Performance Measures for Dynamic Portfolio Management

This paper proposes instantaneous versions of the Sharpe ratio and Jensen’s alpha as performance measures for managed portfolios. Both are derived from optimal portfolio selection theory in a dynamic model. The instantaneous Sharpe ratio equals the discrete Sharpe ratio plus half of the volatility of the fund. Hence, it does not penalize fund managers for taking risks as much as the discrete ratio does. This is justified by dynamic portfolio theory. Unlike their discrete versions, the instantaneous performance measures take leverage correctly into account in a dynamic setting, and they take into account investors rebalancing their portfolios over time.