Abstract
We derive expressions for the Information Ratio (IR) that can be expected from directional market timing strategies. Our results hold as accurate approximations and lift Grinold’s [1989] “Fundamental Law of Active Management” to an operational level. In addition, we separate “time series breadth” (the timing frequency per strategy) from “cross-section breadth” (the number of separate markets) because they contribute differently to performance. We show that implementing volatility-weighted bet sizes, both in the time series context of a single underlying market and in the cross-section context of multiple markets, increases the expected timing IR. Our theoretical results can be used as a benchmark for and reality check on the back-tested performance of timing strategies. We confirm the accuracy of our results by simulating timing strategies for equities and fixed income.
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