We model how investors allocate between asset managers, managers choose portfolios of multiple securities, fees are set, and security prices are determined. Investors are indifferent between higher-cost informed managers and lower-cost uninformed managers, interpreted as passive managers as their portfolio is linked to the " expected market portfolio." We make precise Samuelson's dictum by showing that active investors reduce micro-inefficiencies more than they do macro-inefficiencies. In fact, all inefficiency arises from systematic factors when the number of assets is large. Further, we show how the costs of active and passive investing affect macro- and micro-efficiency, fees, and assets managed by active and passive managers. Our findings help explain the rise of delegated asset management and the resultant changes in financial markets.

中文翻译：

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主动和被动投资：理解萨缪尔森的格言

我们对投资者如何在资产经理之间进行分配进行建模，经理选择多种证券的投资组合，设定费用并确定证券价格。投资者对成本较高的知情经理和成本较低的不知情经理无动于衷，他们被解释为被动经理，因为他们的投资组合与“预期市场投资组合”相关联。我们通过展示积极的投资者减少微观低效率比减少宏观低效率来准确地表达萨缪尔森的格言。事实上，当资产数量很大时，所有的低效率都是由系统因素引起的。此外，我们展示了主动和被动投资的成本如何影响由主动和被动经理人管理的宏观和微观效率、费用和资产。