Dynamic Trading Volume

Abstract

We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a large investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian, mean-reverting diffusion, and increases with depth, volatility, and risk aversion. Unlike the frictionless theory, finite depth excludes leverage and short sales because such positions may not be solvent even with continuous trading.

Trading With Small Price Impact

“…REMARK 3.5. The asymptotic scalings for the value function and the optimal policy are motivated by the corresponding results of Guasoni and Weber (2017).…”

“…Thus, the current position θ t is pushed back more aggressively to the frictionless target θ 0 t if i) the current deviation θ t − θ t is large, ii) market volatility σ S t is high, iii) trading costs t are low, or iv) the investor's risk tolerance R t is low. For constant market, cost, and preference parameters, this reduces to the formulas obtained by ; Almgren and Li (2011); Guasoni and Weber (2017). In the general setting considered here, these quantities are updated continuously with the current volatility, price impact, and (indirect) risk tolerance.…”

Portfolio choice with small temporary and transient price impact

“…These models were originally developed for optimal execution problems, where the goal is to split up a single, exogenously given order in an optimal manner. More recently, dynamic portfolio choice and hedging problems with price impact have also received increasing attention (Collin-Dufresne, Daniel, Moallemi, & Saglam, 2012;Garleanu & Pedersen, 2013;Almgren & Li, 2016;Garleanu & Pedersen, 2016;Bank, Soner, & Voß, 2017;Guasoni & Weber, 2017;Guéant & Pu, 2017;Moreau, Muhle-Karbe, & Soner, 2017). This means that the target orders to be executed are no longer assumed to be given, but are instead derived endogenously from a dynamic optimization problem.…”

Nonlinear price impact and portfolio choice

“…an ordinary differential equation, the solution of which consists of the scalar and the shape function ( ). For = 1, the shape function is linear, and the model recovers the optimal policy for linear impact in Guasoni and Weber (2017). In the limit ↓ 0, the shape function gives rise to the classical trading policy of Dumas and Luciano (1991) for bid-ask spreads.…”

“…The impact of trades on execution prices is a critical determinant of portfolio rebalancing policies: Frictionless models assume a single price, insensitive to sales and purchases of any size, resulting in policies with infinite trading volume (Merton, 1969). Models that acknowledge bid-ask spreads preclude trading when a portfolio is near its target (Constantinides, 1986;Davis & Norman, 1990), whereas linear price impact models recommend a trading rate proportional to its distance from the target (Guasoni & Weber, 2017;Moreau, Muhle-Karbe, & Soner, 2017). Yet, empirical evidence suggests that price impact is nonlinear.…”