What Grinold means by the above formula is that a manager’s value-added (Information Ratio) is a function of his selection skill (Information Coefficient) and the number of opportunities (N) he has.
No doubt thousands of CFA candidates have read this, memorized the formula and nodded sagely. They may have even tried to apply it in their working lives. Let's look at some of the underlying assumptions behind this model and understand how a blind application of this work may lead to suboptimal results.
What do you mean by IC? Most quants think they know how to measure IC, at least mathematically. However, the Information Coefficient for any selection process will vary according to time horizon. Is your IC the same for 1 day as for 1 month or 1 year? If you assume a flat IC for any time horizon and not incorporate trading cost assumptions this model will generate portfolio turnover that is uncontrollably high. Grinold in his later works elaborated on this turnover issue (see Grinold and Stuckelman, 1993; also Grinold and Kahn, 1995).
What do you mean by N? N is the number of independent opportunities available. If you are running a 100 stock portfolio does that mean that the number of independent opportunities, or ideas, is 100? What if you were picking stocks based on some fundamental criteria (e.g. low P/E) or macro theme (e.g. rising inflationary expectations). Is N equal to 1, 100 or somewhere in between?
Putting it into English
No doubt thousands of CFA candidates have read this, memorized the formula and nodded sagely. They may have even tried to apply it in their working lives. Let's look at some of the underlying assumptions behind this model and understand how a blind application of this work may lead to suboptimal results.
What do you mean by IC? Most quants think they know how to measure IC, at least mathematically. However, the Information Coefficient for any selection process will vary according to time horizon. Is your IC the same for 1 day as for 1 month or 1 year? If you assume a flat IC for any time horizon and not incorporate trading cost assumptions this model will generate portfolio turnover that is uncontrollably high. Grinold in his later works elaborated on this turnover issue (see Grinold and Stuckelman, 1993; also Grinold and Kahn, 1995).
What do you mean by N? N is the number of independent opportunities available. If you are running a 100 stock portfolio does that mean that the number of independent opportunities, or ideas, is 100? What if you were picking stocks based on some fundamental criteria (e.g. low P/E) or macro theme (e.g. rising inflationary expectations). Is N equal to 1, 100 or somewhere in between?
Putting it into English
While I am a math geek as much as the next quant, I like to put the ideas into English when I apply them to the real world. The idea behind the Fundamental Law of Active Management is to size the bets according to the edge you have.
Grinold's work is actually a thematic variation on Kelly’s Criterion. John Kelly was a Bell Labs engineer in the 1950s who posed the following problem. Supposing a gambler overheard underworld types fixing a horse race on the telephone, but there was noise on the line. What should the gambler bet given this knowledge and the level of noise (= probability of correct information) on the line? This discussion could then be generalized to a treatise on information content, signal-to-noise ratio, etc.
Grinold's work is actually a thematic variation on Kelly’s Criterion. John Kelly was a Bell Labs engineer in the 1950s who posed the following problem. Supposing a gambler overheard underworld types fixing a horse race on the telephone, but there was noise on the line. What should the gambler bet given this knowledge and the level of noise (= probability of correct information) on the line? This discussion could then be generalized to a treatise on information content, signal-to-noise ratio, etc.
