Shorting in Speculative Markets

Abstract

In models of trading with heterogeneous beliefs following Harrison‐Kreps, short selling is prohibited and agents face constant marginal costs‐of‐carry. The resale option guarantees that prices exceed buy‐and‐hold prices and the difference is identified as a bubble. We propose a model where risk‐neutral agents face asymmetric increasing marginal costs on long and short positions. Here, agents also value an option to delay, and a Hamilton‐Jacobi‐Bellman equation quantifies the influence of costs on prices. An unexpected decrease in shorting costs may deflate a bubble, linking financial innovations that facilitated shorting of mortgage‐backed securities to the collapse of prices.

Asset pricing with heterogeneous beliefs and illiquidity

“…In this case, we drop the requirement of absolute continuity in the definition of the admissible portfolios and we also do not enforce the initial holdings (in any event, agents can instantaneously adjust their position after without incurring costs). The following result, which is a special case of Nutz and Scheinkman (2020, theorem 2.1 and remark 3.5), shows that the corresponding equilibrium corresponds to the price of a representative agent with a view defined by the averaged drift and volatility coefficients. Proposition Let and .…”

“…Considering a holding cost on risky positions as in Cartea and Jaimungal (2016), Choi, Larsen, and Seppi (2019), Nutz and Scheinkman (2020), and Sannikov and Skrzypacz (2016) further simplifies the analysis compared to models where the corresponding risk penalty is imposed on the variance of the risky positions as in Garleanu and Pedersen (2013, 2016) and Herdegen et al. (2019).…”

Liquidity in Competitive Dealer Markets

“…In general, the reduced-form holding cost in (2.1) is more tractable than models with risk aversion. Similar criteria are used in [30,26,28], for example.…”

“…As in Garleanu, Pedersen, and Poteshman [14], the first assumption means that the equilibrium price is "competitive", which is reasonable if the representative dealers correspond to a large number of small liquidity providers, whose individual actions cannot affect the overall market equilibrium. 2 Quadratic holding costs are also used in [30,26,28], for example, because this "inventory aversion" is considerably more tractable than risk aversion, yet still penalizes the accumulation of large and thereby risky positions. The martingale assumption on the fundamental price, also made in [18,15], ensures that the dealers focus on inventory management rather than speculative investment in the end-user market.…”

Liquidity in competitive dealer markets

“…Second, agents have quadratic inventory costs rather than preferences modeled by concave utility functions. Such quadratic holding costs are also used in (Choi, Larsen, & Seppi, to appear; Muhle‐Karbe & Webster, 2017; Nutz & Scheinkman, 2020; Rosu, 2019; Sannikov & Skrzypacz, 2016), for example, because this reduced‐form modeling of “inventory aversion” is considerably more tractable than risk aversion, yet still penalizes the accumulation of large and thereby risky positions. Third, the exogenous price in the open market has martingale dynamics, complemented by quadratic trading costs on the total and individual order flows.…”