The Short-Run Monetary Equilibrium with Liquidity Constraints

A theoretical framework is presented to characterise the money demand in deregulated markets. The main departure from the perfect capital markets setting is that, instead of assuming that investors can lend and borrow any amount of capital at a single (and exogenously determined) interest rate, a bounded money supply is considered. The problem of capital allocation can then be formulated in actuarial terms, in such a way that the optimal liquidity demand can be expressed as a Value-at-Risk. Within this framework, the monetary equilibrium determines the rate at which a unit of capital is exchange by a unit of risk, or, in other words, it determines the market price of risk. In a Gaussian setting, such a price is expressed as a mean-to-volatility ratio and can then be regarded as an alternative measure to the Sharpe ratio. Finally, since the model depends on observable variables, it can be verified on the grounds of historical data. The Black Monday (October 1987) and the Dot-Com Bubble (April 2000) episodes can be described (if not explained) on this base.