Crypto-Currency Volatility

Volatility estimates for leading crypto-currencies versus benchmarks for Gold and Equities (US S&P 500) are compared in the following chart.

Volatility outcomes for crypto-currencies are relatively high but vary significantly. There is a significant difference in the persistence of volatility across currencies and their sensitivity to shocks. In the absense of shocks, volatilities are highest for Solana, Dogecoin and XRP, and lowest for TRON, Bitcoin and BNB (formerly Binance). TRON however has a very high sensitivity to shocks and is therefore more risky than more liquid and popular crypto currencies such as Bitcoin. Tether is a stable coin linked to US currency and should have zero volatility, its trading prices can vary modestly.

Volatility Ranges

Selected based on the crypto-currencies with the largest market capitalisation, see yahoo.

Measuring and Comparing Volatility

The variation in volatility over time is quantified using a autoregressive conditional heteroskedasticity (ARCH) models. In these models an index's value (for example daily return ) is a function of past observations and a random draw from a normal distribution the variance () of which changes over time. The speed of change is a decomposed into the sensitivity to new shocks () and the persistence of previous volatility (). The following is the simplest model, multiple lags of both α and β can be introduced to better capture dynamics.

Using the full sample of the data as illustrated above, the following table summarises the derived parameters.

Value-at-Risk

Value-at-Risk (VaR) describes the loss that could be incurred when holding an instrument during extreme market conditions. As crypto-currencies have much higher price volatilities than gold or shares, an investment in crypto-currenices also carries with it significantly higher probabilities of extreme losses.

The distribution provides an insight into the impact of kurtosis, the frequency of extreme events, on the Value of Risk of each instrument/index.

VaR Ranges

The VaR for all instruments excludes any mean drift (general long term price appreciation) or not capital growth returns (eg for shares). All instruments are compared only in terms of inherent volatility risk.

Returns