“Lies, Damn Lies, and Statistics”

This article is one of those times where writing down my own thoughts really helps clarify what those thoughts are.

I distinctly remember being in my high school AP Macroeconomics class and hearing my teacher say there were three types of lies: lies, damn lies, and statistics. It’s also the title of a West Wing episode. 

The sentiment behind the statement is that statistics can be used to bolster any sort of argument. Let’s look at scenarios involving the stock market.

On any given day, if you turn on CNBC you’ll see a swirl of tickers, charts, and people talking about why stocks are up or down. Many times the reasoning is only attributed after the fact, but that’s a story for another time.

Two of the main indexes that allegedly track the health of the overall stock market are the Dow Jones Industrial Average (DJIA) and the S&P 500 Index (SPX). 

What are they, exactly?

The Dow is composed of 30 blue-chip companies that are among the largest in the U.S. The S&P 500, as the name suggests, is composed of 500 of the largest publicly-traded companies in the U.S. Right off the bat, we’re comparing the performance of 30 companies vs 500 companies. 

How are these indices measured? Good question. There are multiple ways to measure the performance of an index fund. The Dow is a price-weighted index, and the S&P 500 is a capitalization-weighted index.

Here’s the difference.

A price weighted index rises and falls based on the change in price of each stock in the index. Say we had an index of two stocks: Company A and Company B. Company A has a share price of $10, and Company B has a share price of $50. Now, we don’t know which company is bigger. That depends on the number of shares outstanding for each company.

For example, there can be 1,000 shares total for Company A, and 100 shares total for Company B. 

Regardless, if the index holds one share of each company, it’s sitting at $60. Now, let’s say Company A’s share price doubles from $10 to $20, and company B’s share price falls to $40. Notice the index is still trading at $60, it’s like nothing has changed.

However, as you can probably guess, something big did change. 

In isolation, Company A doubled its market capitalization from $10,000 (1,000 x $10/share) to $20,000. Company B, on the other hand, fell 20% (from $5,000 to $4000). This is a gross oversimplification, but the point is that the Dow gives more weight to the price of a single share of a company than other indices.

If this were the S&P 500, we’d be averaging the change in share prices given relative market capitalizations. So, if Company A went up 100% and had a market cap that was already double that of Company B, the change in index price would be positive. A significant difference than if price-weighted. 

So, if you hear something like “biggest single-day point decrease (or increase) in Dow history,” keep it in context. There are many ways to frame financial market performance.