The Valuation of Long-Dated Assets

The fundamental equation of asset pricing states that the expected timeand risk-adjusted cumulative return on any asset equals one at all horizons. This paper shows that for a typical asset, the realized timeand risk-adjusted cumulative return tends to zero with probability one. Just two assumptions are required: limited liability and no arbitrage. This apparent paradox is resolved by a further result, which shows that the long-run value of such an asset is driven by the possibility of extremely good news at the level of the individual asset or extremely bad news at the aggregate level. In the case of the aggregate market, its high Sharpe ratio implies that disasters are the relevant consideration in practice. ∗[email protected]; http://www.stanford.edu/ iwrm. First draft: 14 April, 2007. I thank Brandon Bates, John Campbell, John Cochrane, Darrell Duffie, Lars Hansen, Steve Ross and Martin Weitzman for their comments.