The U.S. stock market is a complex system.

Contrary to the assertions of the efficient market theorists and random walk advocates, we find that price behavior in the U.S. stock market is not entirely efficient or random. Active investing can be rewarding. However, simple rules—buy low-P/E stocks, buy "value," buy small-cap—cannot provide superior returns on a consistent basis.

In a 1989 Journal of Portfolio Management article, we introduced the concept of the market as a complex system, in which prices are driven by numerous interacting factors. These include specific company fundamentals, such as earnings and growth rates; macroeconomic variables, such as interest rates and inflation; and behavioral factors, such as investors' tendency to overreact and to herd. As a result, the market is permeated by a complex web of return regularities.

Regularity in stock price movements implies predictability, which may be exploited to produce superior investment performance. Given the complexity of the market, detection of such investment opportunities is beyond the scope of the human mind alone. It requires computerized statistical modeling of a large number of theoretically plausible and intuitively sensible return-predictor relationships over a broad and diverse range of stocks.

The market's complexity requires a rich, multidimensional model.

We model a large number of potentially valuable return-predictor relationships across the broadest possible equity universe. This unified approach, which we introduced in a Journal of Investing article in 1995, has several benefits over a narrower, more segmented approach. It takes advantage of all the information provided by a diverse range of securities. The effect of interest rate changes on growth stocks, for instance, may tell us something about the behavior of value stocks, information that a focus on value stocks alone would not reveal. A unified approach is thus able to provide more robust insights.

The modeling process also considers variations in the relationships between returns and potential return predictors over different types of stocks and different market environments; earnings revisions, for example, may have a greater impact on growth than on value stocks. It also allows for nonlinearities in effects; a series of earnings surprises, for instance, may have a diminishing impact on stock price.

Breadth of inquiry combined with depth of analysis increases the number of potentially profitable investment opportunities we can detect and the accuracy of the predicted returns from those opportunities. This allows us to build portfolios that are diversified across many small exposures to numerous opportunities, maximizing the potential for superior investment performance.

A unified approach preserves the law of one alpha.

Our unified approach affords us a coherent framework for analysis. The “law of one alpha,” which we introduced in a 1995 Journal of Portfolio Management article, says that every stock has one and only one alpha. Although this would seem to be obvious, it is not always the case in practice; segmented approaches may use different models for different style or size categories, resulting in multiple estimated alphas for the same stock. With a unified approach, each stock in the universe can be consistently related to every other stock.

Return-predictor relationships must be disentangled.

Robust insights into stock price behavior emerge only from an analysis that carefully considers numerous factors simultaneously. In defining “value,” for example, a model that grapples with the market's complexity does not confine itself to a dividend discount model (DDM) estimate of value, but also examines earnings, cash flow, sales, and dividend yield, among other variables. These variables may be closely correlated with each other, as well as with industry effects. For example, a simple low-P/E screen would select a large number of bank and utility stocks.

Naïve attempts to relate returns and potentially relevant predictors do not take correlation into account. Quintiling or univariate analysis, for instance, naïvely assumes that prices are responding only to the variable under consideration. By contrast, simultaneous analysis of all relevant variables takes into account and adjusts for any correlations; the results of such analysis provide a truer picture of real return-predictor relationships.

We developed the concept of disentangling in the 1980s, and described it in a Graham and Dodd Award winning article in Financial Analysts Journal in 1988. Disentangling forms a cornerstone of our approach. Analyzing return-predictor relationships simultaneously, in a multivariate framework, allows us to extract “pure” returns—that is, the expected return to each predictor, uncontaminated by the possible influences of other factors.

Pure returns are superior to naïve returns.

As we demonstrated in a series of Financial Analysts Journal articles in 1988 and 1989, pure returns, unlike naïve returns, distinguish real effects from mere proxies. Based on naïve analyses of returns to market capitalization, for example, investors long thought that small- cap stocks delivered abnormal returns in the month of January. A sophisticated, multivariate analysis shows that these returns really reflect the tax-related trading habits of investors, not firm size.

Pure returns also reveal real investment opportunities, and avoid spurious ones. Based on univariate analysis, naïve returns to high book/price exhibit a negative correlation to market movements. Pure returns to book/price, however, exhibit little correlation to the market. Based on the results of multivariate analysis, investors seeking shelter in a storm would be better off buying stocks with high yields.

By controlling for cross-correlations, multivariate analysis produces pure returns that are less noisy than naïve returns. Thus pure returns are less volatile, and more predictable, than naïve returns.

An integrated investment process helps to preserve the value of investment insights.

No matter how potentially valuable the insights derived from research and the security selection process, they are only as good as the processes used to implement them. Poor portfolio construction and careless trading can erode or even obliterate the return potential of good insights.

A portfolio optimization process that is customized to include exactly the same dimensions found relevant by the stock selection process helps to ensure that all the opportunities detected by the modeling process are exploited, while all the risks detected are accounted for and controlled. A monitoring system feeds transaction cost estimates back to the portfolio optimizer in order to protect value-added from being eroded by trading costs. And a performance attribution system customized along the same dimensions as security selection and portfolio optimization offers the transparency needed to ensure that all systems are working as expected. We introduced these ideas in a Journal of Investing article in 1995.

In portfolio construction, allowing residual risk to vary opportunistically within a given range can enhance portfolio returns.

The optimal level of residual risk for a portfolio is the level that allows the portfolio to provide the highest expected return, given the manager's skill level and the investor's risk tolerance parameters. Placing too much emphasis on risk can result in sacrificing potential return, as we demonstrated in a 1996 Journal of Portfolio Management article.

For example, index-plus portfolios (and similarly constrained enhanced passive portfolios) seek modest levels of alpha (typically less than 1%) with a hard limit on residual risk (usually 2%). Such hard and fast limits on portfolio risk can encourage investors to take less risk than their real risk tolerances may allow, or to ignore more skillful managers in favor of less skillful ones just because the latter's portfolios have less residual risk. Managers facing such constraints may feel motivated to take less risk than their skill warrants. In these cases, the result is often needless sacrifice of potential return.

For market-neutral long-short and enhanced active 120-20, 130-30, and 200-100 portfolios, integrated optimization can create added flexibility in enhancing return and controlling risk.

Short selling allows the manager to exploit underperformers as well as outperformers. When Jacobs Levy added market-neutral long-short to our repertoire of strategies in 1990, we recognized that the full benefits of this strategy emerge only from an integrated optimization. As we showed in a number of articles that have appeared in the Financial Analysts Journal and the Journal of Portfolio Management since the mid-1990s, the construction of optimal long-short portfolios considers potential long and short positions simultaneously. While a separately optimized long portfolio can be combined with a separately optimized short portfolio, each portfolio remains benchmark-constrained and offers none of the real benefits of market neutral long-short construction.

In a 1998 Financial Analysts Journal article, we extended this concept beyond market neutral portfolios to include long-short portfolios that maintain a full market exposure. Long-short portfolios with any given exposure to the underlying market benchmark should be constructed with an integrated optimization that considers simultaneously both long and short positions and the benchmark asset. Rather than combining a long-only portfolio with a market neutral portfolio, it is better to blend active long and short positions so as to obtain a desired benchmark exposure.

That 1998 article laid the foundation for Enhanced Active Equity Strategies, deriving precise formulas for optimally equitizing an active long-short portfolio when exposure to a benchmark is desired. Our Enhanced Active Equity 120-20, 130-30, and 200-100 Strategies employ integrated optimization and short selling to take fuller advantage of our investment insights. In a 2006 Journal of Portfolio Management article, we highlighted the advantages of Enhanced Active Equity portfolios over long-only and other long-short approaches. The benefits of integrated optimization accrue to any long-short portfolio, including market neutral and enhanced active.

The alpha available from security selection is separable from the asset class from which the securities were selected and transportable to any asset class.

A market-neutral long-short portfolio reflects the manager's security selection skills, abstracted from the performance of the asset class from which those securities were selected. The excess return/residual risk of a long-only portfolio can also be isolated by combining the portfolio with short derivatives positions that offset the portfolio's market return component. The characteristics of virtually any asset class can be added back to the long-short or neutralized long-only portfolio via the use of derivatives. We described “alpha transport” in a 1999 article in the Journal of Portfolio Management.

Jacobs Levy was among the first money managers to offer “equitized” long-short portfolios, created by combining an active long-short portfolio with equity futures. Other derivatives could be used to create exposure to other asset classes—bonds, international equity, etc. With the use of derivatives, the active return, or alpha, available from selecting securities from one asset class can be transported to any asset class.

Alpha transport affords the investor increased flexibility in asset allocation because it separates the manager selection decision from the asset allocation decision. The investor can select the manager best able to add value, in whatever asset class, and transport that performance, via derivatives, to achieve any desired asset allocation.

Investment insights can be realized as profits only if portfolio holdings are sufficiently liquid and efficiently traded.

Asset managers can succeed for their clients. Asset gatherers only handicap themselves and their clients' returns by amassing ever-larger position sizes, which become increasingly costly to trade. We maintain strict capacity limits in order to remain liquid and nimble.

We are also a leader in implementing sophisticated electronic trade execution and monitoring systems. As we discussed in Investment Management Technology in 1992, these  systems are designed to minimize trading costs and maximize our ability to exploit investment insights.