The Effective Number of Securities in an Active Portfolio: Why a Passive Benchmark Should Be Equally Weighted
6 Pages Posted: 29 Apr 2021 Last revised: 8 Apr 2022
Date Written: April 28, 2021
If an active equity manager's task is to pick stocks from a benchmark index, then only equal weighting reflects an appropriate benchmark reflecting no prior knowledge of which stocks will outperform others. I use Shannon's entropy to formalize this idea and show how any deviation from equal weighting reflects a smaller effective number of securities than contained in the benchmark, even if each security receives some weight, an appealing notion of the stock picker's task.
Keywords: investment management, active, passive, performance
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