double inflection utility function

Hi everyone,

this double inflection utility function has been bothering me for quite sometime now. The cfai textbook’s explanation is not quite intuitive to me. can someone please explain why individual exhibit risk-averse behaviar (i.e why they buy insurance to avoid small losses) and why exhbit risk-seeking behavior (i.e. why they buy lottery tickets)? a more intuitive example would much much appreciated! please relate the decision making process to the expected utility of the gamble and the utility of the expected outcome. This is where i’m confused, when the textbook says utility of the expected outcome, what exactly it is referring to?



I think you need to make a difference between the double inflection utlility curve and the combination of risk seeking and risk averse behaviour.

Looking at the risk seeking and risk averse behaviour I think this is to do with the way in which the invividual is framing the decision. For example: Wow I could win $5,000,000 seems like a good idea, unless you think of it the other way round where it’s more crap I’m almost certain to lose the price of the ticket. The same can be applied to the insurance contract, you know if a meteor falls on your house you’ll lose everything and for the low low price ofr $1 a month we con completely cover you if the dreadful event happens.

Looking a double inflection utlility curves, this is more to do with the change in risk seeking behaviour as total wealth changes. So at low levels of wealth we are risk averse because we cannot afford to lose our money as wealth increases our ability to take risk increase as does our willingnessto take risk (we need to grow the portfolio), however as we become Warren Buffet wealthy, whlist the ability to take risk is enourmous the willingness is no longer there, we do not need to grow the portfolio at high rates it becomes more important to protect the value for future generations.

Hi Monito,

I appreciate your response. I kinda understand the concept of changing risk behavior as levels of wealth changes. But i’m confused when the CFAI textbook tries to show the changing in behavior using the double inflection utility graph. They demonstrate the problem by saying two lotteries are available, one that lies within the risk-averse section and one that lies within the risk-seeking section. When the individual is risk-averse, the expected utility of the first lottery is less the the utility of the expected outcome, so the individual will pay a premium to avoid it; when the inidivudal is risk-seeking, the expected utility of the second lottery is more than the utilitiy of the expected outcome, so the person will pay a premimum to undertake it. trying to explain the concept by using the terms expected utility confuses me a great deal. If the person is risk-averse, why he would pay a premium? what does this mean? does it mean that he’ll still buy the lottery? I’m thinking, if he’s risk-averse, he wouldn’t pay anything to buy the lottery… more confused… please help.

Do not spin your wheels in Behavioral Finance. The CFAI books dedicate a lot of pages relative to the amount of points you could win on exam day. Move on and if you’re really interested then come back after you pass and spend all the time you want.