Executive Summary

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The Risk Protocol is a specialized investment platform that focuses on addressing some of the risks inherent in investing in cryptocurrencies. As we all know, there are many different types of investment risk including liquidity, volatility, interest rate, counterparty, operational, regulatory risk etc. Initially, at launch, our products shall be focused on the one risk that is most problematic for crypto – volatility. In this paper, we examine several aspects of volatility for the 50 largest cryptocurrencies. For instance, we study the standard deviation and variance of returns, the autocorrelation of absolute and squared returns, the beta of returns vis-à-vis Bitcoin, the leverage effect of cryptocurrency returns versus the standard deviation of returns and how calendar effects impact the magnitude of cryptocurrency price returns. As far as we know, this is the most exhaustive study done to date on cryptocurrency returns and volatility. 

Using data and insights gleaned from this exercise, we have developed highly sophisticated statistical volatility models that have been empirically proven to provide more accurate forecasts of crypto volatility than either implied or realized volatility. Part II of this report, to be published in the near future, will focus on the design and development of these models and their initial results. 

A primary motivation for undertaking this research is to be able to reliably forecast volatility. That is one of the critical inputs impacting pricing of certain very unique and sophisticated tokenized risk-solutions created by The Risk Protocol. Before one can forecast, one must first understand the properties and the attributes of the underlying returns distribution. However, we were surprised at how little is understood of crypto volatility. Industry participants are blindly applying known properties of equity market volatility to crypto. Not only that, popular lore has ascribed specific properties to crypto but precious little research has been done to date to either prove or disprove them. It is our hope that this research serves to better inform investors and advisors about this nascent sector and provides a solid foundation for further research initiatives. 

Our study shows that most stylized facts associated with other financial returns are also exhibited in cryptocurrency returns. However, crypto’s behavior is distinctly different in certain cases as illustrated in the summary findings below:

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1. Inconsistent Leverage Effect: Equity markets exhibit a widely observed “leverage” effect, the phenomenon that an asset’s volatility is negatively correlated to its returns. Typically, rising asset prices are accompanied by declining volatility, and vice versa. We did not observe such a consistent effect in our analysis of cryptocurrencies. We generally found that 1/3rd of our universe exhibited a leverage effect, 1/3rd exhibited an "antileverage" effect and 1/3rd was inconclusive. This has potentially significant implications. It means that one can’t necessarily hedge long underlying crypto exposure by being long volatility. If the underlying crypto happens to be one that exhibits an anti-leverage effect, such a strategy would essentially double one’s downside exposure instead of hedging it.
2. ‍Strong Persistent Calendar Effect: We also found that cryptocurrencies exhibit significant calendar effects. Specifically, there are distinct and persistent “hour of the day” and “day of the week” patterns in cryptocurrency volatility. We found that intraday volatility was persistently and significantly higher during hour 2 and hours 15 – 18 (UTC) each day. A similar analysis looking at daily returns across the week revealed that Saturdays and Sundays exhibited significantly lower volatility and volume relative to weekdays. The lower volumes on weekends makes intuitive sense. However, one would ordinarily expect the lower volumes on weekends to lead to higher volatility -- our analysis indicates otherwise. We also found that US and Chinese holidays exhibited volatility patterns similar to weekends. These findings naturally have implications for crafting effective trading/investment strategies centered around optimal inter and intraday periods for buying/selling volatility and entering or exiting trading positions.‍
3. The Curious Case of LEO: In looking at correlations among the top 50 cryptocurrencies, LEO (Unus Sed Leo) stands out as a confoundingly unique case. The average correlation among all the 50 currencies is 0.524 while Bitcoin and Ethereum have the highest correlation at 0.872. LEO has the lowest correlation with other cryptocurrencies across our universe. The average correlation between LEO and the 49 other cryptocurrencies is only 0.013, the maximum correlation is 0.03 and the minimum correlation is -0.014. So LEO is basically not correlated to any of the other cryptocurrencies in our universe. LEO, by way of quick background, is a utility token of centralized exchange Bitfinex and was issued through an IEO in 2019. Bitfinex is owned by iFinex, which is also the parent company of Tether. There have been reports in the past of inappropriate transfers between affiliated companies Bitfinex and Tether to cover losses at Bitfinex . Tether of course has been the subject of consistent speculation regarding the adequacy and liquidity of its stablecoin reserves. Is it mere coincidence that LEO has the unique trading pattern it does? This issue bears further examination given the controversial past of both Bitfinex and Tether.
4. ‍Volatility is Predictable: Our analysis reveals that while cryptocurrency returns themselves are not predictable using their own past, their magnitude, hence their volatility, is strongly predictable. Overall, the study shows that cryptocurrency volatility is similar to volatility patterns exhibited by other financial asset returns. However, they behave more like equities than currencies. The volatility has a long memory structure as shown by Ding, Granger and Engle in their 1993 paper for S&P 500 returns. 
5. ‍Returns have Leptokurtic Distribution: Unsurprisingly, cryptocurrency returns have a non-normal distribution and are fat-tailed with greater likelihood of extreme events occurring. As with most other financial asset returns, they exhibit the so-called leptokurtic property with fat tails. Out of the 50 cryptocurrencies analyzed, 40% have a negative skewness number. The standard deviations over the sample period are also very different for different cryptocurrencies. LEO has the lowest annualized standard deviation at 76% while MANA (Decentraland) has the highest at 338%. As a reference point, the annualized standard deviation over the past two decades is 20% for the S&P 500 and 25% for Nasdaq.
6. ‍Magnified Gain/Loss Asymmetry: Cryptocurrencies exhibit gain/loss asymmetry, which refers to the observation that it usually takes less time for a financial instrument to drop a certain amount than it takes to move up by the same amount. This attribute of crypto is similar to broader equity markets and in contrast to FX exchange rates which exhibit greater symmetry in up/down moves.  
7. ‍Increasingly Correlated with Broader Equity Markets: In comparing returns against other asset classes, it is observed that prior to 2019, there was no significant correlation between BTC returns and broader stock market returns. However, for the past three years from 2020 to 2022, the return correlation has become very significantly positive, especially between BTC and Nasdaq.
8. ‍Evidence of Negative Correlation to USD: While there is little correlation between BTC and the Dollar Index for daily frequencies, the correlation gradually becomes significantly negative as one goes from daily to monthly data, and from monthly to annual. The annual return correlation between BTC and the Dollar Index reached a very significant -0.75 level. This lends credence to the popular narrative that over a longer horizon, if the US dollar weakens, one would expect BTC returns to be stronger with negative correlation to the dollar.
9. ‍One-way Volatility Spillover: Finally, we found significant volatility spillover from the broader US stock market to crypto, especially in recent years. This is more pronounced for some of the more mature cryptocurrencies. Our hypothesis is that the spillover currently is unidirectional i.e. while volatility in traditional financial markets has an impact on crypto markets, volatility in crypto is self-contained and does not flow into traditional finance (“TradFi”). However, we could not statistically establish that there was no spillover from crypto to broader markets.

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These findings have profound implications for risk managers, portfolio allocators, investors and traders as far as investing in cryptocurrencies is concerned. 

For instance, the study suggests that constructing “diversified portfolios” of various crypto assets is harder to accomplish given the higher average correlations between crypto assets and their universally high correlation with Bitcoin. There is always the possibility that there are other tokens like LEO or CVX with little or no correlation with the broader universe of cryptocurrencies, but a broader analysis needs to be conducted to prove/disprove that hypothesis. Risk managers shall be similarly challenged to construct hedges by being long volatility. In TradFi, higher volatility is synonymous with market declines. However, this phenomenon, called leverage effect, is inconsistent within the crypto universe. It is applicable for some cryptocurrencies, the opposite is true for others and for the remainder, there is no statistically significant relationship. We also found that the volatility of crypto volatility is significantly higher than the “vol of vol” of other asset classes. That makes it more difficult to forecast, compounding the woes of risk managers. 

From a trader’s perspective, taking into account the calendar effects of crypto volatility would be a key data point in timing of trades. Our study reveals that there are specific times during the day and certain days in the week when volatility is markedly lower. A trader trying to build a large position would want to do it in a period of low volatility. Similarly a trader selling options would want to do so when volatility is observed to be higher and buy options in periods of low volatility. 

Finally, from an allocator’s perspective, the increasing correlation between cryptocurrencies and the broader equity markets presents a sticky problem. How much should they allocate to a category that adds volatility to the portfolio without getting much in the way of diversification benefits? 

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