Active and Passive Investing

The Arithmetic of Active Management A negative sum game? Not so fast... "It must be the case that: - before costs: average active return = passive return - after costs: average active return < passive return ...these assertions... depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required." Sharpe's arithmetic is often cited as proof that active management is doomed William Sharpe, 1991 Not so fast... Sharpe assumes passive investors never trade Assumption does not hold in the real world: IPOs, index inclusions/deletions, etc. This breaks the equality: when passive investors trade, they may get worse prices So active management can be worth positive fees in aggregate Empirical questions: Do they actually add value? If so, how much? Also, it should be called the arithmetic of active investing Active investors do not only include delegated managers, but also retail and institutional internal investing: latter are large, not publicly measured ● (AQR) P Sharpening the Arithmetic of Active Management and NY пах Lasse Heje Pedersen Lalat AQR Capital Management Greenwich Connect, un progen Rino Somal Ichallenge William F. Sharpe's famous equality that "before costs. the return on the average actively managed dollar will equal the return on the average passively managed dollar. This equality is based on the implicit assumption that the market portfolio never changes, which does not hold in the real world because new shares are issued, others are repurchased. and indexes are reconstituted-so even passive investors must regularly trade. Therefore, active managers can be worth positive fees in aggregate, allowing them to play an important economic role helping allocate resources eff dently Passive investing also plays a useful economic role: creating low-cost access to markets. Die Theerthoris a principa at AQR Capital Management, a dob investment management firm, which may or may not apply similar invest tachometheads of analysis a described in The views expressed necessarily those of A CEC05 * See for example Fama, Eugene F., and Kenneth R. French (2010), "Luck versus skill in the cross-section of mutual fund returns," The Journal of Finance. 41/635 For illustrative purposes only. Image courtesy of http://www.nobelprize.org/nobel prizes economic-sciences/laureates/1990/sharpe-bio.html (Ra) Perspectives harpe's (1991) famous "arithmetic of active management states it must be the case that (1) before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar, and (2) after costs, the return on the average actively managed dollar will be less 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. (p. 7: italics in the originall Sharpe's arithmetic has been invoked by Warren Buffett is often stated as incontrovertible fact by speakers at conferences followed by a triumphant "QED!"), and is cited as proof that active management is "doomed" in aggregate (French 2008). If active management is doomed in aggregate, then so is our market-based financial system because we need someone to make prices informative. However, we may avoid doom on the basis of my arithmetic. Sharpe's powerful insight is that one active investor's gain is another active investor's loss, which aggregates to zero for all active investors. This useful insight is correct when considering a fond set of securities over a single time period, but in the real world, the set of securities in the market changes over time. fdcom Anbu C Ashute Devid Tttarita rosur Mms Clickr MG Com Sartond Se Devid Jon Debet C Martin Tidy Moireet, Li Pe Bag Scotchon Wien F. Sharpe, S Articipo a CFAS Det the sty at Drag ere Come ant at the New Desi Larg:amaCurt 21 LO 5

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