Bernoulli's Hypothesis: What it Means, How it Works

What Is Bernoulli's Hypothesis?

Bernoulli's Hypothesis states a person accepts risk not only on the basis of possible losses or gains, but also based upon the utility gained from the risky action itself.

Understanding Bernoulli's Hypothesis

The hypothesis was proposed by mathematician Daniel Bernoulli in an attempt to solve what was known as the St. Petersburg Paradox. The St. Petersburg Paradox was a question that asked, essentially, why people are reluctant to participate in fair games where the chance of winning is as likely as the chance of losing. Bernoulli's Hypothesis solved the paradox by introducing the concept of expected utility and stating that the amount of utility from playing a game is a significant factor in whether or not to participate.

Bernoulli's hypothesis also introduces the concept of diminishing marginal utility gained from having increasing amounts of money. The more money a person has, the less utility they gain from getting more money. This will make a person who has won several rounds of a game and gained additional money less likely to participate in the future as the utility factor is no longer present even though the odds have not changed. 

Bernoulli's Hypothesis in Finance

Bernoulli's Hypothesis can be applied to the financial world when looking at an investor's risk tolerance. As the amount of money a person has grows, the person may become more risk-averse (despite their ability to take on risk increasing due to their increase in capital) because they are experiencing diminished marginal utility with every extra dollar earned. Since they no longer feel the sense of utility from their gains, they no longer want to play the risky game. Rationally speaking, there is no reason to stop playing a game that has fair odds. Put another way, there is no reason to stop investing at the higher end of the risk and reward spectrum in order to maximize returns. In practice, however, the amount of money that can be won/earned is no longer worth it for a person eventually as the utility of each dollar decreases as you have more than enough of them.

Related closely to the idea of diminishing marginal returns, Bernoulli's hypothesis essentially states that one should not accept a highly risky investment choice if the potential returns will provide little utility or value. A young investor who still has their highest income-earning years ahead can be expected to accept greater investment risk, as the potential returns could be very valuable compared to such a person's relative lack of wealth. On the other hand, a retired investor with ample savings already in the bank should not be looking for a highly volatile or risky investment, as the potential benefits are unlikely to be worth the risk.