In the simplistic two factor model, this type of analysis would result in a total of nine outcomes. The most common type of random factor analysis is called "Monte Carlo" analysis, where factor values are not estimated but are chosen randomly from a set bounded by the variable's own probability distribution.

For example a simple two factor analysis: We would expect that the value corresponding to the mean, in this case being BB, would appear the most times since the mean is the value with the highest probability of occurring.

Standards set for reporting investment performance ensure that investors are provided with the risk profile variability of performance for past performance of investments. Although both investments may provide the same overall return for a given investment horizon , the periodic returns demonstrate the risk differentials in these investments.

For example, because variability equates to risk, an investment that provided the same return every year is deemed to be less risky than an investment that provided annual returns that fluctuated between negative and positive. The output of any forecast will only produce the expected or mean value of that initiative - the outcome that the analyst believes has the highest probability of occurrence.

By forming the upside and downside cases we begin to get an understanding of other possible return outcomes, but there are many other potential outcomes within the set bounded by the extreme upside and downside already estimated. Related Articles.

We illustrate with financial statements from Apple Inc. The figure below presents one method for determining the fixed number of outcomes between the two extremes. Overview Historical performance data is required to provide some insight into the variability of an investment's performance and to help investors understand the risk that has been borne by shareholders in the past.

By assigning the probability of occurrence, let us assume: To finalize this study, the analyst would assign the probabilities for each outcome and then add those probabilities for any like values. The more factors one has in a model and the more factor scenarios one includes, the more potential scenario values are calculated resulting in a robust analysis and insight into the risk of a potential investment.

A three-factor model using three potential outcomes for each variable would end up with 27 outcomes, and so forth.

Risk analysis is concerned with trying to determine the probability that a future outcome will be something other than the mean value. Strict regulations over the calculation and presentation of past returns ensure the comparability of return information across securities, investment managers and funds. Drawbacks of Scenario Analysis The major drawback for these types of fixed outcome analyses are the probabilities estimated and the outcome sets bounded by the values for the extreme positive and negative events.

This method can help refine probability estimates using an intuitive process. For more insight, read Measure Your Portfolio's Performance.

By conducting scenario analysis an investor can produce a risk profile for a forecasted investment and create a basis for comparing prospective investments. Although they may be low probability events, most investments, or portfolios of investments, have the potential for very high positive and negative returns. Random factor analysis is completed by running thousands and even hundreds of thousands of independent trials with a computer to assign values to the factors in a random fashion.

A method to circumvent the problems inherent in the previous examples is to run an extreme number of trials of a multivariate model.