8 factor model

8 factor model - What Practitioners Need To Know . . ....

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What Practitioners Need To Know . . . About Factor Methods cc Z) g < < < 12 Mark Kritzman Windham Capital Management Financial analysts are concerned with factors, or common sources of risk that contribute to changes in security prices. By identifying such factors, analysts may be able to control a ponfolio's risk more efficiently and perhaps even im- prove its return, I will describe in general terms two approaches often used to identify factors. The first ap- proach, called factor analysis, al- lows analysts to isolate factors by observing common variations in the returns of different securities. These factors are merely statisti- cal constructs that represent some underlying source of risk; that source may or may not be observable. The second ap- proach, called cross-sectional re- gression analysis, requires that we define a set of security at- tributes that measure exposure to an underlying factor and deter- mine whether or not differences across security returns corre- spond to differences in these se- curity attributes. Factor Analysis I begin with a nonfinancial, hope- fully intuitive, example. I wilt ap- ply the insights gained by this example to show how we might go about identifying the factors that underlie the stock market. Suppose we wish to determine whether or not there are com- mon sources of scholastic apti- tude, based upon the grades of 100 students in the following nine courses—algebra, biology, calcu- lus, chemistry, composition, French, geometry, literature and physics. We proceed as follows. First, we compute the correlation between the algebra grades of students 1 through 100 and their grades in each of the other eight courses. Then we compute the correlations between their biol- ogy grades and their grades in each of the seven other courses. We continue until we have com- puted the correlations between the grades of every pair of cours- es—36 correlations in all. Table I displays these hypothetical corre- lations. That all these correlations are positive suggests the presence of a pervasive factor, which is prob- ably related to intelligence or study habits. In addition to this pervasive factor, there appear to be three other factors, or com- monalities, in performance. First, the variation in algebra grades is highly correlated with the variation in calculus and ge- ometry grades. Moreover, perfor- mance in calculus is highly corre- lated with performance in geometry. The grades in these three courses, however, are not nearly as highly correlated with the grades in any of the other six courses. We might thus conclude that there is a common aptitude that underlies performance in these three courses. Second, performance in biology is highly correlated with perfor- mance in chemistry and physics, and performance in chemistry is highly correlated with perfor- mance in physics. Again, perfor- mance in these courses does not correspond as closely with per- formance in any of the other courses. We might conclude that there
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8 factor model - What Practitioners Need To Know . . ....

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