Here we explain the concept and reasons of the games on our risk tool introduction page.
This series of games were modified from Christoph Hauert’s “Gamelab”. These games themselves originally were formed to question the expected utility theory in economics. Here we used them to show how irrational people’s behaviors are when it comes to dealing with risk.
The first set of questions is called Allais paradox, designed by Maurice Allais.
Please choose between:
• A: A chance of winning $40,000 with probability 0.2 (expected value $8,000)
• B: A chance of winning $30,000 with probability 0.25 (expected value $7,500)
Now please choose between:
• A: A chance of winning $40,000 with probability 0.8 (expected value $32,000)
• B: A chance of winning $30,000 with certainty.
A rational risk averse person would choose B for both questions while a risk lover would choose A for both questions. Surprisingly, empirical data shows most people pick A for the first question, then B for the second, which shows inconsistency when facing risk or risk-free opportunities. Our risk tool help analyze the risk level of your portfolio, no matter how risky the underlying assets are.
The second set of questions is called Preference Reversal. This game was proposed by cognitive psychologists and studied by many economists. It shows the anomaly when people make choices under a losing or depressing environment.
Now please choose between:
• A: Obtaining $2,400 with certainty (expected value $2,400)
• B: A chance of winning $10,000 with probability 0.25 (expected value $2,500)
Now please choose between:
• A: Losing $7,500 with certainty (expected loss $7,500)
• B: A chance of losing $10,000 with probability 0.75 (expected loss $7,500).
Again for both questions, a risk averse person would choose A and a risk lover would choose B. Survey data shows most people choose A for the first question then B for the second. That’s where the anomaly lies when people face the same losses as gains. In a losing situation, people tend to forget about the risk and take chance to avoid losses. As investors, we need to keep track of the underlying risks all the time and make the rational move. That’s where our risk tool helps.
The next question is essentially a combination of the choices from preference reversal,
• A: Obtaining $2,400 with certainty, at the same time a chance of losing $10,000 with probability 0.75
• B: A chance of winning $10,000 with probability 0.25, at the same time losing $7,500 with certainty.
In this case, most people choose the rational choice B, which is really a combination of 1B and 2A of the previous two questions. That’s clearly a better choice than 1A and 2B, which most people chose when asked separately.
The last set of questions also tests on gaining vs losing.
Now assume you are given $3,000. Please choose between
• A: a sure gain of $1,000.
• B: a 50% chance to gain $2,000.
Now assume you are given $5,000. Please choose between
• A: a sure loss of $1,000
• B: a 50% chance to lose $2,000
Also in both scenarios people with choice A will end up with $4000 and people with choice B will end up with either $3000 or $5000 with a 50-50 chance. Interestingly, most people tend to pick A for the first scenario and B for the second, which again shows how our mind works differently when seeing the word “lose” from seeing the word “gain”.
These questions are not set up to trick you, but rather to show the human nature and how our rationality works dealing with risks. That’s why we design this risk tool, for people to monitor the risk in their portfolio objectively. By knowing the current risk level, investors will be able to make more rational decisions and not fall into the fallacy of our human mind sets.
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