On the Fundamental Law of Active Portfolio Management: How to Make Conditional Investments Unconditionally Optimal

摘要

The fundamental law of active portfolio management pioneered by Grinold [1989] tells an active manager how to transform his alpha forecasts into valued-added for his active portfolio by using a linear strategy with active positions proportional to the forecasts. This linear strategy is conditionally optimal because it is optimal each period, conditional on the forecasts at that time. However, the unconditional value-added (the valued-added over the long haul or over multiple periods) is usually what the manager strives earnestly for. Under this unconditional objective, the linear strategy can generate zero unconditional value-added or even a negative value if the forecasts or signals have a high kurtosis. To overcome this problem, we provide an investment strategy that maximizes the unconditional value-added -with the optimal use of conditional information, with the help of important insights from Hansen and Richard [1987], and especially from Ferson and Siegel [2001], as well as Chiang [2008]. Our strategy is nonlinear in the forecasts, but has a simple economic interpretation. When the alpha forecasts are high, we invest less aggressively than the linear strategy, and when the forecasts are low, we invest more aggressively. In this way, we tend to smooth our value-added over time and, hence, on a risk-adjusted basis, our long-term unconditional value-added will in most cases be substantially higher than that based on the linear strategy, particularly when the alpha forecasts experience high kurtosis.