# Fundamental Law of Active Management

A measure of the effectiveness and quality of a manager’s skill set and his/her ability to apply the knowledge actively at work

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## What is the Fundamental Law of Active Management?

Developed by Richard Grinold and Ronald Kahn, the Fundamental Law of Active Management states that an active manager’s productivity depends on the quality of his/her skills and, consequently, the frequency in which the skills are applied at work. The law can also be expressed in an equation. The active manager should produce the Information Ratio (IR), which is the added value in every unit of risk added.

### Information Ratio Formula

To produce the Information Ratio (IR), the manager’s skillset is expressed by the Information Coefficient (IC)2. The extent of skill application is expressed as Breadth, which is the manager’s derived independent signals. The formula is given below:

Where:

• IC is the Information Coefficient
• Breadth is the number of investment decisions in a year

In the equation, the risk is the input, the strategy’s productivity is IR, and the value-added is the output. At a particular risk level, the value-added should be the specified risk multiplied by the IR. Therefore, the active manager needs to increase the frequency of utilizing his/her skills at work, which is positive Breadth, or he/she can increase the quality of his/her skill set, which is positive IC.

### Summary

• The Fundamental Law of Active Management measures the effectiveness and quality of a manager’s skill set and his/her ability to apply the knowledge actively at work.
• The law enables the appraisal of a manager’s productivity and comparability with other factors of management of an entity.
• Information Ratio (IR), Information Coefficient (IC), and Breadth help in determining the factors that are vital in the fundamental law of active management.

### Transaction Costs

Information Coefficient (IC) can be defined as the level of correlation in a forecast with returns realized. The correlation shows how good a manager is at forecasting. The higher the correlation, the better a manager is rated in their forecasting ability. Forecasting, however, is just the tip of the iceberg in rating a manager’s ability. Transaction costs determine a manager’s success rating in a portfolio.

Transaction costs offset profits realized in a successful campaign in forecasting. However, they reduce the bets available for the manager to undertake. Such circumstances of reduction tend to make rather skillful managers fail in their forecasting campaigns, especially in asset management.

Transaction costs are a vital concern for an active manager. He/She is interested in the net in transaction costs that have been realized in that instance. Managers who take transaction costs into account while maximizing IC are successful in maximizing IR. The alpha obtained in a skilled forecast can be much less than the ones measured in IC due to the presence of transaction costs.

An adjustment of the IC is prudent for the proper presentation of the fundamental law equation to reflect the prioritized bets that the manager needs to act upon. The prioritized bets should be those that have more forecasted returns than the transaction costs projected.

### Weaknesses in the Fundamental Law of Active Management

The simplicity of the law exposes it to a lot of weaknesses. For example, most of the assumptions in the law prove to be an omission. The equation seems to have been developed in the absence of transaction costs. When the transaction cost is put into perspective, there arises the urgent need to redefine Breadth and IC. Breadth should be taken into account for a complete equation and should not be influenced by other factors. However, independence cannot be precisely measured without an estimation error.

So, the equation conceals technical activities, such as asset allocation, and it can be difficult since the results will be inaccurate. The formula also ignores important portfolio considerations as it takes the expected IR of each manager in isolation.

Information Ratio does not need to show a correlation with the rest of the portfolio. When IR is uncorrelated to the rest of the portfolio, even a negative value can contribute positively to the portfolio.

### Conclusion

The focus should be concentrated on the effects of transaction costs and independence on Breadth. Also, the effects of transaction costs on adjusted cost skill measure and the adjusted cost IC should be considered to properly measure productivity. There is no precise metric that offers definite error-free estimation, and caution should be exercised on metrics that claim to be error-free.

Therefore, forecasting a manager’s skill and Breadth is approximate and can sometimes be disappointing. The best strategy in using the equation is by aiming at the marginal impact of an additional manager on the performance of a fund, instead of focusing on the isolated measure of IR of a manager or a strategy.