Bitcoin Bubble Trouble

Forthcoming in Wilmott Magazine, 2018

Swiss Finance Institute Research Paper No. 18-24

17 Pages Posted: 20 Mar 2018 Last revised: 19 Jun 2018

See all articles by Jerome L Kreuser

Jerome L Kreuser

ETH Zurich

Didier Sornette

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

Date Written: January 12, 2018


We present a dynamic Rational Expectations (RE) bubble model of prices with the intention to evaluate it on optimal investment strategies applied to Bitcoin. Our bubble model is defined as a geometric Brownian motion combined with separate crash (and rally) discrete jump distributions associated with positive (and negative) bubbles. The RE condition implies that the excess risk premium of the risky asset exposed to crashes is an increasing function of the amplitude of the expected crash, which itself grows with the bubble mispricing: hence, the larger the bubble price, the larger its subsequent growth rate. We use the RE condition to estimate the real-time crash probability dynamically through an accelerating probability function depending on the increasing expected return. We examine the optimal investment problem in the context of the bubble model by obtaining an analytic expression for maximizing the expected log of wealth (Kelly criterion) for the risky asset and a risk-free asset. Using our bubble model on Bitcoin from 8-Jul-2013 until 19-Dec-2017 would have generated a CAGR of 140% with a maximum drawdown of 69% giving a Calmar Ratio of 2.03. It would have moved out of Bitcoin gradually since 25-Apr-2017 to be completely out on 19-Dec-2017, three days before the crash. The outperformance of the Efficient Portfolio over just investing in Bitcoin was 265%, accomplished over 117 rebalances from 08-Jul- 2013 to 20-Dec-2017. This strategy could thus afford a cost of 2.27% at each rebalancing period and still outperform investing only in Bitcoin.

Keywords: bitcoin, financial bubbles, efficient crashes, positive feedback, rational expectation, Kelly

JEL Classification: C53, E47, G01, G17

Suggested Citation

Kreuser, Jerome L and Sornette, Didier, Bitcoin Bubble Trouble (January 12, 2018). Forthcoming in Wilmott Magazine, 2018; Swiss Finance Institute Research Paper No. 18-24. Available at SSRN:

Jerome L Kreuser (Contact Author)

ETH Zurich ( email )

Rämistrasse 101
Zürich, 8092

Didier Sornette

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

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


Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

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