• Extreme-Value-Theory
• GARCH
• DeFi
• EVT
• Copula
• Cryptocurrency

The aim of this thesis is to give the reader an introduction to the emerging ecosystem of
Decentralized Finance. Furthermore, the financial characteristics and properties of cryp-
tocurrencies used in DeFi are assessed by means of various quantitative methods.
The Extreme-Value-Theory, its theoretical background, peculiarities, and various methods
are outlined. Hereby the focus is put on the Block-Maxima and Peaks-Over-Threshold
method. The dependence of the EVT on iid data is elaborated and the GARCH-EVT
approach presented as a alternative to circumvent this prerequisite.
The reader is given an up-to-date risk assessment of the cryptocurrencies comprising
Aave´s treasury. The analysis is based on 683 daily returns of the nine positions. The re-
sults indicate contradiction properties of the returns of the stablecoins and non-stablecoins
in the portfolio. The stablecoins exhibit characteristics, appropriate to their value propo-
sition of reflecting a stable value close to one USD. All show a daily mean return close
to 0% and a low daily volatility around 0.3%. The remaining cryptocurrencies are char-
acterized by a positive mean daily return and a high daily volatility up to 9% around
the mean. Hence, the possibility of larger positive returns, come at the cost of increased
market risks.
The return distribution of the nine cryptocurrencies are heavy-tailed and outlier-prone.
All exhibit a kurtosis of larger than 3 and hence are not well described by normal distri-
bution. To further prove the high riskiness of the cryptocurrencies, the Value-at-Risk and
the corresponding Expected-Shortfall are computed. The findings indicate that investor of non-stablecoins are exposed to high possible losses, up to 22%. Stablecoins are charac-
terized by low market risks which are compensated by additional risks, related to credit or
third party risk, and should not be neglected, as can be seen in the collapse of the Terra
Luna ecosystem. Reasoned by the high riskiness, the Extreme-Value-Theory, based on the
GARCH-EVT approach for non-iid data is applied. Consistent with the prior analysis all
non-stablecoins are subject to extreme tail risks, with possible daily losses up to 56%. It
can be concluded that an investment in individual cryptocurrencies is not suitable to risk
averse investors and needs to be closely monitored in order to avoid adverse returns.
Furthermore, the joint density function of all portfolio positions are modeled by a t-
Student Copula. 10,000 densities are simulated via a Monte-Carlo Simulation, to assess
the market risks of a portfolio and to test for possible diversification effects. The findings
indicate that all non-stablecoin positions are highly correlated, whereby stablecoins are
almost independent of the movement of other cryptocurrencies. The analysis shows that,
by aggregating market risks a small diversification benefit can be achieved, that leads
to lower possible losses for most quantiles of the return distribution. Consistent with
prior research, investing in a cryptocurrency portfolio increases the probability of joint
extreme values on both sides of the distribution´s tail. This must be incorporated into
an investor’s risk management to avoid adverse events, such as margin calls due to the
failure to provide sufficient funds to cover against tail risks. Additionally, the results
have important implications for the optimal portfolio composition of a DeFi protocols´s
treasury. The determined property of non-stablecoins could harm the treasuries ability
to provide stability during times of stress. Stablecoins on the contrary can reduce the
contagion risks, but impose new types of risks. Investors in DeFi protocols must be aware
of the inherent risks of cryptocurrency treasuries and their ability to harm the value of
their investment. Well diversified treasuries should be valued accordingly.
This thesis has identified multiple topics for future research that could widen the un-
derstanding of the cryptocurrency market, especially regarding the sector of DeFi. First,
the optimal composition of a portfolio with stablecoins remains to be investigated. Their
hedging ability and an extended risk assessment comprising further risk categories could
be of great help. The desired properties of a DeFi protocol´s treasury and the best suited
portfolio positions, extend this research field. Furthermore, the identification of the best-suited Copula, to model the joint density function of a cryptocurrency portfolio should
be evaluated.