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Would you play this game?

A coin is unfair in the sense that it will land on heads 53 percent of the time. If the coin lands on head, then I will give you $10. Otherwise, you will have to give me $10.

While the expected return of this game is positive for the player ($0.60), most people will not play this game. Why is that? Behavioural scientists, Daniel Kahneman and Amos Tversky suggested that on average we experience pain from losing $10 twice as intense as the pleasure generated from winning $10. Roughly speaking, the odd of winning has to increase to 67 percent of the time before most people will start playing the game. This fear of loss, is known as loss aversion.

To demonstrate this idea of loss aversion, Antonio Damasio and George Loewenstein devised a clever investing game, which they played with three different groups of participants. The first group had suffered damage to part of their brain linked to emotion. The second group had suffered damage to non-emotional brain. And the third group was a control group.

Each participant was given $20. In each round, the participants can choose between two options: invest $1 or invest nothing. If they decide to do nothing, they keep the dollar and advance to the next round. If they decide to invest, they would hand in a dollar to the experimenter. A fair coin is tossed. If a head is landed, the participants will lose that dollar invested; otherwise, $2.50 will be given to them. The game stopped after 20 rounds.

Observe that the expected return is a gain of $0.25 for each round, so the rational thing to do is to play every round. What did the third group do? They played the game 58 percent of the times, earning an average of $22.80. On the contrary, the participants with emotional impairment played 84 percent of the time, earning an average of $25.70. Damasio and Loewenstein observed that fear seems to play a crucial role in making decision. In fact, the fear of losing is so great in the control group that their willingness to play the game dropped dramatically immediately after losing the last round.

So, what is a consequence?

A simple fact of life that many people don’t realise is this: We don’t play this type of game just once. We play this type of game repeatedly. And this has a long term consequence. Go back to the original game. If you play once, your chance of coming out positive is 53 percent. If you play 20 times, that chance increases to 68.9 percent. If you play 252 times, that chance improves to 84.5 percent. Now, imagine playing it 2520 times. The odd of losing is down to 0.12 percent! Further, expected gain for your account will be $1512!

Why do I use these numbers?

In Markets Never Forget (But People Do), Ken Fisher analysed the index that tracks the top 500 companies in the US (or S&P 500 index) from 1926 to 2010. This is what he found.

  • A chance of having a positive daily return is 53.0 percent.
  • A chance of having a positive monthly return is 62.3 percent.
  • A chance of having a positive yearly return is 72.9 percent.
  • A chance of having a positive 10-yearly return is 94.0 percent.
  • A chance of having a positive 20-yearly return is 100.0 percent. That’s right. Even if you invest at the blink of Great Depression, you will still come out on top 20 years later!

Imagine investing like playing the above game. Each round last for one day. There are roughly 20 trading days in a month, and 252 trading days in a year. Compare previous numbers and those of Fisher’s, and we can see that they are in the same ballpark.

The key lesson from this is that by refusing to take part in a game that have low positive expected gain because of loss aversion, you are refusing yourself from large future gain. The more times you play the game, the more certain you are of achieving positive gain. When face with this type of decision, ask yourself: will I play this type of game once? If not, then always play it. After all, from small things big things grow.

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