Measuring Risk with Probability Distributions

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Risk is an integral part of everyday human life. We both seek, and are unwillingly exposed to varying degrees of risk. Risk can be defined as being a situation with more than one outcome. Risk should be quantifiable, in that, that the risk taker should have an idea of the probabilities of the possible outcomes occurring. For Example, investing in a stock. Investing in a stock can give the investor multiple outcomes, it can give a negative outcome, like when the stock performs badly in the market and the stock decreases in value. Or it can give a positive outcome , like when the stock performs strongly in the market and the stock increases in value. The performance of a stock can be measured through past data gathered from the stock, or from similar stocks.
Uncertainty can also be defined as being a situation with more than one outcome. However, uncertainty is not quantifiable. Instead uncertainty is a situation where the participant is not aware of the probabilities of the outcomes. Frank Knight, an economist from the University of Chicago, summarized the differences of Risk and Uncertainty by stating:
“Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated. The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating. It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an un-measurable one that it is not in effect an uncertainty at...

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...like the one represented at the end of the paper) to find area under the curve the represents the values between $600 and $500. After looking through the table we will find the area of the specified region is .4222 which translates to a probability of occurance being 42.22%. The standard score is positive, like that above, when outcome is above the mean, but it will be negative when it is below the mean. For example, , if we want to know the probability that the profit from Investment A will fall between $400 and $500, we will get a standard score of -1.42. Even though the standard score is negative we can find the probability in the same way, using the table, which will give us 42.22% probability. Since a normal distribution is symmetric about the mean, the probability of two separate outcomes on either side of the mean will have the same chances of occurring.

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