Characteristics are covariances: A unified model of risk and return

Factor Crowding and Liquidity Exhaustion

“…To capture correlated trading, we use a multifactor model based on conventional empirical asset pricing factors to generate the types of signals that many active portfolio managers and factor-based investment strategies employ when selecting and weighting stocks. 2 These factor strategies link cross-sectional variation in returns to stock characteristics, and the positive average returns typically documented for them are consistent with conclusions in Daniel and Titman (1997) and Kelly, Pruitt, and Su (2018). Throughout this article, we use the term "multifactor model" to refer to an empirically motivated cross-sectional model of returns, rather than a theoretical equilibrium asset pricing model based on expected comovement of returns with systematic factors (e.g., the arbitrage pricing theory of Ross, 1976, or time-series models widely used for risk adjustment such as the four-factor model of Carhart, 1997).…”

Deep Learning in Asset Pricing

“…,i are q characteristic managed factors. Such characteristic managed factors based on linearly projecting onto quantiles of characteristics are exactly the input to PCA in Kelly et al (2018) or the elastic net mean-variance optimization in Kozak et al (2018). 13 The solution to minimizing the sum of squared errors in these moment conditions is a simple mean-variance optimization for the q characteristic managed factors i.e θ = E F t+1F t+1…”

“…Our approach also yields the conditional mean-variance efficient portfolio, but based on all stocks. Gu et al (2019) extend the linear conditional factor model of Kelly et al (2018) to a non-linear factor model using an autoencoder neural network. 5…”

“…Kozak et al (2018) apply mean-variance optimization with an elastic net penalty to characteristic sorted factors. 6 Kelly et al (2018) apply PCA to stock returns projected on characteristics to obtain a SDF that is linear in the characteristics. Pelger (2019) combines highfrequency data with PCA to capture non-parametrically the time-variation in factor risk.…”

“…Fundamentally, our object of interest is the pricing kernel. Kelly et al (2018) obtain a multi-factor factor model that maximizes the explained variation. The linear special case applies PCA to a set of characteristic based factors to obtain a linear lower dimensional factor model, while their more general autoencoder obtains the loadings to characteristic based factors that can depend non-linearly on the characteristics.…”