Crash-sensitive Kelly Strategy built on a modified Kreuser-Sornette bubble model tested over three decades of twenty equity indices

37 Pages Posted: 9 Oct 2020 Last revised: 16 Oct 2020

See all articles by J-C Gerlach

J-C Gerlach

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC)

Jerome L Kreuser

ETH Zurich

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute; Southern University of Science and Technology; Tokyo Institute of Technology

Date Written: October 8, 2020

Abstract

We present a modified version of the super-exponential rational expectations “Efficient Crashes” bubble model of (Kreuser and Sornette, 2019) with a different formulation of the expected return that makes clearer the additive nature of corrective jumps. We derive a Kelly trading strategy for the new model. We combine the strategy with a simplified estimation procedure for the model parameters from price time series. We optimize the control parameters of the trading strategy by maximizing the return-weighted accuracy of trades. This enables us to predict the out-of-sample optimal investment, purely based on in-sample calibration of the model on historical data. Our approach solves the difficult problem of selecting the portfolio rebalancing time, as we endogenize it as an optimization parameter. We develop an ex-ante backtest that allows us to test our strategy on twenty equity asset indices. We find that our trading strategy achieves positive trading performance for 95% of tested assets and outperforms the Buy-and-Hold-Strategy in terms of CAGR and Sharpe Ratio in 60% of cases. In our simulations, we do not allow for any short trading or leverage. Thus, we simply simulate allocation of 0-100% of one’s capital between a risk-free and the risky asset over time. The optimal rebalancing periods are mostly of duration around a month; thus, the model does not overtrade, ensuring reasonable trading costs. Furthermore, during crashes, the model reduces the invested amount of capital sufficiently soon to reduce impact of price drawdowns. In addition to the Dotcom bubble, the great financial crisis of 2008 and other historical crashes, our study also covers the most recent crash in March 2020 that happened globally as a consequence of the economic shutdowns that were imposed as a reaction to the spread of the Coronavirus across the world.

Keywords: financial bubbles, efficient crashes, positive feedback, rational expectation, Kelly criterion, optimal investment, Covid-19 crash

JEL Classification: C53, G01, G17

Suggested Citation

Gerlach, Jan-Christian and Kreuser, Jerome L and Sornette, Didier, Crash-sensitive Kelly Strategy built on a modified Kreuser-Sornette bubble model tested over three decades of twenty equity indices (October 8, 2020). Swiss Finance Institute Research Paper No. 20-85, Available at SSRN: https://ssrn.com/abstract=3708035 or http://dx.doi.org/10.2139/ssrn.3708035

Jan-Christian Gerlach

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
SEC
Zürich, 8092
Switzerland

Jerome L Kreuser

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Didier Sornette (Contact Author)

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
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Switzerland

Southern University of Science and Technology

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Tokyo Institute of Technology

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

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