Applications & Limitations of VaR

Value at Risk (VaR) is the most popular risk metric in the world, but it is not perfect. It is like the speedometer of a car—essential, but it won't tell you if the bridge ahead has collapsed.

Applications of VaR

1. Regulatory Capital (Basel Accords)

• Banks: Regulators (RBI, Basel Committee) mandate that banks hold capital based on their VaR.
• Rule: If your 10-day 99% VaR is $100 Million, you must hold a multiple of that (e.g., $300 Million) in cash reserves.

2. Risk Limits & Control

• Trading Desks: Every trader has a "VaR Limit".
• "You can trade whatever you want, as long as your daily VaR stays below $5 Million."
• This allows decentralized risk management.

3. Performance Evaluation (RAROC)

• Risk Adjusted Return on Capital:
  • Trader A makes $10M profit taking huge risks (High VaR).
  • Trader B makes $8M profit taking tiny risks (Low VaR).
  • VaR helps adjust profits to see who is actually better. Trader B likely has a higher RAROC.

4. Comparison Across Assets

• VaR is a universal number. You can compare the risk of a Bond Portfolio vs a Crypto Portfolio vs a Gold Portfolio using a single currency figure (Rs.).

Limitations of VaR

1. "Silent on the Tails" (The 1% Problem)

VaR tells you the minimum loss in the worst 1% of cases, but not the maximum.

• Statement: "99% VaR is 1 Crore."
• Meaning: "You will lose at least 1 Crore."
• Reality: You could lose 1 Crore, or 50 Crores, or 100 Crores. VaR doesn't distinguish between a bad day and doomsday.
• Fix: Use Expected Shortfall (ES).

2. Assumes History Repeats Future

Historical VaR assumes the past 500 days are a good predictor of tomorrow.

• Problem: Structural breaks (Covid, 2008 Crisis) are never in the data until after they happen.

3. Illusion of Safety

VaR gives a precise number ("Risk is exactly 1,234,567 Rs"). This false precision makes managers overconfident.

4. Non-Subadditivity (Not Coherent)

• Mathematically, VaR(Portfolio) can sometimes be greater than VaR(A) + VaR(B).
• This implies that "Diversification increases risk", which is insane and theoretically wrong. (Expected Shortfall fixes this).

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