Why Long-Term Index Charts Hide Historical Volatility
Summary
The document explains why an index can look nearly flat in its early history on a chart that shows many decades of prices. As an index’s level grows, equal percentage moves represent larger absolute changes. On a linear vertical axis, earlier movements are therefore compressed and may look much smaller than comparable recent movements. The answers recommend viewing prices on a logarithmic or semi-logarithmic scale, where equal percentage changes occupy equal vertical distances.
The evidence is an illustrative comparison of the Nasdaq’s approximate level in the mid-1970s with its much higher level decades later. Other answers suggest that stock prices, adjusted for corporate actions and inflation where appropriate, can also clarify long-run comparisons. The discussion corrects the chart-reading impression; it does not present a volatility study or establish that volatility was identical across periods. A log scale makes proportional changes easier to compare, but does not by itself account for dividends, inflation, or changes in index composition.
Key ideas
- A rising index level can make earlier price changes look small on a linear chart.
- Equal percentage moves correspond to larger point changes when the index level is higher.
- A logarithmic vertical axis makes equal proportional price changes appear at equal heights.
- Chart scaling clarifies visual comparisons but does not measure or explain every source of historical volatility.
Tags
Full text
# Why was NASDAQ(or other index) not fluctuating in 70s and 80s? # Why was NASDAQ(or other index) not fluctuating in 70s and 80s? Today I have a search of historical NASDAQ back to 70s and noticed the index was slightly increasing in 70s-early 90s and rising up and down in recent decade of years. Why would that happen? The only reason I can think of is there isn't much computer trading involved so the market wasn't crazy like today? How do you think ## Answer by QPG (score 12, accepted) https://quant.stackexchange.com/a/10563 The volatility in the indices long ago was similar in magnitude to what it is today. The problem you are seeing in your plots is one of compounding and scaling. Think of it this way- back in the mid 70's the magnitude of NASDAQ pricing was around \$100. Today it is on the order of \$4000, a change of 40x. In linear terms, a 1% change in the index today (\$40) would have been a 40% change in the index back in 1975. This goes the other way as well, so on a linear y-axis plot, a moderate swing in value in 1975 (say 1%, or \$1.00) is indistinguishable in 2014 terms. There is a way to see the relative volatility over the years in a plot, and that is to use a logarithmic y-axis. I see you are using google's charting app. Under the chart there is a "settings" button. Click it, and select "logarithmic vertical axis." It makes a big difference. ## Answer by not.so.quanty (score 1) https://quant.stackexchange.com/a/10596 Always use a semi-logarithmic scale when looking at prices. It makes percentage moves of equal heights on your graphs. ## Answer by PabTorre (score 0) https://quant.stackexchange.com/a/10608 try to get a chart with prices for stocks that are not adjusted for dividends and splits, (from quandl, or yahoo) and you will see that the stocks were moving just like they do today, and even more since they didn't trade in decimals. ## Answer by Peter Summersett (score 0) https://quant.stackexchange.com/a/27824 I plotted my own long term stock market price chart, nearly half a century ago, using semi-logarithmic scale and adjusting for inflation. So, I figure that now people are half a century late, in figuring out the obvious. But, at least people are starting to ask questions. ## Answer by Peter Summersett (score 0) https://quant.stackexchange.com/a/27825 Here is the logic: Think of your investment as doubling and doubling again, and doubling again, rather than as going up a thousand, and then another thousand, and then another thousand. In other words, everything about investing is proportional, and that is EXACTLY what semi-logarithmic chart is.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.