having some insider information that is not yet reflected in the price.

The random walk hypothesis sparked controversy: sceptics pointed out that the fact that it is difficult to estimate the factors influencing prices does not mean that regularities do not exist and that it is impossible to establish them. But Malkiel's practical advice (that it is generally more profitable for investors to follow the market than to try to outperform it) is reflected in the growing popularity of passive investing and index funds, which follow the general market trend and compose portfolios of the same financial instruments and in the same proportions as in the indices.

One of the first index funds was Vanguard, which invested in the S&P 500. It was founded in 1975 by John Bogle, influenced, in part, by the ideas of Malkiel, who became the head of the company. ‘When my book was first reviewed by a professional [in 1973], …they said it was the biggest piece of garbage in the world, ridiculous advice. Well, now in mutual funds the index share is now more than 50%,’ recalls Malkiel, the ‘father of passive investing’.

Experiments with investors

The implications of the random walk hypothesis turned out to be even more controversial: it implied that even randomly picking assets could be just as profitable as following an active investment strategy. ‘A blindfolded monkey throwing darts at a newspaper's financial pages could select a portfolio that would do just as well as one carefully selected by experts,’ wrote Malkiel.

This paradoxical statement has attracted the attention of journalists and professional investors. Some have tested it, and although their experiments have not always met scientific standards, the results have shown that the random portfolio idea deserves more attention than it might seem at first sight.

One of these experiments was conducted in 2001 by the British psychologist Richard Wiseman, a professor at the University of Hertfordshire. He picked three people, a professional trader, an astrologer, and a four-year-old child, and asked them to invest a notional £5,000 in stocks of their choice traded on the British stock market. By the end of the year, the virtual portfolio of the trader, who relied on mathematical models, turned out to be non-performing (it had lost almost 50%). The same happened with the portfolio of the astrologer, who relied on the positions of the stars (minus 6.2%). Only the portfolio of the four-year-old girl, who picked her stocks at random, was profitable (5.8% growth).

In the early 2010s, British journalists conducted a similar experiment: a team of financiers competed with a group of schoolchildren and a cat. Recently, the list of experiments has been extended to include a semi-serious study, in which Bruce Sacerdot, a professor at Dartmouth College, and his colleagues compared the investment returns of U.S. congressmen and ‘Santa's reindeer’. In the first instance, the professional financiers lost to the cat in terms of portfolio returns; in the second, the reindeer outperformed the S&P 500 index, unlike the congressmen.

Some have followed a more thorough approach. The most famous example is a multi-year experiment by journalists from The Wall Street Journal. Modelling Malkiel’s dart-throwing monkey scenario, the journalists threw darts at financial pages hung on the wall (giving darts to actual monkeys could be dangerous, the newspaper explained, so the journalists performed the role of the chimps). Their rivals were professional investors. The contest, which began in the late 1980s, lasted 14 years, and in the end, the professionals won: their returns were higher in 87 of 142 six-month contests, and in 76 rounds their returns were higher than the Dow Jones Industrial Average. The returns of the professional team's portfolios averaged 10.2% over the rounds, outperforming the Dow Jones’ rise of 5.6% and the dart throwers’ gain of 3.5%.

Technically, this experiment confirmed the obvious fact: professional investing is more effective than random.

However, critics noted that the performance of the dartboard portfolio was quite impressive: 55 wins out of 142, and the rules of the contest tilted the odds in the professionals’ favour. In particular, at the beginning of each round, The Wall Street Journal published the picks of the investors. According to subsequent research, these expert picks pushed prices up, contributing to abnormal returns due to increased demand for the stocks picked by the professional investors. This was attributed to the ‘noise effect’, the distorting effect of publications on the result of the experiment.

Some researchers also insisted that simply comparing portfolio returns is fundamentally wrong, most of all because it does not take risks into account. Returns reflect the investment strategy, a deliberate decision involving the possibility of both higher returns and higher losses, so simply comparing the returns of a professional portfolio to a random portfolio, critics noted, is like comparing ‘apples to oranges’.

Testing portfolios

The experiments have resulted in growing attention from researchers to Malkiel's idea as well as in new experiments.

In 2012, analysts from Research Affiliates and Towers Watson ran a large-scale simulation of Malkiel's dart-throwing monkeys using data from 1964 to 2012 to see why random investing may beat the market. For each year, they created more than a hundred portfolios, each including 30 out of 1,000 US companies. One type of portfolio was based on one or another investment strategy; the second type was composed using the ‘upside-down’ versions of the first-type strategies (for instance, inverted weighted algorithms). There was also a cap-weighted benchmark portfolio based on the whole sample.

It turned out that carefully crafted investment strategies work well. But their upside-down versions also work, even better than the right-side-up ones. For example, the maximum-diversification index portfolio grew by 11.99% per year, while its upside-down version grew by 12.48%. The average return on the ‘monkey-managed’ portfolios was 11.26% versus the 9.66% generated by the cap-weighted benchmark portfolio.

Malkien was wrong in arguing that a monkey could select a portfolio that would perform no worse than one carefully selected by experts, said Rob Arnott, CEO of Research Affiliates, introducing the study: ‘The monkeys have done a much better job than both the experts and the stock market.’ One of the lessons learned, the authors conclude, is that investment strategies themselves, no matter how thoughtful or intuitive, are not the source of incremental returns. Many rational investment strategies outperform the cap-weighted benchmark; but the same is true for irrational inverted versions of these rational strategies.

According to the researchers, the success of the random portfolios is attributable to the fact that they include more small and undervalued companies with higher returns than the benchmark portfolio, which influenced their performance. In the benchmark portfolio including 1,000 companies, the top 30, with annual returns of 8.6%, accounted for about 40% of the weight, while the average return of the other 970 companies was 10.5%. At the same time, any portfolio of 30 companies would include a higher proportion of smaller companies.

Economists from the University of Catania and the Swiss Federal Institute of Technology in Zurich have also compared the performance of portfolios based on popular investment strategies and randomly composed ones using data from several markets from 1989–1998 to 2012 and concluded that in the long run, their performance was comparable. The reason is that in the long run, the disadvantages of a random portfolio can be offset by its advantages, i.e. it does not have the disadvantages inherent in investment strategies and investor behaviour, such as ‘herd behaviour’. In other words, a random investor will miss some opportunities, but will make fewer mistakes.

Another study has found that a strategy based on past stock performance can also be less successful than a random one, but adding some randomness leads to significantly enhanced performance.

But do not rush to the pet store to get a dart-throwing monkey hoping to beat the market, warns Rick Ferri, the author of a series of books on index funds and passive investing, in his comment on the Research Affiliates study. Random portfolios’ higher concentration of small-cap securities and ‘value stocks’ (with a low price/earnings multiple, that is, undervalued by investors, as opposed to ‘growth stocks’) makes these portfolios riskier, and therefore, more profitable.

The small-cap premium is widely recognised in academia, Ferri writes. It is the extra return expected for taking risks by investing in smaller companies. These companies may not be well known, may not have large distribution networks for their products, and may have to pay more than large companies when borrowing money, and the cost of capital reflects investors’ return. All this makes investing in these companies riskier, which is shown in a model well-known among investing consultants (the Fama-French Three Factor Model). The model suggests that portfolio return is influenced by three factors: beta—which is the co-movement of all stocks in general; size—which is the ratio of the return on the stocks in the portfolio relative to the return of the most-capitalised companies in the market; and value—which compares the book value to capitalisation ratios of the companies in the portfolio and those of the most overvalued companies in the market. The return on any portfolio is a combination of these three risks, Ferri concludes: ‘There is no such thing as a free lunch on Wall Street.’