We are going to analyze several of the major cryptocurrencies as an asset class. And, we are going to address several related questions: Do they provide diversification benefits relative to the stock market (S&P 500)? How do their diversification benefits compare with Gold’s diversification benefit vs. the stock market? Do cryptocurrencies provide diversification benefits when you really need it… during market downturns? Are cryptocurrencies truly “digital Gold”? Do they behave in a similar way given that their supply is constrained (supposedly in a similar way as Gold is)?

1. Cryptocurrencies as an asset class
Gaetan Lion, April 14, 2022
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2. 2
Introduction
We are going to analyze several of the major cryptocurrencies as an asset class. And,
we are going to address several related questions:
• Do they provide diversification benefits relative to the stock market (S&P 500)?
• How do their diversification benefits compare with Gold’s diversification benefit vs.
the stock market?
• Do cryptocurrencies provide diversification benefits when you really need it… during
market downturns?
• Are cryptocurrencies truly “digital Gold”? Do they behave in a similar way given that
their supply is constrained (supposedly in a similar way as Gold is)?

3. 3
The Data
The data is very limited. Even though Bitcoin was innovated back in 2009, I could not find publicly available
data before 2014. And, many other cryptocurrencies have been innovated in just the past few years.
Nevertheless, considering the above data limitations, I could find much data at Yahoo Finance that sources
the data from CoinMarketCap. Additionally, Yahoo Finance facilitates historical data download.
Meanwhile, CoinMarketCap does not.
I conducted my analysis on two data sets:
a) Monthly data from September 2015 to March 2022;
b) Daily data from January 3d 2019 to April 8, 2022.
When analyzing diversification benefits, correlations, scaled growth, etc. we focus on periodic % change
(either monthly or daily % change). When looking at growth patterns, we often look at nominal level
variables.

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Looking at monthly data from
September 2015 to March 2022
Cryptocurrencies time series data is limited. I did not find any data earlier than 2014. And, by starting the
time series in September 2015, I was able to add additional cryptocurrencies to an otherwise limited data
set.

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• Gold has a near zero correlation with the S&P 500 (diversification benefit).
• The cryptocurrencies have low correlations with the S&P 500 (diversification benefit).
• The correlations between cryptocurrencies range from 0.25 to 0.70.
• The correlations between cryptocurrencies and Gold are very low. Cryptocurrencies behave completely
differently than Gold. They can’t be considered the equivalent of digital Gold.
• Cryptocurrencies do not correlate with anything. The latter can be interpreted as a diversification
benefit. However, this benefit should be tempered by the cryptocurrencies huge volatility.
Cryptocurrencies
have very low
correlations with
the S&P 500

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Three different growth patterns among the reviewed asset classes
Incremental Explosive till hit-the-wall Peaks and Valleys
Growth is paced over time. The
investment remains within the
same numeric scale for a long
time (in the 1,000s for the S&P
500 and also for Gold).
Growth is explosive at some point.
Over time, the investment value
crosses through numerous numeric
scales (0 – 10, 10 – 100, 100 – 1000,
etc.). But, at some point the
investment appears to hit a wall and
just goes up and down within the
same numeric scale.
Growth and contractions are both
explosive. The investment does
cross numerous numeric scales on
both the way up and down.
History generates a very volatile
peak and valley pattern.

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Incremental growth: S&P 500 and Gold
Both the S&P 500 and Gold show a paced incremental growth over time. As reviewed earlier, when
detrended these time series are not correlated. However, they may be somewhat cointegrated (over
time their respective trends have a mean-reverting component that aligns them with each other).

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Explosive till hit-the-wall: the majority of cryptocurrencies

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Peaks and Valleys:
Litecoin and XRP
Contrary to the majority of
cryptocurrencies, these two have several
sets of peaks and valleys. Thus, they do not
appear to have explicitly hit a wall. Their
respective patterns suggest they may be
more likely to rebound than other
cryptocurrencies.
Remember that these two cryptocurrencies
had the highest correlation at 0.70 (within
the correlation matrix shown earlier). And,
visually the time series graphs do show a
tight visual similarity between these two
time series.

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From the beginning to the end of the reviewed period (close to 7 years), the majority of the cryptocurrencies
have more than doubled in value every year. That pace is unsustainable. For these investments to keep on
doubling in value every year over the next 7 years, their value would have to increase by 128 times.
The above statistics reflect the cryptocurrencies incredibly fast historical growth and volatility. Cryptocurrencies
are at times referred to as the digital Gold because of their limited supply associated with supposed inflation-
protection quality. However, as reviewed the cryptocurrencies behave completely differently than Gold.

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A complete distribution of monthly % change showing again the volatile
and explosive monthly % change in cryptocurrencies
The cryptocurrencies’ explosive behavior relative to the S&P 500 and Gold is apparent when looking at the
Max, Min, and Range. Also, the cryptocurrencies 75th percentile monthly % changes are a lot higher than
the 95th percentiles for the S&P 500 and Gold. Similarly, the cryptocurrencies 25th percentiles reflect deeper
downturns than the S&P 500 and Gold 5th percentiles.

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Looking at daily data from
January 3d, 2019 to April 8, 2022
Because of the shorter time series, we were able to add Binance among the cryptocurrencies.

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• Overall this correlation matrix is consistent with the one based on monthly data over a longer time
series.
• Both Gold and cryptocurrencies have again low correlations with the S&P 500.
• Cryptocurrencies have low correlations with Gold.
• We note that the correlations between cryptocurrencies are now quite a bit higher than when
looking at the monthly data over a longer time period.

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The “explosive” growth-behavior of cryptocurrencies relative to the S&P 500 and Gold

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The “explosive” behavior of cryptocurrencies relative to the S&P 500 and Gold
As reviewed within this daily time series, it is not uncommon for cryptocurrencies to increase or decrease by + or
– 25% in a single day. The cryptocurrencies’ volatility is far greater than the one for Gold or the S&P 500.

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A complete distribution of daily % change showing again the volatile and
explosive daily % change in cryptocurrencies
The explosive behavior of the cryptocurrencies relative to the S&P 500 and Gold can be readily characterized by
looking at the Max, Min, and Range. Also, the cryptocurrencies 75th percentile daily % changes are all a lot higher
than the 95th percentiles for the S&P 500 and Gold. Similarly, the cryptocurrencies 25th percentiles reflect deeper
downturns than the S&P 500 and Gold 5th percentiles.

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Do cryptocurrencies provide you diversification protection when you need it?
Wow, as shown the cryptocurrencies’ losses were far greater than the stock market’s. In this
one instance (the only one available within the data), the cryptocurrencies provided no
diversification benefit whatsoever… to the contrary, they actually exacerbated the stock market
losses.
Granted this is a “sample of one” study associated with an uncertain large sample error.
However, this single data point has to give you pause. Does it make sense to attempt to
diversify your equities risk with an asset class that is 5 to 10 x riskier (as measured by standard
deviation), and appears to actually correlate with stock market downturns (even though in
general it is rather uncorrelated with the market)?

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Considerations: are Cryptocurrencies just a Zero-sum game over time?
The stock market generates cumulative gains over time.
As the economy and related corporate profits keep on
growing, the overall stock market pie keeps on growing.
Just investing in a stock index creates value over time.
Cryptocurrencies do not appear to generate reliable
cumulative gains. They have generated explosive gains
for early investors. Meanwhile, for the past couple of
years, unlike the stock market, cryptocurrencies have
stopped generating cumulative gains. Investing in a
diversified portfolio of cryptocurrencies, unlike a
diversified portfolio of stocks, may not create value over
time.

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The current cryptocurrency bubble burst
The maximum value for cryptocurrencies have occurred 2 to 9 months earlier than for the S&P 500. And, the
resulting contraction have been far more pronounced. The cryptocurrencies have lost between – 33% to – 79% of
their respective values vs. only – 6% for the S&P 500.
Going forward you may have serial periods of crashes of – 70% or worse, and booms of + 233% that bring back an
investment to break even (see calculations below) without creating incremental sustainable value over time.
1 x (1 – 70%) = 0.3
0.3 x (1 + 233%) = 1
At such a stage, the cryptocurrencies would be a zero-sum game where the early
speculators buying during one of the serial bottoms would extract gains from the
latecomers buying near the top of the bubble. And, this cycle is likely to repeat for
quite a while. Timing this bubble cycle may be challenging.

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Appendix Section:
Data Visualization of Volatility

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The Y-axis indicates that the cryptocurrencies volatility, as measured, is truly amazing.
7.5 means that the annualized standard deviation of % change is 750%! The main point is how much higher is the
volatility of cryptocurrencies relative to the S&P 500. Over the reviewed period, the S&P 500 has an average annual
standard deviation of 14% vs. 80% for Bitcoin, 149% for Ethereum, 307% for Ethereum and Dodge, and 116% for Litecoin.

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How can annualized standard deviations get > 700%?!
Here is one example among many, starting with the monthly values
of the XRP coin from December 2016 to December 2017. We derive
the monthly % change in the right hand column.
Next, we calculate the standard deviation of these monthly %
change. And, it is 251%.
Next, to convert this monthly standard deviation into an annualized
standard deviation, we multiply the 251% by the SQRT(12) and we
get 869%.
One may argue this extremely high annualized standard deviation is
in good part caused by the last observation in December 2017
associated with a monthly % change of 817%. Well, let’s redo this
exercise on the next slide by eliminating this one data point by
moving the data series from November 2016 to November 2017.

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Redoing this calculation by eliminating the extremely high monthly %
change in December 2017 still result in an extremely high annualized
standard deviation of 458%.
As shown on the earlier graph, both XRP and Dodge experienced
annualized standard deviations of > 458% for several months or close
to a year (XRP in 2018, and Dodge in 2021).

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When focusing on the Y-axis (the level dimension), we see how much more volatile are the XRP and Dodge
coins. But, even Bitcoin, that appears tame by comparison, is a lot more volatile than the S&P 500.

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When focusing on the time dimension,
the graph shows that XRP had a huge
spike in volatility in 2018. Meanwhile,
Dodge experienced a similar huge
spike in volatility, 3 years later, in 2021.

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This graph simply shows how much more volatile the cryptocurrencies are relative to the S&P 500.
As shown, XRP is at times 200 times more volatile than the S&P 500.

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Again, XRP stands out. But, even the “relatively” tame Bitcoin is at times 25 times more volatile than the S&P
500.

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When focusing on the time
dimension, we see a huge
spike in volatility relative to
the S&P 500 for all
cryptocurrencies near the
end of 2017.
And, Dodge had a pretty
good spike in such volatility
in 2021.

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The table above summarizes how much more volatile are the cryptocurrencies compared to the S&P 500.