Month of the year effect in the cryptocurrency market and portfolio management

Purpose – to investigate the Month of the year effect in the cryptocurrency market. Design/Method/Research Approach. A number of parametric and non-parametric technics are used, including average analysis, Student's t-test, ANOVA, Kruskal-Wallis statistic test, and regression analysis with the use of dummy variables. Findings. In general (case of overall testing – when all data is analyzed at once) calendar the Month of the Year Effect is not present in the cryptocurrency market. But results of separate testing (data from the period “suspicious for being anomaly” with all the rest of the data, except the values which belong to the “anomaly data set”) shows that July and August returns are much lower than returns on other months. These are the worst months to buy Bitcoins. Theoretical implications. Results of this paper claim to find some holes in the efficiency of the cryptocurrency market, which can be exploited. This contradicts the Efficient Market Hypothesis. Practical implications. Results of this paper claim to find some holes in the efficiency of the cryptocurrency market, which can be exploited. This provides opportunities for effective portfolio management in the cryptocurrency market. Originality/Value. This paper is the first to explore Month of the Year Effect in the cryptocurrency market.


Introduction
alendar anomalies (the Day of the Week Effect, the Turn of the Month Effect, the Month of the Year Effect, the January Effect, the Holiday Effect, the Halloween Effect etc.) is something that shouldn't exist according to the Efficient Market Hypothesis (EMH, see Fama, 1965). However there are many evidences that they exist in real life (Fields, 1931;Cross, 1973;Jensen, 1978;French, 1980;Bildik, 2004;Mynhardt & Plastun, 2013;many others).
However to date no study has analysed such issues in the context of the cryptocurrency market.
Cryptocurrency market is rather new and might still be relatively inefficient and it might be a good basis for the Month of the Year Effect existence.
We focus in particular on the Month of the Year Effect, and apply a variety of statistical methods (average analysis, Student's t-test, ANOVA, the Kruskal-Wallis, and regression analysis with dummy variables) to examine whether or not it exists in the cryptocurrency market. The object of analysis is Bitcoin monthly returns over the period 2013-2019.
The paper is structured as follows: Section 2 briefly reviews the literature on the Month of the Year Effect; Section 3 outlines the methodology; Section 4 presents the empirical results; Section 5 offers some concluding remarks. For example, there are evidences that January show higher returns than any other month of the year (Rozeff and Kinney, 1976;Wachtel, 1942).

Theoretical background
One of the calendar anomalies based from the "month of the Year Effect" family is so called Mark Twain effect. It claims that stock returns in October are lower than in other months. Bildik (2004) use Turkish stock market as an object of analysis and also find that calendar anomalies existed in stock returns and trading volume. Giovanis (2008) using GARCH estimation tested the month of the year effect using data from Athens Stock Exchange Market. They found evidences in favor of the January effect.  But at the same time returns during summer months (May-September) tend to be significantly higher than returns during other months of the year (October-April). (2006) based on Singapore stock market data over the period 1993-2005 reveals that the Month of the Year Effect has largely disappeared.

Wong et al
Silva (2010) explored Portuguese stock market during 1998-2008 and also find no evidences in favor or the January anomaly.
As can be seen the evidences are mixed. Possible explanation is market evolution -anomalies are fading in time .
The cryptocurrency market represents a particularly interesting case being rather new, relatively unexplored and at the same time extremely vulnerable to anomalies, given its high volatility relative to the FOREX, stock and commodity markets etc. (Cheung et al., 2015;Urquhart, 2016;Aalborg et al., 2019).
Only few market anomalies are already discussed for the case of the cryptocurrency market. For example Caporale and Plastun (2019) explore overreactions in the cryptocurrency market and find evidence of price patterns after overreactions. Chevapatrakul and Mascia (2019) using the quantile autoregressive model show that days with extremely negative returns are likely to be followed by periods characterised by negative returns and weekly positive returns as Bitcoin prices continue to rise.
As for the calendar effects, Kurihara and Fukushima (2017) and Caporale and Plastun (2018) explored the day of the week effect in the cryptocurrency market and find evidences in its favor. But the Month of the Year Effect is still unexplored.

Problem statement
he purpose of this paper is to investigate the Month of the year effect in the cryptocurrency market. CoinMarketCap provides volume-weighted average prices reported for each crypto exchange (for example, BitCoin prices are the average of those from 400 markets). As the result this is the most reliable source of information about prices in the cryptocurrency market.

Methods and Data
We use Bitcoin data because this cryptocurrency has the highest market capitalisation and longest span of data (see Table 1). Returns are computed as follows: where -returns on the і-th day in %; Close -close price on the і-th day; Close -close price on the (і-1)-th day.
Average analysis provides preliminary evidence on whether there are differences between returns on different months of the year.
A number of statistical tests, both parametric (in the case of normally distributed data) and non-parametric (in the case of nonnormal distributions); they include Student's t-tests, ANOVA analysis, and Kruskal-Wallis tests are carried out for further evidences in favor or against differences between returns on different months of the year.
We test Null Hypothesis (H0): analyzed data sets (returns of specific month) belong to the same general population (the whole data set). In case of H0 rejection we get evidence in favor of anomaly. In other case (H0 can not be rejected) no anomaly is observed.
We use Student's t-tests, ANOVA and Kruskal -Wallis test in two variants: -overall testing -when all data is analyzed at once; -separate testing -we compare data from the period "suspicious for being anomaly" (month of interest) with all the rest of the data, except the values which belong to the "anomaly data set" (month of interest returns).
We also run multiple regressions including a dummy variable to identify certain calendar anomaly: where -return on the period t; -mean return for each month; -dummy variable for each month, equal to 0 or 1. is 1 when mean return occurs on n-th month otherwise it is 0. -random error term for month t.
The size, sign and statistical significance of the dummy coefficients provide information about possible anomalies.

Empirical results
isual analysis (Fig. 1) gives clear signals in favor of this anomaly. Returns on March and October are 3-4 times higher than on other months. July, August and September look like the worth months for Bitcoin buyers. A "W" pattern is observed in Bitcoin monthly returns with peaks in March and October. As for the January effect and Mark Twain effect, there are no evidences of them in the Bitcoin returns.
Statistical tests show mixed results. According to t-test ( Table 2) returns for some of the months statistically differ from the all other data. This evidences in favor of the anomaly and confirms the Month of the Year Effect.
ANOVA analysis (Table 3) overall does not confirm the anomaly. Overall data set analysis shows no statistically significant differences between different months and the whole data set. Nevertheless for the case of separate testing returns of August happened to be statistically different from the all other data excluding returns on August. So anomaly is only partially confirmed.
Non-parametric Kruskal-Wallis test (Table 4) for the case of overall data set does not confirm the anomaly. But separate testing results show the presence of statistically significant differences in returns on February, July and August which can be treated as evidence in favor of the Month of the Year Effect.
Regression analysis with dummy variables of the Month of the Year Effect finds no evidences in favor of this anomaly ( Table 5). All the slopes are statistically insignificant (p-values are much higher than 0,05) as well as overall model (F is very low).
To summarize empirical results we form the following table (See Table 6).