Open Questions Introduction For 20 chapters, we have aspired to be magicians. We have attempted to present a comprehensive and seamless theory: covering every aspect of active portfolio management, and smoothly flowing from foundations to expected returns and valuation to information processing to implementation. We must now confess—if you don't already know—that the theory isn't seamless. We have swept aside, ignored, or simply assumed away the poorly understood aspects of portfolio management— the open questions—that require additional work. Successful active management efficiently utilizes superior information. The search for the next source of superior information is an inherent open question all the time for every active manager, but it isn't an open question for active management. We will not deal here with any specifically focused valuation questions (e.g., what combination of accounting variables correlates most closely with future returns?). Instead, we wish to highlight open questions for the process of active management. Our goal is to emphasize that we haven't completed the theory of active portfolio management. It is still fertile ground for research.1 1In 1900, the mathematician David Hilbert presented a now-famous list of important open questions as a challenge and a research plan for the mathematics community for the twentieth century. This book is appearing at the beginning of the twentyfirst century, but we cannot claim ambitions quite as lofty.
Page 574 These open questions will cover the general topics of • Dynamics • Transactions costs • Liabilities, asset allocation, and risk over time • Nonlinearities • After-tax investing • Behavioral finance Dynamics Active portfolio management is a dynamic problem. We manage portfolios over time. We confront a flow of information (and noise). Risk changes as volatilities change and as our exposures change over time. (Benchmark timing is just the most obvious example.) Transactions costs change over time and with our speed of trading. Active portfolio management confronts these changing parameters simultaneously. With a proper frame, managers should make investment decisions now, accounting for these dynamics and interactions now and in the future. This full dynamic problem is both complicated and important. One simple open question is, when should we trade? This simple question demands more than just a static analysis. If transactions costs were zero, the solution would be obvious: Trade every time the alpha changes. But transactions costs aren't zero. When should we trade, given the dynamics of returns, risks, and costs over time? Another open question concerns dynamic strategies and risk. Even if single-period returns are normal or lognormal, dynamic strategies can generate skewed and optionlike return patterns. Portfolio insurance is one example. So another open question is, how should we decide on an appropriate dynamic strategy, and what are its implications for our return distribution? Transactions Costs As we stated in Chap. 16, there is no CAPM or Black-Scholes model of transactions costs. A complete and practical model of transactions costs would cover three important aspects: tightness, depth, and resiliency. Tightness measures the bid/ask spread. Depth measures
Page 575 market impact. Resiliency measures how depth or market impact evolves over time. An investor buys a large block and pushes up the price. How long will it take for the price to sink back to equilibrium? What factors influence resiliency? One open question is, how do we model tightness, depth, and resiliency? A second open question is, how do transactions costs in one stock influence transactions costs in other stocks? Liabilities, Asset Allocation, and Risk Over Time Investors choose assets based on their future liabilities. This is most obvious in strategic asset allocation. Accurate liability modeling is one open question. Liabilities aren't certain. They are often contingent on other factors (e.g., inflation, dead or alive). Another question concerns managing assets against fixed-horizon liabilities. How should our asset allocation change as we approach retirement, and move past it? Nonlinearities Nonlinearities arise in at least two contexts in finance. We empirically observe nonlinear responses to certain exposures, particularly size. Relative behavior along the size dimension is still poorly understood. How do small stocks behave relative to midcap, large, and megacap stocks? Size is a pervasive issue in portfolio management. It enters into benchmarks and market averages. It is linked to the typical long-only constraint. The open question is, How do we adequately capture the nonlinear (and multidimensional) behavior of size? Quite separately, researchers have investigated the applicability of nonlinear dynamic models like chaos or catastrophe theory to finance. An open question: Do nonlinear models offer any predictive power for understanding financial market behavior? After-Tax Investing Managing after-tax returns is extremely complicated. It combines all the intricacies of dynamic portfolio management with wash sale
Page 576 rules, multiple tax rates dependent on holding periods, and even calendar date dependencies. We should respond differently to a set of alphas we receive in January from the way we respond to one we receive in December. We will never solve this problem exactly. The current approaches to after-tax investing are reasonable but simplistic. Most analyze the oneperiod problem, placing a penalty on net realized capital gains each period. There are two open questions here: How good are these simple approaches, and how much better can we do? Behavioral Finance Our final question touches on a topic related to valuation, but from a very broad perspective. Traditional finance theories assume perfectly rational investor behavior. Underneath that assumption is perhaps the idea that while investors aren't perfectly rational, their departures from rationality are unique and random and should wash out across the marketplace. Investment psychologists have now demonstrated, however, that investors are irrational in systematic and predictable ways. They have even named and cataloged these systematic effects. So far, behavioral finance has mainly served as an argument for why some anomalies (e.g., residual reversal) continue to work over time. It has helped explain several known market phenomena. The open question for behavioral finance is whether it has predictive ability. Can first principles of psychology lead to new investment strategies? Summary We have presented several open questions concerning the process of active management. Many of them involve the interaction of several separately solvable phenomena (e.g., changing alphas and transactions costs), often dynamically over time. Others involve the potential application of new methodologies to finance. Some of these open questions are technical. All have important implications. The process of active portfolio management is still a vibrant area of research.
Page 577