For a long while now, having watched bubbles form and pop, I have found it frustrating how people pile into assets with straight line trajectories.  I first noticed it in the time of the dot-com bubble of the late 1990s.  During that time, as I recall, returns in the market were frighteningly close to straight line, not only highly positive, but with a low volatility of returns from month to month.

A more frightening version of this, in terms of risk to our way of life, was in residential real estate.  Prior to the popping of the real estate bubble, residential real estate in the United States had also had fairly straight line appreciation over a considerable number of years.  Again, not only was the appreciation significantly positive, it had little variance.

It reminds me of a favorite "simple wisdom that is obvious but that we tend to forget" type quote:
"If something cannot go on forever, it will stop."
~ Herbert Stein

I'll not be at all surprised if what I'm about to propose has been done before, as it seems so simple.  If so, forgive me.

It would seem that one can represent the degree to which a return has been straight line fairly easily as R/V, where R is some measure of return and V is some measure of volatility, likely for the same period of time, but not necessarily so.  As this ratio increases, I propose that tail probability, the probability of a significant move, call it a black swan or gray swan event to use Nassim Taleb's term, increases (tail obesity).  My theory is that significant moves become more probable as tension increases, similar to how a major earthquake becomes more likely as tension grows between tectonic plates, and that in some situations this tension increases following periods of straight line appreciation.

It might also be that a formula like (R / R2) /  (V / V2), where R is some return, R2 is some return prior, V is some measure of volatility, and V2 is this measure for some period prior (again, likely for the same periods, but not necessarily so), would identify this tail probability more accurately, as it would serve to measure the change in return versus the change in volatility over a period of time.

This, to some degree, goes against conventional wisdom that higher volatility implies higher risk.  Note that I'm not proposing that lower volatility implies higher risk, but that high returns over a period of time, when combined with low volatility of those returns, serves to change the shape of the parabola of possible returns.  In other words, I'm merely proposing that there may be a way to identify a time when a black swan or gray swan type price movement, to use Nassim Taleb's term, is more probable than usual.

Also note that I've concentrated on straight line positive returns, ignoring similar moves downward, likely to the chagrin of statistical purists.  Intuitively, I feel that the tail probability increase is more likely with straight line appreciation, and that the increase in probability at the tail is isolated or at least heavily weighted to the down side.  Capitulation happens both ways, of course, but given that there is no limit to upside, while the downside always has to contend with zero, there is simply more opportunity for straight line returns to the upside.

If this is some sort of common knowledge, which I fear as it seems to simple, then egads, and sorry.  If not, call it the Hawkins Ratio; my kids will think it is cool.