Crypto with Style!
Can we identify relevant Factors to explain crypto returns?
AlphabetIM Research, February 2023
1. Style Investing
Style or Factor investing is a concept that can be applied to a wide range of asset classes, including cryptocurrencies. Like with equity factor investing, the goal of cryptocurrency factor investing is to identify and invest in specific styles or factors that are thought to explain a significant portion of the returns of individual cryptocurrencies and portfolios beyond the asset class benchmark.
This field has massively grown on equity this last decade, even if it was already studied in the 1990s where a theory like the Fama-French three-factor model received a considerable attention [4]. This model has made an original contribution to the field of equity factor investing by providing a new framework for explaining the returns of individual stocks and portfolios. It is built upon the capital asset pricing model (CAPM) by adding two additional factors to explain the returns of individual stocks and portfolios. The CAPM model, developed by William Sharpe in the 1960s [8], suggests that the expected return of a stock is a function of its beta, which measures the stock’s systematic risk, and the risk-free rate. However, the CAPM model was criticized for its inability to explain the returns of individual stocks and portfolios, as well as its reliance on a single factor to explain the risk of a stock.
The Fama-French model addresses these criticisms by adding two additional factors to the CAPM model: size and value. The size factor measures the return of small-cap stocks relative to large-cap stocks, while the value factor measures the return of value stocks relative to growth stocks where value stocks are stocks with low price versus earnings ratio and growth stocks are stocks with high growth of revenues. Fama and French argue that these two factors are relevant for explaining the returns of individual stocks and portfolios, as they capture the differences in risk and return between these groups of stocks. In other words, it suggests that the expected return of a stock is a function of its beta, size, and value. The model also suggests that there is a positive relationship between the size and value factors and expected returns, meaning that small-cap and value stocks are expected to have higher returns than large-cap and growth stocks, respectively. This relationship is commonly referred to as the size and value premiums, and it has been widely observed in empirical studies.
One of the most significant impacts of the Fama-French model has been the growth of factor-based investing, which seeks to invest in specific factors, such as size and value, that have been shown to have a persistent impact on returns. Factor-based investing has become a popular investment strategy, as it allows investors to construct portfolios that are diversified across multiple factors, which can help to reduce risk and enhance returns.
After this original contribution, Cahart proposed to add a new decisive style based on a momentum[2] factor differentiating up-trending and down-trending stocks, which proved to be a robust factor studied intensively since then. Other factors like low-volatility and quality have also been added to the most commonly used styles to explain behaviors of stocks portfolio and have been extensively studies like in [1].
Regarding crypto currencies, literature is relatively new on factor investing but we begin to explore the same approach and Liu, Tsyvinski, and Wu, have suggested to use a three-factor model [6,7] to describe returns of crypto currencies. Beyond crypto market they proposed to use size and momentum to get a better fit to weekly crypto returns. Following this framework, Cong & al. tested a five factors model [3] with the add-on of network and value factors, which performs even better and point to the importance of alternative features like network adoption to address the value of a given crypto currency.
In this study, we will focus on top market cap coins and try to constitute some potential factors on a weekly basis to compare to above mentioned papers. We’ll investigate first if they bear individually some investing interest and then try to isolate the most relevant ones through PCA and features selection methods. Finally, we’ll suggest a three-factor model and compare it to other crypto factors theories.
2. Data and Factors definition
Our universe selection has been driven by proposing a realistic investing approach, that’s why we consider only biggest market capitalization where liquidity is above a given threshold and where we can collect reliable and meaningful network and flow data (note that survival bias can affect dramatically results in such an immature market where thousands of coins have disappeared in a short period of times). We end up with a perimeter of 62 coins* with a mix of sectors: L1/L2, DeFi, Web3, Gaming…
We retrieved prices and volumes from Binance api from the 1st November 2020 to 31st January 2023, which gives a non-overlapping sequence of 116 weeks. Regarding alternative features like flow and network, we use data provider IntoTheBlock analytics to constitute Flow, Sentiment, Network and Value factors.
We define 10 potential factors: Market, Momentum, LowVol, Size, Liquidity, Positioning, Flow, Sentiment, Network and Value as follow:
- Market: we take our universe and weight the coins by their market capitalizations.
- Momentum: we choose a mix of 7d-reurn, 30d-return, 7d-return/7d-volatility, 30d-return/30d-volatility, 7d-ewma return of residuals (residuals come from the regression of daily return against bitcoin with a 30d-beta).
- LowVol: a mix of 7d-realized volatility, 30d-realized volatility, and 30d-Beta. We want here to test if there is a premium associated to risk measured by volatility given that crypto assets are very volatile and exhibit big discrepancies among them. It’s an identified factor in equity world and we would like to see if it can be on similar interest here.
- Size: market capitalization. Like equity size factors, we will rank coins inversely to exhibit a small versus big premium. Note that we have already chosen a perimeter of big caps to deal only with tradable assets for decent amount of money. Size factor will be then less relevant in our study.
- Liquidity: a mix of 7d-volume/30d-volume and (7d-volume — 7d-volume of previous week)/30d-volume. The idea here is to examine a potential liquidity premium.
- Positioning: a mix of premium defined as (perpetual price-spot price)/spot price and premium speed = premium — premium of previous week. Here, we want to address if a biased supply/demand imbalance on the perpetual can explain a part of next return. As a reverting signal, we will rank coins inversely to this feature.
- Flow: we take both log of whales net flow addressing accumulation or reduction of on-chain holding by whales; and log of exchange net flow, which gives an indicator of on-chain flows in and out centralized exchanges. The idea is here to see if on-chain moves could constitute a tangible factor. For more details, please read specification at intotheblock.io.
- Sentiment: we use “technical” sentiment by looking at token GitHuB. We use a mix of first difference of log of GitHub commits and first difference of log of GitHub stars. We test here if developer community strength and activity contribute to return determination. Note that we explored social media sentiment but at this stage of our research, signals are too noisy and clearly do not fit a weekly sampling.
- Network: as suggested by Cong & al in [3] we will use first difference of log values of total addresses with balance and the first difference of log values of total transaction volume on chain in USD. Note that unlike their paper, we do not retain neither total addresses without any balances nor volume in coins as they appear redundant and less relevant than the chosen ones. We want to estimate here if growth and activity of the network can be a robust factor.
- Value: we specify a Value factor like [3] where we compare the coin price with its network size through a user-to-market ratio (where user is approximated by the total addresses with balance) and its network activity via a transaction-to-market ratio (where the transaction is the aggregate volume of transactions recorded on-chain). We try here to define an equivalent to the well-known value factor on the equity side by building some factors on intrinsic value of protocols.
We then windsorize all the features by remoing 2-%iles extreme values and normalize the remaining features cross-coins at each sampling time.
For each of these factors, we look at the forward weekly performance of our coins when we are in every quintile of the distribution of the factors. A good factor will increase monotonously the performance from bottom to top quintile and will especially discriminate bottom quintile and top quintile. We give below the weekly performance mean for each quintile and the t-stat associated:
We note that Momentum, Size, Liquidity, Value, Flow and Network are almost monotonous with a mean continuously increasing along the quintiles. Another interesting result stands in the good segregation of bad and good performances between low and high quintiles for Momentum, Value, Flow and Network, where t-stats are meaningful. Conversely Sentiment and Positioning seem to struggle in the low quintiles with probably some reversal effect.
Now we can form the High-Low portfolio for every feature and this portfolio will then be called factor. We are exhibiting below the mean and its t-stat for all our factors:
We can note that Momentum, Network, Flow, Value and Network display a positive mean with relatively good t-stat. Positioning is clearly an outlier and do not bring any positive performance as illustrated on the graph below where can observe cumulative performances of the different factors:
We also represent on chart 3, risk premium opportunities that can represent these factors with a bubble scatterplot on (volatility, return) axis with the size of the bubble proportional to the Sharpe Ratio of a given factor risk premium. All these results do not take into account any rebalancing fees, which are always critical in the crypto space and usually represent an important proportion of the performance.
Consistently with Table 2, Momentum and Value Risk Premiums lead the board with Flow and Network just below in term of Sharpe ratios. LowVol, Size and Liquidity are quite similar, and Sentiment is differentiating itself by a much higher volatility. We can interpret it by the more versatile nature of community sentiment which drives this factor.
3. PCA and Factors selection
As seen in section2. Some factors seem less relevant in explaining cross-sectional coin returns. We try now to remove those factors from further studies to focus on more promising styles.
To achieve this, we conduct a PCA on weekly return on our universe to see if some factors correlate with eigenvectors. We retain the first 5 components as they account for more than 85% of portfolio variance:
Unsurprisingly, first component is very correlated with the market and reach a correlation of +87% as illustrated on Chart 4. Second component is clearly dominated by Value factor with a correlation of +37%. Third component is not that transparent and do not bring a straightforward explanation, but the fourth component has an important correlation with Liquidity factor with a correlation of +29% and the fifth component has its higher correlation of +16% with the Flow factor. We find out again Value and Flow as relevant factors compared to section 2. We may have expected to see Momentum factor playing a bigger role, but we can assume that it has suffered some eviction effect against Liquidity factor as both factors are the more correlated among all the factors set (we will investigate this behavior in further research). Another potential explanation relies on the change in dynamics this last couple of year where crypto markets appear less driven by momentum than it was up to 2021.
It can also be interesting to run some automatic features selection method to isolate most contributive factors. We test first a mutual information estimation for our factors and measure dependency between factors. We use scikit-learn mutual_info_regression to estimate entropy from k-nearest neighbors’ distances and filter the factor:
# Instantiate the SelectKBest model
selector = SelectKBest(mutual_info_regression, k=5)
# Fit and transform the data using SelectKBest
X_new = selector.fit_transform(X, y)
df_select=pd.DataFrame(X_new)
slectColumns = pd.DataFrame()
for i in range(X.shape[1]):
col = X.iloc[:,i]
for j in range(df_select.shape[1]):
selectCol = df_select.iloc[:, j]
if list(col.values)==list(selectCol.values):
slectColumns=slectColumns.append(col)
slectColumns.transpose() bench_mktCap FLOW_style MOM_style NET_style LIQ_style
0 0.077713 0.000000 -0.015501 0.000000 0.028072
1 0.202123 0.000000 -0.014612 0.000000 0.186210
2 -0.018212 0.000000 0.089466 0.000000 -0.230900
3 0.072943 0.000000 -0.009947 0.000000 0.062531
4 -0.033112 0.000000 -0.067193 0.000000 -0.034698
... ... ... ... ... ...It returns the chosen factors where we retrieve the market, Flow factor, Momentum factor, Network factor and Liquidity factor. We only miss Value factor in this selection.
Another selection relies on embedded method through Lasso penalized regression. From the different types of regularization, Lasso or L1 has the property to shrink some of the coefficients to zero and then removed less useful factors to our selection.
# Embedded Factors selection with L1 regression
selection = SelectFromModel(Lasso(alpha=0.001))
selection.fit(X, y)
selected_feat = X.columns[(selection.get_support())]
print('Total factors: {}'.format((X.shape[1])))
print('Selected factors: {}'.format(len(selected_feat)))
print('Factors with coefficients shrank to zero: {}'.format(
np.sum(selection.estimator_.coef_ == 0)))Total factors: 10
Selected factors: 3
Factors with coefficients shrank to zero: 7# Retrieving selected Fcators
list(selected_feat)
['bench_mktCap', 'LIQ_style', 'VALUE_style']We end up with only 3 factors (out of possible 10) with non-null coefficients in our L1 regression: Market benchmark, Value factor and Liquidity factor.
To sum-up, we find that beyond Market factor which is obviously the main driver of coins portfolio, Value and Liquidity factors are both selected factors in our embedded features selection and they also appear clearly in the PCA we run on the whole portfolio. We can also consider Flow, which appears in the PCA and the mutual information selection method and to a lower extent to Network and Momentum factors that are selected by the mutual information method and exhibit good performances in section 1.
4. Multi-Factors Model
Now that we have identified interesting factors, let’s look at regression models to explain portfolio cross-coins returns.
We begin with what we can call the crypto-CAPM where we use only the Market as the only possible factor to explain returns:
Along our omnibus sample of more than two years, this model achieved a R-squared of 0.356 with a significative Beta(Market) of 1.12 and a t-stat of 63. This is improved when using a multi-factors model where we put all together the 10 potential factors:
We note an increase in R-squared, now at 0.365 with some significative Betas on Market obviously but also on Liquidity factor and Value factors particularly (t-stats of respectively -7.8 and 5.5). We can observe an adjusted R-squared below the regular R-squared indicating that some factors are useless and deteriorate the model. Likewise, we test all possible models by combining different numbers of factors, and we then rank them according to their adjusted R-squared. The best model is a 3-factors model using Value factor and Liquidity factor:
We note that adjusted R-squared reaches 0.367 equals to regular R-squared. This represents a minor improvement compared to crypto-CAPM but confirms conclusion of section 2, by identifying Value and Liquidity as the two main crypto factors on our universe. Compared to [7] we do not identify Size and Momentum as the most valuable factors. Our 3-Factor model using Momentum and Size only got an adjusted R-squared of 0.357. A 5-Factors models, adding Value and Network as suggested by [3] do not perform much better with a metric of 0.359 even if we share the conclusion on the interest of Value factor. As discussed earlier, Size factor is not relevant for our universe limited to the biggest coins but the absence of Momentum in our best models and earlier features selection is probably due to the recent dynamics of market with less volatile market and not established deep trend. Conversely, Liquidity factor seems a good fit to the current nature of crypto market with important periods of calm and abrupt volatility driven by volume peaks that feed short term trends. An interesting study would bet to combine volume and momentum through OBV (On Balance Volume) to see if it brings more explanatory power.
We also look at the granularity of our model among coins. When we test our 3-Factor model through top coins we get the following adjusted R-squared:
If we have a relative strong model for historical coins, we can see heterogeneity in the results with DOGE as a clear outlier with a R-squared of just 0.16. It is not surprising that a model driven by Value is not that robust for a meme coin like DOGE more reactive to tweets. Indeed, Sentiment, Flow and Momentum are the three biggest Betas for this behavioral biased asset. Another interesting example is UNI (not displayed here) with a quite good 3-Factors model R-squared of 0.5 but with a clearly missing Network factor which exhibits the strongest Beta. A characteristic we can observe on many DeFi native tokens as we can expect. For Gaming/Metaverse coins like SAND, we have weaker results for the 3-Factors models (0.383 in this case) but there is notable surge in the Sentiment factor Beta, suggesting that returns of these coins are more impacted by social media and community behaviors. All these results suggest that a further study should be done on a broader universe with a segregation by sector to identify which relevant factors drive a given thematic.
Final Thoughts
We have built in this study some factors that can be relevant to explain major crypto currency returns over the past couple of years. Obviously, cryptocurrency market is still relatively young and less established compared to traditional markets, and as such, the factors and their explanatory power may change over time. Yet, we have observed that some of them can constitute good risk premium investing strategies and we will dig into specific research on risk premium and smart beta investing using these factors. We then tried some methods to select best factors to construct a robust factor model that brings added value to a simple cryto-CAPM and find out that a 3-Factor model completing Maket with Value and Liquidity is the best fit on our universe. Another interesting result relies on differentiation of coin factors dependencies, which seems to be linked to the fundamental nature of a given token and invite to broader sectorized study of our model.
As usual, we would be happy to hear your thoughts.
Questions and comments can be addressed to: contact@alphabetim.io
*62 coins: BTC, ETH, BNB, XRP, SOL, ADA, DOT, DOGE, AVAX, TRX, MATIC, LTC, NEAR, UNI, BCH, XMR, LINK, XLM, ATOM, ETC, ALGO, HBAR, VET, EGLD, MANA, XTZ, FIL, SAND, ZEC, AAVE, EOS, MKR, THETA, GRT, RUNE, NEO, CHZ, KSM, DASH, ENJ, WAVES, BAT, CRV, ONE, KAVA, COMP, XEM, QTUM, 1INCH, OMG, ZRX, YFI, SNX, ONT, STORJ, SUSHI, REN, DENT, BAKE, REEF, BAND, TOMO
References
[1] Asness, C. S., Moskowitz, T. J., & Pedersen, L. H. Value and momentum everywhere (2013). The Journal of Finance, 68(3), 929–985.
[2] Carhart, M. M. On persistence in mutual fund performance (1997). The Journal of Finance, 52(1), 57–82.
[3] Cong & al. Value Premium, Network Adoption,and Factor Pricing of Crypto Assets (2022). European Financial Management Association (EFMA) conference.
[4] Fama, E.F. and French, K.R. Common risk factors in the returns on stocks and bonds (1993). Journal of Financial Economics, 33(1), pp.3–56.
[5] Fama, E.F. and French, K.R. Size, value, and momentum in international stock returns (2012). Journal of Financial Economics, 105(3), pp.457–472.
[6] Liu, Y. and Tsyvinski, A. Risks and returns of cryptocurrency (2021). The Review of Financial Studies, 34(6), pp.2689–2727.
[7] Liu, Y., Tsyvinski, A. and Wu, X. Common risk factors in cryptocurrency (2022). The Journal of Finance, 77(2).
[8] Sharpe William F. Capital asset prices: a theory of market equilibrum under condition of risk (1964). The Journal of Finance.
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