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Which of these 4 options is the MOST RISKY?
1. Gain $100 at 100% probability (guaranteed), and lose nothing 7%  7%  [ 3 ]
2. Gain $200 at 75% probability, or lose $200 at 25% probability 37%  37%  [ 16 ]
3. Gain $300 at 50% probability, or lose $100 at 50% probability 28%  28%  [ 12 ]
4. Gain $400 at 25% probability, or gain/lose $0 at 75% probability 28%  28%  [ 12 ]
Total votes : 43
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 Post subject: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 23, 2012 10:34 am 
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I am interested in how people intuitively judge the level of "risk" in making decisions. The following 4 hypothetical options are each worth an expected (probability-weighted average) value of $100, but which option is the MOST RISKY in absolute terms? In other words, which option is the *least* attractive, assuming you're risk averse?

1. Gain $100 at 100% probability (guaranteed), and lose nothing
2. Gain $200 at 75% probability, or lose $200 at 25% probability
3. Gain $300 at 50% probability, or lose $100 at 50% probability
4. Gain $400 at 25% probability, or gain/lose $0 at 75% probability

Please note that the gains and losses given in each case are NET gains/losses, including any upfront investment.

Also, assume this is a "one-shot scenario" - you only get to play the game once based on the option you choose.

Please place your vote in the poll above!

PS. You can change your vote if you make a mistake.

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Last edited by KelvinS on Wed Jan 25, 2012 7:32 am, edited 11 times in total.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 11:00 am 
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Kelvin, in order to correctly assess the risk of these scenarios, don't you have to consider how much you are investing in the first place? It is very different if you start with $200 or $200,000.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 11:31 am 
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Gus wrote:
Kelvin, in order to correctly assess the risk of these scenarios, don't you have to consider how much you are investing in the first place? It is very different if you start with $200 or $200,000.

No details on upfront investment are assumed or required: these 4 options include upside and downside returns NET of any upfront investment...

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 12:04 pm 
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Just for clarification: Obviously you are talking about a one shot scenario?
Otherwise we could repeat the $100 gain at 0 risk infinitely.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 12:29 pm 
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Konrad wrote:
Just for clarification: Obviously you are talking about a one shot scenario?
Otherwise we could repeat the $100 gain at 0 risk infinitely.

Yes, correct, and good point, thanks. Sorry if that wasn't clear.

PS. I have set up the poll so that votes can be changed at any time, in case this would have affected anybody's response...

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 1:35 pm 
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As poker player, just looking at the expected value, if you were to play an infinate number of times, you'd average losing $200 with option 4. The others you either gain money or break even in the long run.

-d


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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 1:40 pm 
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Sorry Kelvin I ticked no.1 by mistake, meant to tick 4.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 2:08 pm 
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I'm rather risk adverse. I would prefer option 1, a guaranteed gain of my expected result. Barring that, i'd play for option 4, since I wouldn't want to risk losing any money. Now, if these values were for $10 instead of $100, I would probably play the lottery and go for broke, since I have $10 to lose. Keep in mind when extrapolating your data that the utility of money is not proportional to it's monetary value.


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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 2:24 pm 
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darryl wrote:
As poker player, just looking at the expected value, if you were to play an infinate number of times, you'd average losing $200 with option 4. The others you either gain money or break even in the long run.
No, you would actually gain $100 per game on average and in the long run, regardless of the option. That's because I defined each option so that the expected (probability-weighted average) value is always $100:

Option 1: Expected value = 100% * $100 = $100
Option 2: Expected value = 75% * $200 + 25% * (-$200) = $150 - $50 = $100
Option 3: Expected value = 50% * $300 + 50% * (-$100) = $150 - $50 = $100
Option 4: Expected value = 25% * $400 + 75% * $0 = $100 +/- $0 = $100

The options differ only in terms of the risk involved in a single game. Therefore, the goal here is to choose the option that would be most risky (least attractive) if you could only play this game once...

Tony Fisher wrote:
Sorry Kelvin I ticked no.1 by mistake, meant to tick 4.
No problem, I set up the poll so that you (or anybody else) can change your/their vote, please, in case of such mistake...

URodent wrote:
I'm rather risk adverse. I would prefer option 1, a guaranteed gain of my expected result. Barring that, i'd play for option 4, since I wouldn't want to risk losing any money.
Fair enough, but please remember to vote for the option that you consider to be MOST RISKY (i.e., LEAST ATTRACTIVE) - NOT the one you would prefer (as you seem to describe).

URodent wrote:
Now, if these values were for $10 instead of $100, I would probably play the lottery and go for broke, since I have $10 to lose. Keep in mind when extrapolating your data that the utility of money is not proportional to it's monetary value.
You make an interesting and valid point here, that people are generally willing to take more risk if they have more money available to lose in the first place. But in this case I am trying to keep things simple, by asking what is the most risky option in absolute terms, regardless of how much money you can afford to lose, if that makes any sense...

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Last edited by KelvinS on Mon Jan 23, 2012 3:08 pm, edited 1 time in total.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 23, 2012 3:03 pm 
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From a players point of view here is how I'd rate the risk.

1. Gain $100 at 100% probability (guaranteed), and lose nothing

No risk. You can't lose anything

2. Gain $200 at 75% probability, or lose $200 at 25% probability

High Risk. You can lose $200.

3. Gain $300 at 50% probability, or lose $100 at 50% probability

Moderate Risk. You can lose $100.

4. Gain $400 at 25% probability, or gain/lose $0 at 75% probability

Low risk. You can't lose anything but you have a 75% change of not getting the $100 you would get if you picked option 1.

Carl

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Tue Jan 24, 2012 8:34 am 
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KelvinS wrote:
darryl wrote:
As poker player, just looking at the expected value, if you were to play an infinate number of times, you'd average losing $200 with option 4. The others you either gain money or break even in the long run.
No, you would actually gain $100 per game on average and in the long run, regardless of the option. That's because I defined each option so that the expected (probability-weighted average) value is always $100:


Oops, I did the math really quick on my lunch break and misread the amounts. So based on rereading the amounts, option 2 is the riskiest because you can lose the most.

-d


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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Tue Jan 24, 2012 11:39 am 
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Has anybody an example for option 4 in real life?
Quote:
4. Gain $400 at 25% probability, or gain/lose $0 at 75% probability
I do not risk / invest anything, but I have a 25% chance of winning. The only risk is that I do not win :roll: Life is not really full of such opportunities, is it? :roll:

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Tue Jan 24, 2012 2:09 pm 
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Konrad wrote:
Has anybody an example for option 4 in real life?


To bring up poker again, (probably a bad example, but it happens a lot) suppose you are in the middle of a Texas Hold 'Em hand, all of your money is in the pot already and the pot is worth $400. Since the money is all in the pot already, you can't lose any more money. So everyone flips their cards over and there is one more card that the dealer must flip face up for everyone.
You notice that 1 out of 4 of the cards remaining in the deck will make it such that you win the entire hand and the $400. The remaining 3 out of 4 cards will make it such that you lose the hand and someone else wins the $400

-d


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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 1:08 am 
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Also is a bit circumstantial.

To me, $100 is one hell of a lot of money. Pardon the language. Losing that would be a tremendous blow. And at 50% loss?

$100, however, to most people on this forum, is probably peanuts.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 3:25 am 
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darryl wrote:
Konrad wrote:
Has anybody an example for option 4 in real life?
To bring up poker again, (probably a bad example, but it happens a lot) suppose you are in the middle of a Texas Hold 'Em hand, all of your money is in the pot already and the pot is worth $400. Since the money is all in the pot already, you can't lose any more money. So everyone flips their cards over and there is one more card that the dealer must flip face up for everyone.
You notice that 1 out of 4 of the cards remaining in the deck will make it such that you win the entire hand and the $400. The remaining 3 out of 4 cards will make it such that you lose the hand and someone else wins the $400

-d
I'm not a poker player. So, I cannot follow the details. My perception of this example is somewhat different: I'm in the game because I have paid some money into the pot previously. If I loose at the very end, I would loose that money. My consideration would always include the start and the end of the situation, when I calculate my net win or loss.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 3:34 am 
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wwwmwww wrote:
From a players point of view here is how I'd rate the risk.

2. Gain $200 at 75% probability, or lose $200 at 25% probability

High Risk. You can lose $200.



Exactly my consideration too: in a single play I don't want to enter the risk of losing $200,-.....
(option 2 is highest potential loss)

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 6:58 am 
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OK, I've given people a good chance to vote and comment with rationale.

Currently the votes stand as follows:

1. 6% [ 2 ]
2. 41% [ 14 ]
3. 24% [ 8 ]
4. 29% [ 10 ]

Now here's some analysis...

Clearly, Option 1 has no risk at all: $100 is guaranteed and there is no uncertainty, and no possibility to lose anything - just get $100 for free! Nice deal if you can get it, but hey, this is only theoretical. On that basis, the two people who voted for this option as "most risky" either have no understanding of what risk is, or (more likely, I suspect) didn't read the question properly! Oh well, it happens...

You might wonder why I included this Option. Well, it was precisely for this reason: to act as a negative control and discount/ignore votes where the question has clearly been misread - although I'm tempted to keep them, because not understanding the objective properly is a common source of risk! :lol:

Anyway, the real decision is choosing between options 2-4...

Most people (41%) have chosen option 2 as most risky, apparently based on greatest potential loss/downside, but regardless of probability. Many people (29%) also chose option 4, based on the greatest probability of loss/downside (relative to average/expected gain of $100) and/or lowest probability of gain/upside, but regardless of the potential loss. Both of these perspectives appear very rational, in some sense.

But now, let us rephrase Option 1, and add an Option 5, so that all 5 options follow a clear mathematical trend:

1. Gain $100 at 100% probability, or lose $300 at 0% probability
2. Gain $200 at 75% probability, or lose $200 at 25% probability
3. Gain $300 at 50% probability, or lose $100 at 50% probability
4. Gain $400 at 25% probability, or lose $0 at 75% probability
5. Gain $500 at 0% probability, or lose -$100 at 100% probability

Now you can clearly see through options 1-5: potential gain increases and potential loss decreases by $100 per option, while probability of gain decreases and probability of loss increases by 25% per option, so that average expected value is always a net gain of $100.

But here's the interesting part: Option 5 is actually equivalent to Option 1, so that a gain of $100 is guaranteed in each case, with no risk or uncertainty. Now think again about why you chose your option as the most risky...

If your original choice was based on the greatest potential loss/downside vs expected value, while ignoring the probability, then you would now choose Option 1 as the most risky. And if your choice was based on the greatest probability of loss/downside or the lowest probability of gain/upside, while ignoring the potential loss/downside, then you would now choose Option 5, which is equivalent to Option 1.

In effect, based on the same rationale for choosing options 2 or 4, more than 75% of us could have easily chosen Option 1, where there is actually no risk at all!

The fact is that risk is a combination (and balance) of both these factors: probability * impact

In other words, risk is the potential loss/downside (relative to expected value), multiplied by the probability of that loss.

On that basis, the "downside risk" of each option can be calculated as follows:

1. [$100 - (-$300)] * 0% probability = 0
2. [$100 - (-$200)] * 25% probability = 75
3. [$100 - (-$100)] * 50% probability = 100
4. [$100 - ($0)] * 75% probability = 75

These numbers represent the expected (probability-weighted average) downside risk relative to your expected gain. You can also calculate the expected "upside risk" and the numbers will be exactly the same, because upside and downside risk always balance to give the expected value on average. Makes sense, right?

On that basis, Option 3 is actually the most risky, and yet only 8 people (24%, including me) voted for this as the most risky option. And with 4 options available, that's slightly worse than a random guess!

In case you have any doubt about this, you can see that the difference between the potential loss and potential gain of each option (if you consider 0% probability of $300 loss in option 1) is always $400. However, what makes these options different is that the distribution between upside and downside scenarios is completely random (50% probability) in option 3, so the uncertainty (and therefore risk) is greatest for this option.

Essentially this means we have no information to predict whether there will be a positive or negative outcome for option 3, so the risk is greatest, whereas we must have better information to predict the outcome in options 2 and 4, while we already know the outcome of option 1.

The amazing thing is that, despite the general level of intelligence on this forum, fewer than 25% (equivalent to a random guess!) chose the right answer. But even if you are still not convinced by these arguments, you should find it quite disturbing that the votes are so scattered.

Indeed, risk is a very complicated subject, and humans are very poor at judging risk even when the options are very simple and well defined. We are programmed to judge risk at a very primitive, emotional and irrational level, and even the brightest usually get it wrong! :wink:

PS. Congratulations to those who went for Option 3 - would be interested to hear how you arrived at your choice. :D

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 1:28 pm 
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Konrad wrote:
I'm not a poker player. So, I cannot follow the details. My perception of this example is somewhat different: I'm in the game because I have paid some money into the pot previously. If I loose at the very end, I would loose that money. My consideration would always include the start and the end of the situation, when I calculate my net win or loss.


If you play poker regularly, you have to completely ignore the money you already put in the pot once it's in there (it's already in there and you can't do anything about it) and you have to look at the total amount in the pot at the time to see if it's worth the amount you put in based on the percentage of time you get the amount coming out. If this makes any sense.

-d


Last edited by darryl on Wed Jan 25, 2012 1:58 pm, edited 1 time in total.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Wed Jan 25, 2012 1:48 pm 
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darryl wrote:
If you play poker regularly, you have to completely ignore the money you already put in the pot once it's in there (it's already in there and you can't do anything about it) and you have to look at the total amount in the pot at the time to see if it's worth the amount you put in based on the percentage of time you get the amount coming out. If this makes any sense.

-d
That's right: all decisions should only consider future outcomes and probabilities, ignoring any prior investment. Such "sunk costs" tend to cloud otherwise good logical decision making with emotional perspectives (fear of an overall loss), but what's done is done, and should have no impact on any subsequent decisions once an investment has already been made and the game is in play.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Thu Jan 26, 2012 5:34 am 
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Quote:
That's right: all decisions should only consider future outcomes and probabilities, ignoring any prior investment.


Sounds as advice for the stock market. :wink:


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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Thu Jan 26, 2012 6:29 pm 
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By the way, regarding the poll, I should make a living trading options between those who voted for Option 2 and those who voted for Option 4... :wink:

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 1:36 am 
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I voted 3 before reading Kelvin's post. I judged the risk based on the probability that you will come out at a loss. 50% is obviously higher than 25% so that made the choice easy.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 2:01 am 
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This topic could be about how you perceive / measure risk but I think it's actually more about how you define risk.

Options 1 and 4 have no risk because you can't lose anything. Options 2 and 3 both have risk because you can lose $200 and $100 respectively. Option 2 is riskiest because it has the greatest downside. To me risk is potential loss, regardless of the expected value (which is a $100 gain in all 4 options).

Put another way, if I was walking on the street minding my own business and doing just fine on my own and somebody came up to me with this proposal I'd choose 1. Why not, I don't need the money but sure, a free $100 is nice. The next likely choice I'd make would be 4 because hey, I didn't need the money but having the chance at $400 is nice.

Given only a single chance to play I'd never choose 2 or 3 because I don't need the gain and I'm not willing to take a loss for the chance to gain.

Of course, if you could play this game once a day, every day then it doesn't matter what you choose. I'd play every day and gain an average of $100 a day in the long run.

If you dispute my analysis above as incorrect or less correct than some other analysis then we are likely using different definitions of risk.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 5:18 am 
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Option 4 does have some risk because you could lose the $100 that you would expect to gain on average (or by choosing option 1). In other words, loss is measured vs what you would expect at the end, not what you start with. It's called "opportunity cost".

So, option 2 has biggest potential loss, option 4 has biggest probability of loss, and option 4 has biggest expected loss (probability x impact), so what you voted says more about how you define risk than anything else, as you said.

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 30, 2012 10:37 am 
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KelvinS wrote:
The amazing thing is that, despite the general level of intelligence on this forum, fewer than 25% (equivalent to a random guess!) chose the right answer.
I'd argue the "right" answer depends on one's definition of risk so I wouldn't go so far as to say most got this question wrong.

Carl

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 30, 2012 3:01 pm 
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wwwmwww wrote:
KelvinS wrote:
The amazing thing is that, despite the general level of intelligence on this forum, fewer than 25% (equivalent to a random guess!) chose the right answer.
I'd argue the "right" answer depends on one's definition of risk so I wouldn't go so far as to say most got this question wrong.

Carl

That is correct, but as I explained above, any definition of risk that is based on either greatest potential loss or greatest probability of loss (rather than the product of probability x potential loss) is inherently irrational and inconsistent:

KelvinS wrote:
But now, let us rephrase Option 1, and add an Option 5, so that all 5 options follow a clear mathematical trend:

1. Gain $100 at 100% probability, or lose $300 at 0% probability
2. Gain $200 at 75% probability, or lose $200 at 25% probability
3. Gain $300 at 50% probability, or lose $100 at 50% probability
4. Gain $400 at 25% probability, or lose $0 at 75% probability
5. Gain $500 at 0% probability, or lose -$100 at 100% probability

Now you can clearly see through options 1-5: potential gain increases and potential loss decreases by $100 per option, while probability of gain decreases and probability of loss increases by 25% per option, so that average expected value is always a net gain of $100.

But here's the interesting part: Option 5 is actually equivalent to Option 1, so that a gain of $100 is guaranteed in each case, with no risk or uncertainty. Now think again about why you chose your option as the most risky...

If your original choice was based on the greatest potential loss/downside vs expected value, while ignoring the probability, then you would now choose Option 1 as the most risky. And if your choice was based on the greatest probability of loss/downside or the lowest probability of gain/upside, while ignoring the potential loss/downside, then you would now choose Option 5, which is equivalent to Option 1.

In effect, based on the same rationale for choosing options 2 or 4, more than 75% of us could have easily chosen Option 1, where there is actually no risk at all!

In other words, unless you define risk as expected loss = probability x impact (loss vs expected value), you can end up identifying cases as being "most risky" when there is clearly no risk at all.

So there is really only one rational and consistent definition of risk! :D

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 Post subject: Re: Poll: how do you perceive/judge RISK?
PostPosted: Mon Jan 30, 2012 3:23 pm 
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I view some of your arguements as irrational...
KelvinS wrote:
If your original choice was based on the greatest potential loss/downside vs expected value, while ignoring the probability, then you would now choose Option 1 as the most risky.
Why? Option 1 has no downside. Or are you telling me I can't ignore the loss of $300 at 0% probability? We appear to be ignoring the small probability that the earth gets destroyed by an asteroid impact before we can collect our winnings in all these options. So why is it I can't ignore something you state has 0% probability?
KelvinS wrote:
And if your choice was based on the greatest probability of loss/downside or the lowest probability of gain/upside, while ignoring the potential loss/downside, then you would now choose Option 5, which is equivalent to Option 1.
Again there is NO probability of loss/downside with option 5. You consider the loss of a dept of $100 (that is in effect what the minus sign means) a downside? Your definitions of "greatest" and/or "downside" are irrational and you come here and appear to be saying the majority of the members who took part in your poll have an irrational definition of "risk". Your conclusions are flawed IMHO.

Carl

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 7:18 pm 
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Because:

Gain $100 at 100% probability

is virtually indistinguishable (mathematically) from:

Gain $100.0001 at 99.9999% probability, or lose $299.9999 at 0.0001% probability

as well as:

Gain $499.9999 at 0.0001% probability, or lose -$99.9999 at 99.9999% probability

Just keep adding more (or less) decimal places and you will see, as you reach a point where there is an abrupt inconsistency in your rationale for defining risk.

In other words, you can't judge risk only by potential loss while ignoring probability (or vice versa), otherwise you could judge virtually identical options as "highly/most risky" and "no risk at all". But that's exactly what you did!

So now who's being irrational? :P

PS. Losing -$50 is equivalent to gaining $50, but that's still a downside or loss relative to your expected gain of $100 (which would be giuaranteed if you go with Option 1), so again there is no inconsistency in my logic.

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Last edited by KelvinS on Mon Jan 30, 2012 8:06 pm, edited 1 time in total.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 8:01 pm 
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KelvinS wrote:
Gain $100 at 100% probability

is virtually indistinguishable (mathematically) from:

Gain $100.0001 at 99.9999% probability, or lose $299.9999 at 0.0001% probability
This strikes me as crazy logic. They are close but not the same. The second has a chance of risk and the first does not. It's like instead of using discrete numbers you've chosen to use an infinite series that converges on gaining $100 at 100% probability. Similar to Renormalization.


The problem I have with your characterization of risk is that you are factoring in the certainty of money in option 1 as added risk to the other options.

We don't have the same baseline. I say that right now I have $0 and if I choose option 1 or option 4 they have no risk because I can't end up with less than what I started with.

You seem to be setting your baseline as considering the $100 of option 1 as a done deal and saying option 4 is more risky because you might not get any money with option 4.

The chance of not gaining money is not the same thing as risk.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 8:04 pm 
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None of the above. Your risk machine is fair; additionally, I lose nothing for trying. The slot machine at the casino is not fair, because it takes more tokens than it dispenses. Every time. For every person that wins $1000, well more than a thousand people lose their $1 deposit. Even at 99% payout, they can still make a profit of at least a penny on every dollar. The casino is also correct to bet that most of the few people who win will put their money back into the system and lose it again, which happens more often than not.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 8:09 pm 
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bmenrigh wrote:
KelvinS wrote:
Gain $100 at 100% probability

is virtually indistinguishable (mathematically) from:

Gain $100.0001 at 99.9999% probability, or lose $299.9999 at 0.0001% probability
This strikes me as crazy logic. They are close but not the same. The second has a chance of risk and the first does not. It's like instead of using discrete numbers you've chosen to use an infinite series that converges on gaining $100 at 100% probability. Similar to Renormalization.


The problem I have with your characterization of risk is that you are factoring in the certainty of money in option 1 as added risk to the other options.

We don't have the same baseline. I say that right now I have $0 and if I choose option 1 or option 4 they have no risk because I can't end up with less than what I started with.

You seem to be setting your baseline as considering the $100 of option 1 as a done deal and saying option 4 is more risky because you might not get any money with option 4.

The chance of not gaining money is not the same thing as risk.
Option 4 does have risk, because you have to consider your downside of no gain/loss relative to your expected gain of $100 (probability-weighted average value of each option), rather than your current wealth ($0). In economic terms this is called your "opportunity cost".

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Last edited by KelvinS on Mon Jan 30, 2012 8:18 pm, edited 1 time in total.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 8:18 pm 
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KelvinS wrote:
Option 4 does have risk, because you have to consider your downside of no gain relative to your expected gain ($100), rather than your current wealth ($0). In economic terms this is called your "opportunity cost".
Yes but I don't call that risk. We're using different definitions. I agree that there is a potential opportunity cost to option 4 however that cost is perfectly offset (because they have the same expected value) by the $400 payout.

This paper characterizes the issues:

Payne, J.W. (2005) It is Whether You Win or Lose: The Importance of Overall Probabilities of Winning or Losing in Risky Choice. Journal of Risk and Uncertainty, Vol. 30, pp. 5-19.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 8:36 pm 
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Interesting paper, thanks. However it is mainly focused on people's *perception* of risk, and the psychological focus on avoiding absolute/strict loss vs current wealth, rather than relative loss vs expected value, which is consistent with what you are saying.

But mathematically speaking, downside risk/loss must be measured relative to expected value (opportunity cost), so that upside and downside risk/uncertainty (probability x deviation) are equal and opposite, otherwise they wouldn't balance to give the expected value!

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Mon Jan 30, 2012 9:37 pm 
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Okay, I just had a brainstorm. The $200/300 dollar options are better investment in the long haul than the $100/400 options.

Four random people vote the $100 option and all four walk away with $100
Total earnings (average) for four people = $100 x 4 = $400

Four random people vote the $200 option and three of them walk away with $200
Total earnings (average) for four people = $200 x 3 = $600

Four random people vote the $300 option and two of them walk away with $300
Total earnings (average) for four people = $300 x 2 = $600

Four random people vote the $200 option and one of them walks away with $400
Total earnings (average) for four people = $400 x 1 = $400

So clearly, averaged across many attempts, the $200 and $300 options net 50% more profit than the $100 and $400 options. I'd probably take the $200 option myself. Twice as much dough for a 1-in-4 chance of losing.

EDIT: Crap, I didn't read the question correctly. You can actually LOSE Money with option 2 & 3. :?

How about we raise the stakes a bit? I happen to have at my disposal two mafia henchmen and a silver dollar. One henchman is holding a loaded handgun and the other henchman has a safe full of non-sequential bills, totalling $100,000,000. You call heads or tails and I will toss the coin onto the pavement. No tricks, all fair and square: 50/50 chance you have of netting $100,000,000 dollars and living in luxury for the rest of your life if you win the coin toss, 50/50 chance you will be forfeiting your life immediately if you lose the coin toss (shot to the back of the head). Your call, heads or tails... :twisted:

As it turns out, the odds are actually in your favor: You are more likely to die in a car crash on your way home from work, than to win the lottery. :shock:

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Tue Jan 31, 2012 12:52 am 
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stardust4ever wrote:
Okay, I just had a brainstorm. The $200/300 dollar options are better investment in the long haul than the $100/400 options.
[...]
EDIT: Crap, I didn't read the question correctly. You can actually LOSE Money with option 2 & 3. :?
The expected value of each option is $100. Do this a million times and you make $100 million on average. Personally I'd still go for option 1 or 4 every time even if I got to play millions of times because 2 and 3 allow you to go really deep in the hole even if you're expected to gain in the long run.

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 Post subject: Re: Poll: how do you perceive/judge RISK? - ANSWER
PostPosted: Wed Feb 01, 2012 1:35 am 
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In your question you make it clear:
Kelvin wrote:
Also, assume this is a "one-shot scenario" - you only get to play the game once based on the option you choose.
so I think any concept of expected or averaged gains over time are not relevant.

I see risk as more than just an assessment of the probability of a negative outcome, but also the magnitude of that negative outcome without respect to probability.

I don't agree that lack of gain is equal to risk, so to me losing $50 is not the same as not gaining $50. To anyone with finite resources these can't be equal, particularly when you have removed the opportunity of averaging losses over time.
Regarding opportunity cost, there are innumerable ways I am not making money right now but none are risks, just unfulfilled opportunities.

So I would answer option #2 is the most risky, as regardless of the probabilities you are *risking* $200. This is what you stand to lose, and you have only one shot at it.

I think your question is really "are you risk averse, risk neutral or risk loving?" (from Wikipedia)

Me? I'm risk averse (if you couldn't already tell) :)

Dave

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