In a coin-tossing experiment that was rigged to give a 60/40 probability of winning, 60 per cent of financially sophisticated players managed to lose money.istockphoto/Getty Images/iStockphoto
Most investors are aware that when they move into the financial markets they are dealing with decision-making under uncertainty. As a result, a great deal of time and money is devoted to analysis and research in the hopes of reducing that uncertainty and improving the quality of decisions. Not all investments unfold according to plan, of course, but we tend to assume that with more or better research, mistakes could be avoided.
But, what if the error did not arise from a poor calibration of the uncertainty, but from poor execution of the investment decision once it is made? A recent article in the Social Science Research Network (SSRN.com) suggests that even when we know with certainty the probability and size of the payoff, many of us still manage to lose money.
The authors, Victor Haghani of Elm Partners and Richard Dewey of Pimco, set up an experiment with 61 subjects who bet on a simulated coin-flip game where they were told explicitly that heads had a 60-per-cent chance of occurring. They were also given a $25 (U.S.) pot to start, were told they could wager any amount in increments of 1 cent and that the game would last for 30 minutes. The subjects were primarily finance and economics students, plus young professionals at finance firms. The opportunity to play a reward-based game biased in your favour for an extended period should have been irresistible.
With these facts at our disposal, the obvious strategy is to bet on heads every time. The only tricky issue is how much of your increasing fortune you should bet on each flip so as to avoid losing all of your money on the non-trivial possibility of a run of tails. Fortunately, there is a simple formula to address the second decision: It is the Kelly criterion, developed by John Kelly at Bell Labs in 1955. It considers the probability of a successful outcome (heads) and the expected payoff. You can look it up on Wikipedia or elsewhere, but the answer in this situation is that you should bet 20 per cent of the pot on every flip.
Needless to say, the participants in this experiment did not cover themselves with glory. The maximum payout was capped at $250 because a nimble player using the Kelly criterion could theoretically amass a fortune of more than $3-million in 30 minutes. Only 21 per cent of participants reached this goal. One third of the players finished with less money in their account than what they started with, and 28 per cent went bust. In other words, in a game that was rigged to give a 60/40 probability of winning, 60 per cent of financially sophisticated players managed to lose money! The unsuccessful players made a series of errors that are familiar to us as investors: betting the entire pot on a single flip, betting on tails after a run of heads in the belief that it was time for a reversal, and varying the size of the bet erratically. The authors concede there is a world of difference between flipping a coin for 30 minutes when the entire fund at risk is $25 and investing your entire savings in the stock market over a 30-year period, but there are some lessons here for the individual investor.
First, the regulators and investment industry commentators who think that more education is the solution to poor investor outcomes may be disappointed. The participants in this experiment were already far more financially literate than any part-time investor with a full-time job and they still fell prey to the usual behavioural biases of a retail investor.
Second, although the Kelly criterion indicates that betting 20 per cent of the pot is the optimal strategy in this situation, a simulation using 10 per cent and 15 per cent of the total as a constant proportion worked almost as well. So, the exact amount of our market exposure to a specific investment is less crucial than the emotional fortitude to stick with the strategy when the market is moving against you.
Finally, if you have been investing for some time, it would be helpful to look back over several years of statements to develop an informal sense of your predictive ability. According to the Kelly formula, the higher your confidence in the predicted outcome and the greater the ratio of potential gain to loss from the investment, the larger the position in your portfolio. You already knew that, of course. What you now need to develop is a realistic assessment of your ability in these two areas so that the formula output is a useful tool and not simply a reaffirmation of your adviser's perennial optimism.
Robert Tattersall, CFA, is co-founder of the Saxon family of mutual funds and retired chief investment officer of Mackenzie Investments.