• Table of Contents • Introduction • 1-Time Value • 2-Risk/Return • 3-Accounting • 4-Securities • 5-Business • 6-Regulatory • Case Studies • Student Papers
 2.2 Risk of a Single Asset 2.2.2 Expected Return

## 2.2.1 Probability Distribution

Assessing the risk of an asset requires that we have some sense for the range of possible outcomes. For example, a judge sentencing a youthful offender might consider the likelihood of different scenarios:
• worst case (pessimistic), the offender will commit only another minor crime;
• expected case (normal), she will commit no more crimes
• best case (optimistic), she will prevent others from committing crimes

Given this distribution, the judge might suspend the youthful offender's sentence.

Predicting a range of outcomes and assigning to them different probabilities can give further insight into risk. Using a probability distribution, we can model different outcomes. For example, the probability distribution of the results of throwing two dice is shown in the table to the right --

Example

 Result Probability 2 1/36 = 2.8% 3 2/36 = 5.6% 4 3/36 = 8.3% 5 4/36 = 11.1% 6 5/36 = 13.9% 7 6/36 = 16.7% 8 5/36 = 13.9% 9 4/36 = 11.1% 10 3/36 = 8.3% 11 2/36 = 5.6% 12 1/36 = 2.8% Total 36/36 = 100%

The most likely throw is a 7 - but it happens only one-sixth of the time. Possible outcomes range from 2 to 12, although the likelihood of throwing a 2 or 12 is significantly lower than throwing a 7. What if you wanted to throw at least a 7? You would have to consider variability in assessing risk. Even though 7 would be the most frequent throw, you might throw less. In fact, there is a 41.6% chance that you will throw less than a 7.

 2.2 Risk of a Single Asset 2.2.2 Expected Return