FRED offers some historical time series that the Bank of England has compiled, including the series shown above that tracks the price of stock market shares. The series starts way back in 1709 with the shares of the South Sea Company and the British East India Company. Other companies have been added and subtracted as they’ve entered and left the U.K. stock market. Just glancing at the graph reveals two things: First, the series is close to zero most of the time and then explodes. Second, there are wild fluctuations in recent decades.
For both these “observations,” though, there’s a mirage at work. Don’t worry: This optical illusion is common in very long time series. But let’s clear it up. Back in the 18th century, all prices, including share prices, were much lower And when a long time series includes regular growth, recent changes are amplified while initial changes aren’t readily visible.
One way to sidestep these visual pitfalls is to use logarithms. Their big advantage is that any change you can measure on a graph, such as those mentioned above, is a change in percentages: Anywhere in the graph, one inch corresponds to the same percentage change. In this graph, the share price doesn’t look explosive at all; actually, it seems quite stable except for growth periods in the mid 19th century and second half of the 20th century. Also, the recent wild fluctuations have been tamed. (But note the blip in 1720, due to the South Sea Bubble.)
An even better way to represent the data is to remove the growth of the general price level so the growth of stock prices themselves is better captured. A tip of the hat to the Bank of England for offering a time series on the consumer price index that, remarkably, begins in 1206. By dividing share prices by this series (shown in the graph below), we can see that there are longer periods where the real share price has actually declined.
That concludes our historical data literacy lesson for today. Your homework? Convert the units in the graph below to logarithms.
How these graphs were created: For the first graph, search for “share price UK.” For the second, take the first, click on “Edit Graph,” and select units “natural logarithm.” For the third, take the first, click on “Edit Graph,” add a series by searching for “CPI UK” (selecting the one with the earliest start date), and then apply formula a/b.
Suggested by Christian Zimmermann.