# FLAM or ... FLAW ?

**Nachiket Garde, CFA and Dr Tim Wilding**

The Fundamental Law of Active Management formalizes the concept of information ratio for a fund. It distills the value of active management, as expressed by the information ratio, into only two variables.

The first variable is the portfolio managers ‘skill’ in selecting securities. In other words, how well is the portfolio manager at assessing investment opportunities, expressed via forecasts ? In practice, the IC represents the manager’s estimated correlation of forecast with ex post residual return

The second variable is breadth; the number of independent investment opportunities. In other words, it represents the number of independent bets or factors associated with the strategy

The second variable, breadth, drives fund managers to express their view over multiple stocks, as the law stipulates that the alpha increased with the breadth, where the breadth was the number of stocks with forecast returns.

There are a couple of potential drawbacks to following this approach for a fundamental portfolio manager. Firstly, simple common-sense suggests that it’s hard work to generate information for a stock, and therefore, your opinion on the fiftieth stock is likely to be much worse (lower information) than the 1st. Given limitations of time and resources, it is highly unlikely that the analyst’s average IC is the same for an expanded coverage universe. Hence, a lower average IC may cancel any gains made from increasing breadth. Secondly, the requirement to have independent opportunities or sources of information, is seldom met in practice. Analysts typically rely on valuation frameworks for forecasting alpha. These valuation frameworks often have common factors used to derive forecasts, thereby reducing the number of independent sources of information. For example, if earnings yield is one of the factors used to evaluate stocks, there is only one independent source of information and breadth equals one.

The other motivation to increase the number of stocks in the portfolio is the premise that all managers should seek to have widely diversified portfolios. But this drive for diversification can actually hurt performance due to lower information on non-core assets included into the portfolio not for their alpha potential but due to their diversification potential. Therefore a fundamental portfolio manager has a better chance to outperform the benchmark when they run concentrated portfolios that are a true reflection of their stock picking skills.

Quantitative portfolio managers often employ optimization in their portfolio design. In this context, there are two further limitations of the principles associated with the FLAM in practice: 1) the formula ignores the impact of estimation error in investment information on out-of-sample optimized investment performance; 2) the formula assumes a quadratic utility unconstrained optimization framework that ignores the necessity of including mandate constraints required for defining portfolio optimality in practice.

In reality, constraints and inequality constraints in particular, are necessary. Long-only constraints limit liability risk which, although largely unmeasured in most portfolio risk models, is often an institutional requirement. Regulatory considerations may often mandate the use of no-shorting inequality constraints. Performance benchmarks may often mandate index related sets of constraints for controlling and monitoring investment objectives.

On the flip side, there are risks to running concentrated portfolios. In particular, during times of under performance, these portfolios, relative to larger portfolios, will suffer more . But this is a risk management challenge. It is worth noting that even a portfolio of well-diversified assets cannot remove risk completely. It will still be exposed to systematic risk, which is the uncertainty that faces the market as a whole. Also known as “undiversifiable risk,” “volatility,” or “market risk,” systematic risk cannot be diversified away. However, it can be mitigated somewhat by diversifying beyond equities into asset classes such as cash, fixed income, and alternative investments such as real estate and private equity, all within a suitable risk management framework.

Sapiat, through its EMA system, can be utilized to assist with this challenge. Sapiat, provides a range of factor models that can be used to analyse and break down the risk of investment portfolios. The EMA factors are generated using the EM (Expectation Maximisation) algorithm, one widely used in the AI (Artificial Intelligence) field. The EM algorithm is a learning algorithm that produces the most relevant set of factors without human input. The resultant factor models contain a set of factor loadings for each security. Through these loadings a risk profile can be inferred which can then be used for decision making. The factor loadings represent exposures to systematic underlying factors and the factor models can be used to perform an instantaneous Style Analysis of a portfolio showing sources of risk.

By not pre-imposing a factor structure in the risk models, the EMA factor model can be used to essentially pick up latent factors that are driving the returns of assets. For a concentrated portfolio, a lot of these risks are unknown to a large extent and utilizing a risk model with a pre-imposed factor structure runs the risk of missing out on some of these factors. Further, by incorporating a multi-dimensional GARCH framework, the EMA volatility forecast can be used to hedge systematic risks of concentrated portfolios accurately and more importantly, in a timely fashion. This is a critical enabler for managers of concentrated portfolios to react quickly to changing market conditions, and avoid extended periods of under performance.