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Bitcoin, Currencies, and Fragility Nassim Nicholas Taleb†‡ †Universa Investments ‡Tandon School of Engineering, New York University Forthcoming, Quantitative Finance

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Bitcoin, Currencies, and Fragility Nassim Nicholas Taleb†‡ †Universa Investments ‡Tandon School of Engineering, New York University Forthcoming, Quantitative Finance 1 Bitcoin, Currencies, and Fragility Nassim Nicholas Taleby z yUniversa Investments zTandon School of Engineering, New York University Forthcoming, Quantitative Finance BTC Volatility 2013-2021 INTRODUCTION/ABSTRACT 1.2 This discussion applies quantitative finance methods and economic arguments to cryptocurrencies in general 1.0 and bitcoin in particular —as there are about 10; 000 cryptocurrencies, we focus (unless otherwise specified) 0.8 on the most discussed crypto of those that claim to hew to the original protocol [1] and the one with, by far, the 0.6 largest market capitalization. 0.4 In its current version, in spite of the hype, bitcoin failed to satisfy the notion of "currency without govern- 0.2 ment" (it proved to not even be a currency at all), can be neither a short nor long term store of value (its expected 0.0 value is no higher than 0), cannot operate as a reliable 2016 2018 2020 inflation hedge, and, worst of all, does not constitute, not even remotely, a safe haven for one’s investments, Fig. 1. BTC return, 3 months annualized volatility. It does not seem to drop over time. a shield against government tyranny, or a tail protection BTC Capitalization Volatility 2013-2021 vehicle for catastrophic episodes. 1×10 12 Furthermore, bitcoin promoters appear to conflate the success of a payment mechanism (as a decentralized 11 mode of exchange), which so far has failed, with the 8×10 speculative variations in the price of a zero-sum maxi- mally fragile asset with massive negative externalities. 6×10 11 Going through monetary history, we show how a true numeraire must be one of minimum variance with respect 4×10 11 to an arbitrary basket of goods and services, how gold and silver lost their inflation hedge status during the Hunt 2×10 11 brothers squeeze in the late 1970s and what would be required from a true inflation hedged store of value. 0 2016 2018 2020 arXiv:2106.14204v2 [econ.GN] 4 Jul 2021 Fig. 2. Too volatile to fail? We show the volatility of the capitalization of THE BLOCKCHAIN BTC. At higher levels of capitalization, return volatility compounds. In 2021 a swing of half a trillion dollars in the capitalization of bitcoin took place. First, let us consider what cryptocurrencies do by examining the notion of blockchain and its intellectual and mathematical appeal. The concept behind such a chain is quite intuitive to [2]. Indexing sequences by t = 1; 2; : : : n, with a seed at early practitioners of quantitative finance. Consider that be- t, a variable xt on the real line generates via nonlinear fore efficient software for Monte Carlo simulations became transformations r : R ! R, an output variable r(xt). widely available, some of us were using methods to generate This output variable can serve as a pseudorandom seed to pseudorandom variables via some forms of chained nonlinear generate another pseudorandom variable, r(xt+1). For all transformations, in the spirit of Von Neumann’s original idea t, knowledge of r(Xt) allows knowledge of all subsequent variables r(xτ )τ>t and replication of the entire sequence, thus [email protected] probabilistically mimicking the arrow of time. It is also crucial The author thanks Gur Huberman, Mark Spitznagel, Brandon Yarkin, Arthur that the same seed produces exactly the same pseudorandom Breitman, Trishank Karthik Kuppusamy, Jim Gatheral, Joe Norman, Zhuo Xi, David Boxenhorn, Antonis Polemitis, Joe Shipman, and others for useful variable, allowing verification of sequence, but disallowing discussions. easy reverse engineering. 2 What the blockchain added, thanks to the hash function, As we will see, mathematical and combinatorial qualities is the condition that r(:) must be functionally and proba- do not necessarily translate into financial benefits at either bilistically bijective: no two seeds should produce the same individual or systemic levels. output (or should produce a vanishingly low probability of that happening), what, in computer science terminology, is called Comment 1: Why BTC is worth exactly 0 collision. This hard-wired attribute and absence of supervision of the Gold and other precious metals are largely maintenance blockchain allow the storage of activities on a public ledger to free, do not degrade over an historical horizon, and facilitate peer-to-peer commerce, transactions, and settlements. do not require maintenance to refresh their physical The blockchain concept also allows for serial record keeping. properties over time. This is supposed to help create what the original white paper Cryptocurrencies require a sustained amount of inter- [1] described as: est in them. A purely peer-to-peer version of electronic cash would allow online payments to be sent directly VULNERABILITY OF REVENUE-FREE BUBBLES from one party to another without going through a financial institution. A central result (even principle) in the rational expectations and securities pricing literature is that, thanks to the law of From that paper, bitcoin makes use of three existing tech- iterated expectations, if we expect now that we will expect the nologies: 1) the hash function, 2) the Merkle tree (to chain price to vary at some point in the future, then by backward blocks of transactions tagged by the hash function), and 3) the induction such a variation must be incorporated in the price concept of proof of work (used to deter spam by forcing agents now. When there are no dividends, as with growth companies, to use computer time in order to qualify for a transaction) there is still an expectation of future earnings, and a future — technologies that, ironically, all came out of the academic expected reward to stockholders — directly via dividends, or literature[3]1. The idea provides a game theoretic approach to indirectly via reverse dilutions and buybacks. It remains that mitigate the effects of the absence of custodian and lack of a stock is a claim on accumulated assets and their residual trust between participants in the maintenance of a permanent value. shared public ledger — attenuating or circumventing the coor- Earnings-free assets with no residual value are problematic. dination quandary known as the "Byzantine general problem". The implication is that, owing to the absence of any explicit The bitcoin transactional currency (BTC) system establishes yield benefitting the holder of bitcoin, if we expect that at an adversarial collaboration between the so-called "miners" any point in the future the value will be zero when miners are who validate transactions by getting them on a public ledger; extinct, the technology becomes obsolete, or future generations as a reward they get coins plus a fee from the underlying get into other such "assets" and bitcoin loses its appeal for transactions, transfers of coins between parties. The proof them, then the value must be zero now3. of work method has an adjustable degree of difficulty based The typical comparison of bitcoin to gold is lacking in on the speed of blocks, which aims, in theory, to keep the elementary financial rigor4. We will see below how precious incentive sufficiently high for miners to keep operating the metals lost their quality as a medium of exchange; gold and system. Such adjustments lead to an exponential increase in other dividend-free precious items (such as other metals or computer power requirements, making at the time of writing stones) have held some financial status for more than 6; 000 onerous energy demands on the system — energy that could years, and their physical status for several orders of magnitude find alternatives in other computational and scientific uses. longer (i.e., they did not degrade or mutate into some other Miners derive their compensation from both seignorage alloy or mineral). So one can expect one’s gold or silver (the market value of a bitcoin minus its mining costs) and possessions to be around physically for at least the next transaction fees upon validation — with the plan to switch to transaction fees as the sole revenues upon the eventual 3Using a traditional rational bubble model (see [4] and the review by depletion of the coins, which are limited to a fixed number. [5]), we get the following conditions. Let rd be a discount rate and π be A central attribute is that bitcoin depends on the existence a probability of absorption over a period. To escape the barrier, bitcoin must grow at er+π forever, but no more, without remission, and with total certainty. of such miners for perpetuity. Should it grow then stabilize, it still would be prone to extinction. We note Note that the entire ideological basis behind bitcoin is that traditionally, models rule out any continuous growth at an exponential rate complete distrust of other operators — there are no par- faster than r + π because the security or asset would then represent the entire economy. Bitcoin distinguishes itself from other assets because of its fragility tial custodians; the system is fully distributed, though prone as a mere book entry on a virtual ledger that requires constant refreshing ad to concentration2. Furthermore, by the very nature of the infinitum. blockchain, transactions are irreversible, no matter the reason. 4It is also a reasoning error to claim that an innovation, bitcoin, can become the "new gold" ab ovo, when gold wasn’t decided to be so by fiat thanks Finally, note that bitcoins are zero-sum by virtue of the to a white paper; it organically became a reserve asset ex post, through numerus clausus. centuries of competitive selection against other modes of storage, payment, and collectibles. Gold elicited an aesthetic fascination and had been used as 1As this discussion is focused on proof of work, we exclude from it jewelry and store of value for more than two millennia before it became, Ethereum and other cryptocurrencies.
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