Risk Metrics - Methodology
How we calculate risk indicators for cryptocurrencies
Table of Contents
Overview
CoinRisqLab provides a comprehensive suite of risk metrics to help investors understand and quantify the risk profile of cryptocurrencies. These metrics are based on Modern Portfolio Theory and industry-standard risk management practices.
Metrics use different calculation windows based on their purpose: VaR and Beta use 365 days for more stable risk estimates, while Skewness, Kurtosis, and SML use 90 days to capture recent distribution characteristics.
VaR/CVaR
Downside Risk
Beta/Alpha
Market Sensitivity
Skew/Kurtosis
Distribution Shape
SML
CAPM Valuation
Value at Risk (VaR)
Value at Risk (VaR) is a statistical measure that quantifies the potential loss in value of an asset over a defined period for a given confidence level. It answers the question: "What is the maximum loss I can expect with X% confidence?"
Definition
VaR at confidence level α represents the (1-α) percentile of the return distribution. For example, VaR 95% indicates the loss that will not be exceeded 95% of the time.
Historical VaR Method
We use the Historical Simulation method, which makes no assumptions about the distribution of returns:
- Collect up to 365 days of daily logarithmic returns
- Sort returns from lowest to highest
- Find the return at the (100-α) percentile position
- Report the absolute value as potential loss
Note: The volatility (standard deviation) used in VaR calculations is computed over a 365-day window, unlike the standalone volatility metric which uses a 90-day window and is then annualized. This longer window provides more stable risk estimates for downside risk measurement.
Confidence Levels
| Level | Percentile | Interpretation |
|---|---|---|
VaR 95% | 5th percentile | Loss exceeded only 5% of days (1 in 20) |
VaR 99% | 1st percentile | Loss exceeded only 1% of days (1 in 100) |
Example
Conditional VaR (CVaR) / Expected Shortfall
CVaR, also known as Expected Shortfall (ES), addresses a key limitation of VaR: it tells you the average loss when VaR is exceeded. It answers: "When things go bad, how bad do they get?"
Formula
VaR vs CVaR Comparison
| Metric | Question | Property |
|---|---|---|
| VaR | What's the threshold loss? | Single point estimate |
| CVaR | What's the average extreme loss? | Tail average (coherent risk measure) |
Note: CVaR is always greater than or equal to VaR. It provides a more complete picture of tail risk.
Beta (Market Sensitivity)
Beta measures the sensitivity of an asset's returns to market movements. It indicates how much an asset tends to move relative to the overall market (CoinRisqLab 80 Index).
Formula
Beta is calculated using Ordinary Least Squares (OLS) regression of asset returns against market returns.
Beta Interpretation
| Beta Value | Category | Meaning |
|---|---|---|
β < 0 | Inverse | Moves opposite to the market |
0 < β < 1 | Defensive | Less volatile than market |
β = 1 | Market | Moves exactly like the market |
1 < β < 2 | Aggressive | Amplifies market movements |
β > 2 | Speculative | Extreme market sensitivity |
Additional Regression Metrics
R-Squared (R²)
Percentage of asset variance explained by market movements. Higher R² means the asset tracks the market more closely.
Correlation
Strength and direction of linear relationship with the market. Ranges from -1 (perfect inverse) to +1 (perfect positive).
Alpha (Excess Return)
Alpha measures the excess return of an asset beyond what would be predicted by its beta. A positive alpha indicates outperformance; negative alpha indicates underperformance.
Formula
Interpretation
- Positive Alpha: Asset generates returns above what beta predicts (skilled selection or unique value)
- Negative Alpha: Asset underperforms relative to its market risk
- Zero Alpha: Returns fully explained by market exposure
Security Market Line (SML)
The Security Market Line is a graphical representation of the Capital Asset Pricing Model (CAPM). It shows the theoretical relationship between systematic risk (beta) and expected return.
CAPM Formula
Note: We use Rf = 0 (simplified model for crypto markets where traditional risk-free rates are less relevant).
Jensen's Alpha
The vertical distance between an asset's actual return and the SML represents Jensen's Alpha:
| Position | Interpretation |
|---|---|
Above SML | Undervalued - Generates excess returns for its risk level |
On SML | Fairly valued - Return matches risk |
Below SML | Overvalued - Insufficient return for risk taken |
Skewness
Skewness measures the asymmetry of the return distribution. It indicates whether extreme returns are more likely to be positive or negative.
Fisher's Skewness Formula
Interpretation
| Value | Type | Meaning |
|---|---|---|
< -0.5 | Negative Skew | Left tail is longer - more extreme losses than gains |
-0.5 to 0.5 | Symmetric | Balanced distribution of returns |
> 0.5 | Positive Skew | Right tail is longer - more extreme gains than losses |
Risk Implication
Negative skewness is concerning for investors because it means the asset has a higher probability of extreme negative returns (crash risk). Most cryptocurrencies exhibit negative skewness during market stress periods.
Kurtosis
Kurtosis measures the "tailedness" of the return distribution - how likely extreme values (outliers) are compared to a normal distribution.
Excess Kurtosis Formula (Fisher)
Interpretation
| Value | Type | Meaning |
|---|---|---|
< -1 | Platykurtic | Thin tails - fewer extreme events than normal |
-1 to 1 | Mesokurtic | Normal-like tails |
> 1 | Leptokurtic | Fat tails - more extreme events than normal |
Risk Implication
High kurtosis (leptokurtic) is important for risk management because it means extreme moves happen more often than a normal distribution would predict. Cryptocurrencies typically have high positive kurtosis, meaning "black swan" events are more common than in traditional markets.
Stress Test
Stress testing estimates the potential impact of historical crisis events on an asset, using its beta to project how it would react to similar market shocks.
Formula
Historical Scenarios
| Event | Period | Market Shock |
|---|---|---|
| COVID-19 Crash | Feb-Mar 2020 | -50.42% |
| China Mining Ban | May 2021 | -25.07% |
| UST/Luna Crash | May 2022 | -4.73% |
| FTX Collapse | Nov 2022 | -2.64% |
Example
Calculation Parameters
| Parameter | Value | Description |
|---|---|---|
| VaR / Beta Window | 365 days | Longer window for stable risk estimates |
| Skew / Kurtosis / SML Window | 90 days | Shorter window to capture recent distribution |
| Return Type | Logarithmic | Natural log of price ratios |
| Market Benchmark | CoinRisqLab 80 | Index used for Beta/SML calculations |
| Risk-Free Rate | 0% | Simplified assumption for crypto markets |
| Min. Data Points | 7 days | Minimum required for statistical validity |
| Update Frequency | Daily (2 AM) | All metrics recalculated daily |