The Value at Risk Analyzer is a parametric, single-asset risk measurement tool that uses the normal distribution to answer the most fundamental question in financial risk management: what is the maximum loss I should expect on this position over a given time period, at a given level of confidence?
Every parameter — mean return, volatility, time period, asset value, and confidence level — updates the chart and all six result metrics live as you move a slider or type a number. There is no Calculate button. The distribution redraws instantly, letting you explore the entire risk landscape of an asset in seconds.
This tool models a single asset using the parametric (normal distribution) method only. It assumes returns are normally distributed, which underestimates tail risk for assets with fat-tailed or skewed return distributions (equities during crises, options, cryptocurrencies). It does not compute historical simulation VaR or Monte Carlo VaR, and it does not model multi-asset portfolio VaR. These limitations are standard to the parametric approach and are discussed further in Section 8.
The tool computes VaR and Expected Shortfall live — no button click required after the initial load. You can run a complete parametric VaR analysis in under a minute.
Type a name for the position in the Asset Name field at the top of the
parameters panel — for example, Reliance Industries or
Nifty 50 ETF. This name appears as a gold italic watermark on the
chart and in the PDF report. It is optional; leaving it blank has no effect on
the calculations.
Enter the asset's annualised mean return and annualised standard deviation (volatility), select the time period from the dropdown, enter the current market value of your position, and set your desired confidence level. Every field has a paired slider for ±50% adjustment. The results update instantly with each change.
The dark results box below the parameters panel shows six metrics: Period Mean, Period Volatility, VaR (Absolute), Asset Value at VaR, VaR as % of Asset, and Expected Shortfall. The chart visualises the full return distribution, with the loss tail shaded green, the profit region shaded teal, and the VaR threshold marked by a gold dashed line.
Five parameters drive all calculations. Each has a numeric input box for precise entry and a paired slider that adjusts the value ±50% of its current level for rapid sensitivity analysis. The Time Period parameter uses a dropdown instead of a numeric input.
Directly below the parameters panel sits the dark-background results box, showing six metrics arranged in a 2×3 grid. All six update live as you change any parameter. The teal-coloured metrics are descriptive statistics; the red-coloured metrics are risk measures. The green/red Asset Value at VaR changes colour based on whether the floor value is above or below the original position value.
The chart plots the normal probability distribution of asset values at the end of the chosen holding period. The x-axis shows the asset value at each possible return outcome; the y-axis shows the probability density at that value. The entire area under the curve sums to 1 (100% of all possible outcomes).
The smooth bell-shaped curve is the normal probability density function of the asset's return over the period, scaled by the asset value to display on the x-axis in currency terms. The peak of the curve is at the Period Mean (Asset Value × (1 + Period μ)). The width of the curve is determined by Period σ — a higher volatility asset has a flatter, wider bell, meaning outcomes are spread over a much larger range of asset values. The entire curve is rendered with a teal-to-dark gradient fill for readability.
The left portion of the distribution — from the minimum x-axis value up to the VaR threshold — is filled with a green gradient. This region represents the (1 − confidence)% worst outcomes: the scenarios where losses exceed the VaR level. For a 95% confidence level, this green tail contains exactly 5% of the total probability mass. The label inside this region displays the exact tail probability (e.g., "10.0% prob below VaR" for a 90% confidence level). The average loss within this tail is the Expected Shortfall.
The right portion of the distribution — from the VaR threshold to the right side of the chart — is filled with a lighter teal gradient. This region represents the confidence% of outcomes where losses are less than VaR or the position ends in profit. The larger the confidence level you set, the more of the distribution sits to the right of the VaR line, and the more extreme the VaR figure becomes to capture the remaining left tail.
The gold dashed vertical line marks the VaR level — the asset value at the confidence threshold. Everything to the left of this line is the loss tail; everything to the right is within the confidence range. The label above the line shows "VaR XX%" where XX is the current confidence level. As you raise the confidence level, this line moves further left (deeper into the tail), and the VaR amount increases.
A muted grey dashed line marks the expected (mean) asset value at end of period — the peak of the bell curve. This is Asset Value × (1 + Period μ). When the mean return is positive, this line sits to the right of the original asset value, indicating expected growth. The gap between the mean line and the VaR threshold line is the expected-return buffer that reduces VaR: a higher expected return shifts the distribution rightward, moving the left tail further from the loss zone.
If you enter a name in the Asset Name field, it appears as a gold italic watermark in the top-right area of the chart. This name also carries through to the PDF export header. It has no effect on calculations — it is a labelling convenience for reports and presentations.
Hovering anywhere over the chart displays a tooltip showing four values at the cursor's x-position: the Asset Value at that point, the Return % relative to the original position, the Probability Density (height of the curve at that point), and the Prob ≤ this (the cumulative probability — the fraction of outcomes that are at or below this asset value). The Prob ≤ this value is most useful: when the cursor is at the VaR line, it will read exactly (1 − confidence).
The following concepts are the building blocks of the parametric VaR framework. Understanding them converts the tool's outputs from numbers into a coherent risk management language.
VaR is a statistical measure of the maximum expected loss over a defined period at a given confidence level. "Maximum expected loss" is a slightly misleading phrase — VaR is really a threshold: losses exceed it with probability (1 − confidence). A 95% one-month VaR of ₹80,000 means there is a 5% chance the loss will exceed ₹80,000 in any given month. VaR says nothing about how large the loss is when it does exceed the threshold — that is the role of Expected Shortfall.
The parametric method assumes asset returns follow a normal (Gaussian) distribution, characterised by mean μ and standard deviation σ. This assumption makes VaR computation analytically tractable — a single formula yields the exact answer. The limitation is that real asset returns have fat tails (extreme losses are more common than the normal model predicts) and negative skew (large losses are more likely than large gains of the same magnitude). The normal model underestimates tail risk during market stress.
ES is the average loss conditional on the loss exceeding VaR — the mean of the left tail. It is mathematically defined as: E[Loss | Loss > VaR]. ES is always larger than VaR and provides a more complete picture of tail risk. For a normal distribution, ES at confidence c is: ES = −[μ − σ × φ(z) / (1 − c)] × Asset Value, where φ is the normal PDF. ES is a coherent risk measure (VaR is not) and has been adopted by Basel IV as the primary regulatory capital metric.
The confidence level determines how far into the left tail VaR is measured. Raising confidence from 90% to 99% does not mean the risk is "ten times safer" — it means you are capturing a more extreme tail event. The z-score for 90% is −1.28; for 95% it is −1.645; for 99% it is −2.326. The VaR roughly doubles from 90% to 99.9% confidence for a normal distribution. The choice of confidence level should match its intended use: 95% for internal management, 99% for Basel regulatory capital, 99.9% for operational risk and stress testing.
Under the assumption that returns are independent and identically distributed (i.i.d.) over time, volatility scales with the square root of the time horizon: σ_T = σ_annual × √t. Returns (means) scale linearly: μ_T = μ_annual × t. This is the basis for converting annual parameters to any sub-annual holding period. The rule breaks down in practice when returns are autocorrelated (trending or mean-reverting), which is common over short horizons for many assets.
Parametric VaR (this tool) fits a distribution to return data and computes VaR analytically. It is fast, elegant, and produces a smooth risk surface — but inherits all assumptions of the chosen distribution. Historical simulation VaR uses actual past returns directly — no distribution assumption — and therefore captures fat tails and skewness automatically. Most large institutions use historical simulation or Monte Carlo as their primary method, and parametric VaR as a fast cross-check or for instruments with limited history.
Parametric VaR and Expected Shortfall are foundational tools across risk management, treasury, trading, and regulatory compliance:
The VaR (Absolute) result is a currency loss amount, not a forecast. A monthly 95% VaR of ₹75,000 on a ₹10 lakh position means: in the worst 5% of months (approximately one month every twenty months, or roughly once every 1.7 years), losses are expected to exceed ₹75,000. In the remaining 95% of months, losses are less than ₹75,000 — and in most of those months, the position gains value.
The choice of confidence level should be driven by the purpose of the VaR calculation:
Using 99% when 95% is more appropriate will produce a VaR that looks much larger and may unnecessarily constrain trading positions. Using 90% for regulatory purposes will understate the required capital. Match the confidence level to the context.
Always look at both. VaR tells you the probability of a loss exceeding the threshold; ES tells you the average severity of losses when they do exceed it. If VaR is ₹80,000 and ES is ₹82,000, the loss tail is thin — losses rarely extend far beyond VaR. If ES is ₹1,40,000 against a VaR of ₹80,000, the tail is fat — when losses exceed VaR, they tend to be dramatically larger. The ES/VaR ratio is a practical measure of tail severity. For a standard normal distribution, ES/VaR at 95% confidence is approximately 1.25.
The mean return acts as a buffer. An asset with a 15% annual mean return and 20% annual volatility has a meaningfully lower monthly VaR than one with a −5% mean and 20% volatility — even though the volatility is identical. This is because the positive expected return shifts the entire distribution rightward, moving the left tail further from the loss zone. For short holding periods (weekly, monthly), the mean effect is small relative to volatility because mean scales with t while volatility scales with √t. For annual horizons, mean return becomes significant.
Two productivity features — Save Model and Export PDF — are available to Trial and Premium users. Free users can run the full parametric VaR analysis and view all six results on screen; saving and PDF export require an account.
| Feature | Free | Trial | Premium |
|---|---|---|---|
| VaR Calculation | ✓ Unlimited | ✓ Unlimited | ✓ Unlimited |
| Live Chart & Results | ✓ Unlimited | ✓ Unlimited | ✓ Unlimited |
| Export PDF | ✗ Not available | ✓ Unlimited | ✓ Unlimited |
| Save Model | ✗ Not available | Up to 3 models | ✓ Unlimited |
| Load Saved Model | ✗ Not available | ✓ All saved models | ✓ All saved models |
Click the ⬇ Export PDF button after reviewing the on-screen results. The tool generates a formatted A4 landscape PDF entirely in your browser using jsPDF — no data is sent to a server — and downloads it immediately.
A model is a named snapshot of all your current inputs: Asset Name, Annual Mean Return, Annual Standard Deviation, Time Period, Asset Value, and Confidence Level. Saving a model lets you return to a previous risk analysis in any future session with a single click.
The Save Model button appears once you are logged in with a Trial or Premium account. Click it after setting up the VaR analysis you want to preserve — for example, after entering a specific asset's risk parameters for a recurring monthly risk report.
Choose a short, descriptive name — for example REL-MONTHLY,
NIFTY-95, or GOLD-ANN. The name identifies the
model in the dropdown. Saving under an existing name prompts you to confirm
overwrite.
Select any saved model from the Load saved model dropdown. All inputs are restored instantly — Asset Name, mean, volatility, time period, asset value, and confidence level — and all six results update immediately. No recalculation step required.
During a Trial, you can save up to three distinct risk scenarios. Overwriting an existing model does not consume an additional slot. When the three-model limit is reached, overwrite an existing model or upgrade to Premium. A practical approach: save the three most commonly used positions (e.g., your largest equity holding, your bond position, and a benchmark index).
Premium users can save as many models as needed — one per position in a portfolio, one per asset class, or a series of stress scenarios for the same position with different volatility assumptions. Premium is ideal for risk managers maintaining a library of position-level VaR scenarios.
A quick-reference table of every technical term used in the tool and this guide.
| Term | Definition | In this tool |
|---|---|---|
| Value at Risk (VaR) | The maximum expected loss over a defined holding period at a specified confidence level. Not a worst-case loss — losses exceed VaR with probability (1 − confidence). Introduced by J.P. Morgan's RiskMetrics in 1994. | Primary output. Shown as VaR (Absolute) in the results box (red). |
| Expected Shortfall (ES) | The average loss conditional on the loss exceeding VaR — the mean of the left tail. Also called CVaR or Conditional VaR. Always larger than VaR. A coherent risk measure. Adopted by Basel IV (FRTB) at 97.5% confidence. | Sixth result metric. Shown in red. Computed as −[μ_T − σ_T × φ(z) / (1−cl)] × Value. |
| CVaR | Conditional Value at Risk — another name for Expected Shortfall. The conditional expectation of loss given that the loss exceeds VaR. | Same as Expected Shortfall in the results box. |
| Normal Distribution | A symmetric, bell-shaped probability distribution characterised by mean μ and standard deviation σ. The parametric VaR method assumes asset returns follow this distribution, enabling analytical computation of VaR. | The teal bell-shaped curve on the chart. Computed using the standard normal PDF and CDF. |
| Confidence Level (cl) | The probability that the actual loss will not exceed the VaR figure. Common values: 90%, 95%, 99%, 99.9%. The complement (1 − cl) is the probability the loss exceeds VaR — i.e., the size of the left tail. | VaR Confidence Level parameter. Determines the z-score and the size of the green loss tail. |
| Parametric VaR | A VaR method that assumes a parametric distribution (usually normal) for returns and computes VaR analytically using the distribution's parameters. Fast and elegant, but sensitive to the distributional assumption. | The method used throughout this tool. |
| σ (Sigma) | Standard deviation of returns — the primary measure of volatility and risk in financial models. Annualised σ is the input; period σ is derived using the square-root-of-time rule. | Std Deviation (Annual) input. Period σ shown in results box (teal). |
| μ (Mu) | Mean (expected) return of the asset. Annualised μ is the input; period μ is derived by multiplying by t. A positive μ reduces VaR by shifting the return distribution rightward. | Mean Return (Annual) input. Period μ shown in results box (teal). |
| z-score (z_VaR) | The number of standard deviations from the mean corresponding to a given confidence level. For VaR, z_VaR = Φ⁻¹(1 − cl). Always negative for loss-side VaR. Examples: z at 90% = −1.282, at 95% = −1.645, at 99% = −2.326. | Computed internally via the inverse normal CDF (rational approximation). Used in the VaR and ES formulas. |
| Φ⁻¹ (Inverse CDF) | The inverse of the standard normal cumulative distribution function. Given a probability p, Φ⁻¹(p) returns the z-score such that P(Z ≤ z) = p. Used to convert a confidence level into a VaR z-score. | Computed using a rational polynomial approximation (Beasley-Springer-Moro algorithm). Used for z_VaR. |
| φ (Normal PDF) | The standard normal probability density function. φ(z) = (1/√2π) × exp(−z²/2). Appears in the Expected Shortfall formula as the height of the normal curve at the VaR z-score. | Computed in the ES formula: φ(z_VaR) / (1 − cl) scales the ES calculation. |
| Square-Root-of-Time Rule | The scaling rule for converting volatility across time horizons under i.i.d. return assumptions: σ_T = σ_annual × √t; μ_T = μ_annual × t. Volatility grows with √t because variance is additive but standard deviation is not. | Applied when computing Period σ and Period μ from annual inputs for any chosen time period. |
| Holding Period (t) | The time horizon over which VaR is measured, expressed as a fraction of a year. Annual = 1.0, Quarterly = 0.25, Monthly = 0.0833, Weekly = 0.0192. Longer horizons produce larger absolute VaR because uncertainty compounds. | Time Period dropdown. Determines t used in all scaling formulas. |
| Probability Density | The height of the probability distribution at a given outcome. Does not directly represent probability — the probability of an outcome in a range is the area under the density curve over that range. | Y-axis of the distribution chart. Shown in the hover tooltip as "Density". |
| Cumulative Distribution (CDF) | The probability that the random variable takes a value less than or equal to a given point. For a normal distribution, the CDF at the VaR point equals (1 − confidence level). Φ(x) denotes the standard normal CDF. | Shown in the hover tooltip as "Prob ≤ this". At the VaR threshold, reads (1 − confidence). |
| Fat Tails | A property of return distributions where extreme outcomes occur more frequently than predicted by the normal distribution. Measured by excess kurtosis (kurtosis > 3). Equity returns typically exhibit fat tails, meaning the normal model underestimates the probability and magnitude of large losses. | A key limitation of this tool's parametric model. Discussed in Section 8. |
| Basel III / IV | International banking regulatory frameworks (Bank for International Settlements). Basel III required 10-day, 99% VaR for market risk capital. Basel IV (Fundamental Review of the Trading Book, FRTB) replaced this with 97.5% Expected Shortfall. | Context for the 99% confidence level and the regulatory importance of ES alongside VaR. |