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Where can I find the most accurate closing and opening prices for the S&P500 and other major indices?

I have been reading in a book called Machine Learning (author Ernest Chan) that many places are using "consolidated closing prices" at the end of the day which distorts the closing price.

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    $\begingroup$ The only way to get an accurate, tradeable, S&P500 open price is to use futures. $\endgroup$ – noob2 Feb 27 '17 at 17:40
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Tldr: Any broker can give you after-hours trading, but consolidated data probably works fine.

This is actually something of a tricky question - it's often not clear when a data provider is using consolidated data, and what the actual "closing price" is tends to vary between exchanges, and it's also unlikely to matter.

From an SEC webpage:

A number of markets offer after-hours trading trading and some financial publications and market data vendors use the last trade in these after-hours markets as the closing price for the day. Others use the 4:00 p.m. price as the closing price and display prices for after-hours trading separately.

They go on to mention consolidated information:

To avoid confusion, the central distributor of transaction prices for exchange-traded securities - the Consolidated Tape Association - implemented a system designed to make closing prices uniform. Under this system, the regular session closing price for stocks is the 4:00 p.m. price.

It's really up to you as to what you want your closing price to be, but the consolidated close price makes all close prices across every exchange comparable which, often times, may be more important, and it's unlikely that any variance caused by after-hours trading will skew your trading significantly.

The SEC also states that the NASDAQ close price uses similar rules to the consolidated tape close price, so it stands to reason that any close price from the NASDAQ is an "accurate" close price.

I think the most important thing to do is to define why you want unconsolidated tape data. I would be interesting in seeing specifically what Dr. Chan says about consolidated tape data, because it strikes me as odd - there are a million reasons I can think of to simply use the consolidated close price over trying to work out what the "real" close price is.

So this is not really a simple question, because the concept of a close price, if you reject the consolidated price, is highly malleable. Is it:

  1. The last trade of the trading day (4pm)?
  2. The last trade of the calendar day (midnight)?
  3. The last trade processed in the market (because this may differ)?

I also performed a brief search of academic literature on this topic, and I didn't turn anything up on close price and the consolidated tape or close price in

If you are still interested in getting all information on the close price, any data provider like Interactive Brokers should be able to provide you with after-market data you can use to cherry-pick the closing price that works best for your analyses.

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