You may have noticed that the questions are framed so that one has positive expected value (if you flipped enough coins you should come out ahead) and one has negative expected value (flipping more coins will not help you here as the odds are stacked against you in every scenario). First lets take a look at question #1 and see how you did.

## Expected Values for Prospect Theory Question #1:

50% * \$300 + 50% * -\$200 = \$50

50% * \$75 + 50% * \$0 = \$37.50

100% * \$35 = \$35

If you picked the first answer, congratulations! That means you either made a rational decision to take the choice with the highest expected value over time or you simply like higher risk activities such as jumping out of airplanes. If you picked the third answer, don’t fret, this just means that you don’t like risking money when you can have a sure thing. Remember that the wider the range is between the best and worst outcome, the higher the risk (the first answer has a range between -\$200 and \$300 (\$500) which makes it the highest risk answer while the third answer has a range of \$0 and therefore it has no risk).

If you picked the third answer, it turns out that you are not alone. Daniel Kahneman and Amos Tversky found in their Nobel Prize winning paper “Prospect Theory: An Analysis of Decision under Risk” that when given the choice between two scenarios with positive expected value, people tended to chose the less risky outcome or the “sure thing” over a riskier bet even though the riskier bet had a higher expected value.

A rational gambler should always take the bet that results in the highest expected value because he knows he will flip the coin many times and eventually he will win more money over time. Despite what appears to be the “rational” course of action, people tend to behave quite differently in reality, which leads to the realization of lower expected value. Relating prospect theory to the stock market, people tend to sell winning stocks too early because they want to “lock in a gain” or a sure thing even through the odds of the stock going even higher may be greater than 50%.

## Expected Values for Prospect Theory Question #2:

50% * -\$100 + 50% * \$20 = -\$40

50% * -\$60 + 50% * \$0 = -\$30

100% * -\$25 = -\$25

While Kahneman and Tversky found that most people chose to take the sure thing when given scenarios with positive expected values, people tend to do the exact opposite when given scenarios with negative expected value. If a person must choose between a guaranteed loss and the chance of breaking even, they will more likely take the chance not to lose anything even when taking the guaranteed loss would result in a higher expected value.

You may have realized at this point that something seems off; people tend to take the low risk bet when given the option to make money and the high risk bet when they must lose money. Now you are seeing prospect theory in action.

As it pertains to the stock market, the negative side of prospect theory results in investors holding onto losing companies because they would rather take the chance that the stock rises back to even than sell the stock and take a definite loss.

Prospect theory is often represented by a graph (left) that shows how people’s utility (happiness derived) from gains become less and less as they gain more money while the greater the losses become the less happiness they lose by losing more money. When given a set of options it’s rational to select the option that returns the highest value over time, yet Kahneman and Tversky’s paper shows that people tend to be motivated by their own happiness instead of strict monetary gain (expected value). For this reason, prospect theory is dubbed a behavioral bias, meaning that human behavior, in this instance, does not reflect rational action.

## How does prospect theory affect investing?

Prospect theory provides reasoning to why people tend to sell their winning investments too early while holding onto losing investments. Once the pain of losing money sets in (the money is already lost) it becomes easy for us to gamble on getting back to even. We think: “It will probably get back to what I paid for it eventually and I will be angry with myself if I sell it here if I could have sold it at a higher price”. Can you see the irrationality of this argument? Instead of hoping the investment will return to it’s former value so you can avoid the pain of losing money, you should be assessing the probability that the stock falls versus the probability that it rises.

On the flip side of this argument, prospect theory results in selling investments too early because the happiness gained from a further rise in the stock does not outweigh the fear that the stock will return to it’s original value. If you have tried your hand at buying and selling stocks or even mutual funds/ETFs then you probably know that joyous feeling you get when your stocks are up. Chances are you also have felt the sinking feeling of defeat when your stocks fall in value. Investing evokes all sorts of emotions which may turn into emotional biases that are hurting your investment performance.