标题： 关于气泡的起源 显示英文标题

标题： On Origins of Bubbles

摘要： 我们以一种旨在具有教育意义的方式讨论了一个标准，该标准是某一比率的一个下界，用于判断何时某只股票（或类似工具）在长期内不是一个好的投资标的，即使其预期回报为正也可能发生这种情况。 根本原因在于价格为正且具有偏斜、长尾分布，这与波动性相结合会导致长期的不对称性。 这涉及到股票价格中的泡沫，我们使用一个简单的二叉树模型来讨论这一问题，而无需诉诸随机微积分工具。 我们展示了上述比率的经验性质。 市场总市值的对数和行业似乎对该比率具有相关解释力，而市净率（或其对数）则不然。 我们还讨论了波动性的短期效应，即金融领域海森堡不确定性原理的类比，并利用二叉树给出了一个简单的推导。 显示英文摘要

摘要： 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.