Article by Durga Nand Jha
The fundamental law of active portfolio management helps to explain the value addition of any investment strategies.
Fundamental Law of Active Management, developed by Richard Grinold and Ronald Kahn, states that an active manager’s productivity depends on the quality of the manager’s skill and, consequently, the frequency in which the skills are applied at work in a portfolio management.
Active portfolio management is typically mixed with the constraints that limit the portfolio manager from fully exploiting their forecasting abilities. Constraints, such as long-only, industry or sector mandated concentration or the value-growth neutrality further limit a portfolio manager from taking independent bets or to the construction of an active portfolio’s composition.
Expected value addition to the portfolio depends on both the portfolio manager’s forecasting skills and the manager’s flexibility in taking the independent bets, which reflects those forecasts. The “fundamental law of active management” gives higher value addition for an actively managed portfolio based on the forecasting ability of the portfolio manager and the breadth of the application.
Active Security Returns
The return of any portfolio ultimately depends on the ability of the portfolio manager to forecast the security returns.
The triangular correlation above reflects the relationships between forecasted and realized returns and security active weights. The base represents the value addition of the portfolio through active management. The correlation of the active returns is majorly attributable to active weights:
The portfolio would add value through active weight in the security with positive active returns and negative active weights with the negative active return. Alternatively, the performance of the portfolio is related to the cross-sectional correlation of the portfolio active security weights and the portfolio realized active returns - the security data in the bottom two corners of the correlation triangle.
Information Coefficient (IC)
Further, the manager can only add value to the portfolio, if he can correctly forecast the return. Therefore, the correlation of the forecasted active return and the realized active returns will add value to the portfolio. This cross-sectional relation at the top of the triangle and the realized active returns at the right corner is commonly called the information coefficient (IC).
- Information coefficient range between +1 to -1.
- The ex-ante IC must take the positive value otherwise an investor would not pursue active portfolio management.
Managers with high information coefficients will be able to add more value to the portfolio over time as the portfolio manager will be able to correctly forecast the performance of the stock. An information coefficient (IC) measures the strength of the manager’s forecasting abilities or bets in the portfolio management process.
Transfer Coefficient (TC)
A portfolio manager with high information coefficient (high forecasting ability) will be able to add value to the portfolio over time – but only to the extent that a portfolio manager can exploit those forecasts in the construction of the managed portfolio. The correlation between the forecasted active returns on the top of the triangle and the active weights in the left corner measures the degree to which managers' forecasts are translated into active weights. This cross-sectional relationship is termed the transfer coefficient (TC).
Transfer coefficient measures the degree to which the manager’s bet (signal) is transferred to active portfolio weights. The transfer coefficient turns out to be a simple scaling factor in the generalized fundamental law and is an intuitive way to measure the extent to which portfolio construction constraints reduce the expected value of forecasting ability. In the ideal world without any constraints on portfolio construction, a well-constructed portfolio will have a transfer coefficient of 1.0. However, in the real world, a portfolio manager often works under portfolio construction constraints, such as no short selling, sector or industry concentration, turnover limit, or benchmarking of a portfolio, which produces the transfer coefficient of less than 1.0. The transfer coefficient suggests why the portfolio performance in practice is often lesser than what is predicted by the original form of the fundamental law.
The Basic Fundamental Law
The fundamental law of active management identifies the ex-ante relationship between the portfolio manager's expected performance and the actual performance of the portfolio.
Where BR (breadth) is the number of independent “bets” in an actively managed portfolio. Breath is the number of times a portfolio manager uses his/ her bets in a year. The information coefficient measures the accuracy of those independent bets of the portfolio manager. Information ratio (IR) is the active return (E(RA)) per unit of active risk (σA). Therefore, another form of the equation can be:
The important lesson of the fundamental law is that breadth of application, as well as the quality of the manager’s forecast, dictates the value to be added through active management.
The Full Fundamental Law
In the absence of constraints, the transfer coefficient is 1 in the portfolio construction. However, including the impacts of portfolio constraints such as no short sell, industry or sector-specific concentration or turnover limit leads to transfer coefficient lower than 1. After, including the impact of constraints, the full fundamental law can be arranged as:
Similar to the information coefficient, the transfer coefficient is also a simple scaling factor for the measurement of value addition to the portfolio. Transfer coefficient is an additional adjustment to the breadth, which is reflected as a constraint to the independent bets.
The fundamental law of active management is quite intuitive. The expected active return of the portfolio is the product of below four key parameters:
- The transfer coefficient, which measures the structuring of the portfolio
- The information coefficient, which measures the manager's forecasting skill
- Breadth, which measures the number of independent bets, active decisions available to an active manager per year
- Portfolio active risk, which measures the level of aggressiveness
Jha is currently the Chief Investment Officer of Prabhu Capital Limited and has more than 8 years of experience in the Investment Banking domain with MNCs like KPMG, Mercer, and Infosys. Mr. Jha is an MBA graduate and a former CFA charter-holder and former FRM charter-holder.