What is Value at Risk (VaR)?
Value at Risk (VaR) is a statistical measure that estimates the maximum expected loss of a portfolio over a defined time horizon at a specified confidence level. Put simply: VaR answers the question, "What is the most I can expect to lose over the next N days, 95% (or 99%) of the time?"
The definition has three essential parts — loss amount, time horizon, and confidence level — and all three must be specified for a VaR statement to be meaningful. A statement like "the portfolio has a VaR of $10,000" is incomplete. The full statement is: "The portfolio has a 1-day 95% VaR of $10,000" — meaning there is a 5% probability of losing more than $10,000 in any single trading day.
VaR was formally developed at JPMorgan in the late 1980s as part of the RiskMetrics framework and became the industry standard for market risk measurement following its adoption by the Basel Committee on Banking Supervision in the 1990s. Today it underpins the regulatory capital requirements for every major bank in the world.
Example: 1-Day 95% VaR = $10,000 on a $500,000 portfolio
Statement 1 (Loss probability):
"There is a 5% chance of losing more than $10,000 in one day."
Statement 2 (Confidence):
"We are 95% confident that the daily loss will NOT exceed $10,000."
Statement 3 (Frequency):
"On average, we expect to lose more than $10,000 on approximately
1 in every 20 trading days (5% × 252 ≈ 12.6 days per year)."
All three statements are mathematically equivalent.
The framing changes; the number does not.
The Three Core Components of VaR
1. Maximum Potential Loss (the VaR amount)
This is the dollar or percentage threshold that VaR estimates. It is not the worst possible loss — it is the loss threshold below which losses will remain a specified percentage of the time. For a 95% VaR of $10,000: losses will be below $10,000 on 95% of days and above $10,000 on the remaining 5% of days. The VaR amount is always a positive number representing a loss. In practice it is often written as negative (−$10,000) to emphasize that it is a loss, or as positive with the loss context implied.
2. Time Horizon
VaR is always horizon-specific. The choice of horizon depends on the use case:
| Horizon | Common Use | Scale from 1-day via √T rule |
|---|---|---|
| 1 day | Daily trading risk monitoring, hedge fund risk reports | Baseline — no scaling needed |
| 10 days | Basel III regulatory capital requirement for market risk | 1-day VaR × √10 = × 3.162 |
| 1 month (21d) | Monthly portfolio risk reviews | 1-day VaR × √21 = × 4.583 |
| 1 year (252d) | Annual risk budgeting, stress testing | 1-day VaR × √252 = × 15.875 |
The square-root-of-time rule is the standard method for scaling VaR across horizons. It assumes returns are independent and identically distributed (i.i.d.) — an approximation that holds reasonably well for short horizons but breaks down over longer periods where mean-reversion and volatility clustering become important.
3. Confidence Level
The confidence level defines how far into the loss tail VaR reaches. It is the probability that actual losses will not exceed the VaR threshold. Three confidence levels dominate in practice:
| Confidence Level | Exceedance Probability | Z-Score | Primary Use |
|---|---|---|---|
| 90% | 10% chance of exceedance | 1.282 | Internal risk monitoring, conservative initial screening |
| 95% | 5% chance of exceedance | 1.645 | Standard for asset managers, hedge funds, internal risk |
| 99% | 1% chance of exceedance | 2.326 | Bank internal models, conservative risk reporting |
| 99.5% | 0.5% chance of exceedance | 2.576 | Insurance regulatory capital (Solvency II), extreme risk |
Portfolio: $500,000 | Daily σ: 1.2% | μ: 0.03%
1-Day VaR at different confidence levels:
90% VaR = $500,000 × (1.282 × 1.2% − 0.03%) = $7,542
95% VaR = $500,000 × (1.645 × 1.2% − 0.03%) = $9,720
99% VaR = $500,000 × (2.326 × 1.2% − 0.03%) = $13,806
Reading the 95% VaR:
→ We are 95% confident daily losses stay below $9,720.
→ There is a 5% chance of losing MORE than $9,720 today.
→ On ~12.6 trading days per year, losses will exceed $9,720.
Scaling to 10-day (Basel regulatory horizon):
10-Day 95% VaR = $9,720 × √10 = $30,730
VaR Synonyms and Related Terms
Value at Risk appears under several names and abbreviations across different contexts and languages. Recognizing these synonyms helps when reading regulatory filings, academic papers, or risk reports from different institutions:
| Term | Context | Equivalent to VaR? |
|---|---|---|
| Value at Risk (VaR) | Universal — finance, banking, regulation | ✅ Standard term |
| Giá trị rủi ro / Giá trị chịu rủi ro | Vietnamese translation used in financial literature | ✅ Direct translation |
| Market Risk Capital (MRC) | Basel III regulatory framework — VaR × multiplier | Derived from VaR — regulatory capital requirement |
| Loss Quantile | Academic statistics — describes VaR as a percentile | ✅ Same concept, different framing |
| Potential Loss Estimate (PLE) | Some corporate treasury departments | ✅ Same concept |
| Earnings at Risk (EaR) | Corporate finance — applied to earnings instead of portfolio value | Related — measures earnings volatility, not portfolio loss |
| Cash Flow at Risk (CFaR) | Corporate treasury — VaR applied to future cash flows | Related — same methodology, applied to cash flows |
| Expected Shortfall (ES) / CVaR | Basel III post-2016, academic risk management | Extension of VaR — measures average loss beyond VaR threshold |
Applications of VaR in Finance
1. Regulatory capital requirements (Basel III)
Under Basel III, banks must hold capital proportional to their market risk VaR. The regulatory formula requires a 10-day 99% VaR multiplied by a scaling factor (minimum 3). Banks with poor VaR model performance in backtesting receive higher multipliers, increasing their capital requirement as a penalty. The transition from VaR to Expected Shortfall (CVaR) is underway under Basel IV's Fundamental Review of the Trading Book (FRTB).
2. Portfolio risk monitoring
Fund managers use daily VaR reports to monitor whether their portfolio risk is within mandated limits. A fund with a $1 billion portfolio might have a risk limit of "daily 95% VaR below $15M." Exceeding this limit requires immediate de-risking — reducing positions or adding hedges to bring VaR back within bounds.
3. Position sizing and risk budgeting
VaR provides a common unit of risk across different assets and strategies. A risk manager can allocate a "VaR budget" across desks or strategies — each allocation unit gets a maximum VaR they can use, forcing explicit risk trade-offs when new positions are added. Adding a position that doubles the VaR contribution of one desk forces that desk to reduce risk elsewhere.
4. Stress testing supplement
VaR works alongside stress testing (scenario analysis) in institutional risk management. VaR captures normal-market risk; stress tests capture extreme-tail risk. Together they give a complete picture — VaR tells you the everyday risk, stress testing tells you the crisis risk.
5. Performance attribution — Sharpe vs Risk-Adjusted Return
VaR enables more sophisticated performance evaluation. Instead of comparing returns, risk managers compare return-per-unit-of-VaR across strategies — identifying which strategies generate the most return for each unit of downside risk consumed.
Method 1 — Historical VaR (Historical Simulation)
Historical VaR is the simplest and most transparent method. It requires no distributional assumption — it simply sorts the actual historical return observations from worst to best and reads off the relevant percentile directly.
Step 1: Collect N periods of actual returns.
Step 2: Sort returns from worst (most negative) to best.
Step 3: Find the return at the (1−confidence) percentile.
Step 4: VaR = |return at that percentile| × Portfolio Value.
Example — 25 daily returns, $500,000 portfolio, 95% VaR:
Returns sorted (worst to best):
−3.1%, −2.8%, −2.2%, −1.9%, −1.7%, −1.5%, −1.2%, −1.0%,
−0.8%, −0.6%, −0.4%, −0.3%, 0.2%, 0.3%, 0.5%, 0.6%, 0.7%,
0.8%, 0.9%, 1.1%, 1.4%, 1.8%, 2.1%, 2.4%, 3.2%
95% VaR → look at 5th percentile of 25 obs = (1−0.95)×25 = 1.25th obs
→ 2nd lowest return = −2.80%
95% Historical VaR = $500,000 × 2.80% = $14,000
95% CVaR → average of returns BELOW the VaR:
tail returns: −3.1%, −2.8% → avg = −2.95%
95% CVaR = $500,000 × 2.95% = $14,750
Key characteristics:
✅ No distributional assumption — captures actual fat tails and skewness
✅ Simple to explain and verify
✅ Directly incorporates historical crisis periods if they are in the sample
❌ Limited by sample size — rare events not in the window are invisible
❌ Past return patterns may not reflect future risk
❌ Equally weights 5-year-old and yesterday's returns (unless EWMA used)
EWMA weighting — making recent data matter more
The standard equal-weighted historical simulation treats a return from five years ago the same as yesterday's return. Exponentially Weighted Moving Average (EWMA) historical simulation assigns higher weights to recent observations, with weights decaying geometrically at rate λ (typically 0.94 as used by RiskMetrics). This makes VaR more responsive to recent changes in market volatility — rising faster during stress and falling faster when conditions normalize.
Method 2 — Parametric VaR (Variance-Covariance Method)
The parametric method assumes that portfolio returns follow a normal (Gaussian) distribution. Under this assumption, VaR can be computed analytically from just two parameters: the portfolio's expected return (μ) and its volatility (σ). This makes it fast, simple, and mathematically elegant — but vulnerable when the normality assumption breaks down.
VaR = Portfolio Value × (Z_α × σ_scaled − μ_scaled)
Where:
Z_α = Normal distribution inverse CDF at confidence level α
(90% → 1.282 | 95% → 1.645 | 99% → 2.326)
σ_scaled = Daily σ × √(holding period)
μ_scaled = Daily μ × holding period
CVaR (Expected Shortfall):
CVaR = Portfolio Value × [φ(Z_α) / (1−α)] × σ_scaled − μ_scaled
Where φ(Z_α) = standard normal PDF at Z_α
Example — $500,000 portfolio, σ=1.2%/day, μ=0.03%/day, 1-day:
VaR 95% = $500,000 × (1.645 × 0.012 − 0.0003) = $9,720 (1.944%)
CVaR 95% = $500,000 × (0.1031/0.05 × 0.012 − 0.0003) = $12,222 (2.444%)
Scaling to different horizons (square-root-of-time rule):
10-day: VaR 95% = $9,720 × √10 = $30,730
Annual: VaR 95% = $9,720 × √252 = $154,342
Key characteristics:
✅ Fast — computes instantly from just μ and σ
✅ Simple to understand and communicate
✅ Consistent and reproducible — no simulation randomness
✅ Easy to scale across time horizons
❌ Assumes normal distribution — underestimates fat-tail losses
❌ 2008 GFC losses were 4–6σ events — parametric VaR missed this badly
❌ Cannot handle non-linear instruments (options, convertibles)
Method 3 — Monte Carlo VaR (Simulation Method)
Monte Carlo VaR generates thousands of hypothetical portfolio return scenarios by drawing random samples from a specified distribution. The VaR is then computed empirically from the simulation results — exactly as in historical simulation, but using simulated rather than historical returns.
Step 1: Specify the return distribution parameters (μ, σ).
Step 2: Generate N random return scenarios using Box-Muller or similar.
Step 3: Sort the N simulated returns from worst to best.
Step 4: Read off the (1−confidence) percentile → this is VaR.
Step 5: Average the tail returns → this is CVaR.
Example — 5,000 simulations, μ=0.03%/day, σ=1.2%/day, $500,000:
Generate 5,000 random daily returns from N(0.03%, 1.2%).
Sort results. The 250th worst (5% × 5,000) ≈ −1.89%.
MC VaR 95% ≈ $500,000 × 1.89% ≈ $9,450
(vs parametric $9,720 — close but not identical due to randomness)
CVaR: average of 250 worst returns ≈ −2.39%
MC CVaR 95% ≈ $500,000 × 2.39% ≈ $11,950
Fat-tail multiplier (t-distribution approximation):
Normal multiplier × 1.3 → σ_effective = 1.2% × 1.3 = 1.56%
This makes extreme scenarios more likely, better capturing real markets.
MC VaR 95% with fat-tail×1.3 ≈ $12,285 vs parametric $9,720
Key characteristics:
✅ Most flexible — can handle any distribution shape
✅ Captures fat tails with fat-tail multiplier
✅ Works for complex portfolios with non-linear instruments
✅ Produces full distribution of outcomes, not just the tail
❌ Results vary between runs (simulation randomness) — use 10,000+ sims
❌ Computationally intensive for large portfolios
❌ Quality of output depends on quality of input distribution assumptions
Comparing the Three VaR Methods
| Criterion | Historical | Parametric | Monte Carlo |
|---|---|---|---|
| Distributional assumption | None — uses actual data | Normal distribution required | User-specified (flexible) |
| Data requirement | Historical return series (min 250 obs ideal) | Only μ and σ needed | Only μ and σ needed (or copulas for multi-asset) |
| Fat tail capture | ✅ If crisis in sample | ❌ Underestimates tails | ✅ With fat-tail multiplier |
| Speed | Fast (sort operation) | Instant (formula) | Slow (10,000 simulations) |
| Non-linear instruments | ✅ Captures options, etc. | ❌ Assumes linearity | ✅ Most flexible |
| Regulatory acceptance | ✅ Basel accepted | ✅ Basel accepted | ✅ Basel accepted |
| Best for | Liquid portfolios with rich return history | Quick estimates, linear portfolios | Complex portfolios, stress testing |
In practice, sophisticated institutions run all three methods simultaneously and compare the results. Large divergences between methods signal that the normality assumption is being violated or that the historical sample contains unusual periods that dominate the result. Our VaR Calculator Pro implements all three, allowing direct comparison in one tool.
CVaR / Expected Shortfall — Going Beyond VaR
VaR's most fundamental weakness is that it says nothing about the magnitude of losses when its threshold is breached. A 95% VaR of $10,000 could mean losses cluster just above $10,000 on bad days — or that losses occasionally reach $100,000 on catastrophic days. VaR cannot distinguish between these two scenarios.
CVaR (Conditional VaR), also called Expected Shortfall (ES) or Tail Loss, solves this problem by measuring the average loss in the scenarios where VaR is exceeded:
CVaR = E[Loss | Loss > VaR]
= Average of all losses that exceed the VaR threshold
CVaR is always ≥ VaR for the same confidence level.
Example — $500,000 portfolio, σ=1.2%/day, 95% confidence:
Parametric VaR 95% = $9,720
Parametric CVaR 95% = $12,222 (on the 5% of days when VaR is breached,
the average loss is $12,222)
Historical example (25 returns):
Historical VaR 95% = $14,000 (2nd lowest return: −2.8%)
Historical CVaR 95% = $14,750 (avg of 2 worst: (−3.1%+−2.8%)/2 = −2.95%)
Why regulators prefer CVaR (ES):
VaR at 99% for Portfolio A: $10,000 — tail losses cluster just above $10K
VaR at 99% for Portfolio B: $10,000 — tail losses can reach $100K
→ Same VaR, completely different risk! CVaR differentiates them.
Basel IV (FRTB) has replaced VaR with Expected Shortfall at 97.5%
as the primary regulatory risk measure for exactly this reason.
Multi-Asset Portfolio VaR and Diversification
For a portfolio of multiple assets, VaR cannot be calculated by simply summing individual asset VaRs — this would ignore the diversification benefit of holding assets that do not move in perfect lockstep. The correct approach uses the full covariance matrix.
Portfolio daily σ² = Σᵢ Σⱼ wᵢ wⱼ σᵢ σⱼ ρᵢⱼ
Portfolio VaR = Portfolio Value × Z_α × σ_portfolio
Example — 3-asset portfolio, $500,000, 95% confidence:
SPY: weight 60%, daily σ 1.0%
AGG: weight 30%, daily σ 0.3%
GLD: weight 10%, daily σ 0.8%
ρ(SPY,AGG)=−0.20 | ρ(SPY,GLD)=0.05 | ρ(AGG,GLD)=0.10
σ_p² = 0.6²×0.01² + 0.3²×0.003² + 0.1²×0.008²
+ 2×0.6×0.3×0.01×0.003×(−0.20)
+ 2×0.6×0.1×0.01×0.008×0.05
+ 2×0.3×0.1×0.003×0.008×0.10
= 0.000036 + 0.00000081 + 0.00000064 − 0.00000216 + ≈0 + ≈0
= 0.0000349
σ_portfolio = √0.0000349 = 0.591%/day
Portfolio VaR 95% = $500,000 × 1.645 × 0.00591 = $4,860
Portfolio CVaR 95% = $500,000 × (0.1031/0.05) × 0.00591 = $6,100
Weighted avg individual VaR (no diversification):
→ 0.6×1.0% + 0.3×0.3% + 0.1×0.8% = 0.770%/day
→ Undiversified VaR = $500,000 × 1.645 × 0.0077 = $6,329
Diversification benefit = $6,329 − $4,860 = $1,469 per day
VaR reduction from diversification = 0.179%/day of portfolio value
Key insight: The negative correlation between SPY and AGG (−0.20)
provides a meaningful hedge — when equities fall, bonds cushion
the loss, reducing portfolio VaR significantly below the standalone sum.
VaR Backtesting — How to Know If Your Model Works
A VaR model is only useful if it is well-calibrated — meaning breaches actually occur at the frequency the model predicts. A 95% VaR model should be breached on approximately 5% of days. VaR backtesting systematically checks this by comparing predicted VaR against actual realized returns over a test window.
Breach = Day when actual loss > predicted VaR threshold
Expected breaches = N × (1 − confidence level)
Example — 95% VaR model, 25-day test window:
VaR threshold: $1,500 (= 0.30% of $500,000)
Actual returns enter: 11 days had losses > 0.30%
Expected breaches: 25 × 5% = 1.25
Breach rate = 11/25 = 44.0% (actual) vs 5.0% (expected)
Ratio = 44%/5% = 8.8× — model severely underestimates risk
Scaled to 250-day window: 11/25 × 250 = 110 breaches
Basel III classification: RED ZONE (10+ breaches → model rejected)
Basel III Traffic Light System (250-day standard window):
🟢 Green Zone (0–4 breaches): Model accepted — capital multiplier = 3.0
🟡 Amber Zone (5–9 breaches): Increased scrutiny — multiplier rises 3.4–3.8
🔴 Red Zone (10+ breaches): Model rejected — multiplier = 4.0+ (maximum)
Kupiec POF Test (simplified model assessment):
Actual breach rate ÷ Expected breach rate:
0.50–2.00×: Model acceptable
< 0.50× or > 2.00×: Model biased (over- or under-conservative)
→ Well-calibrated: model predicted 5% breaches, got 4–6% ✅
The backtesting example above illustrates why VaR model choice matters: a VaR of $1,500 on a $500,000 portfolio with 1.2% daily volatility is far too low — the parametric 95% VaR should be approximately $9,720. A model set at $1,500 will be breached on nearly every bad day, immediately entering the Red Zone. This is not a flaw in backtesting — it is backtesting working exactly as designed, detecting a miscalibrated model.
Critical Limitations of VaR — What It Does Not Tell You
VaR is powerful and widely used, but every practitioner must understand where it fails — and use it accordingly:
1. VaR does not tell you what happens when it is breached
This is VaR's most important limitation. A 99% VaR of $15,000 says losses will stay below $15,000 on 99% of days. It says nothing about whether the remaining 1% of days produce losses of $16,000 or $160,000. During the 2008 financial crisis, losses on many "low-VaR" portfolios were 10–20× the predicted VaR — not because VaR was wrong about frequency, but because it gave no information about severity. CVaR/Expected Shortfall partially addresses this, which is why Basel IV is transitioning away from VaR toward ES.
2. VaR assumes normal market conditions
Parametric VaR explicitly assumes a normal distribution. Historical VaR is only as good as the history it contains — if the sample period was calm, the VaR will be low. Real financial returns have fat tails (kurtosis greater than 3) and negative skew — extreme losses occur more frequently and are larger than the normal distribution predicts. The Monte Carlo fat-tail multiplier and EWMA weighting address this partially, but no model fully captures crisis-era behavior.
3. VaR does not capture correlation breakdown in crises
Multi-asset VaR assumes stable correlations. During market crises, correlations between asset classes typically spike toward 1.0 — diversification disappears exactly when it is needed most. A portfolio VaR calculated with normal-market correlations severely underestimates crisis risk. Stress testing with crisis-era correlations is the only partial solution; our Portfolio Volatility Calculator's Stress Test tab applies historical crisis scenarios to address this.
4. VaR is not additive across risk types
Market risk VaR, credit risk VaR, and operational risk VaR cannot simply be added together. Different aggregation methods (simple sum, square root of sum of squares, full copula) produce dramatically different total risk estimates. This is why enterprise-wide risk management requires specialized systems beyond what any single VaR calculation can provide.
5. VaR can create perverse incentives
Because VaR ignores losses beyond the threshold, traders can technically "reduce VaR" by replacing large, frequent small losses with rare catastrophic losses — selling deep out-of-the-money options being the canonical example. The position looks safer by VaR metrics while actually creating far greater tail risk. CVaR, being sensitive to the magnitude of tail losses, is more resistant to this manipulation.
How to Use Our VaR Calculator Pro — Tab by Tab
Our Value at Risk Calculator Pro implements all five dimensions of professional VaR analysis in one integrated tool. Here is how to use each tab:
Tab 1: Parametric VaR — Instant analytical calculation
Enter portfolio value, expected daily return, and daily volatility (or enter annual volatility to auto-fill daily σ). Set holding period and select confidence levels. Results show:
- VaR and CVaR at each selected confidence level with Z-score, dollar loss and percentage
- Daily volatility dollar range and 1σ band
- 10-day and annual VaR via square-root-of-time scaling
- Normal distribution chart with VaR threshold markers
- VaR 95% (1-day): −$9,720 (1.94%) | CVaR 95%: −$12,222 (2.44%)
- VaR 99% (1-day): −$13,806 (2.76%) | 10-Day VaR 95%: −$30,730
Tab 2: Historical VaR — Empirical simulation from actual returns
Enter portfolio value and a comma-separated series of historical percentage returns (minimum 20 recommended). Choose equal or EWMA decay weighting. Results show:
- VaR and CVaR at 90%, 95% and 99% from empirical percentiles
- Observation count, mean return, worst and best day
- Return distribution histogram with VaR percentile markers
- Historical VaR 95%: −$14,000 (2.80%) | CVaR 95%: −$14,750 (2.95%)
- Worst Day: −3.10% | Mean: −0.060%
Tab 3: Monte Carlo VaR — Simulation with fat-tail option
Enter portfolio value, daily return, daily volatility, number of simulations (up to 10,000) and optional fat-tail multiplier. Click "Run Simulation." Results show:
- VaR and CVaR at 90%, 95% and 99% from simulation results
- Comparison column: Monte Carlo vs equivalent Parametric VaR
- Simulated mean, worst and best scenario in dollars
- Simulated return distribution histogram
- MC VaR 95%: ≈ −$9,400 (1.89%) | vs Parametric: −0.06% difference ✅
- Simulated Mean: +0.055% | Worst: −$18.1K | Best: +$23.9K
Tab 4: Multi-Asset VaR — Portfolio VaR from covariance matrix
Add up to 6 assets with ticker, weight (%) and daily volatility (%). Enter pairwise correlations. Click "Calculate Portfolio VaR." Results show:
- Portfolio VaR and CVaR at selected confidence level
- Portfolio daily volatility from full covariance matrix
- Weighted average standalone volatility (pre-diversification)
- Diversification benefit in volatility percentage
- VaR contribution bar chart per asset
- Portfolio σ: 0.599%/day vs weighted avg 0.770%/day
- Portfolio VaR 95%: −$4,900 | CVaR: −$6,200 | Div. Benefit: −0.171% vol
Tab 5: Backtesting — Test your VaR model against real outcomes
Enter portfolio value, the predicted VaR dollar amount, confidence level, and actual realized daily returns. Results show:
- Breach count, expected breaches, breach rate
- Largest breach loss in dollars
- Model assessment (Well-Calibrated / Acceptable / Biased)
- Basel III traffic light zone (Green / Amber / Red) scaled to 250 days
- Daily P&L bar chart with VaR threshold line and breaches highlighted
- Breaches: 11 actual vs 1.3 expected | Breach Rate: 44.0%
- Assessment: Model Biased | Basel: 🔴 Red Zone (110 scaled breaches)
→ VaR $1,500 is far too low for a $500K portfolio with 1.2% daily vol. Use parametric VaR ~$9,720 for a calibrated model.
Frequently Asked Questions
What is Value at Risk (VaR)?
Value at Risk (VaR) is the maximum expected loss of a portfolio over a specified time horizon at a given confidence level. For example, a 1-day 95% VaR of $10,000 means there is a 5% probability of losing more than $10,000 in a single trading day. VaR requires three components to be fully specified: the loss amount, the time horizon, and the confidence level.
What is the difference between VaR and CVaR?
VaR gives the loss threshold (the point below which losses stay X% of the time). CVaR (Conditional VaR, also called Expected Shortfall) gives the average loss in the scenarios where that threshold is exceeded. CVaR is always larger than VaR for the same confidence level and provides more information about tail risk severity. Basel IV is replacing VaR with Expected Shortfall at 97.5% as the regulatory standard for exactly this reason.
Which VaR method is most accurate?
No single method is universally most accurate. Historical VaR requires no distributional assumption and captures real fat tails if they are in the sample, but is limited by sample size. Parametric VaR is fast but assumes normality and underestimates tail risk. Monte Carlo is the most flexible and can incorporate fat tails, but depends on the quality of input assumptions. Professional risk managers typically run all three and compare the results.
Why does VaR not capture the full risk?
VaR's critical limitation is that it says nothing about the magnitude of losses when the threshold is breached. A 99% VaR of $15,000 could mean tail losses are $16,000 on bad days, or $160,000 on catastrophic days — VaR cannot distinguish between these. This is why CVaR is preferred by sophisticated risk managers and regulators. VaR also assumes stable correlations that break down during crises, and it does not capture liquidity risk or non-linear instrument behavior under the parametric method.
How does the Basel III traffic light system work?
Basel III requires banks to backtest their internal VaR models against 250 trading days of actual returns. The traffic light classifies models by breach count: Green zone (0–4 breaches) means the model is accepted; Amber zone (5–9 breaches) triggers increased regulatory scrutiny and higher capital multipliers; Red zone (10+ breaches) means the model is rejected and the maximum capital multiplier (4.0×) applies. This creates a direct financial incentive for banks to maintain well-calibrated VaR models.
How do you scale VaR across different time horizons?
The square-root-of-time rule scales 1-day VaR to longer horizons: T-day VaR = 1-day VaR × √T. For example, 1-day 95% VaR of $9,720 scales to a 10-day VaR of $9,720 × √10 = $30,730. This rule assumes returns are independent and identically distributed, which holds reasonably well for short horizons but breaks down over longer periods where volatility clustering and mean-reversion become important.
Is this VaR calculator free?
Yes. The Value at Risk Calculator Pro on StockToolHub is completely free with no registration, account, or subscription required. All five tabs — Parametric VaR, Historical VaR, Monte Carlo VaR, Multi-Asset VaR, and Backtesting — are fully accessible.
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