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Performance measures for dynamic portfolio management

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This paper propses instataneous 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 as much for taking risks as th discrete ratio does. This is justified by dynamic portfolio theory. Unlike their discrete versions, the instantaneous performance measures take levrage corrcetly into account in a dynamic setting, and they take into account the fact that investors rebalance their portfolios over time. We calculate the discrete and instantaneous Sharpe ratios for a sample of six mutual funds and the S and P 500 index. They illustrate that the two versions of the Sharpe ratio may rank funds differently and that funds high volatility look better when evaluated by the instatntaneous than by the conventional Sharpe ratio

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