## Even if you're sure it's a bubble …

As well explained on the Wikipedia page, an economic bubble occurs when the market price of an asset spends a time substantially above its presumed "intrinsic value" before returning to that value. Such bubbles can only be identified in retrospect. Whether or not a substantial recent price increase constitutes a bubble which will later burst is always a matter of debate. At the time of writing (June 2017) there is extensive discussion (e.g. this Economist article) surrounding the rapid appreciation of bitcoin: is this a bubble? Suppose you are sure that a bubble is in progress; to make up some numbers, suppose the current price is 2,000 and you are sure it will return to 1,000 within one or two years. In principle you can profit by "selling short", receiving 2,000 today in exchange for having to pay 1,000 later. Your first thought might be "my only risk is that it's not a bubble after all, and the price never drops". But this is wrong.

Even if you knew for certain that the bubble would burst, you cannot guarantee to make money via this knowledge.

The mathematical point is that bubbles are in principle consistent with the martingale theory underlying the efficient market hypothesis, and this theory predicts, in our "suppose" setting above,

with probability $$\frac{1}{x-1}$$ the price will reach at least $$x$$ thousand before dropping down to 1,000.
The graphic below shows 5 representative possibilities for the future prices (until a return to 1,000). The point is that in short selling you need to post collateral to cover the current price, and you have some limit on collateral available. If your limit were 7,000 then in one of the representative cases you would be forced to cover your position by paying 7,000. Thus (under the martingale theory and ignoring various practical costs) you are essentially just making a "fair bet" with chance $$5/6$$ to gain 1,000 and chance $$1/6$$ to lose 5,000.

### Footnotes

This is somewhat similar to the St. Petersburg paradox but pays attention to reality -- no-one has an unlimited amount of money.