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But Many Vanguard managed fund quietly out perform many Vanguard ETFsBasic Math
William Sharpe’s arithmetic of active management is admirably direct: “After costs, the return on the actively managed dollar will be less than the average passively managed dollar,” wrote the good professor in 1991. “These assertions will hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication, and division. Nothing else is required.”
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However, it is also one of the largest managers of active funds.
Vanguard's AUM for actively managed funds was more than $1.7 trillion as of February 28, 2022.
Some of its mutual funds advised by Wellington, Primecap, and Baillie Gifford are quite attractive.
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Nothing else is required
Something rather important is required. The assumption that active management costs more than passive management. If I manage my portfolio myself, I am actively managing my assets with 0.00% assessed management costs. OTOH, if I invest passively, I'm paying someone something to determine what is in my passive portfolio and/or to execute it, unless I rely on a published index and personally buy and sell securities to track the index.
The full statement by Sharpe was that: What may have appeared sensible in 1991 may not be so sensible in 2022. Now there are all sorts of esoteric high cost indexes and active ETFs having costs as low or sometimes lower than passive ETFs (e.g. the second and fourth lowest cost ultrashort term ETFs in M*'s table are actively managed - ICSH and VUSB).
While it is likely true that actively managed dollars are still hit with higher fees (on average) than passively managed dollars, one can no longer show this merely by appealing to common sense as Sharpe did. (Though Sharpe did consider any fund actively managed if it did not cap-weight an entire market; thus, e.g. equal weighted index funds are by his definition actively managed.)