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.

Many financial instruments are designed with embedded leverage, such as options and leveraged exchange-traded funds (ETFs). Embedded leverage alleviates investors’ leverage constraints, and, therefore, we hypothesize that embedded leverage lowers required returns. Consistent with this hypothesis, we find empirically that options and leveraged ETFs provide significant amounts of embedded leverage; this embedded leverage increases return volatility in proportion to the embedded leverage; and higher embedded leverage is associated with lower risk-adjusted returns. The results are statistically and economically significant, and we provide extensive robustness tests and discuss the broader implications of embedded leverage for financial economics.

I present closed-form solutions for prices, portfolios, and beliefs in a model where four types of investors trade assets over time: naive investors who learn via a social network, “fanatics” possibly spreading fake news, and rational short- and long-term investors. I show that fanatic and rational views dominate over time, and their relative importance depends on their following by influencers. Securities markets exhibit social network spillovers, large effects of influencers and thought leaders, bubbles, bursts of high volume, price momentum, fundamental momentum, and reversal. The model sheds new light on the GameStop event, historical bubbles, and asset markets more generally.