The Valuation of Long-Dated Assets

Abstract

The expected time- and risk-adjusted cumulative return on any asset equals one at all horizons. Nonetheless, I show that a typical asset's realized time- and risk-adjusted cumulative return tends to zero almost surely. As a corollary, the value of a typical long-dated asset is driven by extreme events: either by good news at the level of the individual asset or by bad news at the aggregate level. In the case of the aggregate market, the fact that its Sharpe ratio is higher than its volatility suggests that bad news is the relevant consideration in practice.