Utility Theory and Prospect Theory

Updated: 5 days ago

If you read our previous article on the Utility Theory, you may be asking yourself, how does it tie into investing?


Risk and Return


It introduces risk and return since due to its direct relationship, there are trade-offs. Depending on how much cash the investor is willing to shell out, risk aversion can differ. Someone who has little wealth will be much more risk tolerant because they have a limited amount of money and are seeking higher returns to get more capital. Someone who has more wealth will be more risk averse because they already have capital.

The risk averse graph on the left (in red) represents the diminishing marginal returns as wealth increases. This makes sense since the graph is concave as the individuals who are risk averse look for higher expected returns to offset any possible loss they might incur.


The investor who is risk-neutral is in the middle (in blue) does not experience any form of concavement as they only seek for returns.


The individual who actively seeks out risks is on the far right-hand side (in green) and demonstrates increasing marginal utility for each accumulation of wealth. Notice how the graph on the far left is concave while the graph on the far right is convexed.


The Utility Theory and the Traditional Finance Theory


Since the Utility Theory originates from the Traditional Finance Theory, the two share many of the same rationales. Two of the core ideas that have transferred over from the latter to the former is that one, people make calculations based on information that is presumed to be accurate to weigh their investment outcomes and two, all investors are risk-averse.


The Prospect Theory


Meanwhile, the Prospect Theory which is based on the Behavioral Finance Theory, says randomality plays a huge role and that investors value gains and losses very differently. As a result, loss aversion is a bias of the prospect theory. Because of this different approach towards gains and losses, as well as what is happening in the market, this can lead to very different behaviors.


The Prospect Theory replaces utility maximization and instead, substitutes it with loss aversion. To recap, loss aversion refers to people’s tendency of weighing losses more heavily than gains. In short, people care significantly more about the loss of $15 dollars than a gain of $15 dollars.


The Prospect Theory highlights the correlation between the analysis of risk that is relevant to our outcomes. Losses should be avoided at all times and when we have gains, we are oftentimes less likely to continue pursuing gains because we are scared of coming across a loss.


For example, if Paul has already lost money whether it be due to poor risk management or inadequate research, he will have a tendency to hold onto his investments.


Why?


Because according to loss aversion, he is hoping that his shares will rise again. If his shares bounce back, he will be able to avoid an unwanted loss. Another reason is because a loss on paper does not exactly signal a loss in reality. Because Paul is choosing to hold onto his poor performing investments, he is playing a dangerous game.


But on the other hand, if Paul is making money based on his investments, he will do the exact opposite. He will sell to avoid a loss, which leads to selling winners too early on. The graph below manifests the relationship between the Utility and Prospect Theory.



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