Technical Note - Remember Alpha

Comments The venerable straight-line equation Y = Bx + A is again being rediscovered, but this time by economists, mining engineers and geologists. Two economists, William Sharpe and Harry Markowitz, from the University of Chicago and Stanford University, respectively, won the 1990 Noble Prize in economics by showing that the price of individual stocks can be related to the Dow Jones industrial average (DJIA) using the straight-line equation. According to Bill Chidester, Investment Analyst, Scientific Investment, Sharpe and Markowitz strongly emphasized the role of the beta (B) value while considering the alpha (A) value to be "pretty unimportant." Chidester claims that alpha is the "mystery" value that causes individual stocks to behave independently of popular stock-market indices, such as the DJIA. For many years, mining engineers and geologists have routinely called alpha the "nugget" or surprise element in geostatistical analyses in which a designated distance (x-axis) is related to the variance of the grade (y-axis). Because the influence of the independent variable (distance) over the dependent variable (grade variance) is ideal when alpha is equal to zero, any increase in alpha represents a loosening of influence or control within the relationship. This can be good news or bad news - good news if you are an economist sorting out off-trend stocks and bad news if you are a mining engineer trying to predict sulfur in a coal seam. With many mining trends, such as those involving the relationship of distance to the variance of grade, a mathematical relationship can be formed. In geostatistical analysis, the point where a mathematical trend ends is known as the sill. If the difference between the variance of grade at the sill and at alpha can be determined, then an estimate of the relative control for a given distance can be obtained by comparing the sill value to alpha. The extent to which alpha approaches the value of the sill provides an indication of independence or loss of trend. The alpha concept may find application with distance, time or fluid problems. The point of change can be either a change in trend or the trend limit. However, even without a clearly defined point of change or trend limit, increasing alpha values always infer loss of trend. Alpha analysis should be regarded as a valuable tool when sorting out many sets of mining data. The application of this user-friendly concept to reserves, material transport, fluid flow and other areas has been, and will continue to be, the basis of many important past and future developments in mining and geology.