# Four plots of the S&P 500

## Jul 15, 2018 · 374 words · 2 minutes read

These are just a few quick exploratory plots that help to convey some things about the S&P 500.

Here’s the monthly adjusted closing price of the S&P 500 from January 1950 to July 2018. The data comes from Yahoo (via Quantmod) using the `^GSPC`

symbol (side note: there are actually multiple versions of the S&P 500). The adjusted closing price is the price accounting for dividends and corporate actions, like rights offerings. For the monthly values I’m using the values from first trading day of each month. So the adjusted closing price for January 1950 is $16.66, the value from January 3rd which was the first trading day of the month.

The market goes up (except when it goes down). At least that’s the basic trend.

It’s maybe not particularly useful to look at the price over such a long time horizon on this scale - log scale would probably be better. This is because there doesn’t look like there was a lot of change from 1950 to at least the 1980s and then suddenly there is massive growth (and the 2001 and 2008 recessions).

Here’s the same graph but using a log base 2 scale.

Now the trend looks almost linear! (The operative word of course is *almost*.) That is of course because the S&P 500 price has grown exponentially. Log scales can be a little difficult to interpret sometimes. But log base 2 has a nice feature - a 2x change in the price corresponds to a 1 unit change in the log price.

Another way to look at the S&P 500 is to calculate the monthly percent change - the percent increase or decrease from the previous month.

The monthly percent change is centered near zero. Most changes are within 5% of the previous month. The decreases can be more extreme than increases (as shown by the y-axis) but we also know the market generally goes up (except of course when it goes down).

This last plot shows the distribution of monthly percent changes.

Again we can see the distribution is centered near zero but also skewed positive. The median is actually pretty close to 1%. There is a fair amount of variation but large changes, like ±10%, are pretty rare.