Oil Price Fluctuations:   Understanding Price Changes Statistically

Oil drives the world. The Fortune® Global 500 lists seven oil related firms as the top ten revenue generators. The other three companies, Toyota®, ING®, and Wal-Mart® are also deeply influenced by oil prices.

Clearly critical to economic stability, oil price fluctuations govern world priorities. Figure 1 plots oil price vs. time (inflation adjusted to 2010 USD).

Figure 1. Spot West Texas Intermediate (WTI) oil price (free on board - FOB) vs. time. The gold curve plots daily spot price, while the blue curve plots monthly prices. All values adjusted to 2010 USD.

Far from stable, oil prices change drastically with time. Compare oil data to <u>population growth data</u>, which are rock-solid by comparison. Data in figure 1 have no linear trend but for a general increase if averaged over time.

So how can we make erratic data more understandable?

Look at day-to-day price changes (i.e., fluctuations). Fluctuation values vs. time are plotted in figure 2.

Figure 2. WTI price fluctuations. Red, green, and blue intervals show decreasing excursion likelihood as price fluctuation magnitude increases.

The red, green, and blue curves define fluctuation intervals. As the interval widens, the chance a fluctuation exceeds the interval decreases.

We must be careful when looking at the price change in dollar terms. As drawn in figure 2, price changes look increasingly erratic as time evolves.

Plotting asset price change relative to the asset price (ΔP/P) yields an interesting result. Percent change vs. time values are plotted in figure 3.

With price changes scaled by inflation corrected prices, the result is consistent with our expectation (fluctuations have about the same magnitude over time and the net gain grows with global growth). Prices change randomly until new information alters price systematically (e.g., supply data, demand decline data, geopolitical unrest). Randomness accounts for most price changes.

Figure 3. WTI percent change fluctuations. Note the more uniform random fluctuations with proper scaling. Red, green, and blue intervals point to decreasing shift likelihood as price fluctuation magnitude increases.

On most days, prices rattle around zero with no dramatic net change. Dramatic price shifts are considered emotional responses. Extraordinary spikes (read fear and greed) yield significant price fluctuations. As in life, the market is volatile in the short-term and trends towards sensibility later.

Noisy data are easily understood as plotted in figure 3 (percent change for each day), but a more instructive way to plot the data is binning price change data and plotting a histogram. Histograms tell us how probable or improbable we can expect a given fluctuation to be.

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