in the 1980s,richard grinold was seeking a method of relating performance, skill,and breadth in investing. so for instance,you might be a very skilled investor, meaning that you can pick stocks well,but you might not have many opportunities orbreadth to exercise that skill. so grinold felt that there mustbe some equation whereby we could combine skill and breadth tocreate an estimate of performance. he developed a relationship he called the fundamental law ofactive portfolio management.
i'm going to state it here at thebeginning of the lesson, and then spend the rest of the lesson trying to justifyit and show you why it makes sense. and here's his expression, performance is equal to skilltimes the square root of breadth. so we need some measure of skill andsome measure of breadth. so if you want to improve yourperformance you can improve skill, or you can find more andmore applications or methods or opportunities for applying that skill. so, as an example breadth might relateto how many stocks you invest in and
skill relates to yourskill in choosing them. so, again you can invest ineither improving your skill or improving your breadth. so performance is summarized insomething called information ratio, which is very much like the sharperatio that we've discussed before, but it refers to the sharpe ratio of excessreturns, in other words the manner in which the portfolio manager isexceeding the market's performance. skill is summarized in somethingcalled information coefficient and and breadth is just how manytrading opportunities we have.
okay.so, we'll expand more and more onthis as we go through the lesson.
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