On Origins of Bubbles

TL;DR

This paper explores the origins of stock market bubbles, proposing a criterion based on price distribution skewness and volatility, supported by a simple binomial model and empirical analysis of market data.

Contribution

It introduces a new ratio-based criterion for identifying when stocks are poor long-term investments, emphasizing the role of distribution skewness and volatility without complex stochastic calculus.

Findings

Log market cap and sectors explain the ratio well

Price-to-book ratio is not a significant explanatory variable

Short-term volatility effects resemble an uncertainty principle in finance

Abstract

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.