Let's say you enter two lotteries with a chance to win $250. In one, you have a 5% chance of winning; in the other, you have a 30% chance. Now let's say you're faced with two scenarios:
- You can improve your chances of winning the first lottery from 5% to 10%.
- You can improve your chances of winning the second lottery from 30% to 35%.
Which one seems like the more significant change?
Even though they're both the same in terms of the actual change, most people consider the first option to be more significant. Why? And, more importantly, how does that affect your finances?
One of the keystone theories of behavioral finance is prospect theory, first identified by Daniel Kahneman and Amos Tversky. These researchers found that people uniformly violate the classic economic models of decision making under risk: namely, we tend to feel the pain of loss more than we feel the pleasure of gains, and we don't make decisions based on pure probability. Instead, we assign "weights" to various outcomes that are based on our perceptions of those probabilities.
Those perceptions, as you have probably guessed, aren't always in line with reality.
For example, for most people the difference between a 5% and 10% chance is much larger than the difference between a 30% and 35% chance.
Take another example: If you had a 5% chance of losing $10,000 or a 100% chance of losing $501, which would you choose? According to standard economic theory, you should pick the 5% risk because the expected value is lower (the usual method of weighting would be to multiply the probability by the value of the loss, which gives you $500).
However, in experiments most people pick the sure loss. In other words, they overweight the small risk. Similarly, when given the option between a 5% chance of winning $10,000 (expected value $500) versus a sure chance of winning $501, they tend to take the risk. At a low probability we're too concerned with low probabilities and not concerned enough with high probabilities.
It looks kind of like this:
If we're thinking "purely" rationally, we should give an equal weight to each probability -- a 5% chance should be considered a 5% chance, and a 95% chance should be considered a 95% chance. In reality, we tend to overweight the low probabilities, meaning in our heads they are more important or of greater value than they actually are, and we underweight high probabilities.
The economic fallout
What does all this have to do with finance? Consider the case of insurance.
For example, we tend to be a bit overeager in buying insurance for items such as cell phones. If your relatively inexpensive cell phone has a small chance of breaking, it almost certainly doesn't make sense to insure it. But electronics insurance is a very brisk and profitable business for electronics stores. In this case, we're overweighting and thus overinsuring against a low-probability and low-cost event and being overly risk averse.
Similarly, it's common for retirees to hold life insurance policies rather than annuities. As we age in retirement, the benefits of life insurance decrease and the costs increase. After all, the probability of cashing the policy only rises over time. Death in retirement is a high-probability and low-cost event -- especially when compared to death in one's 40s or when the children are young. In other words, retirees are risk-seeking in terms of the potential gains of a life insurance policy when they would generally be better off reducing the risk of outliving their savings by buying an annuity.
These are just two areas where our perceptions of risk mess up our analyses of it. While your iPhone insurance might not set you back so much, the cost of underinsuring your older age (or underinsuring yourself in your working years) could come at a very high price indeed.
For better decision making, realize that your perception of risk might be affecting your calculation of it. Instead of just going with your gut, think about the probabilities involved and the numbers involved -- even if you're just estimating, this will help dial back some of the decision-making biases that could be affecting your judgment.