This article investigates the relationship between market efficiency and liquidity in cryptoasset markets. The empirical evidence is currently scarce, with most existing studies focusing on a small cross section of the most liquid cryptoassets. This, however, offers a limited picture. Therefore, we extend our analysis across a broader spectrum.
Empirical evidence suggests that market efficiency is closely linked to liquidity, and thus has profound implications for market makers and inventory risk. On the one hand, if market makers can detect temporary price deviations from fundamental values, they may manage inventory risk appropriately and incentivise the convergence of prices to their fundamental values. A high degree of liquidity facilitates profits, thus causing low predictability of return and a high degree of market efficiency. In this case, liquidity is positively associated with market efficiency. On the other hand, while liquidity decreases, the market becomes more efficient because prices incorporate more information (Barberis et. al, 1998).
Most academic research on cryptoassets to date has focused solely on the nature of Bitcoin. Selgin (2015) and Baeck and Elbeck (2015) argue that it resembles a speculative commodity rather than a currency. Peterson (2017) and Van Vliet (2018) use Metcalfe’s Law to value Bitcoin based on the size of the network. Grinberg (2012) discusses the impact of macroeconomic factors on Bitcoin’s price.
In this note, we examine market efficiency in cryptoassets, extending the analysis conducted by Urquhart (2016). This paper was first to test the weak form of market efficiency on Bitcoin. Using five tests, it was concluded that Bitcoin returns are indeed market inefficient, which confirmed the intuition of many observers at the time about this new asset.
We first analyse the risk-return profile of cryptoassets sorted by the illiquidity measure, as proposed by Amihud (2002), i.e.,
Where is the number of traded days in month T (this is 30 days for most cryptoassets),is the daily return of asset i on day t in USD, is the daily volume traded of asset i on day t expressed in millions of USD. This measure provides an understanding of the relationship between trading volumes and price changes, which ultimately reflects the price impact of daily aggregate trading activity.
The data consists of the top 408 cryptoassets sorted by market capitalization. Prices and trading volume are sampled daily from July 2015 to January 2021.
Figure 1: Illiquidity Ratios
Source: Aaro Capital Research
Notes: The left panel shows the cross-sectional average illiquidity ratio over time, while the right panel shows the histogram time-series average of the illiquidity ratios. The data consists of the top 408 cryptoassets sorted by market capitalization. Prices and trading volume are sampled daily from July 2015 to January 2021.
The left panel of Figure 1 shows the time series average of the illiquidity ratio across the sample. The period before March 2017 is excluded to avoid issues with fitting the average illiquidity ratio on the chart. One interesting fact emerges; the average illiquidity increased (i.e. liquidity decreased) for the vast majority of 2020. The right panel shows the cross-sectional distribution of the average illiquidity ratios across cryptoassets. Again, one interesting fact emerges; while most cryptoasset pairs show reasonable values of the Amihud ratio, there is are many with outlier illiquidity values.
Market Liquidity and Cryptoasset Returns
Now, we investigate more carefully the relationship between illiquidity and returns. More specifically, the liquidity risk factor is constructed as follows; we calculate the illiquidity ratio at each time t, which we label illiq, for each cryptoasset based on the equation outlined above, and sort each pair into quintiles based on illiq. Then, a portfolio is constructed as an equally weighted average of the returns in each quintile at time t+1.
Figure 2: Market Liquidity and Returns in Cryptoasset Markets
Source: Aaro Capital Research
Notes: The left panel shows the returns on five equally weighted portfolios composed by cryptoassets sorted by the Amihud illiquidity ratio. The right panel shows the corresponding Sharpe ratios for these portfolios. The data consists of the top 408 cryptoassets sorted by market capitalisation. Prices and trading volume are sampled daily from July 2015 to January 2021.
The left panel shows the average returns for each sub-portfolio. Interestingly, the cryptoassets with the lowest illiquidity ratios (i.e. those that are more liquid) have higher average returns. However, there is no clear pattern once returns are adjusted for risk. In this respect, the right panel shows the Sharpe ratios for these portfolios. There is no clear evidence in favour of higher risk-adjusted returns for more liquid cryptoassets. At first sight, this seems counterintuitive as often is there should be a premium, namely higher returns, for less liquid assets in order to make investors willing to hold those assets.
One reason for this could be the fact that we are including smaller cryptoassets in our sample. Many of these, despite considered as part of our liquid bucket, may not actually be that liquid in a traditional sense. Other measures of liquidity may therefore be more suitable to capture true liquidity premiums. We leave that for future research.
Market Efficiency and Liquidity
We now look at things in more detail, by testing for market efficiency across individual cryptoasset pairs and focusing on predictability of returns. Following Urquhart (2016), we employ the same set of statistical tests for randomness. Firstly, return autocorrelation is examined using the Ljung-Box test (Ljung and Box, 1978). Secondly, the variance ratio represents our second measure of price efficiency. The literature shows that the variance of longer horizon returns should equal the variance of shorter horizon returns times the frequency of the short horizon returns, in the absence of autocorrelations (see Lo and MacKinlay 1988). This finding is a property of any random walk process, since variance increases linearly with time. In the market micro-structure literature, variance ratios have been used by Chordia et al. (2008).
We then sort cryptoassets into five quintiles as outlined above based on their Amihud illiquidity ratios and calculate the average p-values of either the Ljung-Box test, or the variance ratio test for each quintile. Figure 3 reports the results.
Source: Aaro Capital Research
Notes: The left panel shows the average p-value of the variance ratio for the cryptoassets sorted on the Amihud ratio. The right panel shows the results for the p-value of the Ljung-Box test for the cryptoassets sorted on the Amihud ratio. The data consists of the top 408 cryptoassets sorted by market capitalisation. Prices and trading volume are sampled daily from July 2015 to January 2021.
The left panel shows the average p-value of the variance ratio for the cryptoassets sorted on the Amihud ratio. The null hypothesis is that the returns are i.i.d., that is, markets are efficient. Two facts emerge. First, the null hypothesis that cryptoasset markets are efficient is rejected at conventional significance levels. Second, the rejection is not concentrated at a given level of liquidity and is rejected across the board, almost independently on the level of the Amihud ratio.
The right panel shows the results for the p-value of the Ljung-Box test for the cryptoassets sorted on the Amihud ratio. The null hypothesis is that there is no autocorrelation in the daily returns. Again, two facts emerge. First, although the evidence is rather weak, the results show there is some weak autocorrelation of the returns, averaged by levels of liquidity. Notice that, instead of testing randomness at each distinct lag, the Ljung-Box test checks the “overall” randomness based on several lags. In this respect, it may seem quite restrictive. The second result is that, again, there is only a limited impact of liquidity. The evidence against market efficiency is somewhat consistent across different levels of (il)liquidity, although as outlined before, the significance of the test statistic is rather small.
We test for the existence of a relationship between market efficiency and liquidity, as proxied by the Amihud illiquidity ratio (2002). The empirical evidence suggests three key findings:
- Price inefficiency is somewhat pervasive in cryptoasset markets.
- There is no apparent relationship between market efficiency and liquidity (i.e., market inefficiency is relatively pervasive in the cross section and does not depend on liquidity).
- There has been a substantial increase in market illiquidity (or price impact) over the last year, i.e., 2020.
The relationship between market efficiency and liquidity is worth further investigation, beyond the use of a single measure, such as the Amihud ratio.
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