Interpreting Independent Bets in the Fundamental Law of Active Management
Summary
The document asks what the number of independent forecasts, N, means in the Fundamental Law of Active Management, commonly expressed as information ratio equal to information coefficient times the square root of N. It quotes a definition that describes N as independent bets over a year, combining cross-sectional bets across assets at a point in time with bets on the same asset across time. The question seeks a practical portfolio example but does not provide one.
The responses disagree about the formula’s practical value. One argues that counting independent bets is not meaningful when strategies rely on a common factor with random payoffs, and points to Ding and Martin’s 2017 reformulation, which relates portfolio information ratio to the information coefficient and its variability. Another offers a rough interpretation as positions in uncorrelated instruments over a year. These are brief comments, not a full derivation or agreed calculation procedure; the document leaves unresolved how to measure independence in a real portfolio.
Key ideas
- The original formulation scales information coefficient by the square root of the number of independent forecasts.
- The cited definition combines bets across assets with repeated bets on the same asset over time.
- A response questions the count when factor payoffs are random and refers readers to a revised formulation.
- Counting positions in uncorrelated instruments is offered as a rough practical interpretation, not a detailed method.
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# About the number of independent forecasts in the Fundamental Law of Active Management
# 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.
## Answer by zack young (score 1)
https://quant.stackexchange.com/a/36541
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.
## Answer by zack young (score 0)
https://quant.stackexchange.com/a/36239
See the paper by Ding and Martin (2017), "The fundamental law of active management, Redux", published in the Journal of Empirical Finance.
## Answer by Amin Saqi (score 0)
https://quant.stackexchange.com/a/50708
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.