# About the number of independent forecasts in the Fundamental Law of Active Management

The original FLAM predicts the information ratio by

$$IR = IC \times \sqrt{N}$$ where $IR$ is the Information Ratio, $IC$ is the information Coefficient and $N$ is the number of independent forecasts. Later this law is improved several times, but the term $IC \times \sqrt{N}$ is always present. I don't seem to understand (and find a good practical example) of what is exactly $N$ and how to calculate it.

I would be grateful if someone explains the exact definition of $N$. What is an independent forecast? It may seem a stupid question to some, but for me it is fundamental.

In Zhou and Jain, Active Equity Management, it is written:

$N$ is the number of independent bets in a year, it has two aspects: the number of cross-sectional bets on different assets at any point in time and the number of independent bets on the same asset across time.

In this context what exactly is cross-sectional bet and independent bet on the same asset? It would be best if someone gives a small portfolio example.

There is no such thing as number of independent bets when one is betting on a common random factor as we quants usually do. Grinold & Kahn’s formula is only relevant when the factor payoff is a constant over time. This is not interesting in practice. When the factor payoff is random, then Ding and Martin The Fundamental Law of Active Management: Redux (2017) showed that the portfolio IR is basically IC divided by IC standard deviations.

To put it more bluntly , the G&K formula is useless and misleading. It is a joke that CFAers have to learn this stuff.

See the paper by Ding and Martin (2017), "The fundamental law of active management, Redux", published in the Journal of Empirical Finance.

• Could you add some detail to make this answer self-contained? Sep 29 '17 at 22:53

You can think of it as the number of trading positions on Uncorrelated instruments, in a year.

So backtest your strategy in some uncorrelated instruments for a year, and sum their positions count.