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

Why GameStop? Why January 2021? 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 at least 2:1 leverage, then aggregate demand for shares can be upward sloping and an equilibrium price therefore unstable. If P0 is an equilibrium price, then there exists a price P1>P0 that also clears the market. P0 is unstable and P1 is stable. Unfortunately, if the price actually is P1, then it will be unstable and there will exist a P2>P1 that clears the market and is stable. This is true for any arbitrarily high proposed price. When some investors are all in, therefore, the sky's the limit. Access to leverage above 2:1 is only possible in the United States using stock options and options trading has only been available for inexperienced retail investors recently. These investors could only trigger unstable equilibria if the company that they targeted was small enough for their wealth to matter but large enough to have traded options. Our theory therefore answers the two questions posed at the start of this abstract.