# How to Calculate S&P Monthly Average Closing Price?

When I look at monthly S&P 500 prices at a site such as Multpl, they state "all prices are monthly average closing prices." e.g. https://www.multpl.com/s-p-500-historical-prices/table/by-month

How does one calculate this "monthly average closing price?"

For example, they report 3,668.10 for December 1, 2020. When I average all the closing prices for December 2020 from https://finance.yahoo.com/quote/%5EGSPC/history/, I don't get that number. When I average all the closing prices for November 2020, I don't get that number.

I see other sites citing 3,668.10 for December 2020, so it looks like there is a canonical method for calculating it.

Is "monthly average closing price" the simple average of all closing prices in the month? If so, why doesn't the reported average match when I calculate it?

MULTPL indicates that the monthly Dec 1, 2020 average is 3,668.10. If you visually scan the Yahoo data for November, most of the days had closes below 3,600 so it's impossible that a simple average of the Yahoo data could result in a MULTPL monthly average of 3,668.10.

My guess is that either the two web sites are looking at different data (not likely), the MULTPL data contains bad data (not likely) or MULTPL is using a proprietary method for calculating the average (more likely).

The only way to have a shot at figuring this out is to get your hands on the MULTPL data and compare.

• It's possible that it's a weighted average (giving prices at the end of the month more weight), but you'd have to infer the weighting method (linear, exponential, etc.) and parameters and see if it's consistent on all months. Jan 4 at 14:58
• Solving that equation could be a Herculean task if it's not a basic weighting or standard EMA. And if it is a weight or exponential MA, the provider should be disclosing that. The path of least resistance might be to just call the source of the data and see if they'll provide their method of calculation. Jan 4 at 15:05