You must have heard or read these couple of lines at some time or the other: Toss a coin three times and you get heads all three times. As you prepare to toss it up the fourth time, what crosses your mind? "This time, it should be tails because the last three were heads  now tails is due". If that's what you thought, you made a logical error  the probability of tails the 4th time around is exactly the same as it was for the first three tosses  50%. Outcomes of the first 3 tosses do not influence the 4th toss.
Gamblers fallacy
One person who seems to have mastered the art of calling tosses correctly is Mahendra Dhoni  maybe we should ask him what logic he uses! Be that as it may, this logical fallacy of calling tosses based on previous outcomes  also known as "gambler's fallacy"  was taken to an interesting new level by Larry Swedroe in his book, "Rational investing in irrational times". Here is an interesting extract from the book.
"Each year a statistics professor begins her class by asking each student to write down the sequential outcome of a series of one hundred imaginary coin tosses. One student, however, is chosen to flip a real coin and chart the outcome. The professor then leaves the room and returns in fifteen minutes with the outcomes waiting for her on her desk. She tells the class that she will identify the one real coin toss out of the thirty submitted with just one guess. With great persistence she amazes the class by getting it correct. How does she perform this seemingly magical act? She knows that the report with the longest consecutive streak of H (heads) or T (tails) is highly likely to be the result of the real flip. The reason is that, when presented with a question like which of the following sequences is more likely to occur, HHHHHTTTTT or HTHTHTHTHT, despite the fact that statistics show that both sequences are equally likely to occur, the majority of people select the later "more random" outcome. They thus write imaginary sequences that look more like HHTTHTHTTT rather than HHHTTTHHHH."
The statistics students in this example were perhaps trying to be too logical, when in fact randomness and not logic governs the outcomes. The main mistake that we make in such cases is that we bring in long term probabilities to forecast short term outcomes. We know that if you toss a coin 1000 times, the probability of getting heads and tails are both 50%. But if you toss it 4 times, can you say that the most likely outcome is 2 heads and 2 tails?
Hot hand fallacy
A variant of gamblers fallacy is "hot hand fallacy"  a mistaken belief that if someone is having a great run, the run will continue. Origins of this behaviour were traced back to the game of basketball, where teams that saw a player score twice or thrice in quick succession, believe that he is on a great run  he has a "hot hand"  and therefore keep passing the ball to him to shoot  believing that his current run makes him the best person to take the shot at the basket. Several studies revealed that the "hot hand" does not give the team any better chance of scoring.
Have your clients fallen prey to hot hand fallacy?
Hot hand fallacy is what many stock market investors must be going through now. The last 15 months have been great in the stock market  particularly in mid and small cap stocks that see a lot of retail interest. An investor who invested tentatively in a couple of small cap stocks 12 months ago, now considers himself as an ace stock picker, after 3 of his bets came good. His confidence is soaring, his investment time horizon is shrinking rapidly and you watch the investor transform into a trader.
How do you, as his advisor, help him protect his gains and not get too reckless in this bull market? Is it right to advise him to stop trading when he thinks he is on a winning streak? Will he listen? Will you put down his winning streak only to luck, which will inevitably run out?
Its not always only luck
The Economist carried a fascinating story that is food for thought for every advisor when faced with this dilemma. Here is an extract from the article that appeared in the 10May2014 edition.
"Using the power of the internet to round up a huge sample, the two researchers examined 565,915 bets made by 776 people on sports such as horseracing and football. Because these were online bets their timing could be established precisely. Ms Xu and Dr Harvey looked at winning and losing streaks up to six bets long.
The probability of a first bet winning was 48% and that of a followup winning again was 49%. After that, the streak took off. The third bet won 57% of the time. The fourth, if the third had won, won 67% of the time, the fifth, 72% of it and the sixth 75%. As for the losers, after ploughing their first bets, their success with their second slipped to 47% and thence held at 45%.
The explanation of the puzzle, Ms Xu and Dr Harvey found, was not that Lady Luck actually does smile on winners and frown on losers. Rather, as winners' winning streaks increased in length they started choosing safer and safer odds, which led them to win more often, though less profitably. In contrast, those who had experienced a losing streak went for ever riskier bets, making it more likely the streak would continue."
How to help clients through hot hand fallacy
This research holds a key to how you may want to help clients who think they have a "hot hand" in this bull market, and that everything they touch will now turn to gold. If you find clients having made good profits on a couple of trades in small cap stocks, encourage them to invest at least the profits into either bluechip "all weather" large cap stocks or into a diversified equity fund, while they continue to invest the original capital in the quest for the next potential multibagger. The money is still in the equity market, but like the researchers showed, it is prudent to choose safer odds when you are in the money.
All content in MasterMind is created by Wealth Forum and should not be construed as an opinion of Sundaram Mutual Fund.
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