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1、 BIS Working Papers No 1087 Crypto carry by Maik Schmeling,Andreas Schrimpf and Karamfil Todorov Monetary and Economic Department April 2023 JEL classification:G12,G13,G15.Keywords:Crypto,Carry,Futures basis,Crash risk,Bitcoin,Ethereum.Restricted BIS Working Papers are written by members of the Mone
2、tary and Economic Department of the Bank for International Settlements,and from time to time by other economists,and are published by the Bank.The papers are on subjects of topical interest and are technical in character.The views expressed in them are those of their authors and not necessarily the
3、views of the BIS.This publication is available on the BIS website(www.bis.org).Bank for International Settlements 2023.All rights reserved.Brief excerpts may be reproduced or translated provided the source is stated.ISSN 1020-0959(print)ISSN 1682-7678(online)Crypto CarryMaik SchmelingGoethe Universi
4、ty&CEPRschmelingfinance.uni-frankfurt.deAndreas SchrimpfBIS&CEPRandreas.schrimpfbis.orgKaramfil TodorovBISkaramfil.todorovbis.orgThis version:March 24,2023AbstractWe document that the carry of crypto futures,i.e.the difference between futures andspot prices,can become very large(up to 60%p.a.)and va
5、ries strongly over time.Thisbehavior is most consistent with the existence of a highly volatile crypto convenience yieldthat stems from two main forces:(i)trend-chasing and attention by smaller investorsseeking leveraged upside exposure to crypto assets in boom periods,and(ii)the relativescarcity of
6、“arbitrage”capital taking the other side through a cash and carry position.Engaging in the latter is risky due to spikes in margins and liquidations amid drawdowns.The interplay between these two forces,and the involved high leverage,may help explainwhy severe market crashes are a frequent feature o
7、f crypto markets.JEL Classification:G12,G13,G15Keywords:Crypto,Carry,Futures basis,Crash risk,Bitcoin,EthereumWe are grateful for helpful comments to Agostino Cappponi,Wenqian Huang,Egemen Eren,Shihao Yu(discussant),seminar participants at the BIS and conference participants at the 2023 SGF conferen
8、ce.We alsothank Giulio Cornelli for excellent research assistance.Maik Schmeling gratefully acknowledges financial supportby the German Science Foundation(DFG).The views expressed in this paper are those by the authors and donot necessarily represent those by the Bank for International Settlements(B
9、IS).The Risk-Free Crypto Trade Is Back In a Big Way Bloomberg,8 October 2021“The closest thing to a risk-free bet has reemerged in the cryptocurrency market as traders.bid up the priceof futures.”1.IntroductionDigital assets such as Bitcoin(BTC)and Ether(ETH)have gained significant attention frommar
10、ket practitioners,academics,and policymakers in recent years due to their extreme growthin market capitalization,trading volume,and the rise of products and applications based onthese crypto assets.This digital ecosystem has matured to a point where cash and derivativeinstruments are now actively tr
11、aded both on native crypto exchanges as well as on traditionalexchanges,i.e.the Chicago Mercantile Exchange(CME).Against this background,the main purpose of our paper is to study one of the most salientfeatures of these instruments in recent years the large difference between spot and futuresprices,
12、the so-called futures basis or“crypto carry”.1Crypto carry encapsulates the return ona simple“cash and carry”strategy:going long in the spot market,while selling forward thesame amount forward via a futures contract.If carry is positive,locking in the higher futuresprice while holding the spot until
13、 expiration of the futures contract generates profit(loss ifcarry is negative).We analyze crypto carry observed for the two major digital assets,Bitcoinand Ethereum,shed light on its economic drivers,and study how these are connected to theboom-and-bust dynamics commonly observed in crypto markets.T
14、he first contribution of our paper is to provide stylized facts about crypto carry,character-izing its variation over time and across various crypto platforms and traditional exchanges.Astriking feature of crypto carry is its size,averaging about 10%p.a.across exchanges from April2019 to January 202
15、2.A simple cash and carry trade would thus have yielded about 10%p.a.while at the same time being hedged against price swings in the underlying asset.The carryfor BTC and ETH is overall quite similar in terms of its level and is highly correlated acrossthe two assets over time.Carry is also highly c
16、orrelated across exchanges,with correlationstypically exceeding 90%.That said,there is some evidence on market segmentation betweencrypto exchanges and the traditional financial system(CME),with correlations of carry on the1We use the terms crypto carry and basis interchangeably in this paper.1forme
17、r and that on the CME being much weaker(only about 60-70%),see,e.g.Makarov andSchoar(2020)for an empirical analysis of price inefficiencies in crypto markets.Crypto carry isalso very volatile at low frequencies with maximum(minimum)values above 40%p.a.(below-20%)over the longer run,while it is quite
18、 persistent at higher frequencies(such as daily).Based on these facts,we seek to provide a deeper understanding of the economic forcesdriving crypto carry.As an organizing framework,we rely on the basic futures pricing equation,slightly adapted to digital asset markets(see Section 2.3 for further de
19、tails):fit,T sit=rt,T r?t,T+t,T+it,where f=logF and s=logS denote log futures and spot prices,respectively,T is the ma-turity of the futures contract,and i indexes exchanges.rt,Tand r?t,Tdenote short-term interestrates for US dollars(USD)and for crypto assets,respectively.The part unexplained by the
20、interest differential conceptually consists of two parts:itdenotes an idiosyncratic(exchange-specific)pricing error,while in turn can be thought of as an aggregate crypto convenienceyield.More specifically,we denote by t,Tthe net(of storage)convenience yield of holding thefutures contract.2This basi
21、c pricing equation tells us that the variation in carry that we observe in the datamust stem from:(i)interest rate differentials between the crypto world and the fiat world,(ii)idiosyncratic variation in pricing errors specific to exchanges(it),(iii)the convenience yield ofholding the future versus
22、the spot().Dissecting these different channels,we first document that interest rate differentials onlycapture 2%of carrys total variation.Likewise,variation in exchange fixed effects only capturesabout 1%of changes in carry.These facts suggest that neither interest rates nor idiosyncraticpricing err
23、ors drive a significant share of crypto carry.Hence,variation in carry must stem fromfluctuations in convenience yields.Going a step further,we run regressions to dissect movements in carry into changes in spot2We depart from the standard convention of defining the convenience yield as referring to
24、holding spot(e.g.,Gorton and Rouwenhorst,2006)for reasons that will become clear later:namely,the convenience of futures asa tool to engage in levered crypto trading.Convenience yields are shown to be important drivers of prices alsoin assets other than commodities:e.g.,Jiang et al.(2021)use currenc
25、y forwards to show that foreign investorsderive a convenience yield from holding U.S.Treasuries.2rates and the futures premium.We do so by regressing realized spot and futures price changeson the current carry(Ft St)in the spirit of Fama(1984)and Fama and French(1987).Thelogic of this regression is
26、based on the fact that carry at time t has to mechanically predict eitherchanges in spot prices or changes in the futures price from t to maturity of the contract T,orboth,since the futures price has to converge to the spot price at T.3The results for these regressions are striking in that a positiv
27、e carry predicts both a declinein the spot as well as in the futures price,albeit to different degrees.Specifically,our estimatesfor 1-month BTC futures imply that a rise in absolute carry by one dollar predicts a five dollardecline in spot prices which is overcompensated by a six dollar decline in
28、futures prices.Theseresults indicate that a high carry predicts future crypto price crashes.They further imply thatthere is“excess volatility”of crypto futures relative to spot prices,i.e.our estimates imply thatchanges in futures prices are about ten times more volatile than changes in spot prices
29、whenmeasured in units of the variance of carry.4In the second part of the paper we then seek to establish a better understanding of theeconomic forces that shape crypto convenience yields.Two main questions guide our work:whydo prices in the futures market decouple so strongly from spot prices?And,w
30、hat prevents“arbitrageurs”that is,cash and carry traders who are short(long)the futures when carry ispositive(negative)to lean against these extreme price dislocations?5We look at investor positioning to shed light on the types of market participants that are ondifferent sides of the trade in crypto
31、 futures.Based on the commitment of traders(COT)dataof the Commodity Futures Trading Commission(CFTC)for the CME,we establish that a risein net long positions by“nonreportable”traders(and“other reportables”)tends to be associatedwith an increase in crypto carry.These nonreportables typically compris
32、e smaller players such asfamily offices,proprietary trading shops that run commodity trend-following strategies,and/orwealthy individuals.Empirically,dealer intermediaries and leveraged funds tend to take the3In a similar vein,a long literature on uncovered interest parity(UIP)in foreign exchange(FX
33、)markets hastested for the ability of FX carry(also often labelled forward discount in that literature)to predict spot exchangerates(see,e.g.,Hassan and Mano,2019,for a recent contribution).4These results are qualitatively similar albeit more extreme to earlier results for commodities markets byFama
34、 and French(1987),notably for precious metals,and suggest a strong role for time-variation in convenienceyields in driving carry.5We put arbitrageurs deliberately into inverted commas here,as we will argue later on that the cash and carrystrategy cannot be regarded as a riskless trade in the sense o
35、f a”free lunch”.3opposite position by being short in crypto futures.These results square well with the notionthat the crypto futures basis tends to be elevated when smaller entities seek leveraged upsideexposure.6This birds eye perspective suggests that two lines of inquiry are important to understa
36、ndfluctuations in crypto convenience yields.The first one is the pressure created by smaller,trend-chasing investors to gain leveraged upside exposure to crypto-assets,which would likely increasecarry.We call these investors”trend-followers”.The second one is factors that prevent a largerdeployment
37、of capital to the cash and carry strategy,which,in turn,by being on the other sidethrough short futures positions,should dampen the upside pressure on the basis.We label theinvestors who are on the other side of the trend-followers as”carry traders”.To investigate the first channel empirically,we st
38、udy the actions of trend followers.Our mainhypothesis is that when there are strong price trends and heightened media attention,more ofthese investors rush into levered crypto futures positions.Consistent with this narrative,wefind that crypto carry is positively correlated with social media metrics
39、 such as Reddit followers(attention)and with past crypto returns(trend chasing or momentum).7If this class of investorshas a preference for leveraged products(cf.Asness et al.,2012;Frazzini and Pedersen,2014),a rise in their demand would go hand in hand with a rise in carry and a convenience yield o
40、nleveraged futures over spot,i.e.,0 in the equation above.Regarding the second channel,the key question is why capital devoted by carry traders who effectively take the other side of trend followers is scarce and slow-moving?To answerthis question,it is essential to examine the risk and return profi
41、le of the crypto cash and carrystrategy.Cash and carry can be seen as a trade on the convergence of spot and futures prices(i.e.,long spot,short futures or vice versa).However,despite being often portrayed as“risk-free”in the financial media(as evidenced by the quote at the start of the introduction
42、),suchtrades are risky in practice due to frictions in how collateral is handled on traditional and cryptoexchanges.Implementing such long-short carry position exposes a trader to the risk of spikes6See Makarov and Schoar(2021)for an in-depth analysis of the bitcoin ecosystem,disaggregated by indivi
43、dualwallets,and the different types of uses over time and Kose et al.(2021)for a recent overview of papers studyingthe economics of blockchain fundamentals.7Liu and Tsyvinski(2021)in a recent paper also find that attention is useful for predicting cryptocurrencyreturns.Kogan et al.(2023)study retail
44、 traders and show that these investors tend to be trend-followers incrypto assets.4in margins(Brunnermeier and Pedersen,2009),e.g.when the basis moves against the traderbefore maturity of the contract.As such,there is a risk that such a trade cannot be funded untilconvergence.This risk is exacerbate
45、d by the fact that the long spot position cannot be usedas collateral for the futures position on traditional exchanges such as the CME to which largerinstitutions have direct access.We then investigate factors limiting the deployment of capital to the crypto cash and carrystrategy.First,we study th
46、e basic return characteristics of the strategy.We construct cashand carry returns by shorting the futures contract and going long spot at time t when carry ispositive(or doing the opposite when it is negative),and holding this position until expiration atT.The Sharpe Ratio of this strategy(before tr
47、ansaction costs)is about 0.59 p.a.for 1-monthfutures traded on the CME,when financing the position at LIBOR.Yet,we also find that thereturns on the futures leg of this strategy exhibit severe drawdowns.Such drawdowns can leadto contract liquidations of the carry traders positions if margin calls can
48、not be met.In linewith this,we find that,in practice,carry is a significant predictor of liquidations in futurespositions.For example,an increase of carry by 10%predicts that liquidations of short futurespositions rise by 44%of total open interest over the next month.These findings indicate thatthe
49、strategy exposes patient carry traders to significant risk as the absence of cross-margining,or other margin frictions could lead to forced liquidations before maturity.These frictions alsoexplain why arbitrageurs oftentimes may not deploy enough capital to lean against a carrywidening during crypto
50、 price booms.Finally,we study the link between carry and crypto crash risk discussed above in more detailby analysing the data on contract liquidations together with(option-implied)return moments.Empirically,we find that carry emerges as a strong predictor of realized and implied skewnesssuch that a