# Volatility metrics

Volatility measures variation of an asset price, thus, indicates its market risk

# Methodology

All volatility metrics are calculated:

• for investors to show long-term volatility

For the detailed description of the difference between short- and long-term calculations see section Investment horizon.

BTC-fiat (including USDT) pairs are based on the USD denominated Aggregated price; ALT-fiat, ALT-BTC, ALT-ETH pairs are based on the BTC Aggregated price.

The volatility metrics are calculated per coin, not per currency pair (symbol).

A metric is displayed on the website only if at least 33% of all observations within a selected period are available.

# Risk scoring

The risk scoring gives a single value with the coloured circle of the risk of an asset or symbol:

• Green circle means low risk

• Orange circle means medium risk

• Red circle means high risk

The resulting metric values are then compared with the metric value for MG50:

• Those assets that have values 2+ times lower than that of MG50 are low volatility (risk) assets

• Those assets that have values 1.5+ times higher than that of MG50 are high volatility assets

• All the rest should be considered mid-volatility assets

# Risk metrics

 Metric Description Meaning Value-at-risk VaR, also named expected loss, measures the amount of potential loss (with a certain degree of confidence) that could happen in an investment over a given time period. Higher value means higher risk Standard deviation of returns Standard deviation is a metric to estimate the extent by which a return varies from its mean Higher value means higher risk Best historical return Largest positive return for the selected interval within the period Higher value means higher risk Worst historical return Largest negative return for the selected interval within the latest period Higher value means higher risk Maximum drawdown A maximum drawdown is the maximum loss from a peak to a trough of an asset price, before a new peak is attained Higher value means higher risk Periods with extreme returns Share of returns for the selected interval within the period exceeding critical value Higher value means higher risk Sharpe ratio The average return for the selected interval, which is calculated within the period, earned in excess of the risk-free rate per unit of volatility or total risk Higher value means higher return per unit of risk

The formulas of the selected metrics are shown below.

Value-at-Risk

We calculate 95% VaR over the specified period based on the historical returns for the interval. E.g., for a long-term investor VaR shows a maximum expected daily loss of investment based on 15-minute returns with the 95% confidence (it means there are 5 cases out of 100 when the loss will exceed this value).

$\operatorname{VaR}_\alpha(X)=\inf\big\{x\in\mathbb{R}:F_X(x)>\alpha\big\}$

where:

• X is a return for the interval

• F is the cumulative distribution function of X

• α is 5% in our case

Standard deviation of returns:

$σ = \sqrt{\frac{\sum\limits^{N}_{i=1} (x_i-\overline{x})^2}{N-1}}$

where:

• x is a return for the interval (e.g., 15-minute or daily return)

• is an average return over the selected period (e.g., 1 day of 3 months)

• N is the number of periods within a period

Maximum drawdown:

$\text{MDD}(T)=\max_{\tau\in (0,T)}\left[\max_{t \in (0,\tau)} X(t)- X(\tau) \right]$

where:

• T is the end of the period

• t is the time of the peak, i.e. highest price within the period

• τ is the time of the lowest price within the period after the peak

Sharpe ratio:

$S = \frac{\overline{r}-r_f}{σ}$

where:

• r is ex-post average return of an asset

• rf is a risk-free rate that we assume equals 0

• σ is standard deviation of returns of an asset over the period