The Wisdom of Crowds and Stock Market Prices
by Brian Durno, CFA – April 8, 2010
“Prediction is very hard, especially about the future” – Yogi Berra
Michael Mauboussin, a professor at Columbia Business School, performs an experiment with his class each year. About three weeks before the Academy Awards, he hands them a two sided form. On the front, there are six major categories (best actor, best picture etc). On the back are six much more remote categories (cinematography, music, make-up etc). Students are asked to predict the winners in each category. Students contribute $1 to a pot and the winner gets the proceeds. The goal is predict the winners and win the pot, not to vote for your favorite in each category. The predictions are then aggregated, allowing for a comparison between the collective vote (defined as the vote occurring most frequently) and the vote of each individual. The most recent results of this experiment revealed that the collective vote correctly named 11 out of the 12 winners, an amazing predictive outcome. The best individual student named only 9 out of 12 winners and the average student guessed only 5 out of 12 winners. In this case, the collective was significantly better than average and even better than the best individual. Mr. Mauboussin’s results have been consistent year after year. This concept is known as the wisdom of crowds and it is a well researched area with very interesting and practical applications 1. The basic idea of the wisdom of crowds is that under certain conditions, the collective is smarter than the average person within the collective.
There are three primary conditions that must be satisfied in order for the wisdom of crowds to work;
- the presence of an aggregation mechanism bringing information together,
- the presence of incentives,
- diversity of opinion.
Looking at the first two conditions in the context of the stock market, (1) by definition the stock market is an aggregation mechanism, in that market participants complete stock trading over exchanges and prices are widely available, (2) the stock market provides monetary incentives for accurate predictions. Dealing with the third condition, diversity of opinion, is the most interesting.
In his book, “The Difference”, Scott Page presents the “diversity prediction theorem” which states that Collective error = Individual Error – Prediction Diversity. This basically states that the accuracy of the collective in making a prediction is made up of two parts. The first part is the accuracy of the individuals within the group. The second part is the degree of diversity within the group. The more diversity within the group, the more accurate the collective’s prediction will be. The implication of this theorem for collective accuracy is that diversity plays an equally important role as the ability of each individual. Relating this to the stock market, in order for stock markets to be efficient (ie prices that are reasonable estimates of fair value), there needs to be diversity of opinion amongst participants. It is this third condition that is most likely to be violated.
When diversity of opinion breaks down, market participants act in a coordinated manner with one view dominating the collective. In the extreme, the technology bubble and the effect on market valuations was one example of diversity breakdown. The credit crisis also saw two instances of diversity breakdown. One before the crisis – that housing prices would not decline, and one in the middle the crisis – that we were headed for another great depression. Common to all diversity breakdowns are a disconnection between expectations and fundamentals. In some cases the breakdown is extreme and obvious, in others it is more subtle. It is the more subtle breakdowns that require careful analysis to recognize.
The outcome of a stock’s return is probabilistic in nature. Any probabilistic system has a random component and a signal. For example, if you flip a coin hundreds of times, you would see 50% heads, 50% tails as a signal. After only 20 trials, however, it is highly probable that the percentage of heads will only be about 35%. If you were to extrapolate this short term outcome (noise), you will make an error and forecast inaccurately. If you were more focused on the signal, you would make predictions more accurately allowing you to confidently ignore the noise.
To make this analysis a little more practical, I will use an example. During the credit crisis, Royal Bank shares touched a low of $25.52 on Feb 4, 2009 (down from its peak of $61.08 in the summer of 2007). Using our models, we can estimate the embedded expectations that are contained in stock market prices, including the market’s expected long term return on equity (ROE) of a business. Based on Royal Bank’s price of $25.52, the collective wisdom of the stock market was estimating the long term ROE of Royal Bank to be around 9.0%. Was this a signal or just noise?
Since 1969, Royal Bank’s ROE has averaged about 16%. In the 10 year period ended 2008, (the only data the market had at the time) Royal’s average ROE was slightly under 20%. Was the market’s estimate of Royal Bank’s long term ROE of 9% reasonable (a signal) or was it noise? Royal finished the year 2009 reporting a 15.2% ROE. Against one of the worst economic backdrops in a generation, Royal’s fiscal 2nd quarter, February-April of 2009, the bank produced an ROE of 12.3%, the lowest level it recorded during the crisis. The consensus view in February 2009 was bleak and almost unanimous. The market’s 9% long term ROE estimate at its lows was not even recorded in a single quarter during the crisis. Royal Bank trades around $60 as I write this.
How magnetic is the pull of the consensus view? A double edged sword of the diversity prediction theorem is the impact of deliberation. If people share their information and criticize one another’s models, they can increase the accuracy of their models. However, they can also reduce their diversity. An experiment conducted by Solomon Asch, shows how easily people will abandon accurate models for inaccurate, but popular models2. Participants were asked to compare the lengths of several lines, A, B, C compared to a reference line. Subjects were asked which lines were longer, shorter and the same length as the reference line. The first subjects were planted by Asch and confidently gave wrong answers. Asch found that others follow the majority – giving wrong answers – about 1/3 of the time and 75% of subjects gave at least one wrong answer.
This is just one of many examples where otherwise rational people abandon their beliefs to follow the opinions of the majority.
The stock market is an incredible aggregator of the opinions of its participants. These opinions are expressed in the prices they are willing to buy and sell businesses every day. During periods when diversity of opinion is high, it is probable that the market is generally efficient. However, under certain conditions the market is inefficient. It is during times of diversity breakdown that yield the most extreme market events and provide the most opportunity to investors that are intensely focused on the signals provided by the market and not the noise.
Brian Durno, CFA
JDM Investment Partners Ltd.
Manager of The Investment Partners Fund
1 For a more rigorous review of the Wisdom of Crowds concept, see Michael Mauboussin,
“The Wisdom and Whims of the Collective”, CFA Institute Conference Proceedings Quarterly,
CFA Institute, December 2007.
2 Asch, S.E. (1956). Studies of independence and conformity: A minority of one against a
unanimous majority. Psychological Monographs, 70: 416.