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I always wondered you to quantify the value of risk in an investment. Before the high tech crash people would often say if want to make more money you got to be willing to take more risks. But how to quantify those risks in terms of an investment. In the context of a mars mission the problem becomes clearer. Each mars mission is worth a given value, if it fails it is worth much less. A successful mission today is worth more then it is tomorrow, in terms of inspiring future generations, accumulating scientific and engineering knowledge. If way say the value of a mission today grows exponentially with time in terms of scientific spin offs, inspiration and cultural enrichment. We could use a typical rate like 10%. If we new the value accumulated by two different programs over time we could compare them by asking a bunch of statistical question?
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An example. A bookie starts with 100 dollars and each bet he takes he has a 60% chance of winning. The bookie gets one customer per day and each customer will not bet more then 100 dollars. What formula should the bookie use to maximize the expected value of his revenue (A.K.A average over a bunch of ensembles) to choose his maximum bet? What formula should the bookie use to maxiumize the curve which is five standard deviations bellow his expected revenue (A.K.A the expected worst case)?
Note that in the above problem the answer will be different depending if we want the expected value for the 10th bet the 11th bet or the expected value of the average of the first 10 bets.
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Why is the bookie example relevant? The bookie example is relevant because NASA on receives a fixed amount of money each year. In order to maximize the benefit produced by the organization it must mitigate risks to an expectable level. For instance it may be considered too risky for NASA to launch all their robotic probes for the year in a single HLLV instead of spreading the risk out over several launches. Or in terms of an investor an investor (baring borrowing) an investor only has a fixed income to invest each year. It will take several years before the return on his investment is equal to his annual contribution. Thus if the investor wants to make sure that he has enough money to retire with he must mitigate some of the risk.
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I'm no statistician, but as I recall, elementary risk assessment can be done any number of ways depending on how you expect your investment to behave.
The "time value of money" method is simple, and useful if you know the investment's behavior over time. Cumulative reliability estimates, and zero-sum matrices can help if you don't know what it's going to do over time but do know how likely it is to fail or how spectacularly it will do so.
If you had a whole bunch of investments of the same type, so that you could watch how they behave as a group, you wouldn't necessarily have to know enough details to predict how each individual investment will perform. You could just use an amortization matrix instead to make predictions using average behaviors.
Discussions of these methods can be found in any business statistics book.
"We go big, or we don't go." - GCNRevenger
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