Lunch Talk: Optimal Dynamic Portfolio Liquidation with Lower Partial Moments

Who: Hassan Anis, M.A.Sc Candidate, University of Toronto

When: Wednesday, December 6th @ 12:00pm – 1:00pm

Where: RS207

Abstract: One of the most important problems faced by stock traders is how to execute large block orders of security shares. When liquidating a large position, the trader faces the following dilemma: a slow trading rate risks prices moving away from their current quote, while a faster trading rate will drive quotes away from the current one leading to a large market impact. We propose a novel quasi-multi-period model for optimal position liquidation in the presence of both temporary and permanent market impact. Four features distinguish the proposed approach from alternatives. First, instead of the common stylized approach of modelling the problem as a dynamic program with static trading rates, we frame the problem as a stochastic SOCP which uses a collection of sample paths to represent possible future realizations of state variables. This, in turn, is used to construct trading strategies that differentiate decisions with respect to the observed market conditions. Second, our trading horizon is a single day divided into multiple intraday periods allowing us to take advantage of the seasonal intraday patterns in the optimization. This paper is the first to apply Engle’s Multiplicative component GARCH to estimate and update intraday volatilities in a trading strategy. Third, we implement a shrinking horizon framework to update intraday parameters by incorporating new incoming information while maintaining standard non-anticipativity constraints. We construct a model where the trader uses information from observations of price evolution during the day to continuously update the size of future trade orders. Thus, the trader is able to dynamically update the trading decisions based on changing market conditions. Finally, we use asymmetric measures of risk which, unlike symmetric measures such as variance, capture the fact that investors are usually not averse to deviations from the expected target if these deviations are in their advantage.