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High Risk Doesn't Imply High Reward

I listened to a talk a while back where the speaker cited his Finance 101 class as a premise.  He drew a graph on the board that looked something like this

Pretty standard stuff right?  I mean, most of use have probably seen this before whether or not we've taken a finance class.  Sometimes I've seen people protest that this is not always true, to which the instructor says something like, "Well this is a general rule, there are always exceptions".  The main problem I have with this graph is two fold: 
  1. This states that increasing risk will increase rewards.  This basically states it doesn't matter what you do, if you are doing risky stuff, you will become rich.  
  2.  This is not a general rule, most riskier things return less reward, not more.  Think about drugs, high risk, low return.

Allow me to offer a new formula, semi-proof, and graph to replace this misleading one.

Theorem 1

Let Risk = R
Let Reward = P (Think P for Profit)
\forallR0\existsP0   R\Rightarrow P0 \land R1 \Rightarrow P0 \land R1 < R0 

For those normal people that haven't studied predicate calculas and have glossed over the fomula, I'll say it in words.  For every risk with a matching reward, there exists another, smaller risk that will get you the same reward.

Pretty bold statement right?  Let me use an example to help clarify this statement.

Imagine there is burning building with a loved one inside and you are watching it burn down.  Which of the follow would you do?
  1. Take off as many clothes as you can while running into the building until you reach your loved one and take them to safety.
  2. Run into the building with all your clothes on.  Try to cover your face until you reach your loved one and take them to safety.
  3. Tell the fully geared fireman who is standing next to you to get your loved one and take them to safety.
The original graph would tell you that you should do number 1 because it has the highest risk and therefore the most rewarding.  That is of course foolish, but how would you get a fully geared fireman to stand next to you?

Corollary 1.1

R1 is harder to get than R0.  Or, in terms of the 3 options above, option 3 is harder to get than option 1.  It is rare that you will have a fully geared fireman right next to you the instant you need him, but it will give you the same reward.  Just because there exists a lower risk option doesn't mean it is an equally probable solution, in fact, they are less common.


Corollary 1.2

Successful people can get the R1s either by ability, luck, influence, or inheritance.  Consider the case of the boy who has a rich dad and inherits all of his money.  He got a lower risk option than the guy who makes the same amount of money through some other venture.  Just because a lower risk option exists, doesn't mean that you have the means to achieve it...I mean, not everyone's a fire chief right?

The Correct Graph

Pretty similar eh?  The main thing to note here is that a reward of 20 maps to any risk 0-20. 

Conclusion

Now that I've bad mouthed the original graph, let me conclude by saying that there is a use for it.  The original graph states what people are willing to pay for a reduction in risk.  As a seller, it is important to know that people are willing to pay (have a lower return) if they think they are getting a sure thing.  However as a buyer (or entrepreneur), you should consider my alternative.

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