Monty Hall walks up to you and offers you a choice. He will will give you $500,000 or the chance to answer a question correctly for $10,000,000. If you answer the question incorrectly, you get nothing. So there are only 3 possible outcomes for you: you get nothing, you get half a million, or you get 10 million.
My position is that there is zero risk to you in this scenario, as you cannot suffer a loss. Others in the thread claim that you may lose an “opportunity”, and hence there is a risk.
I believe the dictionary definition of risk bears me out. This is how the online American Heritage dictionary defines risk:
From a trading standing point your risk is $500,000 once you decide to respond in some way to Monte’s offer. The $500,000 is your base position and immediately represents your investment.
Look at it this way Monte phrased it differntly but what he really did was hand you $500,000 with no strings attached and then offered to let you wager it for a chance to gain $9,500,000
There is a string attached. Once you have the half million, you no longer have the option of earning 9.5 million.
I do agree that if you are given half a million, no strings attached, then offered the chance to bet it against the 9.5 million, you would be facing a risk.
Risk = (magnitude of consequences) x (likelihood of consequences)
This formula or something very close to it was in an article from Journal of the Atomic Scientists a year or two ago. The topic was nuclear terrorism. The likelihood of nuclear terrorism is debatable but the consequences are monstrous. Therefore the risk of nuclear terrorism is something to think about, to say the least.
Incidentally, the article quoted Warren Buffet as saying it’s “… inevitable. I can’t see any way it won’t happen.”
Suppose that you have one chance in twenty of answering the question correctly, so that your expected value in either case = $500,000. Most people would choose the sure $500,000, because it has no risk, defined as the variance (or standard deviation) of possible outcomes. The other option has risk, even though you can’t lose. If you don’t want to call it risk, call it something else, but it exists, and it’s bad for most people, because most people would choose the sure $500,000.
That’s a definition I can accept, with a minor addition. Is it fair to infer the formula could be stated more precisely as (magnitude of negative consequences) x (likelihood of negative consequences)?
I don’t see any negative consequences to accepting either side of Monty’s offer. Therefor the risk = 0.
Therein lies the point of my question. If you can’t lose, what is at risk? I would argue that that you MUST use a different term, because risk necessarily entails the possibility of loss.
And having said this, I have realized this may be the wrong forum. I put it in GQ because I was thinking about the definition of the term. But it probably should be in either IMHO or even GD.
You’ll be fighting a losing battle, though, because the definition of “risk” as “the variability of return from an investment” is too entrenched to change.
As a finance and insurance quant guy, I understand the usefulness of this definition. Given three coin flips with payoffs +200 vs 0, +100 vs -100, and 0 vs -200, it’s very useful to speak of the three having different expected value but the same risk. All would trade at a similar “risk premium” to their expected value.
I understand that this diverges from the vernacular definition of “the possibility of suffering harm or loss”. So be it–a lot of words differ in technical versus vernacular use. You can tell those of us in finance that “we MUST use a different term”, but we aren’t going to.
For your purposes, if you don’t like saying “risk” where there is no possibility of loss, say “uncertainty”.
Care to try for something more authoritative than Wiki?
Or not: the Wiki definition of “risk” is
One might say the two definitions are contradictory. Or it’s arguable that they can be reconciled depending on an agreed definition of the term “bargain”. A bargain as I understand it involves and exchange of goods or services, or possibly obligations among parties. If all parties are actually offering something of value, then they are in fact subjecting themselves to risk.
Here is the results page for a Google search of risk.
Out of 34 definition, I see only 3 that do not explicitly include the possibility of a loss. Those 3 are:
I think I understand what you’re saying, but don’t your examples involve actual or theoretical investments? Not only is there no possibility of loss, there is no investment either.
The negative consequence of accepting the half mill is that you no longer have any chance of winning the ten. And vice versa.
I don’t agree with you as to what constitutes a “string attached”. A “string” is something that devalues what you have after you’ve been given it. So if accepting the half mill meant you were then obliged to kiss Monty’s ass once a year indefinitely, that would be a string. A price that you pay to get something (giving up the chance of the ten mill) is not a “string”. It’s a price you paid.
So, per your second sentence, you have to agree that you are facing a risk.
I’m not sure if this actually relates to my original question or not, but, Freddy the Pig, can you tell me if a risk calculation in finance can end up with a negative result? My guess is that the result will always be from 0.0 to 1.0, inclusive. Is this correct?
You have a chance, if you lose it you’ve suffered a loss.
Say you are in a casino. You have a ticket that says “one free spin of the roulette wheel. If it comes up red, we pay you ten bucks, even though you didn’t put any money down”. Someone steals the ticket. Would you say you’ve lost nothing?
Umm, geez, I was just offering it up as food for chat. :dubious:
Well anyway, forget about wikipedia. Just based on the dictionary definition you gave above, I still think that one “risks” something if one goes for the ten million. I incur the “possibility of suffering loss,” to wit, loss of the opportunity to have half a million dollars.
It seems fairly clear to me that an opportunity is something that can and should be counted as an asset. If someone told me I am never allowed to travel to Germany, I would feel a loss. (To be clear: I’ve never been to Germany. The loss here would be the loss of any opportunity to go to Germany.) If someone offered to pay me five dollars in exchange for my never travelling to Germany, I would not take the offer. If they offered $50,000,000, I’d consider it. From this, I conclude that I apparently assign some value to my posessing the opportunity to go to Germany. So the opportunity is a good. Whose good is it, if not mine? And if it’s mine, isn’t it mine to lose? So it seems it is something I can risk, and risk losing.
Similarly, if someone offers me $500,000 dollars with no strings attached, and I turn it down, then I have lost something–I have lost the opportunity to gain half a million dollars. So then, if I flip a coin beforehand, saying I’ll accept if it’s heads and decline if it’s tails, then I’m risking the loss of something–the opportunity to have $500,000.
I don’t think a string necessasrily devalues the thing it’s attached to. It is simply a condition of acceptance. Monty might say, “I’ll give you a million dollars if you say pretty please”.
I will think about the “price you paid” thing and reply tomorrow as it’s getting toward crash time for me.
Frylock, I apologize for the tone of the last post I addressed to you. It was unnecessarily snarky.
No, risk is always either positive or zero. It’s calculated either as a variance (which involves squaring the deviation from average, resulting in a positive number) or a standard deviation (square root of the variance). The least variance you can have (zero) is when the outcome is certain–regardless of whether that outcome be good or bad.
However, variances aren’t bounded by 1.0. You’re perhaps thinking of correlation coefficients, which range
from -1.0 to 1.0, and can in fact be negative, since two series can be negatively correlated if one goes up when the other goes down.
I still have a a problem with the idea that the OP assumes there is nothing to lose so there is no risk. My issue isn’t with the assessment of risk but with the assumption that there is nothing to lose.
The starting position of the problem isn’t zero dollars in your pocket its $500,000. There is no risk in acquiring $500,000 but the value of perfect information is $9,500,000.
Is there Risk in the following problem?
You work for 5 years until you get paid.
Your boss, Monte, says that he will pay you your salary ($500,000) or give you the chance to draw 20 times your salary if you can answer a question.