Formula & Calculator
Value at Risk (Parametric, Simplified)
Estimates the maximum expected loss on a crypto portfolio over a given time period at a chosen confidence level, using a normal distribution assumption.
Interpretation
VaR = Portfolio Value × z × σ. The maximum expected loss over a given period at a given confidence level. Used for risk management.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| VaR | Value at risk | currency |
| Portfolio Value | Current portfolio value | currency |
| z | Z-score for confidence level | |
| σ | Portfolio standard deviation (period) |
What it means
Value at Risk (VaR) is a statistical measure of the risk of loss in an investment. The parametric form assumes a normal distribution. It is used by financial institutions to assess portfolio risk. Understanding VaR helps in setting risk limits and in stress testing portfolios. It is a key metric in risk management. However, it has limitations and does not capture tail risk.
Worked example
Value at Risk – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Portfolio Value | $50,000 |
| Confidence Level (z) | 1.645 (95%) |
| σ (period) | 0.08 |
| Parameter | Value |
|---|---|
| Portfolio | $100,000 |
| z (99%) | 2.33 |
| σ | 0.10 |
Common mistakes
- Parametric VaR: Assumes normal distribution of returns.
- Portfolio value: The current portfolio value.
- z: Z‑score for the desired confidence level (e.g., 1.645 for 95%).
- σ: Portfolio standard deviation (volatility).
- Limitation: Does not capture tail risk (fat tails).
Applications
Value at Risk (VaR) estimates the maximum loss expected over a given time horizon at a specified confidence level (e.g., 95%). This is a standard risk management tool. By using the parametric approach, traders and investors can quantify downside risk and set capital reserves. VaR is used by funds and institutions to monitor risk exposure. Understanding VaR is essential for professional risk management.
- Quantifying downside risk for portfolio positions
- Setting risk limits and capital allocation
- Stress testing and scenario analysis
- Risk reporting to stakeholders
- Educational understanding of risk measures
Frequently Asked Questions
VaR = Portfolio Value × z × σ. For example, a $50,000 portfolio with a daily volatility of 8% and 95% confidence (z=1.645) has a 1-day VaR of $6,580. This means there is a 5% chance of losing more than that in a day.
Crypto returns have fat tails, meaning extreme moves occur more frequently than a normal distribution predicts. This leads to underestimated VaR. For crypto, consider using historical simulation or EVT (Extreme Value Theory).
A higher confidence level (e.g., 99% vs 95%) gives a higher VaR because you are looking at a more extreme tail. For example, z=2.33 for 99% vs 1.645 for 95%.
VaR gives the maximum loss at a confidence level. CVaR (Conditional VaR) gives the average loss in the worst-case scenarios beyond VaR. CVaR is more informative for tail risk.
Yes, you can size a position so that its VaR does not exceed your risk budget. For example, if your risk tolerance is 2% of portfolio per day, you can limit the position size accordingly.
Use the same period as your holding period. For daily VaR, use daily volatility. For weekly, use weekly volatility (daily σ × √5). Adjust accordingly.
You can set a stop-loss at the VaR level to limit losses to your risk tolerance. However, in crypto, stop-losses may not execute at the exact price due to slippage.
It works best for portfolios with linear exposure (e.g., spot holdings). For portfolios with options or leverage, more advanced methods are needed.