On the fundamental law of active portfolio management: How to make conditional investments unconditionally optimal

The fundamental law of active portfolio management tells an active manager how to transform his alpha forecasts into the valued-added of 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. The unconditional value-added - the valued-added over the long haul or over multiple periods - is what the manager normally strives to achieve. Under this unconditional objective, the linear strategy can approach zero value-added if the forecasts or signals have a high kurtosis. To overcome this problem, the author provides an investment strategy that maximizes the unconditional value-added with the optimal use of conditional information. The strategy is nonlinear in the forecasts, but has a simple economic interpretation. When the alpha forecasts are high, an active manager invests less aggressively than the linear strategy, and when the forecasts are low, an active manager invests more aggressively. In this way, an active manager tends to smooth out value-added over time and, hence, on a risk-adjusted basis, the active manager's long-term unconditional value-added will be substantially higher than the value-added based on a linear strategy, particularly when the alpha forecasts experience high kurtosis.