What constitutes "risk"?

[Boyo_Jim]

@Freddy the Pig

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 was assuming financial risk is measured like a probability, as a percentage from 0% - 100%.

[Boyo_Jim]

@BubbaDog

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.

The starting position is 0 dollars, as you have nothing until you choose to accept $500,000. I agree there is no risk to this.

There is no chance at all you will end up with 9.5 million, or an additional 9.5 million. If you accept the $500,000 you are done. In leiu of accepting the $500,000 you may accept an opportunity to earn 10 million if you answer a question correctly.

At the end of the day, you will have: a) what you started with, or b) $500,000 more than that, or c) 10 million more than your starting point. You lose nothing in any outcome.

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.

Please clarify this. First, you have been taking a risk working for 5 years without pay, accepting a promise of future payment. But let’s assume you’re boss is good for it and puts a pile of cash on front of you.

Scenario 1 has no risk: if your boss says, “Here, take it. I will give you an extra 9.5 million (or 10 million, or just $10 for that matter) if you can answer this question correctly. The cash on the desk is yours either way.”

Scenario 2 does have risk: your boss says, “You can have this money, or have 10 million more if you answer this question correctly, but if you answer wrong you get nothing at all.”

The difference the OP scenario and these two scenarios is that in these latter two scenarios, your starting point IS $500,000. You have earned it before you get to the table. But if there is no penalty for answering the question wrong, there is no risk in attempting to answer it.

[groman]

@Boyo Jim

The starting position is 0 dollars, as you have nothing until you choose to accept $500,000. I agree there is no risk to this.

There is no chance at all you will end up with 9.5 million, or an additional 9.5 million. If you accept the $500,000 you are done. In leiu of accepting the $500,000 you may accept an opportunity to earn 10 million if you answer a question correctly.

At the end of the day, you will have: a) what you started with, or b) $500,000 more than that, or c) 10 million more than your starting point. You lose nothing in any outcome.

You have to make a choice. You either get $500,000, or you get a question. If you choose $500,000 you have $500,000. If you choose the question you have (before answering the question) $0, but you gave up the $500,000 to be at this point. When you answer the question correctly you wind up with $10,000,000 in your pocket, for a net gain from answering the question correctly of $9,500,000. When you answer the question incorrectly you wind up with $0 in your pocket, for a net loss from answering the question incorrectly of $500,000.
We can rephrase this problem. I’ll give you $1 or a raffle ticket. If you take the raffle ticket and win nothing, you lost $1. Sure, the amount of money in your pocket did not change, but that doesn’t mean you did not lose $1. It’s the same as finding a $1 bill and then misplacing it – your net worth did not change, but it’s certainly a loss.