# Modelling (Ir)rational Behavior

Suppose, you are currently making \$80k/year and net worth of \$300k. So, let’s play a hypothetical game. You choose from the following at no cost to you: 1) I give you \$10MM right now (100%) 2) I flip a fair coin,(50%) heads you get \$30MM, (50%) tails you get nothing. You can NOT trade this game (sell the right to someone else). What do you choose and why?

1 even though the rational answer is 2. Before you ask, not sure how its possible to model this irrational behavior as it would be based on case by case subjective risk adverseness.

king_kong Wrote: ------------------------------------------------------- > 1 even though the rational answer is 2. Before you > ask, not sure how its possible to model this > irrational behavior as it would be based on case > by case subjective risk adverseness. I agree. The question now becomes, suppose you COULD trade this. What would a buyer of this option be willing to pay, today? If this game was played before the bubble burst early 2007…what do you think a buyer of this option would be willing to pay?

Even though the expected return on 2 is higher, I would be shocked if anyone making \$80K a year doesn’t choose 1. The more appropriate question would be: Net worth: \$15MM 1)You lose \$10MM right now (100%) 2) I flip a fair coin,(50%) heads you lose \$30MM, (50%) tails you lose nothing. You would see varying answers under that scenario.

Sorry to break it to you, but either outcome can be rational, depending on your marginal utility towards money. For instance, let’s say I offer you \$100 billion for sure or a 50/50 chance of getting \$201 billion. I would take the \$100 billion, since my marginal utility from my current wealth to \$100 billion is huge, but my marginal utility from \$100 to \$201 billion is not that much. In ConvertArb’s example, it is not correct to model the utility payoffs as \$10, and 0.5*\$30, unless you are risk neutral. Most people are not risk neutral. Instead, you have to do it this way (U(x) is the expected utility from choice x). U(1) = U(310) U(2) = 0.5*U(300) + 0.5*U(330) The game would be completely different if you did not have the \$300k savings. It would be: U(1) = U(10) U(2) = 0.5*U(0) + 0.5*U(30) Utility is a function of risk tolerance, so different people will have different answers. This is a well-explored topic in economics. It’s applied to many real world scenarios, such as taxing the rich more than taxing the poor.

former trader Wrote: ------------------------------------------------------- > Even though the expected return on 2 is higher, I > would be shocked if anyone making \$80K a year > doesn’t choose 1. > > The more appropriate question would be: > > Net worth: \$15MM > > 1)You lose \$10MM right now (100%) > 2) I flip a fair coin,(50%) heads you lose \$30MM, > (50%) tails you lose nothing. > > You would see varying answers under that scenario. That is the whole point of the original question. Does an individual’s risk-reward vary by net worth? If so, should everyone “play” (invest) in the market? What can be drawn from this?

ConvertArb Wrote: ------------------------------------------------------- > former trader Wrote: > -------------------------------------------------- > ----- > > Even though the expected return on 2 is higher, > I > > would be shocked if anyone making \$80K a year > > doesn’t choose 1. > > > > The more appropriate question would be: > > > > Net worth: \$15MM > > > > 1)You lose \$10MM right now (100%) > > 2) I flip a fair coin,(50%) heads you lose > \$30MM, > > (50%) tails you lose nothing. > > > > You would see varying answers under that > scenario. > > That is the whole point of the original question. > > > Does an individual’s risk-reward vary by net > worth? If so, should everyone “play” (invest) in > the market? What can be drawn from this? Of course it varies by net worth. Someone worth \$1 billion can afford to take the 50% gamble of making 3% (30M) instead of 1% or 0%. For someone making 80K, you are offering a risk free return of 12,500% right off the bat.

It can all be explained with utility curves!

Bird in hand theory

HMW is right, choice 1 isnt irrational at all. Utility curves always take the for of positive 1st derivative and negative second derivative. Translation, each dollar is valuable to you but less valuable than the previous dollar. This is well explored in micro econ and generally modelled with some function of Ln. Your net work should come into play here as your overall utility is a function of your wealth. I dont have my calc on me but using HMW point, Ln(10) may be greater than 0.5Ln(0) + 0.5Ln(30).