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.

Hedging in a World That Doesn’t Move at the Same Speed

As we enter the final module of my Financial Modeling class, students shift from building models to using them in a way that feels much closer to reality: commodity hedging. Up to this point, much of what we have done relies on structure:

• returns
• distributions
• regressions
• correlations

Hedging forces a different kind of thinking. Because in the real world, relationships between variables are not stable, synchronized, or even visible at first glance

They are messy. And often delayed.

A Simple Example with Big Implications

I have recently been looking at protein prices (e.g., feeder cattle) and oil prices, I started with a straightforward approach:

Weekly returns and contemporaneous correlations (same week). The result tells one story.  See chart below.

This shows a massive oil demand decrease during Covid. On the other hand supply chain disruptions and panic buying made prices of protein go higher. This did not change until the Russian invasion of Ukraine that jolt the system backwards.

But there is an economic problem with that assumption: Why would changes in oil prices affect protein markets immediately?  Costs, transportation, feed, energy inputs take time to work through the system.

So I introduced something very simple: a 2-week lag in oil returns and suddenly, the relationship changes dramatically.

The situation changes dramatically. Now oil becomes a cost driver, going into fertilizer, transportation, energy costs in general. 

Why This Matters for Hedging

This is not just a statistical curiosity. It has direct implications for how we hedge.

If you hedge based on contemporaneous correlations you assume immediate transmission of shocks and you may conclude: “this hedge doesn’t work” or“there is no relationship”

But what if the relationship is real… just delayed?

Now your problem is not only the hedge but also the timing. 

I want students to walk away with two ideas that go beyond formulas:

1. Correlations Are Not Constants, they move. They evolve. They break. A hedge that worked last year may not work today.

2. The World Has Frictions. Information, costs, and shocks do not propagate instantly, there are lags, passthroughs, adjustments. 

Good modeling requires respecting that reality.

If your hedge is not working, ask yourself:

Is it wrong…  or are you just early?