This convexity stuff started to become more clear to me when I read this note from Taleb and that helped me to get convexity to much deeper level
"Take for example the binomial distribution with B[N, p] probability of success (avoidance of failure), with N=50. When p moves from 96% to 99% the probability quadruples. So small imprecision around the probability of success (error in its computation, uncertainty about how we computed the probability) leads to enormous ranges in the total result. This shows that there is no such thing as "measurable risk" in the tails, no matter what model we use.
Case 2: More scary. Take a Gaussian, with the probability of exceeding a certain number, that is, . 1- Cumulative density function.. Assume mean = 0, STD= 1. Change the STD from 1 to 1.1 (underestimation of 10% of the variance). For the famed "six sigmas", the area in the tails explodes by 2400%. For the areas above 10 sigmas (common in economics), the area explodes by trillions."
If the tails are unmesurable (both in terms of % chance and consequences of the tail) and in convexity stocks/bets the tails dominate total returns (heck, that tends to be true even in the indexes, to some extent), it quickly becomes clear that the short sellers, who claim to know the % chance and the size of the tail payoffs, are just delusional. They are being driven more by a mental tick that they have (the contrarian bug) rather than any real analysis. So I started to lean the other way, to try to collect in that ignorance.
If there are so many market participants who seem to be unaware of all of this, and even worse, bet the other way (creating the possibility of short squeezes, etc), it becomes likely that there is some kind of premia to be extracted by betting on these convexity bets. Especially if those bets are being made in periods where that convexity bet is unpopular, then that underapreciation/unawareness factor is being played out even more so the premia might be larger
