Traditional financial theory assumes that investors are rational and utility maximizing. Utility here is a wider concept than just profit, as it can include non-monetary value. For example, an ethical investment could generate a lower return but increase utility for certain individuals.
According to Expected Utility Theory (EUT), an investor will base their decision on the expected utility of different outcomes, and choose the option with the highest expected utility. The expected utility is equal to the probability of the outcome, multiplied by the utility the outcome gives. To keep it simple, I will assume that investors are only investing to maximize monetary profit, i.e. money = utility, the more money, the more utility.
To give an example, if an investor has two investment options to choose between:
The investor will probably choose Investment A, as it has the highest expected value of $500, compared to Investment B that has an expected value of $400 (as 50% x $1,000 = $500, and 20% x $2,000 = $400). Makes sense, doesn’t it? And you got the math too? Awesome, then let’s play around a bit…
Below I give you four bets. You have to choose between A or B for each bet, and if I contact you tomorrow and ask you to honor your bets, you’ll have to do it (I won’t, but that’s how serious I want you to consider them).
Please choose A or B and note it down.
In addition to however much money you have, I give you $10,000, now choose between:
Note down your answer.
In addition to however much money you have at the moment, I’m being even more generous and give you $20,000, now choose between:
Note down your answer please.
Please choose A or B and note it down.
Have you noted down all your answers?
Ok, then scroll down and learn more about your rationality.
In Bet 1, A has an expected value of $50 and B has an expected value of $0. If you’re as described in EUT you should go with A. However, most people go with option B, and the reason for that was explained by Kahneman and Tversky in 1979.
They found that losses hurt more than gains give satisfaction. On average studies have concluded that a loss is about twice as painful as an equal gain which makes you feel as good, i.e. a loss of $50 can feel as bad as a gain of $100. This leads to people trying to avoid losses, i.e. they are loss averse.
Risk Seeking in Losses
In Bet 2 and 3, all choices have the expected outcome; that you walk away with $15,000 in your pocket. In Bet 2 you were given $10,000 up front, and both A and B have an expected value of $5,000. Indifferent of your choice, you’re expected to walk away with $15,000 in your pocket.
In Bet 3 you were given $20,000 up front and both A and B have an expected value of you actually losing $5,000. No matter your choice, again you’re expect to walk away with $15,000 in your pocket.
So, in both Bet 2 and 3, a rational person should be indifferent to A and B, as they have the same expected outcome. However, most people tend to prefer option A in Bet 2, i.e.to get $5,000 with 100% certainty, and A over B in Bet 3, i.e. 50% chance that you lose $10,000 and 50% chance that you get $0.
The only difference is the ‘framing’: Bet 2 is framed as a gain and so people tend to be risk averse and go with A; as you get $5,000 for sure and give up the 50% chance in option B to win $10,000. Bet 3 is framed as a loss and so people tend to be risk seeking, i.e. choosing A to take the 50% chance of not losing anything at the risk of losing $10,000, rather than just taking a $5,000 certain loss.
People tend to again prefer option A over B in Bet 4 even though the expected value is exactly the same; $5. Because $5 isn’t that much money and there is a chance that you’ll win $5,000. You don’t really care about 5 bucks when you see there is an opportunity to win 5 grand! Kahneman and Tversky (1992) found that people tend to overweigh small probabilities and underweigh large probabilities.
So How Rational Are YOU?
You might already have suspected that you aren’t always rational, or you may think that you’re rational but know that people in your surroundings aren’t. In fact, rationality depends on how we define it. I won’t give you a definition of what being a rational individual is right now, I won’t even try.
My only wish with this post is that if you didn’t do it before, begin to question rationality as it’s defined by traditional financial theory and expected utility theory. By doing that, in my view, you have ‘become’ more rational.
And so then, you will also consider how many financial models—which are still used today—rely on traditional financial theory. Which will lead you to maybe question their reliability and accuracy; and that I believe, makes you become a better investor.
Article by Alexander Wetterling, Become A Better Investor