Using Entropy to Forecast Bitcoin’s Daily Conditional Value at Risk

Abstract

Conditional value at risk (CVaR), or expected shortfall, is a risk measure for investments according to Rockafellar and Uryasev. Yamai and Yoshiba define CVaR as the conditional expectation of loss given that the loss is beyond the value at risk (VaR) level. The VaR is a risk measure that represents how much an investment might lose during usual market conditions with a given probability in a time interval. In particular, Rockafellar and Uryasev show that CVaR is superior to VaR in applications related to investment portfolio optimization. On the other hand, the Shannon entropy has been used as an uncertainty measure in investments and, in particular, to forecast the Bitcoin's daily VaR. In this paper, we estimate the entropy of intraday distribution of Bitcoin's logreturns through the symbolic time series analysis (STSA) and we forecast Bitcoin's daily CVaR using the estimated entropy. We find that the entropy is positively correlated to the likelihood of extreme values of Bitcoin's daily logreturns using a logistic regression model based on CVaR and the use of entropy to forecast the Bitcoin's daily CVaR of the next day performs better than the naive use of the historical CVaR.

Uncertainty and Risk in the Cryptocurrency Market

“…For example, Lahmiri et al (2018) applied Shannon's entropy to assess the fractality and randomness of the BTC estimated volatilities and found evidence of a high degree of randomness for the analyzed series. Symbolic time series analysis (STSA) was used by Pele and Mazurencu-Marinescu-Pele (2019) and Takada et al (2019) to compute Shannon's entropy of intraday Bitcoin returns as a measure of uncertainty and to predict VaR and CVaR.…”

“…They provided mixed evidence concerning the dynamics of the volatility of the examined returns. The simultaneous assessment of uncertainty and risk was also only focused on the BTC (Pele and Mazurencu-Marinescu-Pele 2019;Takada et al 2019). In what follows, we extend the joint analyses of the two concepts using a sample of seven cryptocurrencies with distinct characteristics to improve knowledge of this diverse market.…”