Liquidity and Downside Risk in Bitcoin

The likelihood of severe contractions in the price of an asset is inherently linked to liquidity. For instance, funding shocks decrease market liquidity, leading to speculator losses on their initial positions, forcing them to sell more, causing a further price drop, and so on. Such “liquidity spirals” have been investigated by Brunnermeier and Pedersen (2009). They show theoretically that securities speculators invest in have a positive average return and a negative skewness. The positive return is a premium for providing liquidity and the negative skewness arises from an asymmetric response to fundamental shocks, i.e. shocks that lead to speculator losses are amplified. Conversely, shocks that lead to speculator gains are not amplified. Further, Brunnermeier and Pedersen (2009) show that securities where speculators have long positions will move together, as will securities that they short.

Introduction

In cryptoasset markets, we can envision a situation where a sudden price increase attracts more capital. In a frictionless and risk-neutral economy, this should lead to an immediate appreciation of the cryptoasset associated with the capital inflow. In the presence of liquidity constraints, however, capital arrives slowly, such that cryptoasset prices often appreciate slowly, occasionally disrupted by sudden depreciations as speculative capital is withdrawn.

In the long term, however, as speculators hold on to their long positions, the investment may be prevented from leading to a build-up of a “bubble”. As a consequence, the correction is often delayed and occurs as a sudden crash when speculators unwind their net long positions. This deteriorates market liquidity, which in turn can trigger a further sell-off from small retail investors and therefore a liquidity spiral. 

In this note, we investigate the relationship between market liquidity and price crashes in cryptoasset markets. We investigate this through the lens of a dynamic quantile regression model in which liquidity is explicitly linked to the empirical probability of observing large losses, i.e. the value-at-risk. The focus of the study is Bitcoin (BTC). The reason is two-fold: first, Bitcoin represents a market “level” factor as it captures most of the time-series variation of the aggregate returns on the market. That is, BTC is fairly representative of the market when it comes to the relationship between liquidity and returns. Second, BTC is the most traded cryptoasset, perhaps except for Tether (USDT). Although the liquidity of BTC is by no means comparable to the liquidity of more traditional assets, such as equities, BTC/USD likely represents the most liquid pair currently traded in the market. In this respect, the results we provide in this short note can be interpreted as conservative relative to the rest of the market.

Liquidity and Value-at-risk

Our empirical analysis uses daily time-series data on BTC prices relative to USD for the period August 2015 to January 2021. In addition, we consider two alternative liquidity measures based on the high, low, close, and open prices. In particular, we calculate two alternative synthetic bid-ask spreads measures as in Corwin and Schultz (2012) and Abdi and Ranaldo (2017). Both measures have been shown to provide a fairly accurate approximation of bid-ask spreads in equity markets. As the procedures to calculate these bid-ask spreads is somewhat complex, we direct the interested reader to the references at the bottom of the research report.

The VaR is calculated as each time t following Engle and Manganelli (2004). We consider a first-order autoregressive dynamics as follows:



Engle and Manganelli (2004) dubbed this model the Symmetric Absolute Value (SAV) Conditional VaR model. This model assumes past returns have a symmetric effect on the dynamics of downside risk and that the latter is mean reverting. Figure 1 reports the dynamics of Value-at-risk at α=5% confidence level (left panel) and the two alternative measures of bid-ask spread (right panel).

Figure 1: Value-at-risk and Liquidity


Source: Aaro Capital Research

Notes: The left panel shows the daily returns (blue line) and the Value-at-Risk at 5% (red line) for BTC. The right panel shows the two alternative measures of bid-ask spread, the one proposed by Corwin and Schultz (2012) and Abdi and Ranaldo (2017). The sample is from August 2015 to February 2021, daily.

Two interesting observations emerge. First, the number of in-sample violations of the VaR is around 5%, which is in line with the model specification. Second, both specifications of the bid-ask spread gives a similar dynamic. Liquidity tends to significantly deteriorate from 2017/2018, mid-2019 and during the early stages of the Covid-19 pandemic and early 2021. This suggests that the highly volatile market for BTC could be linked with high volatility in liquidity. 
Figure 2 provides a first visual link between liquidity and downside risk in Bitcoin. In particular, the figure plots the correlation between the  and each of the two measures of bid-ask spreads.

Figure 2: Downside Risk and Bid-ask Spreads


 

Source: Aaro Capital Research

Notes: The left (right) panel shows the correlation between the VaR at 5% significance level and the bid-ask spread calculated as in Corwin and Schultz 2012 (Abdi and Ranaldo 2017). The red line is the OLS fitted regression line. The sample is from August 2015 to February 2021, daily.

Two interesting facts emerge. First, there is a strong and positive correlation between downside risk, proxied by the VaR, and market liquidity for BTC. That is, deteriorating liquidity, or higher transaction costs, tend to anticipate large price drops in BTC at the aggregate level. Second, although the relationship between liquidity and downside risk is mostly linear, there is an inverse relationship for very high values of the VaR. This is particularly true for the Corwin and Schultz (2012) bid-ask spread approximation.

Evidence From a Dynamic Quantile Approach

Figure 2 visually provides some indication on the nature of the relationship between downside risk and liquidity, based on a simple correlation analysis. We investigate this relationship further through the lens of an extended Symmetric Absolute Value (SAV) Conditional VaR, whereby the bid-ask spread is directly considered as a regressor in the dynamic quantile approach. More specifically, we consider the following model:



Where  represents one of the two alternative bid-ask spread measures. The coefficient gives a direct interpretation of the effect of liquidity on downside risk. Table 1 below reports the Maximum Likelihood Estimates and the corresponding standard errors and p-values (see Engle and Manganelli 2004 for more details on the estimation procedure).

Table 1: Model Estimates

Source: Aaro Capital Research

Notes: This table reports the estimates of the dynamic quantile autoregressive model as outlined in the main text. We report the results by using as regressors both the bid-ask spread computed as in Abdi and Ranaldo (2017) and in Corwin and Schultz (2012). *,**, and *** indicates that the coefficient is significant at the 10%, 5%, and 1% level, respectively. The sample is from August 2015 to February 2021, daily.
According to Table 1, there exists a moderate mean-reversion in the VaR dynamics, although the persistence is moderate, as measured by the autoregressive estimates of . Turning our attention to liquidity, the regression analysis suggests that higher bid-ask spreads, i.e. lower liquidity, are correlated with one-step ahead higher VaR levels. The overall statistical significance is rather strong, with coefficients that are significant at the 1% confidence level. That is, the null hypothesis is largely rejected at the 1% significance level. Overall, the results show that there is a significant and positive relationship between liquidity and downside risk, as proxied by the daily VaR at 5%.

Conclusion

We test for the existence of a relationship between downside risk, i.e. market crashes, and liquidity, as proxied by the bid-ask spreads proposed by Corwin and Schultz (2012) and Abdi and Ranaldo (2017). We focus on Bitcoin, the largest cryptoasset traded by market capitalisation. The empirical evidence suggests two key findings: 

  1.     Bid-ask spreads tend to be highly volatile and increasing over early 2020 and early 2021. This could possibly explain some of the market volatility observed in the last few months.
  2.     There is a strong and significant correlation between downside risk, or market crashes, and liquidity. This is show both visually, through a simple scatter plot, and statistically through a more complex dynamic quantile regression model.

The relationship between crashes and liquidity has been linked to limited risk capacity and financing constraints by large institutional investors, in the context of traditional asset classes, such as equities, currencies and commodities. It is plausible that something similar is happening in cryptoasset markets as well, with crash risk and liquidity being interlinked with trading frictions and orders by large investors.

Bibliography

Abdi, Farshid, and Angelo Ranaldo. "A simple estimation of bid-ask spreads from daily close, high, and low prices." The Review of Financial Studies 30.12 (2017): 4437-4480.

Brunnermeier, Markus K., and Lasse Heje Pedersen. "Market liquidity and funding liquidity." The review of financial studies 22.6 (2009): 2201-2238.

Corwin, Shane A., and Paul Schultz. "A simple way to estimate bid‐ask spreads from daily high and low prices." The Journal of Finance 67.2 (2012): 719-760.

Engle, R., & Manganelli, S. (2004). CAViaR: conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 22(4), 367–381.
 

Disclaimer

The material provided in this article is being provided for general informational purposes. Aaro Capital Limited does not provide, and does not hold itself out as providing, investment advice and the information provided in this article should not be relied upon or form the basis of any investment decision nor for the potential suitability of any particular investment. The figures shown in this article refer to the past or are provided as examples only. Past performance is not reliable indicator of future results.

This article may contain information about cryptoassets. Cryptoassets are at a developmental stage and anyone thinking about investing into these types of assets should be cautious and take appropriate advice in relation to the risks associated with these assets including (without limitation) volatility, total capital loss, and lack of regulation over certain market participants. While the directors of Aaro Capital Limited have used their reasonable endeavours to ensure the accuracy of the information contained in this article, neither Aaro Capital Limited nor its directors give any warranty or guarantee as to the accuracy and completeness of such information.

 

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