The Sky's the Limit: Asset prices can be indeterminate when margin traders are all in

Abstract

We analyze a setting in which a risky asset is traded by two types of investors: some are all in and buy up to their margin limit and some buy and sell based on the asset's fundamental value. A higher price of the asset increases all-in investor wealth and they borrow against this wealth to buy more shares. All-in investor demand for shares is therefore upward sloping. If all-in investors have (i) enough wealth and (ii) access to enough leverage, then aggregate demand for shares is Z-shaped. If the most recent price was P_1, then there are three equilibrium prices, P_2>P_1>P_0. If the price were to rise to P_2, then there would again be three equilibrium prices, P_3>P_2>P_0. This is true for any arbitrarily high proposed price. If the price were ever to fall to P_0, then P_0 would be the unique market-clearing price in all future periods. Prices will tend to rise repeatedly prior to a permanent collapse. Our theory applies to markets as diverse as the housing market and the market for meme stocks like GameStop Corporation and AMC Entertainment.