# Shorting in Speculative Markets

## TL;DR

This paper develops a continuous-time model of trading with heterogeneous beliefs, incorporating costs-of-carry and short-selling, to analyze their effects on asset prices and bubbles in speculative markets.

## Contribution

It introduces a novel HJB equation capturing costs-of-carry and short-selling effects, linking financial innovations to bubble dynamics and market collapses.

## Key findings

- Increasing marginal costs affect asset prices and bubbles.
- Short-selling can lead to bubble collapse.
- Market prices depend on asset supply and costs-of-carry.

## Abstract

We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case for risk-averse agents. In the equilibrium models of heterogeneous beliefs that followed Harrison-Kreps, investors are risk-neutral, short-selling is prohibited and agents face constant marginal costs of carrying positions. The resulting resale option guarantees that the price exceeds the price of the asset when speculation is ruled out; the difference is identified as a bubble. In our model increasing marginal costs entail that the price depends on asset supply. Second, agents also value an option to delay, and this may cause the market to equilibrate below the buy-and-hold price. Third, we introduce the possibility of short-selling. A Hamilton-Jacobi-Bellman equation of a novel form quantifies precisely the influence of the costs-of-carry on the price. An unexpected decrease in shorting costs may lead to the collapse of a bubble; this links the financial innovations that facilitated shorting of MBSs to the subsequent collapse of prices.