Parametric, historical, and Monte Carlo VaR compared
| VaR Method | Assumption | Strength | Weakness |
|---|---|---|---|
| Parametric | Returns are normally distributed | Fast, simple calculation | Underestimates tail risk (fat tails) |
| Historical | Future resembles the past | No distribution assumption | Misses unprecedented events |
| Monte Carlo | Simulated return paths | Most flexible, handles complex portfolios | Computationally intensive, model-dependent |
| Time-scaling (√t rule) | Daily returns are independent and identically distributed (i.i.d.) | Rescales a 1-day VaR to any horizon by multiplying by √t | Fails when volatility clusters or returns trend, mis-stating multi-day risk |
The parametric VaR formula
Parametric VaR = Portfolio Value × z-score × σ × √t
VaR is a threshold, not the worst case
VaR tells you the threshold of a bad day, not how bad it gets. A 95% 1-day VaR of $50K means you expect to lose more than $50K only 5% of the time — but on that 5%, the loss could be $100K, $500K, or worse.
Calculate your own portfolio's daily VaR
How often losses should exceed VaR
Why VaR fails when you need it most
What a VaR number actually means
Optional deep dive: adverse selection
Going deeper (optional). Up next: a deeper look at how this plays out in practice — an advanced aside you can skip on first pass and come back to anytime. Continue when you're curious.
Going Deeper — this module contains a deep-dive on adverse selection and the Akerlof lemons dynamic. It is promoted to its own module: see 'Adverse Selection and Market Unraveling' (risk-1b) in this path.
Sit with the ideas.
You manage a bond-heavy portfolio. Interest rates have been stable for two years, but you worry about a sudden rate shock. Which VaR method is LEAST appropriate for capturing this risk?