Why Higher-Frequency Data Can Underestimate Risk: A Copper VaR Case

A common question in risk modeling:

If I have weekly or monthly price data, can I scale it to estimate quarterly risk?

In theory, yes. In practice, it depends on what you believe about markets.

Using copper prices (2006–2026), I estimate quarterly VaR for a $1,000,000 short position:

Weekly data (scaled): 29.8%

Monthly data (scaled): 29.6%

Quarterly data (direct): 34.2%

The gap is economically meaningful.

The Standard Scaling Framework

Parametric VaR assumes:

• Returns are independent
• Volatility is stable
• Risk scales with time

This is convenient—and often wrong for commodities.

Why Scaling Breaks in Commodities

• Volatility Clustering - High-volatility periods persist.
• Serial Correlation - Returns are not independent; trends exist.
• Path Dependency - Risk emerges from sequences, not isolated shocks.
• Distribution Effects - Compounding smooths tails and understates extremes.
• Regime Mixing - Averaging across calm and crisis periods biases volatility downward.

A Practical Fix in Excel: Don’t Scale—Aggregate

Instead of scaling returns, construct them at the horizon you care about.

Two practical approaches in Excel:

Method 1: Additive (Rolling Aggregation of Returns)

Method 2: Offset / Rolling Window Formula (Most Practical)

You can construct actual quarterly returns directly from weekly data. Take price today and divide by price 13 weeks ago.  This creates a time series of realized quarterly returns, even from weekly data.

See the calculations and download the file here. 

Scaling answers: “What would risk look like if returns were independent?” 

Rolling aggregation answers: “What has risk actually looked like over this horizon?”

For commodities, those are not the same question.

Why This Matters for FP&A and Treasury

• Hedging - Underestimated VaR lead to undersized hedges
• Liquidity - Commodity exposures drive margin calls lead to insufficient reserves
• Performance Measurement - Volatility understatement leads to overstated risk-adjusted returns

A Simple Diagnostic

If our assumptions hold:

Weekly-scaled VaR ≈ Monthly-scaled VaR ≈ Quarterly VaR

If they don’t:

The gap is a signal, not noise.

Conclusion

When you scale volatility, you are not just changing time—you are imposing a theory of how markets behave.

For copper, that theory is often wrong.

And the cost shows up in decisions—not in formulas.