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Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models

Journal of Finance 2023 78(1), 487-557 open access
We propose a novel framework for analyzing linear asset pricing models: simple, robust, and applicable to high‐dimensional problems. For a (potentially misspecified) stand‐alone model, it provides reliable price of risk estimates for both tradable and nontradable factors, and detects those weakly identified. For competing factors and (possibly nonnested) models, the method automatically selects the best specification— if a dominant one exists—or provides a Bayesian model averaging–stochastic discount factor (BMA‐SDF), if there is no clear winner. We analyze 2.25 quadrillion models generated by a large set of factors and find that the BMA‐SDF outperforms existing models in‐ and out‐of‐sample.

Retail Trading in Options and the Rise of the Big Three Wholesalers

Journal of Finance 2023 78(6), 3465-3514 open access
We document a rapid increase in retail trading in options in the United States. Facilitated by payment for order flow (PFOF) from wholesalers executing retail orders, retail trading recently reached over 60% of total market volume. Nearly 90% of PFOF comes from three wholesalers. Exploiting new flags in transaction‐level data, we isolate wholesaler trades and build a novel measure of retail options trading. Our measure comoves with equity‐based retail activity proxies and drops significantly during U.S. brokerage platform outages and trading restrictions. Retail investors prefer cheaper, weekly options with average bid‐ask spread of 12.6%, and lose money on average.