# LO 64.4: Describe Grinold’s fundamental law of active management, including its

LO 64.4: Describe Grinolds fundamental law of active management, including its assumptions and limitations, and calculate the information ratio using this law.
Portfolio managers create value, and potentially create alpha, by making bets that deviate from their benchmark. Richard Grinold formalized this intuitive relationship in the fundamental law of active management.1 This fundamental law does not provide a tool for searching for high IR plays, but it does present a good mechanism for systematically evaluating investment strategies. The law states that:
IR ~ IC x VBR
The formula for Grinolds fundamental law shows that the information ratio (IR) is approximately equal to the product of the information coefficient (IC) and the square root of the breadth (BR) of an investors strategy. The information coefficient is essentially the correlation between an investments predicted and actual value. This is an explicit evaluation of an investors forecasting skill. A higher IC score means that the predictions had a higher correlation (high-quality predictions). Breadth is simply the number of investments deployed.
Consider an example of an investor who requires an IR of 0.50. If this investor wants to time the market using an index and plans to only make four investments during the year, then he would need an IC of 0.25 as shown:
0.5 = 0.25 x T i
What would happen if this same investor instead decided to deploy a stock selection strategy based on either value or momentum plays? These two strategies both involve taking a high number of bets every year. If they placed 200 bets in a given year, then they would only need an IC of 0.035 instead of 0.25. A lower IC means lower-quality predictions.
0.5 = 0.035×7200
Grinolds fundamental law teaches us about a central tradeoff in active management. Investors need to either play smart (a high IC shows high-quality predictions) or play often (a high BR shows a lot of trade activity). Essentially, investors can be very good at making forecasts and place a small number of bets, or they will need to simply place a lot of bets. 1. Richard C. Grinold, The Fundamental Law of Active Management, Journal o f Portfolio
Management 15, no. 3 (1989): 30-37.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Grinolds framework ignores downside risk and makes a critical assumption that all forecasts are independent of one another. The Norwegian sovereign wealth fund has used Grinolds fundamental law in practice. Their philosophy is to take a high number of bets using a large list of entirely independent asset managers. This helps to keep forecasts independent and allows them to have reduced reliance on forecasting prowess while still endeavoring to achieve their benchmark IR goals.
In practice, it has also been noted that as assets under management go up, the IC tends to decline. This affects mutual funds, hedge funds, private equity firms, pension funds, and sovereign wealth funds alike. This is one reason why some mutual funds close to new investors and turn away new assets once they reach an internally set size.
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