Petrol Price Exploration

Introduction

With the petrol price coming down so rapidly recently I decided to have a look and see what correlation there is between the crude oil price and the price of a litre of petrol sold at a garage.

I'm sure this sort of analysis has come up quite a lot recently. It's certainly nothing new but I thought it would be interesting nonetheless.

The first thing to do is to get hold of the necessary data:

1. Petrol prices - ONS
2. Brent crude oil prices - US Energy Information Administration
3. Dollar to Pound conversion rates - Bank of England

The petrol prices are an average of pump prices collected from four oil companies and two supermarkets on the Monday of each week. The data goes back to 2003.

The Brent crude spot prices are a daily series although there are gaps in the series for holidays etc. The data goes back to 1987.

The dollar to pound conversion rate is again a daily series and again there are gaps on the holidays. The gaps are similar to the gaps found in the Brent crude prices but are not always the same - different country, different holidays.

It's interesting to note that the drop in price in 2008 was much larger than the recent drop. The two series are show similar trends but they're not currently directly comparable. Let's see if we can improve on that.

Manipulation

First we need to convert the Brent crude prices to pounds per barrel. For this we use the Bank of England conversion rate data.

Next we take only the Brent crude prices from the Monday of each week so that we are comparing prices on the same day of each week.

For both of these data series I had to interpolate some data points for holes in the series. This was done using the SplineInterpolate macro from the SurveyScience excel add-in. There's no particular reason to use this over a straight line interpolation. I just thought I would.

The fourth adjustment to the data was to the pump prices of petrol. I removed the taxes. There are two taxes added - a duty and VAT. I've assumed here that duty is added first and then VAT.

The result is below:

As you can see, the correlation is remarkably good. Some of this apparent correlation is due to the way Excel has chosen the scales but it still looks good.

I did also try a smoothing algorithm on the data but I think it hides too much of the detail for the analysis.

Correlation

So taking the data from the beginning of 2011, there appears to be a fairly stable set of prices. Let's see if how much time lag there is between crude oil price and pump prices.

To do this, I've taken the prices and calculated the correlation for the two original series and then calculated the correlation for the two series when the pump prices are shifted back by a number of weeks.

We get the following two charts:

The first chart shows the data when shifted back by -14 to +14 weeks. The second chart shows the peak in more detail with interpolated points (spline).

This shows that pump prices follow crude oil prices most closely 2 weeks and 5 days later i.e. there is a lag of 2 weeks and 5 days.

Accounting for this lag, let's plot the two series against each other:

The plot looks indicative of a strong relationship between the two prices. However note that there are very few points towards the bottom left. This is the recent drop in prices. Taking these out we get:

Still a strong relationship but the R squared value has dropped from 0.9 to 0.64. So you can predict the price given the crude oil price but you will be off by quite a bit a lot of the time. Much of this is due to the volatility of the crude oil prices compared to the pump price as the plot below shows. It is a plot of the two series accounting for the lag:

Further Analysis

One of the questions often raised is whether the price at the pump rises quickly on a rise in crude oil but drops slowly when crude oil prices decline.

There are two related ways to look at this:

• Are the peaks in the two series closer together than the troughs,
• Are the positive gradients of the pump prices more steep than the negative gradients.

Unfortunately I'm going to have to leave that for another time. Until then.