Using trading strategies to detect phase transitions in financial markets

We show that the log-periodic power law singularity model (LPPLS), a mathematical embodiment of positive feedbacks between agents and of their hierarchical dynamical organization, has a significant predictive power in financial markets. We find that LPPLS-based strategies significantly outperform the randomized ones and that they are robust with respect to a large selection of assets and time periods. The dynamics of prices thus markedly deviate from randomness in certain pockets of predictability that can be associated with bubble market regimes. Our hybrid approach, marrying finance with the trading strategies, and critical phenomena with LPPLS, demonstrates that targeting information related to phase transitions enables the forecast of financial bubbles and crashes punctuating the dynamics of prices.

Figure 1

Price trajectory of the SPY (blue and left scale) together with the average of the signal over the SP500 constituents (as of 2003) (red and right scale) as a function of time.

Figure 2

Example of a strategy applied on Deere and Co. (DE). We see a successful example of going short with a signal threshold $\overline{s}$ of 0.025, as manifested by the predominance of green bars on the upper figure. The size of the positions changes due to reallocation of resources on the other assets of the portfolio. Notice that most green bars coincide with the end of a strong price appreciation that the LPPLS signal qualifies as a mature bubble ready to burst.

Figure 3

Annualized returns of the LPPLS-based strategies vs the random ones on a basket of 50 assets between 1 January 2008 and 31 December 2012. Each point represents the annualized return of a single strategy.

Figure 4

Each polygon represents the fraction of LPPLS $>$ shuffle positions of a cloud plot of Fig. 3. The vertical bars on the $yz$ projections represent the standard deviation of the fraction of LPPLS $>$ shuffle positions over ten different choices of assets. In the vast majority of cases, LPPLS is above the 50% plane and thus significantly differs from shuffle positions. Although LPPLS vs shuffle signals is not shown here, the results are qualitatively the same.