when it comes to statistics in finance investors often turn to metrics such as correlation when discussing diversification and the variation of portfolios over time however according to s p dow jones indices the measure known as asset dispersion has strong qualifications as a complementary tool 1 understandably since the dispersion of possible returns on an asset provides insight about the volatility and risk associated with holding that asset the more variable the return on an asset the more risky or volatile it is 
for example an asset whose historical return in any given year ranges from 10 to 10 can be considered more volatile than an asset whose historical return ranges from 3 to 3 because its returns are more widely dispersed measuring dispersionthe primary risk measurement statistic beta measures the dispersion of a security s return relative to a particular benchmark or market index most frequently the u s s p 500 index a beta measure of 1 0 indicates the investment moves in unison with the benchmark a beta greater than 1 0 indicates the security is likely to experience moves greater than the market as a whole a stock with a beta of 1 3 could be expected to experience moves that are 1 3x the market meaning if the market is up 10 the beta stock of 1 3 climbs 13 the flip side is that if the market goes down that security will likely go down more than the market although there are no guarantees of the magnitude of the moves a beta of less than 1 0 signifies a less dispersed return relative to the overall market for example a security with a beta of 0 87 will likely trail the overall market if the market is up 10 then the investment with the lower beta would be expected to rise only 8 7 alpha is a statistic that measures a portfolio s risk adjusted returns that is how much more or less the investment returned relative to the index or beta a return higher than the beta indicates a positive alpha usually attributed to the success of the portfolio manager or model a negative alpha on the other hand indicates the lack of success of the portfolio manager in beating the beta or more broadly the market 