Is liquidity risk priced in cryptocurrency markets?

ABSTRACT

This paper investigates the pricing of liquidity risk in the cross-section of cryptocurrencies from January 2017 to December 2020. The cryptocurrencies with high liquidity risk (beta) earned a risk-adjusted return of 4.4% higher weekly than those with low liquidity risk after controlling for the market, size, and reversal factors. Furthermore, the positive relation between expected cryptocurrency returns and liquidity risk is robust when I use cross-sectional regression tests for individual cryptocurrencies and alternative liquidity measures. The results suggest that liquidity risk is an important determinant of expected cryptocurrency returns.

KEYWORDS:

• Liquidity risk
• cryptocurrency
• asset pricing
• Cross-sectional returns

JEL CLASSIFICATION:

• G12
• G14

Disclosure statement

No potential conflict of interest was reported by the author(s).

2. Liquidity betas

I first calculate the aggregate liquidity, $\mathit{LI}{Q}_{\mathit{M},\mathit{t}}$ for week t by averaging individual liquidity measures across all eligible cryptocurrencies,

(A3) $\mathit{LI}{Q}_{\mathit{M},\mathit{t}}=\frac{1}{N_t}{\sum }_{\mathit{i}=1}^{N_t}\mathit{LI}{Q}_{\mathit{i},\mathit{t}},$(A3)

where $\mathit{LI}{Q}_{\mathit{i},\mathit{t}}$ are weekly liquidity measures (AR and CS) for cryptocurrency i in week t and $N_t$ is the number of available cryptocurrencies in week t. To eliminate inactive and small cryptocurrencies, only those with a market capitalization of at least $100 thousand at the end of the previous week are included if they are traded on at least five trading days each week. Following Lin, Wang, and Wu (2011), I winsorize $\mathit{LI}{Q}_{\mathit{i},\mathit{t}}$ at 1st and 99th percentiles each week to control for outliers.

The unexpected changes in scaled aggregate liquidity are obtained from the time-series regression:

(A4) $\mathrm{\Delta LI}{Q}_{\mathit{M},\mathit{t}}=\mathit{c}+{\epsilon }_t+{\phi }_1\mathrm{\Delta LI}{Q}_{\mathit{M},\mathit{t}-1}+{\phi }_2\frac{{\mathit{M}}_{\mathit{t}-1}}{M_1}\mathit{LI}{Q}_{\mathit{M},\mathit{t}-1}+{\theta }_1{\epsilon }_{\mathit{t}-1}+{\theta }_2{\epsilon }_{\mathit{t}-2},$(A4)

where $\mathrm{\Delta LI}{Q}_{\mathit{M},\mathit{t}}=\left(\frac{M_t}{M_1}\right)(\mathit{LI}{Q}_{\mathit{M},\mathit{t}}-\mathit{LI}{Q}_{\mathit{M},\mathit{t}-1})$ and $M_t$ and $M_1$ are the market capitalization of eligible cryptocurrencies at the end of week t – 1 and the beginning of the sample, respectively.⁶ I use the negative residuals ($-{\hat{\epsilon }}_{\mathit{t}}$) as the aggregate liquidity innovations ($L_t$).

3. Risk factors construction

Following Shen, Urquhart, and Wang (2020) and Shahzad et al. (2021), I construct tradable risk factors such as $\mathit{MK}{T}_t$, $\mathit{SM}{B}_t$, and $\mathit{DM}{U}_t$. The market factor ($\mathit{MK}{T}_t$) is the excess return on the market computed as the difference between the equally-weighted market return and the risk-free rate (the one-month Treasury bill rate from the Federal Reserve Board).⁷ For size and reversal factors, I form six value-weighted portfolios on market capitalization and the prior one-week return. The independent 2 × 3 sorts on size and reversal use breakpoints every week. The size breakpoints are the 10th and 90th percentiles of market capitalization, while the reversal breakpoints are the 30th and 70th percentiles of prior return. The size factor ($\mathit{SM}{B}_t$) is the average return on the three small portfolios minus three big portfolios, where SMB = 1/3(Small Up + Small Medium + Small Down) − 1/3(Big Up + Big Medium + Big Down). The reversal factor ($\mathit{DM}{U}_t$) is the average return on the two low prior return portfolios minus two high prior return portfolios, where DMU = 1/2(Small Down + Big Down) − 1/2(Small Up + Big Up).

Table A1 reports descriptive statistics of marketwide liquidity ($\mathit{LI}{Q}_{\mathit{M},\mathit{t}}$) and its liquidity innovations ($-{\hat{\epsilon }}_{\mathit{t}}$) from Eq. (A3). The sample includes weekly variables over 249 weeks from 1 April 2016, to 1 January 2021. Panel A reports time-series statistics of variables (mean, standard deviation, minimum, first quartile, median, third quartile, and maximum). The average of market liquidity does not seem to be close to zero, but the average of liquidity innovations is nearly zero, which means that the extended autoregressive integrated moving average model in Eq. (A3) effectively isolates unexpected variations in aggregate liquidity. Panel B reports contemporaneous, lead, and lagged correlations among innovations. I find statistically insignificant first- and second-order autocorrelations in both AR and CS innovations. Interestingly, the contemporaneous correlation between two liquidity innovations ($L_t^{AR}$ and $L_t^{CS}$) is 0.851, showing common unpredictable variations in marketwide liquidity measures.

Table A1. Descriptive Statistics of Marketwide Liquidity and Liquidity Innovations

Notes

¹ Like Acharya and Pedersen (2005) and many others, I define liquidity level as the ability to trade large volume quickly at low cost, while liquidity risk is defined as the covariance of its returns and unexpected changes in aggregate liquidity.

² Main findings are robust to beginning the daily sample on 21 May 2016 (the first day after other missing values in weekly factors) or 17 June 2017 (the first day having a complete dataset of weekly factors without missing values).

³ To avoid any look-ahead bias from two-day corrected $\mathit{A}{R}_d$ and $\mathit{C}{S}_d$, I averaged these for six days.

⁴ I also find statistically significant alphas of 10 liquidity-beta sorted portfolios on MKT, SMB, and DMU by Gibbons, Ross, and Shanken (1989).

⁵ To reduce the concern from errors-in-variables problem, I also calculate standard errors by Shanken (1992) and the results are quantitatively and qualitatively robust.

⁶ Bayesian information criterion is used to select p (= 1) of the order of the autoregressive model and q (= 2) of the order of the moving-average model.

⁷ The main findings remain robust when I use value-weighted excess market returns.