Strengths and Limitations of Fundamental Law

Strengths and Limitations of Fundamental Law

Strengths of Fundamental Law

As discussed in the previous section, the fundamental law of active management can be employed in sectors such as security selection, sector rotation, and market timing.

Limitations of Fundamental Law

I. Ex-ante Skill Measurement

The information coefficient (IC) is the correlation between investors’ forecasts and the actual outcomes of a portfolio. It is a critical element of the fundamental law. Besides investors have the tendency to overestimate their skills in the assumed IC. We should, therefore, acknowledge the challenge of accurately assessing an investor’s skills. Besides, ability forecasts are not constant across the asset segments. In fact, ability forecasts vary over time.

Since the information coefficient varies over time, Qian and Hua (2004) added uncertainty about the level of skill to the basic form of the fundamental law. They showed that:

$$ \sigma_A=\sigma_{IC}\sqrt N\sigma_{RM} $$


  • \(\sigma_A\) is the realized active portfolio risk.
  • \(\sigma_{RM}\) is the benchmark tracking risk predicted by the risk model.
  • \(\sigma_{IC}\) is the additional risk induced by the uncertainty of the information coefficient.

II. Independence of Investment Decisions

The number of individual assets does not adequately measure the strategy breadth in cases where there is a correlation of the active returns between individual assets, and forecasts are dependent from period to period. For instance, applying the fundamental law concepts to hedging strategies using any form of arbitrage increases the breadth beyond the number of securities.

Clarke, de Silva, and Thorley (2006) proposed a more practical measure of breadth given by:

$$ BR=\frac{N}{1+\left(N-1\right)\rho} $$


  • \(N\) is the number of decisions.
  • \(\rho\) is the same correlation between the decisions.


Two active investment managers, A and B, construct a portfolio every quarter by selecting individual stocks of the S&P 500. Both managers calculate their information ratios based on the fundamental law of active management. Manager A has a substantially higher information ratio relative to manager B. In a bid to establish why manager A’s information coefficient is higher, the two managers come up with the following possible reasons:

  1. Correlation of the active returns on the stocks of the S&P 500 stocks.
  2. Correlation of the stocks from quarter to quarter.
  3. Different information coefficients for different stocks.

Based on the limitations of the fundamental law, which of the following statements gives the most accurate reason for manager A’s higher information ratio relative to manager B?

  1. I and II
  2. II and III
  3. I, II and III


The correct answer is C.

Statement I is correct. The active returns on the individual stocks in the S&P 500 are probably correlated. For this reason, the number of independent monthly decisions is lower than 500. This is referred to as cross-sectional dependence.

Statement II is correct. A stock that is forecasted to outperform in one quarter is likely to retain the outperformance forecast for several consecutive quarters. This is referred to as time-series dependence.

Statement III is correct. The fundamental law of active management assumes an identical information coefficient for all forecasts. However, there is a possibility of information coefficient changing with time. Indeed, it could vary between different sets of stocks.

Reading 45: Analysis of Active Portfolio Management

LOS 45 (f) Describe the practical strengths and limitations of the fundamental law of active management.

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop GMAT® Exam Prep

    Daniel Glyn
    Daniel Glyn
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.
    Nyka Smith
    Nyka Smith
    Every concept is very well explained by Nilay Arun. kudos to you man!
    Badr Moubile
    Badr Moubile
    Very helpfull!
    Agustin Olcese
    Agustin Olcese
    Excellent explantions, very clear!
    Jaak Jay
    Jaak Jay
    Awesome content, kudos to Prof.James Frojan
    sindhushree reddy
    sindhushree reddy
    Crisp and short ppt of Frm chapters and great explanation with examples.