Abstract : Ether is 40 times riskier than EURUSD, Bitcoin 9 times !


Given the exponential development of cryptocurrencies such as Bitcoin or Ethereum, and the absence of articles on market risk aspects, we propose to fill this gap modestly by publishing this article to get an idea of ​​the risk incurred by an investor willing to build a portfolio of digital currencies.

The most well-known risk indicator for managers and traders is Value at Risk (VaR).

VaR is an estimate of the losses an investor (invested on an asset or portfolio of financial assets) can suffer and that can only be exceeded with a given probability over a given time horizon.

To calculate this, we must model the distribution of portfolio profits and losses, which are most of the time assumed to follow a normal distribution. We believe that this assumption commonly accepted for conventional financial assets has limitations when it comes to applying it to a portfolio of digital currencies because of their high volatility.

Suppose, for example, that the distribution of profits and losses associated with holding an asset over a period corresponds to a standard normal distribution.
The Value at Risk (VaR) at the 95% confidence level at 1 day rated VAR (95%, 1 day), equal to 1 million euros means that there is a 95% chance that the loss associated with holding the asset Does not exceed EUR 1 million.
Assuming Gaussian law, graphically, the VAR on a day with a probability of 95% can be represented by the graph below:

VaR can be considered as a quantile of the profit and loss distribution associated with the holding of an asset or portfolio of assets over a given period.

If we consider a 95% coverage rate, the one-day VaR corresponds to the 95% level of the distribution of profit and loss over the period of holding the asset.


Virtual currencies are often criticized for their high volatility, as an example on Bitcoin and Ether, their prices have been multiplied by 2.3 and 25.1 since the beginning of the year, but since the highest levels (from 3000 $ And $ 407 on June 11 and June 13, 2017 respectively) they lost more than 23% and 50% of their value in 30 days.


BTC graphe

ETH graphe

In the normal yield assumption, the VaR (99%; 1j) followed by the traders is equal to

VaR(99%,1j) = Nominal()*2.33*stddev()/Sqrt(time)

Which gives for a $ 100 portfolio of Bitcoin with an annualized volatility of 82.8% and knowing that the Bitcoin ribs every day:

  • VaR(99%,1day)=100*2.33*82.8%/sqrt(365) = 10,1 $
  • VaR(99%,10days)=10.1*sqrt(10) = 31.9 $

These Value at Risk are important when compared to risk indicators on other underlying assets such as gold or the EurDollar exchange but they only reflect a high risk linked to the high volatility of digital currencies such as Bitcoin and the Ether.


Risk comparison

Based on a 3-year history on GOLDUSD, EURUSD, and calculating annualized volatility for each instrument, we deduce the following 99% 10j VaRs (always assuming Gaussian law of returns) :

VaR(10j;99%) EURUSD               3.6  
VaR(10j;99%) GOLDUSD                 6,4  
VaR(10j;99%) BTCUSD              31,9  
VaR(10j;99%) ETHUSD            144,0  


As expected Ethereum is the most risky of the instruments studied, the VaR reaches very quickly 99 $, in other words on a horizon of 10j there is 5.45% probability of losing more than 99% of the sum invested.

For a 1-year investment, an investor has:

  • 11,6% chance to lose more than 99% of its capital invested in Bitcoin
  • 39,6% chance to lose more than 99% of its invested capital in Ether

The prices of cryptocurrencies are inherently very volatile, their associated yields have the defect of the tails of distribution (tail risk). Then to take this risk into account, the VaRs are even higher!