Business and Personal Finance Dictionary

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• INDEPENDENCE
  
  Is a very important concept in probability and statistics. When the occurrence or nonoccurrence of an event has no impact or statistical influence on another event then the events are said to be independent of one another. When stock market or other asset returns are substituted for events, these observations are assumed to be independent. This assumption simplifies the mathematics of many pricing and portfolio models. However, it may be inaccurate, particularly during periods of high or increasing volatility. While the majority of observations may fall within the defined assumption, the occurrence of big change days has been demonstrated to occur more frequently than normally expected. Moreover, these relatively large price or rate changes tend to cluster within relatively narrow time frames. As a quick illustration, if a three standard deviation event is normally expected to occur once every 40 years or 10,000 trading days then the likelihood of two such events in a short time frame is expected to be 1 in 100,000,000 (10,000 x 10,000). This clearly has not been the case. It is critical to take into account the statistical interdependence for Value at Risk Programs, hedging, and derivative pricing models.
  
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