Detecting Bubbles in Financial Markets: Fundamental and Dynamical Approaches

Abstract

The subject of this thesis has been the detection of bubbles in financial markets through two fundamentally different approaches. The first approach consisted in quantifying bubbles as the difference between the market value and fundamental price of an asset, taking Zynga, a social networking company, as a case study. By recognizing the centrality of its users in its revenue structure, we were able to determine an upper bound for the value of the company by forecasting its future user base as well as the revenue each of them would generate with nonlinear dynamical models. Our valuation led to our diagnosis of a bubble which in turn, combined with a financial event known as the end of the lock-up period, allowed us to successfully predict Zynga’s downward price trajectory within a specific time-window. In addition, Zynga’s long-term price dynamics have been consistent with our valuation performed shortly after its IPO. The generality of our methodology was emphasized by its successfully application to a different problem : the forecasting of the future oil production of Norway and the U.K. The strengh of this approach lied in the absence of a need to postulate a mechanism for the emergence of a bubble : while this made the detection of bubbles possible, forecasting their burst was difficult, except in rare cases such as the one described here. Our second approach was based on the log-periodic power law model (LPPL), a model taking its roots in critical phenomenas, defining bubbles as transient super-exponential regimes punctuated by phase transitions. Our contribution has been to show in a systematic way and on a large scale that LPPL’s predictive power was robust across a wide range of strategies, assets and time periods. This predictive power was defined as the persistent deviation between LPPL-based strategies and their random counterparts. We went on to generalize the importance of super-exponential regimes in the pricing of assets : we showed, in a factor regression model, that the first difference of past returns, in other words the difference between two consecutive growth rates, yielded significant predictive power over future returns. This phenomenon was captured by a new factor called Γs that outperformed and explained the momentum factor, a pillar of classical finance. This suggests that price acceleration (Γs) clearly dominates price velocity (momentum) in the pricing of assets, supporting the LPPL paradigm. In summary, the work presented in this thesis supports a view of markets out-ofequilibrium, permeated by unsustainable regimes in which the detection of bubbles and the forecast of their crashes is possible.