Value At Risk (VAR) Calculator
This calculator helps you estimate the potential downside risk of an investment or portfolio using the parametric (variance-covariance) Value At Risk method.
Enter your portfolio value, its volatility, and your desired confidence level. The calculator will estimate the maximum expected loss over the specified time period at that confidence level.
Calculate VaR
Understanding Value At Risk (VAR)
What is VaR?
Value At Risk (VaR) is a statistic used to quantify the level of financial risk within a firm, portfolio, or position over a specific time frame. It estimates the maximum potential loss that is expected to occur with a given confidence level.
Parametric VaR Formula Explained
The parametric method (also known as the variance-covariance method) assumes that asset returns are normally distributed. The basic formula is:
VaR = Portfolio Value × Z-score × Volatility
- Portfolio Value: The current market value of your investment.
- Z-score: A statistical value corresponding to your chosen confidence level from a standard normal distribution. It represents how many standard deviations away from the mean the VaR is.
- Volatility: The standard deviation of the investment's returns over the specific time period you are analyzing (e.g., daily, weekly, annual). It must be expressed as a decimal (e.g., 1.5% volatility = 0.015).
Common Confidence Levels and Z-scores
Here are the Z-scores for commonly used confidence levels (for a one-tailed distribution looking at losses):
- 90% Confidence Level: Z-score ≈ 1.282
- 95% Confidence Level: Z-score ≈ 1.645
- 99% Confidence Level: Z-score ≈ 2.326
The calculator uses these specific Z-scores.
Interpretation
A VaR result is typically interpreted as: "There is a (100 - Confidence Level)% probability that the portfolio will lose at least the calculated VaR amount over the specified time period." For example, a 95% 1-day VaR of $1,000 means there is a 5% chance the portfolio will lose $1,000 or more over the next day.
Limitations of Parametric VaR
It's important to be aware of the limitations:
- Assumes normal distribution of returns, which may not hold true, especially during market crashes (heavy tails).
- Historical volatility may not predict future volatility.
- Doesn't capture "tail risk" well (losses beyond the VaR level).
- Sensitive to input data quality.
VAR Calculation Examples
Click on an example to see the step-by-step calculation:
Example 1: Simple Stock Portfolio
Scenario: Calculate the 1-day VaR for a stock portfolio.
1. Known Values: Portfolio Value = $100,000, Daily Volatility = 1.5% (0.015), Confidence Level = 95%.
2. Formula: VaR = Portfolio Value × Z-score (95%) × Volatility (decimal)
3. Calculation: VaR = $100,000 × 1.645 × 0.015
4. Result: VaR ≈ $2,467.50
Conclusion: There is a 5% chance (100% - 95%) the portfolio could lose $2,467.50 or more over the next day.
Example 2: Mutual Fund Risk
Scenario: A fund manager wants to know the 1-week VaR for a mutual fund.
1. Known Values: Portfolio Value = $5,000,000, Weekly Volatility = 2.1% (0.021), Confidence Level = 99%.
2. Formula: VaR = Portfolio Value × Z-score (99%) × Volatility (decimal)
3. Calculation: VaR = $5,000,000 × 2.326 × 0.021
4. Result: VaR ≈ $244,230
Conclusion: There is a 1% chance (100% - 99%) the fund could lose $244,230 or more over the next week.
Example 3: Single Stock Position
Scenario: Evaluate the daily VaR for holding shares of a single volatile stock.
1. Known Values: Portfolio Value = $15,000, Daily Volatility = 3.0% (0.03), Confidence Level = 90%.
2. Formula: VaR = Portfolio Value × Z-score (90%) × Volatility (decimal)
3. Calculation: VaR = $15,000 × 1.282 × 0.03
4. Result: VaR ≈ $576.90
Conclusion: There is a 10% chance (100% - 90%) the stock position could lose $576.90 or more over the next day.
Example 4: Comparing Risk (Lower Volatility)
Scenario: Calculate the daily VaR for a less volatile investment.
1. Known Values: Portfolio Value = $100,000, Daily Volatility = 0.8% (0.008), Confidence Level = 95%.
2. Formula: VaR = Portfolio Value × Z-score (95%) × Volatility (decimal)
3. Calculation: VaR = $100,000 × 1.645 × 0.008
4. Result: VaR ≈ $1,316.00
Conclusion: Compared to Example 1, lower volatility leads to a lower VaR, indicating less potential downside risk at the same confidence level.
Example 5: Different Confidence Level
Scenario: Re-calculate Example 1's portfolio VaR at a higher confidence level.
1. Known Values: Portfolio Value = $100,000, Daily Volatility = 1.5% (0.015), Confidence Level = 99%.
2. Formula: VaR = Portfolio Value × Z-score (99%) × Volatility (decimal)
3. Calculation: VaR = $100,000 × 2.326 × 0.015
4. Result: VaR ≈ $3,489.00
Conclusion: A higher confidence level results in a higher VaR because it captures a larger potential loss quantile (1% worst case vs 5% worst case).
Example 6: Larger Portfolio
Scenario: Calculate the weekly VaR for a significant portfolio.
1. Known Values: Portfolio Value = $10,000,000, Weekly Volatility = 1.8% (0.018), Confidence Level = 95%.
2. Formula: VaR = Portfolio Value × Z-score (95%) × Volatility (decimal)
3. Calculation: VaR = $10,000,000 × 1.645 × 0.018
4. Result: VaR ≈ $296,100
Conclusion: There is a 5% chance the portfolio could lose $296,100 or more over the next week.
Example 7: Lower Confidence Level
Scenario: Calculate the 1-day VaR at a lower confidence level (less strict).
1. Known Values: Portfolio Value = $50,000, Daily Volatility = 2.5% (0.025), Confidence Level = 90%.
2. Formula: VaR = Portfolio Value × Z-score (90%) × Volatility (decimal)
3. Calculation: VaR = $50,000 × 1.282 × 0.025
4. Result: VaR ≈ $1,602.50
Conclusion: There is a 10% chance (a higher probability than 5% or 1%) the portfolio could lose $1,602.50 or more over the next day.
Example 8: Long-Term VaR (Annual)
Scenario: Estimate the annual VaR for a conservative portfolio.
1. Known Values: Portfolio Value = $500,000, Annual Volatility = 7.0% (0.07), Confidence Level = 95%.
2. Formula: VaR = Portfolio Value × Z-score (95%) × Volatility (decimal)
3. Calculation: VaR = $500,000 × 1.645 × 0.07
4. Result: VaR ≈ $57,575.00
Conclusion: There is a 5% chance the portfolio could lose $57,575.00 or more over the next year.
Example 9: Small Investment
Scenario: Calculate the daily VaR for a small personal investment.
1. Known Values: Portfolio Value = $5,000, Daily Volatility = 2.0% (0.02), Confidence Level = 95%.
2. Formula: VaR = Portfolio Value × Z-score (95%) × Volatility (decimal)
3. Calculation: VaR = $5,000 × 1.645 × 0.02
4. Result: VaR ≈ $164.50
Conclusion: There is a 5% chance this investment could lose $164.50 or more over the next day.
Example 10: High Volatility Scenario
Scenario: Evaluate the daily VaR for a highly volatile asset like a cryptocurrency.
1. Known Values: Portfolio Value = $10,000, Daily Volatility = 5.0% (0.05), Confidence Level = 99%.
2. Formula: VaR = Portfolio Value × Z-score (99%) × Volatility (decimal)
3. Calculation: VaR = $10,000 × 2.326 × 0.05
4. Result: VaR ≈ $1,163.00
Conclusion: There is a 1% chance this volatile asset could lose $1,163.00 or more over the next day.
Frequently Asked Questions about Value At Risk (VAR)
1. What does VaR stand for?
VaR stands for Value At Risk. It's a measure used to estimate potential financial loss.
2. What does a 95% VaR of $1,000 mean?
It means there is a 5% probability (100% - 95%) that your portfolio could lose $1,000 or more over the specified time period.
3. What inputs do I need for this calculator?
You need the current value of your portfolio, the volatility (standard deviation of returns) for the specific time period, and the desired confidence level (typically 90%, 95%, or 99%). You can also specify a name for the time period for the interpretation.
4. How is volatility calculated?
Volatility is the standard deviation of the historical returns of the asset or portfolio over a specific time frame. This calculator assumes you provide the volatility figure relevant to your desired time period (e.g., daily volatility for 1-day VaR).
5. Why use a Z-score?
The Z-score is derived from the standard normal distribution and corresponds to the chosen confidence level. It helps determine how many standard deviations away from the mean return the estimated worst-case loss lies, based on the assumption of normally distributed returns.
6. Is parametric VaR always accurate?
No. The parametric method assumes returns are normally distributed, which is often not the case, especially during extreme market events. It may underestimate risk during financial crises (tail risk).
7. What is the difference between VaR and Expected Shortfall (ES)?
VaR estimates the maximum loss at a certain confidence level. Expected Shortfall (or Conditional VaR) is a risk measure that calculates the expected loss *given* that the loss is *worse* than the VaR. ES is often considered a more conservative measure of tail risk.
8. What time period should I use?
The time period depends on your needs (e.g., regulatory requirements, internal risk limits, investment horizon). Common periods are 1 day, 1 week, or 1 year. Crucially, the volatility input must correspond to this chosen time period.
9. Can VaR be used for individual stocks?
Yes, VaR can be calculated for individual assets, positions, or entire portfolios. However, for a diversified portfolio, calculating portfolio volatility requires considering the correlations between the assets.
10. What does a higher VaR indicate?
A higher VaR indicates a greater potential maximum loss at the given confidence level and time period. It suggests the investment or portfolio is riskier in terms of potential downside.
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