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In finance, multiple discriminant analysis (MDA) is used to classify securities into related groups for further analysis. This statistical technique compresses the variance, or distance, of a set of data from a mean value while preserving meaningful information that can be examined by other methods. For example, multiple discriminant analysis might be applied to a range of securities to establish membership in a manageable number of related groups. The behavior between these groups may then be examined by other statistical methods.
In choosing an individual security or assembling a portfolio, there are a number of analyses that might be performed. The accuracy of an analysis can be impaired when there are several variables to be considered simultaneously. Using multiple discriminant analysis, a range of data can be consolidated into three or more groups related by one or more variable factors. The elements around which the groups were formed are effectively eliminated from consideration while other data relations are preserved.
A set of securities might be divided into several groups by MDA according to a price rule defined as significant by the analyst. The behavior of these groups could then be examined relative to other factors, such as historical performance, without having to consider price as a variable. Several variable factors can be screened for and the interplay between related groups examined. Frequently, the goal of such an analysis is to create a Markowitz efficient portfolio.
According to theory, a Markowitz efficient portfolio is one that realizes the highest level of return for a given amount of risk. Further efforts to reduce risk would result in a decline in returns; attempts to increase returns would entail a disproportionate increase in risk. Analysis of the portfolio as a whole rather than the performance of individual securities is necessary to realize this goal. Multiple discriminant analysis is an important tool in implementing this type of statistically based portfolio theory.
Another model that makes extensive use of multiple discriminant analysis is the Altman Z-Score. This is a formula for predicting the odds that a company will go bankrupt in the near future. A Z-Score is based on the analysis of five different financial relations. Each unique ratio provides a different insight into the company's financial health. The combined analysis of these ratios and resultant Z-Score has proven to be 72% accurate in predicting corporate bankruptcy two years prior to filing for protection.
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