Common Risk Factors in Cryptocurrency - BFICommon Risk Factors in Cryptocurrency Yukun Liu Aleh...

Common Risk Factors in Cryptocurrency

Yukun Liu Aleh Tsyvinski Xi Wu

Rochester Simon Yale NYU Stern

Cryptocurrencies and Blockchains ConferenceNovember 2019

Introduction Common Factors Mechanism Implementability Summary

Theory Ahead of Measurement

• Many excellent theoretical papers

• Weber (2016), Huberman, Leshno, and Moallemi (2017), Biais et al. (2018), Chiuand Koeppl (2017), Cong and He (2018), Cong, Li, and Wang (2018), Cong, He,and Li (2018), Sockin and Xiong (2018), Saleh (2018), Schilling and Uhlig (2018),Abadi and Brunnermeier (2018), Routledge and Zetlin-Jones (2018), Makarov andSchoar (2018)

• Relatively few “facts” to calibrate and assess these models

• Our goal:

• Establish a set of stylized facts as benchmark• Test implications of existing models

2


This Paper• Study the cross-section of cryptocurrency returns

• All coins with market cap > 1 mil USD• 1,064 coins in 2019

• Are the characteristics that are deemed important by the markets in the cross-sectionof equity returns also present in the cryptocurrency markets?

• Explore the “crypto” factor zoo (price and market based factors) – 24 factors• 10 factors form successful long-short strategies – directions same as equity market

• Three-factor model with the cryptocurrency market factor (CMKT), a cryptocurrencysize factor (CSMB), and a cryptocurrency momentum factor (CMOM) accounts for theexcess returns of all of the ten successful hedged strategies

• Three common risk factors

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MechanismCryptocurrency size factor (CSMB)

• Liquidity (Amihud (2002); Bali et al. (2005, 2008); Ang et al (2006))• Portfolio characteristics• Strong for high arbitrage cost coins

• Strong at times of high coin market volatility

• Trade-off between capital gain and convenience yield (Cong, Li, and Wang (2018);Sockin and Xiong (2019); Prat, Danos, and Marcassa (2019))• Strong at times of high bitcoin transaction amount

Cryptocurrency momentum factor (CMOM)

• Investor overreaction (Barberis, Shleifer, and Vishny (1998); Daniel, Hirshleifer, andSubrahmanyam (1998); Xiong and Sockin (2019))• Evidence of long-term reversal• However, strong among large coins

4


Data (Jan 2014 – Jun 2019)

Year Number of Coins Market Cap (mil) Volume (thous)Mean Median Mean Median

2014 109 239.83 3.89 1,146.09 36.242015 77 134.53 2.76 1,187.64 11.512016 155 160.60 3.41 1,795.03 23.962017 795 439.42 9.02 18,661.07 131.362018 1,559 363.17 8.85 21,184.20 124.922019 1,064 243.55 5.48 59,599.30 135.29

Full 1,803 329.81 7.17 29,560.01 111.29

Mean Median SD Skewness Kurtosis

Coin Market Return 0.015 0.008 0.115 0.275 4.493

Bitcoin Return 0.015 0.005 0.114 0.425 4.630

Ripple Return 0.033 -0.004 0.255 3.633 23.209

Ethereum Return 0.045 0.012 0.227 1.903 10.723

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Category Factor Definition

Size MCAP Log last day market capitalization in the portfolio formation week

Size PRC Log last day price in the portfolio formation week

Size MAXDPRC The maximum price of the portfolio formation week

Size AGE The number of days that have been listed on Coinmarketcap.com

Mom r 1,0 One-week momentum

Mom r 2,0 Two-week momentum

Mom r 3,0 Three-week momentum

Mom r 4,0 Four-week momentum

Mom r 4,1 One-to-four-week momentum

Mom r 8,0 Eight-week momentum

Mom r 16,0 Sixteen-week momentum

Mom r 50,0 Fifty-week momentum

Mom r 100,0 Hundred-week momentum

Volume VOL Log average daily volume in the portfolio formation week

Volume PRCVOL Log average daily volume times price in the portfolio formation week

Volume VOLSCALED Log average daily volume times price scaled by market capitalization in the portfolio formation week

Vol BETA The regression coefficient βiCMKT in Ri − Rf = αi + βi

CMKT CMKT + εi .

Vol BETA2 Beta squared

Vol IDIOVOL Measured as the standard deviation of the residual after estimating Ri − Rf = αi + βiCMKT CMKT + εi . The model

is estimated using daily returns of the previous 365 days before the formation week.

Vol RETVOL The standard deviation of daily returns in the portfolio formation week

Vol MAXRET Maximum daily return of the portfolio formation week

Vol DELAY The improvement of R2 in Ri − Rf = αi + βi CMKT + βi−1CMKT−1 + βi

−2CMKT−2 + εi , compared to using

only current coin market excess returns. Using daily returns of the previous 365 days before the formation week.

Vol STDPRCVOL Log standard deviation of dollar volume in the portfolio formation week

Vol DAMIHUD The average absolute daily return divided by dollar volume in the portfolio formation week6

Common Factors


10 Significant Predictors

Category Variable 1 2 3 4 5 5-1

Size MCAP 0.057*** 0.019* 0.013 0.013 0.016** -0.042***

Size PRC 0.045*** 0.028** 0.005 0.019 0.015** -0.030**

Size MAXDPRC 0.046*** 0.025** 0.005 0.021* 0.015** -0.031**

Mom r 1,0 -0.003 0.002 0.013 0.045*** 0.022* 0.025*

Mom r 2,0 -0.001 0.004 0.011 0.021** 0.034*** 0.035***

Mom r 3,0 0.000 0.004 0.015* 0.022** 0.045*** 0.045***

Mom r 4,0 0.002 0.007 0.012 0.022** 0.026** 0.023**

Mom r 4,1 0.003 0.009 0.024** 0.014 0.026** 0.023**

Volume PRCVOL 0.040** 0.027** 0.018 0.019* 0.015** -0.024*

Volatility STDPRCVOL 0.038*** 0.032** 0.022* 0.023* 0.015** -0.023**

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Cryptocurrency 3-Factor

• The cryptocurrency market factor (CMKT)

• The value-weighted return of the underlying coins

• A cryptocurrency size factor (CSMB)

• The spread between largest 30% coins and smallest 30% coins

• A cryptocurrency momentum factor (CMOM)

• The spread between the highest 30% 3-week mom coins and lowest 30% 3-weekmom coins

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One-Factor: Only Coin Market Returns

• Essentially, CAPM for cryptocurrency

• Performs poorly in pricing the cross-section of returns (similar to otherasset classes)

• The alphas for most of the ten successful long-short strategies remainlarge and statistically significant; low explanatory power

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Two-Factor Models

• Coin Market and Size

• The long-short alphas for non-momentum strategies are no longer significant• Does not explain any of the momentum factors

• Coin Market and Momentum

• Captures the results of the momentum strategies• Does not explain most of the non-momentum strategies

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Three-Factor Model• None of the long-short strategies is significant controlling for the

cryptocurrency three-factor model

Category Variable Raw 1 2 3 4 5 5-1

Size MCAP -0.042*** 0.007 -0.008 -0.006 -0.005 0.000* -0.007

Size PRC -0.030** 0.015 0.003 -0.017** -0.001 0.001 -0.014

Size MAXDPRC -0.031** 0.016 -0.000 -0.017** 0.000 0.001 -0.015

Mom r 1,0 0.025* -0.016** -0.010* -0.004 0.023 -0.012 0.004

Mom r 2,0 0.035*** -0.007 -0.004 -0.001 -0.002 -0.000 0.007

Mom r 3,0 0.045*** -0.001 -0.006 0.004 0.003 0.002 0.003

Mom r 4,0 0.023** -0.004 -0.005 -0.002 0.002 -0.010 -0.006

Mom r 4,1 0.023** -0.002 -0.002 0.004 -0.004 -0.009 -0.007

Volume PRCVOL -0.024* 0.002 -0.001 -0.006 -0.003 0.000 -0.002

Volatility STDPRCVOL -0.023** 0.008 -0.002 -0.002 -0.005 0.000 -0.007

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Three-Factor Model

• Account for all 10 long-short strategies

• The CSMB factor accounts for the excess returns of

• the market capitalization, price, maximum day price, dollar volume, standarddeviation of dollar volume

• The CMOM factor accounts for all the momentum strategies

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Principal Component Analysis• Principal component analysis of the 24 long-short strategies• Two components emerge to account for 44% of the variations

Component Eigenvalue Difference Cumulative

Comp1 5.81 1.18 0.24Comp2 4.64 1.99 0.44Comp3 2.65 0.84 0.54Comp4 1.81 0.31 0.62Comp5 1.50 0.21 0.68Comp6 1.29 0.40 0.74Comp7 0.89 0.02 0.78Comp8 0.86 0.06 0.81Comp9 0.81 0.14 0.84Comp10 0.67 0.11 0.87

PC1 PC2 CMKT CSMB CMOM

PC1 1.00

PC2 0.00 1.00

CMKT 0.20 0.04 1.00

CSMB 0.69 -0.46 0.14 1.00

CMOM 0.33 0.67 0.07 -0.03 1.0013


Category Variable Comp1 Comp2 Comp3 Comp4 Comp5

Size MCAP -0.229 0.212 -0.145 0.277 -0.217Size PRC -0.316 0.108 -0.114 -0.152 0.370Size MAXDPRC -0.320 0.095 -0.099 -0.157 0.361Size AGE -0.164 -0.001 0.011 -0.137 -0.008Mom r 1,0 0.185 0.241 -0.164 0.033 0.128Mom r 2,0 0.163 0.247 0.016 -0.194 -0.074Mom r 3,0 0.181 0.329 -0.066 -0.240 0.003Mom r 4,0 0.176 0.350 -0.036 -0.205 -0.059Mom r 4,1 0.137 0.314 -0.030 -0.317 -0.087Mom r 8,0 0.079 0.299 0.006 0.100 0.194Mom r 16,0 0.098 0.336 0.069 -0.106 0.121Mom r 50,0 0.068 0.211 0.253 0.183 0.045Mom r 100,0 -0.029 0.072 0.359 0.079 -0.253Volume VOL -0.244 0.243 -0.092 0.265 -0.287Volume PRCVOL -0.331 0.155 -0.097 0.070 0.089Volume VOLSCALED -0.011 0.157 -0.019 -0.014 -0.221Vol BETA -0.062 0.085 0.522 0.115 0.191Vol BETA2 -0.061 0.101 0.521 0.122 0.182Vol IDIOVOL 0.263 0.041 0.119 0.181 -0.227Vol RETVOL 0.213 0.049 -0.157 0.413 0.309Vol MAXRET 0.231 0.116 -0.124 0.407 0.285Vol DELAY 0.194 -0.062 -0.310 0.184 0.008Vol STDPRCVOL -0.333 0.175 -0.034 0.080 0.047Vol DAMIHUD 0.247 -0.240 0.104 -0.213 0.308

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Cryptocurrency Size & MomentumMechanism


Size & MomentumSize-related theories• Traditional

• Weak or non-existent (Dichev (1998); Israel and Moskowitz (2013); Amihud (2002); Pastor and

Stambaugh (2003))

• Liquidity (Amihud (2002); Bali et al. (2005, 2008); Ang et al. (2006))

• Cryptocurrency• Trade-off between capital gain and convenience yield (Cong, Lin, and Wang (2018); Sockin and

Xiong (2019); Prat, Danos, and Marcassa (2019))

Momentum-related theories• Traditional

• Overreaction to news (Barberis, Shleifer, and Vishny (1998); Daniel, Hirshleifer, and

Subrahmanyam (1998))• Underreaction to news (Hong and Stein (1999))

• Risk-based explanation (Li (2017))

• Cryptocurrency• Delayed reaction to the externality of network effect (Cong, Lin, and Wang (2018))

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Size & Momentum

Size-related theories• Liquidity

• Portfolio characteristics• Strong for high arbitrage cost coins

• Strong at times of high coin market volatility

• Trade-off between capital gain and convenience yield

• Strong at times of high transaction amount

Momentum-related theories• Overreaction to news

• Evidence of long-term reversal

• However, strong among large coins

• Delayed reaction to the externality of network effect

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Size – Portfolio Characteristics

• Large size portfolios have higher price, liquidity, age, and lower volatility• Consistent with the liquidity view

• High momentum portfolios have higher price and more liquid

Price Amihud Age SD7 SD30 Idio

MCAP

1 0.636 0.378 492.287 0.121 0.150 0.1422 1.291 0.197 486.765 0.108 0.132 0.1243 2.210 0.067 478.734 0.095 0.113 0.1034 2.568 0.017 490.328 0.081 0.095 0.0845 138.944 0.000 1045.076 0.040 0.045 0.0235-1 138*** -0.377*** 553*** -0.082*** -0.104*** -0.119***

r 3,0

1 16.707 0.046 520.928 0.072 0.094 0.0822 40.175 0.011 714.049 0.051 0.060 0.0443 59.673 0.009 835.355 0.049 0.057 0.0394 78.919 0.021 847.921 0.055 0.062 0.0445 36.956 0.032 671.838 0.104 0.113 0.1015-1 20*** -0.014 151*** 0.032*** 0.019*** 0.018***

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Size – Cost of Arbitrage Index• Create a cost of arbitrage index of each coin

• Five underlying measures: idiosyncratic volatility, coin age, Amihud illiquidity, coin price, and

volume-volatility• Stambaugh, Yu, and Yuan (2015) and Atilgan et al. (2019)

• The size premium is much stronger for coins are hard to arbitrage

• For small coins, coins with high cost of arbitrage index have high expected returns

Size1 2 3 3 - 1

Low High

Arbitrage

Low 1 0.008 0.012 0.014** 0.006(0.97) (1.40) (2.11) (1.02)

2 0.028** 0.015 0.006 -0.021**(2.47) (1.51) (0.65) (-2.26)

High 3 0.083*** 0.021* 0.029* -0.054**(3.22) (1.77) (1.75) (-2.02)

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Size – Time-Series• Stronger at times of high coin market volatility

• Consistent with liquidity view

• Stronger at times of high transaction count• Use transaction count to proxy for the need for transaction• Consistent with the trade-off between capital gain and convenience yield

CSMB CSMB CSMB CSMB

MKTRF 0.046 -0.005 -0.016

(0.100) (-0.011) (-0.033)

SMB 0.309 0.293

(0.406) (0.381)

HML -0.861 -0.910

(-1.161) (-1.111)

MOM -0.081

(-0.143)

fin -0.209

(-0.341)

pead 0.386

(0.330)

σ (CMKT ) 0.968** 0.927** 0.927** 0.968**

(2.474) (2.358) (2.353) (2.474)

log (Trans) 0.076*** 0.077*** 0.077*** 0.076***

(4.827) (4.848) (4.838) (4.826)

R-squared 0.104 0.110 0.110 0.105

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Momentum – Long-Term Past Return

• Long-short zero-investment returns of relatively long-term past returns

• Consistently negative but insignificant• Sample period is short

• Consistent with overreaction

1 2 3 4 5 5-1

60 WeekMean 0.015* 0.018** 0.020** 0.019** 0.012 -0.003

t(Mean) (1.805) (2.105) (2.115) (1.974) (1.103) (-0.325)

70 WeekMean 0.021*** 0.020** 0.029** 0.025** 0.009 -0.012

t(Mean) (2.610) (2.258) (2.458) (2.432) (0.902) (-1.322)

80 WeekMean 0.027*** 0.015* 0.036*** 0.025** 0.007 -0.018

t(Mean) (2.652) (1.693) (2.753) (2.220) (0.697) (-1.639)

90 WeekMean 0.032*** 0.023** 0.029*** 0.021* 0.030** -0.005

t(Mean) (3.349) (2.492) (2.598) (1.936) (2.139) (-0.340)

100 WeekMean 0.030*** 0.025*** 0.026** 0.026** 0.019 -0.009t(Mean) (3.032) (2.655) (2.159) (2.282) (1.618) (-0.723)

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Momentum – Double Sort on Size and Momentum

• Double sort on market cap and 3-week momentum

• Cryptocurrency momentum is much stronger among large coins

Momentum

1 2 3 4 5 5 - 1

Low High

Size

Small 0.042*** 0.016 0.020* 0.013 0.032* -0.011

(2.808) (1.534) (1.948) (1.184) (1.889) (-0.563)

Large -0.001 0.001 0.019* 0.019** 0.040*** 0.042***

(-0.139) (0.124) (1.807) (2.232) (2.743) (2.834)

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Robustness & Implementability


List of Tests• Short bitcoin

• Cryptocurrency exchange

• Adjustment for trading costs

• Largest 20 coins

• Tercile portfolios

• Fama-French factor models; Behavioral factor models

• Controlling for initial coin offering returns

• Alternative variable constructions

• Cryptocurrency industry returns

• Cryptocurrency industry momentum

• Short-term momentum

• Subsample analysis

• Coin age

• ...

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Shorting Bitcoin• Strategies require shorting coins – difficult or impossible to do

• Long the factor – short bitcoin

Category Variable Raw C3 Adj

Size MCAP -0.039*** -0.004

Size PRC -0.034** -0.011

Size MAXDPRC -0.035** -0.012

Mom r 1,0 0.006 -0.016

Mom r 2,0 0.017 -0.004

Mom r 3,0 0.028** -0.001

Mom r 4,0 0.010 -0.013

Mom r 4,1 0.011 -0.012

Volume PRCVOL -0.029** -0.001

Volatility STDPRCVOL -0.028** -0.004

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Cryptocurrency Exchanges

• Using the cryptocurrencies that are traded against USD in at least one of the followingthree cryptocurrency exchanges: Kraken, Coinbase Pro, and Bitlinex

Category Variable 1 2 3 4 5 5-1

Size MCAP 0.046** 0.030* 0.032** 0.030** 0.024** -0.022

Size PRC 0.051** 0.024 0.018 0.027 0.024** -0.026

Size MAXDPRC 0.051** 0.023 0.018 0.029* 0.025** -0.027

Mom r 1,0 -0.006 0.026 0.034** 0.045*** 0.055*** 0.061***

Mom r 2,0 0.005 0.010 0.044** 0.042*** 0.058*** 0.053***

Mom r 3,0 0.017 0.024 0.035** 0.035** 0.058*** 0.040**

Mom r 4,0 0.019 0.016 0.053*** 0.021* 0.065*** 0.046**

Mom r 4,1 0.018 0.036* 0.040** 0.044*** 0.040** 0.022

Volume PRCVOL 0.052*** 0.030 0.028* 0.031** 0.028** -0.025*

Volatility STDPRCVOL 0.063*** 0.032* 0.027* 0.033** 0.023** -0.039**

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Adjusting for Trading Cost

• Top 20 coins, long-only and short bitcoin, rebalancing weekly

• Static adjustment

• Fee: 0.10%• Bid-ask spread: 0.50%• Bitcoin shorting cost: 0.35% per week

• Dynamic adjustment

• Hasbrouck (2009)

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Static Adjustment

Long-Only Short Bitcoin

% Fee Bid-Ask Raw Ret Adj Ret AdjRaw Shorting Raw Xret Adj Xret Adj

Raw

MCAP 0.10 0.50 1.70 1.55 91.33 0.35 0.20 -0.30 -148.68

PRC 0.10 0.50 2.80 2.74 97.70 0.35 1.30 0.89 68.13

MAXDPRC 0.10 0.50 2.70 2.64 97.68 0.35 1.20 0.79 65.62

r 1,0 0.10 0.50 3.20 2.71 84.75 0.35 1.70 0.86 50.71

r 2,0 0.10 0.50 3.90 3.57 91.46 0.35 2.40 1.72 71.55

r 3,0 0.10 0.50 4.50 4.22 93.86 0.35 3.00 2.37 79.13

r 4,0 0.10 0.50 3.70 3.45 93.27 0.35 2.20 1.60 72.77

r 4,1 0.10 0.50 2.90 2.63 90.77 0.35 1.40 0.78 55.88

PRCVOL 0.10 0.50 2.70 2.60 96.25 0.35 1.20 0.75 62.40

STDPRCVOL 0.10 0.50 2.40 2.29 95.27 0.35 0.90 0.44 48.49

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Summary


Conclusion

• Cross-section of cryptocurrencies can be meaningfully analyzed usingstandard asset pricing tools

• A parsimonious three-factor model with market (CMKT), size (CSMB),and momentum (CMOM) that we describe is successful in pricing theanomalies in the cryptocurrency market

• Show evidence of the mechanisms of cryptocurrency size and momentumeffects

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Common Risk Factors in Cryptocurrency - BFICommon Risk Factors in Cryptocurrency Yukun Liu Aleh...

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