Calculating VaR – Methodologies

There are two primary ways to calculate VaR. Each has pros and cons.

1. Historical Simulation

Method: "Let's assume the future will look exactly like the past."

Steps:

1. Gather the last 500 days of returns for your portfolio.
2. Sort them from worst (largest loss) to best.
3. For 95% VaR, pick the 95th percentile worst return. (If 500 days, it's the 25th worst day: 500 * 5%).

Pros:

• Easy to understand.
• No assumptions about Normal distribution (captures fat tails effectively).

Cons:

• Requires a lot of historical data.
• Slow to react to new volatility regimes.

2. Parametric (Variance-Covariance) Method

Method: "Let's assume returns follow a Normal Distribution."

Formula:

VaR = Portfolio_Value * Z_score * Volatility * Sqrt(Time)

Where Z-score depends on confidence level:

• 95% Confidence: 1.65
• 99% Confidence: 2.33

Example:

• Portfolio = ₹1,00,000
• Daily Volatility = 2%
• Confidence = 95% (Z = 1.65)

1-Day VaR = 1,00,000 * 1.65 * 0.02 = 3,300 Rupees.

Meaning: There is a 5% chance you lose more than ₹3,300 tomorrow.

Pros:

• Calculation is instant (just need Volatility).
• Easy to scale with the "Square Root of Time" rule (10-Day VaR = 1-Day VaR * Sqrt(10)).

Cons:

• Assumes Normality (ignores Fat Tails).
• Underestimates risk during crashes.

Loading comparison…

Loading quiz…