If ‘active’ and ‘passive’ management styles are defined in sensible ways, it must be the case that:
- Before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar and
- After costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar.
We observed that based on the way Sharpe defines his terms this argument is both self-evident AND irrefutable.
More recently, Vanguard published The Case for Index-Fund Investing which presents a compelling argument for the soundness and prudence of indexing. Specifically, they make the following points:
- Over short, intermediate and long periods - as well as multiple market cycles - the vast majority of actively managed funds in all categories fail to match or outperform either their benchmarks or low-cost passively managed funds;
- Since investing is, by definition, a zero-sum game – meaning that for every winner there must be a loser and the proportion of the win and loss, before expenses, must be equal – higher expenses (for both active and passive/index strategies) compound the difficulty of “beating” an appropriate, low-cost index fund;
- Picking active managers based on past outperformance doesn’t work: “Persistence” is statistically random for top performing funds (although there is some evidence that the poorest funds as a group do continue with lousy performance);
- Even in market sectors usually thought to be less efficient, and therefore better stalking grounds for active managers to bag the outperformance prize, “a significant majority” underperform;
- That the “common perception” that active managers earn their fees by holding value (losing less) in bear markets is not supported by the data. (Philips lists the following “so-called inefficient sectors”: mid- and small-cap stocks, high-yield bonds, emerging market stocks. See p. 8-9 of original.)
In short, the case against active management as a prudent choice, at least for investment fiduciaries like retirement plan sponsors and trustees of endowment and foundation funds, appears to be both theoretically (Sharpe) and empirically (Philips et. al.) compelling.
Add to this the massive body of research and analysis confirming and corroborating their work, it would seem the answer to the question in the title of this blog post may have to be “Yes” except…
…both Sharpe and Philips explicitly allow (in Sharpe’s words),
"It is perfectly possible for some active managers to beat their passive brethren, even after costs [and it] is also possible for an investor…to choose a set of active managers that, collectively, provides a total return better than that of a passive alternative, even after costs." 
The question, then, for investment fiduciaries who typically delegate investment management to third-parties like mutual funds and professional investment managers may not be, “Is using active management a fiduciary breach?” but “Is there a way to select the right ones?”
The answer may be both simpler and more difficult than most of us, including investment advisors and others who make their livings purporting to do so, imagine.
 Sharpe, William F. The Arithmetic of Active Management, Financial Analysts Journal, January-February 1991, p. 8. Emphasis in the original.