Loss aversion

The previous example is a problem I’ve described in a free risk management awareness course, and from about 3,000 people who have taken the course to date, about 78% of them selected the first game. Is that the best choice?

Let’s see what the expected value of each option is:

• Game A: 50% × €200 + 50% × -€0 = €100
• Game B: 50% × €600 + 50% × -€200 = €200

The expected value of the second option is twice as much as the first one. This means that if we play the games thousands of times, we can have a good level of confidence that the output of the second game would be about twice as much as that of the first one.

It’s relatively simple to think of these games when they are played thousands of times, and I think not many would object to selecting the second option in that case. The problem is that I said we’re going to play this game only once. So how should we reason about it when it’s played only once?

The answer is simple: This game is played once, but we’re playing thousands of games like this in our work and our life. If our strategy is to pick the higher expected value, we may lose some of them, but overall, we’d be the winners. There is, however, an exception to this strategy: Picking the higher expected value is a good idea if it fits within your risk appetite. In other words, if all you have is €200, you should go for the first option, no matter what the expected value of the second option is. This is because the utility of money is not linear.