"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...

"The large asset price jumps that took place during 2008 and 2009 disrupted volatility derivatives markets and caused the single-name variance swap market to dry up completely. This paper defines and analyzes a simple variance swap, a relative of the variance swap that in several respects has...