Fundamental factors versus herding in the 2000–2005 US stock market and prediction

Abstract

We present a general methodology to incorporate fundamental economic factors to our previous theory of herding to describe bubbles and antibubbles. We start from the strong form of Rational Expectation and derive the general method to incorporate factors in addition to the log-periodic power law (LPPL) signature of herding developed in ours and others' works. These factors include interest rate, interest spread, historical volatility, implied volatility and exchange rates. Standard statistical AIC and Wilks tests allow us to compare the explanatory power of the different proposed factor models. We find that the historical volatility played the key role before August of 2002. Around October 2002, the interest rate dominated. In the first six months of 2003, the foreign exchange rate became the key factor. Since the end of 2003, all factors have played an increasingly large role. However, the most surprising result is that the best model is the second-order LPPL without any factor. We thus present a scenario for the future evolution of the US stock market based on the extrapolation of the fit of the second-order LPPL formula, which suggests that herding is still the dominating force and that the unraveling of the US stock market antibubble since 2000 is still qualitatively similar to (but quantitatively different from) the Japanese Nikkei case after 1990.

Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles

“…We do not claim that this changed the failure into a success. Instead, it illustrates the effect of monetary feedbacks that have to be included in improved models incorporating fundamental factors, for instance in the spirit of Zhou and Sornette (2006a). 5.…”

Micro-foundation using percolation theory of the finite time singular behavior of the crash hazard rate in a class of rational expectation bubbles

“…which is the pillar of the JLS model and its extensions [14][15][16][17][18][19][20][21]. Replacing (4) in (2) gives the dynamics of the price dp rice (t)…”

“…This expression (25) again captures a finite-time singularity at time t c , associated with a diverging local growth rate dp p, while the price remains finite at t c since 0 < m < 1. The form is the basis of the parametric model that is used in many empirical calibrations of financial bubbles [10][11][12][13][14][15][16][17][18][19][20][21]. Here, it stems from the rational expectation condition that links the instantaneous return to the crash hazard rate, together with the divergence of the latter.…”

“…The model considers a single asset that is purely speculative and pays no dividends in a market where we ignore the interest rate, and use simplified market-clearing conditions. A number of extensions have been developed in [14][15][16][17][18][19][20][21]. Embedded in the general framework of rational expectation (RE) bubbles, the JLS model views the stock market as divided into investors with rational expectations and noise traders.…”

The Role of Diversification Risk in Financial Bubbles

“…Here, we present an extension of the JLS model, which is in the spirit of the approach developed by Zhou and Sornette [15] to include additional pricing factors.…”