On Origins of Bubbles

We discuss – in what is intended to be a pedagogical fashion – a criterion, which is a lower bound on a certain ratio, for when a stock (or a similar instrument) is not a good investment in the long term, which can happen even if the expected return is positive. The root cause is that prices are positive and have skewed, long-tailed distributions, which coupled with volatility results in a long-run asymmetry. This relates to bubbles in stock prices, which we discuss using a simple binomial tree model, without resorting to the stochastic calculus machinery. We illustrate empirical properties of the aforesaid ratio. Log of market cap and sectors appear to be relevant explanatory variables for this ratio, while price-to-book ratio (or its log) is not. We also discuss a short-term effect of volatility, to wit, the analog of Heisenberg's uncertainty principle in finance and a simple derivation thereof using a binary tree