A more statistically rigorous definition of a bubble is now coming into view. Although it has already been shown that the rational expectations hypothesis is not particularly helpful in this regard, expected stock returns, equity risk premiums, and volatility nonetheless still remain basic descriptive and real-world aspects of trading and investment performance measurement.

In all bubble experiences, though, the one thing (beyond exponentiality) that is readily observed is that price return variance rises relative to its previous pre-bubble baseline. To be more informative, however, this rise in variance ought to be placed in a frame of reference. After all, a 20% increase in price change variance would probably be interpreted differently with interest rates at 5% than at 15%. In this regard, many series might conceivably serve as viable references against which to relate variance changes. The problem, however, is that such series appear to be inconsistently defined and reported.

Although not without measurement problems of its own, the equity risk premium (ERP) is, in contrast, relatively the easiest to implement empirically because a long and consistently defined series is readily available. But more importantly, the ERP directly reflects the market's collective attitudinal balance toward acceptance of risk. As such, it drives the quantities of shares that participants will want to hold.

It is thus proposed that a much more workable definition of a bubble can be derived by analyzing how much the variance rises in relation to a decline in the ERP. This is, in brief, an elasticity concept – one that will be developed here in greater detail.