Question 1

What is Value at Risk (VaR) and how is it used by financial institutions?

Accepted Answer

Value at Risk (VaR) is a standard statistical risk management metric used by commercial banks, hedge funds, and regulators (Basel Accord) to quantify the maximum potential dollar loss in a portfolio over a specified time horizon (e.g. 1 day or 10 days) at a given confidence level (e.g. 95% or 99%).

Question 2

What is the exact mathematical formula for Parametric (Variance-Covariance) VaR?

Accepted Answer

The Parametric VaR formula is: VaR = Portfolio Value × (Z_α × σ × sqrt(t) - μ × t), where Z_α is the standard normal critical value (1.645 for 95%, 2.326 for 99%), σ is periodic standard deviation, t is the time horizon, and μ is expected periodic return.

Question 3

How do Parametric, Historical, and Monte Carlo VaR models compare?

Accepted Answer

Parametric VaR assumes normal (Gaussian) return distributions and calculates risk instantly using mean and variance. Historical VaR sorts actual past return distributions, capturing real non-normal fat tails. Monte Carlo VaR runs thousands of randomized multi-factor simulations, modeling complex derivatives and non-linear options payoffs.

Question 4

What is a worked numerical example of a 1-day 95% and 99% VaR calculation?

Accepted Answer

Consider a $10,000,000 equity portfolio with a daily volatility (σ) of 1.50% and daily expected return assumed to be 0%: 1-Day 95% VaR (Z = 1.645) = $10,000,000 × (1.645 × 0.015) = $246,750. 1-Day 99% VaR (Z = 2.326) = $10,000,000 × (2.326 × 0.015) = $348,900. This means there is a 1% chance the portfolio will lose more than $348,900 on any single trading day.

Question 5

How does the Square Root of Time rule scale VaR across multiple days?

Accepted Answer

Under the assumption of independent and identically distributed (i.i.d.) returns, multi-day VaR scales by the square root of trading days: VaR(T days) = VaR(1 day) × sqrt(T). For example, a 10-day Basel regulatory VaR equals 1-day VaR multiplied by sqrt(10) ≈ 3.162.

Question 6

What are the critical limitations of Value at Risk (fat tails, black swans, CVaR)?

Accepted Answer

VaR tells you the minimum loss in the worst 5% or 1% of cases, but says nothing about how severe losses can become beyond the threshold (tail risk / black swans). In financial crises, real return distributions exhibit extreme fat tails (kurtosis). Financial institutions use Conditional VaR (CVaR / Expected Shortfall) to measure the average loss in the tail.

Question 7

Is my portfolio size, asset allocation, or risk tolerance shared externally?

Accepted Answer

No. All VaR distributions, Z-score quantiles, and portfolio risk calculations are computed 100% locally in your browser with complete data privacy.

Evaluation Criteria	ToolboxDock (Client-Side)	Traditional Online Calculators
Financial Data Privacy	100% Local (Never leaves device RAM)	Logged on remote servers and ad networks
Calculation Latency	Instant real-time update on keystroke	Full page reloads or API round-trips
Offline Usability	Works offline once cached in browser	Fails without active server connection
Cost & Paywalls	100% free with unlimited calculations	Usage caps or financial product paywalls

Value at Risk (VaR) Calculator

$18,653

Expected Shortfall (CVaR)

Protected Capital

Scaled Volatility

Portfolio Capital Tail Risk Exposure Visualizer

What is the Value at Risk (VaR) Calculator?

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How to Use the Value at Risk (VaR) Calculator

1. Enter Portfolio Value ($)

2. Set Confidence Level & Time Horizon

3. Specify Volatility & Expected Return

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Parametric Value at Risk (VaR) Formula

Core Value at Risk (VaR) Calculator Inputs & Terminology

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$18,653

Expected Shortfall (CVaR)

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