A study in certainty equivalent, risk aversion, and utility

**DSchles** · 12-14-2017, 05:41 PM

Will you please vote and help me with a study I'm doing. There will be two polls, of which this is the first.

Suppose you're offered the flip of a fair coin, with the following provisions: Heads, you win $1 million, tails you get nothing. What is the minimum amount of cash in hand (no questions asked) you'd be willing to accept NOT to play the game?

Don

**BJPloppy** · 12-14-2017, 05:43 PM

Originally Posted by DSchles

Suppose you're offered the flip of a fair coin, with the following provisions: Heads, you win $1 million, tails you get nothing. What is the minimum amount of cash in hand (no questions asked) you'd be willing to accept NOT to play the game?

$300,000

(I have to admit that I went back and forth between $250,00 & $300,000)

**DSchles** · 12-14-2017, 05:45 PM

Originally Posted by BJPloppy

$300,000

(I have to admit that I went back and forth between $250,00 & $300,000)

I had some technical trouble. Please vote now.

Thanks.

Don

P.S. Second poll won't appear till we have a good sample of answers to this one.

**Three** · 12-14-2017, 06:36 PM

I assume you get to do this once in a lifetime.

**Midwest Player** · 12-14-2017, 07:48 PM

Option "Less than $100,000" is very misleading. If my choice was only $100 I wouldn't take it. If my choice was $90,000 I would take it.

**DSchles** · 12-14-2017, 08:16 PM

Originally Posted by Midwest Player

Option "Less than $100,000" is very misleading. If my choice was only $100 I wouldn't take it. If my choice was $90,000 I would take it.

So, your answer is less than $100,000!

Don

**Midwest Player** · 12-14-2017, 08:32 PM

Originally Posted by DSchles

So, your answer is less than $100,000!

Don

Yes!

**Jack Jackson** · 12-14-2017, 10:53 PM

Theres No Way, i would take a chance on a 1,000,000 vs. nothing.. 100,000 (or 10%) is all it would take to buy me off..For me 100 Grand is ALOT of money to me and is all i would need to re-invest and live comfortably for years to come..And Although 1,00,000 is 10x as much..It def. wouldnt be 10x as valuable for a person like me..Therefore 100,000 would be the right choice for me.. Its the same reason i always play the "little lotto" and not the Big one..

**Gronbog** · 12-14-2017, 07:59 PM

I think the answer to this depends on what the value of the money is to the person the offer is being made to. With such a large reward for winning, the amount taken not to play has to be life changing in some way otherwise there is no reason to accept it. As MWP says, $100k may not be granular enough. There are lower amounts which would be accepted in a heart beat by some.

I used to think about this when watching the game show "Deal or No Deal". The optimal strategy for the game is always refuse the offer, because the offers are always below EV for the remaining suitcases. However, given that each contestant only gets to play once in their life, they always (wisely, in my opinion) stopped when the offer was for an amount which was significant enough to make difference to their future in some way.

So, to some extent, the results of this poll will reflect the spectrum of that threshold for the members of this forum.

**DSchles** · 12-14-2017, 08:27 PM

Originally Posted by Gronbog

I think the answer to this depends on what the value of the money is to the person the offer is being made to. With such a large reward for winning, the amount taken not to play has to be life changing in some way otherwise there is no reason to accept it. As MWP says, $100k may not be granular enough. There are lower amounts which would be accepted in a heart beat by some.

I used to think about this when watching the game show "Deal or No Deal". The optimal strategy for the game is always refuse the offer, because the offers are always below EV for the remaining suitcases. However, given that each contestant only gets to play once in their life, they always (wisely, in my opinion) stopped when the offer was for an amount which was significant enough to make difference to their future in some way.

So, to some extent, the results of this poll will reflect the spectrum of that threshold for the members of this forum.

You don't think I picked the title of the thread out a hat, do you? :-) All the words were chosen carefully to reflect the full nature of the question. First, most here understand that certainty equivalent, in this context, means the amount of money you would accept, with certainty, to avoid taking any risk whatsoever. But that amount, in turn, depends on two things: 1) one's personal aversion to risk, which is a variable, and 2) the utility of the amount of money chosen to that specific individual.

Some further clarification: In a recent interview, Warren Buffett stated, matter of factly, "money has no utility to me whatsoever." So, presented with this opportunity, it would make little sense for him NOT to flip the coin. On the other hand, a homeless person would consider receiving $100,000 or less as a life-altering event. To him, the utility of even the smallest category offered is so great that gambling would be insane. So yes, the analogy to "Deal or No Deal" is palpable.

So, again, I don't need any of this to be explained to me. I'm interested in what category your personal answer falls. And yes, of course, it's a one-time event. Do you think I'm asking what you'd do if you could do this every hour on the hour? The terms are clear. This discussion isn't going to turn into what anyone had for breakfast. :-)

Don

**Stealth** · 12-15-2017, 10:04 AM

Don, Your poll is an interesting one.

I think you have found an audience where the "utility" function skews the response more than the "risk" function, especially when compared to the wall street guys. If this were a "man on the street" poll I would expect even lower numbers as the risk component becomes larger AND the utility function is more valuable.

Is it not just confirming the underlying premise of CE?

**DSchles** · 12-15-2017, 01:24 PM

Originally Posted by Stealth

Don, Your poll is an interesting one.

I think you have found an audience where the "utility" function skews the response more than the "risk" function, especially when compared to the wall street guys. If this were a "man on the street" poll I would expect even lower numbers as the risk component becomes larger AND the utility function is more valuable.

Is it not just confirming the underlying premise of CE?

If the poll had been for the man in the street, I wouldn't have made the top payoff $1 million.

We'll see what is or isn't confirmed once everyone weighs in. My interest is in the actual responses, which demonstrate that, because of utility, CE, which varies, isn't just e.v., which is the same for everyone.

Don

**BoSox** · 12-17-2017, 04:01 AM

Originally Posted by DSchles

We'll see what is or isn't confirmed once everyone weighs in. My interest is in the actual responses, which demonstrate that, because of utility, CE, which varies, isn't just e.v., which is the same for everyone.

Don

I know this much, I will not be responding to the second question! Don, since your interest is in the actual responses, and most answers are reflective of the utility aspect of the question, which is in my opinion getting too personal, and unnecessary. Frankly I resent even thinking about deciding such a choice "regardless that it is just a poll" whose whole result would affect a charity. Don, what would your choice be under the same scenario?