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?

How risky is a tanker full of oil? A VaR example

 

A recent news headline mentioned that several oil tankers were being allowed to pass through the Strait of Hormuz.

That got me thinking—not about geopolitics—but about something I care deeply about: financial risk.

 A tanker may be “just one shipment,” but financially it is a large floating position in oil.

 

A typical VLCC (Very Large Crude Carrier) carries about 2 million barrels. At today’s price of Brent crude (March 27, 2026) of $107.9 per barrel, that puts the cargo value at roughly: $216 million.

 

From shipment to risk position

Using weekly Brent prices over the last 20 years I found that:

·       Average weekly return: 0.1839%

·       Weekly volatility: 5.2495%

This means the standard deviation of the tanker’s value is about $11 million per week.

So even before doing anything fancy, we already know: A “normal” week can move the value of this cargo by about $11 million in either direction.

 

VaR under the Normal Distribution

If we assume oil returns are normally distributed, the 99% VaR uses a Z-score of 2.3263.

 

 

In other words, a one-week loss of roughly $26 million or more should happen for only 1% of the time (1 out of every 100 weeks)

 

VaR under a Student-t Distribution

But commodity returns are often not well described by the normal distribution. They tend to have fat tails. If instead we use a Student-t distribution with 5 degrees of freedom, the one-week t-critical value (the equivalent to the normal Z-score) is 3.3649, VaR_99% becomes:

 

• Same tanker.
• Same cargo.
• Same price.
• Same volatility.

• Different risk estimate.

The only thing that changed was the assumption about the distribution of returns. One of the hardest lessons for students is that risk is not just calculated, it needs to be modeled. The formula is the easy part; choosing the model is where judgment comes in.

 

Another layer: the data window matters

 

The results also depend on how far back we look.

VaR99% - Weekly Returns
	20 years	10 years	5 years	2 years	1 year
Mean Return	0.184%	0.357%	0.333%	0.371%	0.956%
Standard Deviation	5.249%	5.765%	5.274%	5.548%	6.792%
Normal VaR	$26.75 m	$29.72 m	$27.20 m	$28.66 m	$36.16 m
Student-t VaR	$38.52 m	$42.64 m	$39.02 m	$41.09 m	$51.39 m
Extra VaR	$11.77 m	$12.92 m	$11.82 m	$12.44 m	$15.22 m

 

Shorter samples (especially recent ones) produce higher volatility and higher VaR

 

But we are not done. The horizon matters too: daily vs monthly risk

So far, the analysis used weekly returns. But risk is also shaped by the time horizon over which we measure it. The relevant risk depends on who you are: a trader may care about daily VaR, a vessel owner about weekly or monthly exposure, and an insurance company about even longer horizons tied to extreme events.

 

Below are the same VaR calculations using daily and monthly returns.

 

VaR99% - Daily Returns
	20 years	10 years	5 years	2 years	1 year
Mean Return	0.045%	0.086%	0.070%	0.068%	0.182%
Standard Deviation	2.643%	3.007%	2.320%	2.264%	2.729%
Normal VaR	$13.37 m	$15.28 m	$11.80 m	$11.51 m	$14.10 m
Student-t VaR	$19.29 m	$22.02 m	$17.00 m	$16.59 m	$20.21 m
Extra VaR	$5.92 m	$6.74 m	$5.20 m	$5.07 m	$6.12 m

Even at a one-day horizon, the choice of distribution changes the estimate by millions of dollars

 

VaR99% - Monthly Returns
	20 years	10 years	5 years	2 years	1 year
Mean Return	1.026%	2.035%	1.273%	1.620%	3.915%
Standard Deviation	12.446%	14.434%	10.192%	12.568%	16.539%
Normal VaR	$64.70 m	$76.86 m	$53.92 m	$66.59 m	$91.49 m
Student-t VaR	$92.60 m	$109.21 m	$76.77 m	$94.76 m	$128.56 m
Extra VaR	$27.90 m	$32.35 m	$22.85 m	$28.17 m	$37.07 m

Over longer horizons, both risk and model sensitivity increase dramatically

 

Bottom Line

The cargo does not change. The estimated risk does. The difference comes from:

• The distribution we assume
• The data window we choose
• The time horizon that matches our exposure

 

VaR is often presented as a clean, objective number. It is not. It is a model-driven estimate, and shaped by assumptions. For large exposures like a $216 million tanker—those assumptions can shift the estimate of extreme losses by tens of millions of dollars. That is not a rounding error, it is modeling risk.

 

That is the difference between being prepared… and being surprised.

 

Note. VaR formally includes expected return (the mean). In practice, especially over short horizons (daily), the mean is very small relative to volatility and often ignored. Over longer horizons (months or more), the mean becomes more relevant.