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Measure before cutting: Using CVaR and VaR for cryptocurrencies $BTC.X $ETH.X

October 10, 2018 Comments off

There are many ways to estimate the level of risk one may encounter during trading and investing events.

This short article describes two risk measures that can be easily calculated using historical data and a statistical software (R, Excel):

  1. VaR (Value-at-Risk): The lowest amount of the capital (%) one can lose with a certain level of confidence, in a single event during the period.
  2. CVaR (Conditional Value-at-Risk or Expected Shortfall): The average (%) of all losses greater or equal than VaR for the same confidence level.

CVarR is greater than VaR and is considered more relevant than VaR.

Below, we calculate and discuss these values for three distinct periods in the life of BTCUSD and ETHUSD.

Case #1: September 8 – October 10, 2018 (A very quiet period for cryptocurrencies)

Number of days: 32

VaR95% (BTHUSD) = -1.936% means that every 1.6 days i.e. (1-0.95)*32 days we can lose at least 1.936% of the capital.

CVaR95% (BTHUSD) = -3.005% means that on the day we lose at least 1.936% of the capital, we can expect to lose 3.005% of the capital.

Since CVaR is more relevant than VaR, we calibrate the risk (for a 95% confidence level) for at least 3.005% capital loss on one single event during this period. The same logic applies to each value in the table below, with focus on CVaR.

Case #2: January 1 – October 10, 2018 (Since the start of 2018)

Number of days: 282

VaR99% (ETHUSD) = -14.933% means that every 2.8 days i.e. (1-0.99)*282 days we can lose at least 14.933% of the capital.

CVaR99% (ETHUSD) = -17.26% means that on the day we lose at least 14.933% of the capital, we can expect to lose 17.26% of the capital.

Since CVaR is more relevant than VaR, we calibrate the risk (for a 99% confidence level) for at least 17.26% capital loss on one single event during this period. The same logic applies to each value in the table below, with focus on CVaR.

Case #3: July 10 – December 16, 2017 (A very bullish period)

Number of days: 159

VaR99% (BTCUSD) = -9.651% means that every 1.6 days i.e. (1-0.99)*159 days we can lose at least 9.651% of the capital.

CVaR99% (BTCUSD) = -13.534% means that on the day we lose at least 9.651% of the capital, we can expect to lose 13.534% of the capital.

Since CVaR is more relevant than VaR, we calibrate the risk (for a 99% confidence level) for at least 17.26% capital loss on one single event during this period. The same logic applies to each value in the table below, with focus on CVaR.

To remember

  • Based on historical data, we can calculate expected levels of losses for confidence intervals of our choice (95%, 99%). Value-at-Risk (VaR) and CVaR (Conditional Value-at-Risk or Expected Shortfall) are two measures that can help calibrate the risk.
  • CVaR is higher than VaR for the same confidence level, therefore more representative and its use is recommended.
  • ETHUSD is prone to higher losses than BTCUSD.
  • During trends (Cases #2 and #3), traders may incur higher losses than during quiet periods (Case #1)
  • Focus on losses instead of gains.
  • Same logic can be used for currencies, equities, other cryptocurrencies, other financial instruments.
  • Calculated VaR and CVaR values are not a warranty against future losses. Far more serious losses may occur due to unexpected events.

(Results were generated from GDAX exchange data using the PerformanceAnalytics R package)

 

 

 

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