Mental Models for Handling Risk and Uncertainty
Indicate your preferred choice for the two hypothetical scenarios below:
Scenario 1: Would you rather?
- A: Get 5$ for free.
- B: Flip a coin. If it lands heads, you get 10$. If it lands tails, you get 0$.
- C: Not play this game in the first place.
Scenario 2: Would you rather?
- A: Get 100$ for free.
- B: Have a 95% chance of doubling your current net worth and a 5% chance of losing it all.
- C: Not play this game in the first place.
Scenario Analysis
Scenario 1
Scenario 1 truly gets at the essence of risk. There is zero risk if you decide to go with option A. You have a 100% chance of getting 5$. In a sense, you have zero risk with option B as well. You can’t lose money. The worst outcome is that you walk away with nothing.
I don’t like this way of thinking about it. Given that we’d lose a guaranteed 5$, I think it’s more valid to consider option B as taking a risk to obtain a larger reward. If that doesn’t seem right to you, consider the following variant of scenario 1.
Does it make sense to take that risk? Five million dollars is a life-altering amount of money for most people. The difference between being an average-income earner and a 5-time millionaire is massive compared to the difference between being a 5-time millionaire and a 10-time millionaire. This thought experiment illustrates the decreasing utility of money.
According to the expected value theory, both options are equivalent in terms of how much you would end up with if you played this game an infinite number of times. The difference between the options lies in their variances. Generally speaking, it makes sense to avoid the roller coaster ride and chose the option with the lowest variance when faced with equal expected value options. This is especially true when the guaranteed option provides the desired outcome.
Scenario 2
In scenario 1, both options have the same expected values. In scenario 2, however, the riskier option B has a greater expected value than the safer option A (assuming one’s net worth is above 112$). The expected value of option A is 100$ with a variance of zero. Option B has an expected value of (x)*0.95+(-x)*0.05=0.9x. In order words, choosing option B would result in an average gain of 90% of our current net worth in the long run. That is a sweet deal! Or is it?
The 5% chance of ruin means you could expect to lose everything you own roughly 1 in every 20 times you chose option B. The catch is that losing everything you own would not only negatively impact your life, but it’d also prevent you from being able to participate in the option B game moving forward. Two times zero is zero. You must avoid the chance of ruin at all costs.
Depending on your current net worth, need for money, risk tolerance, and capacity to bounce back from losing it all, it might make sense to take option B.