The idea behind this indicator, popularized by money manager Don Hays and existing with many variations, is that emotional trading takes place at the beginning of the trading day (as traders react to overnight news event and economic releases) while the "smart money" takes the day to evaluate and price action input their orders before the market closes ... Due to that assumed tendency, we want to bet against the opening action and bet with the closing action.

 
The site TradersNarrative.com (or here as a PDF document doc.1443) also states that this index has been popularized by the American analyst Don Hays. Here is their explanation of the basis for this indicator:

The theory behind such a comparison is that the market participants vary in these two time periods. Since the retail crowd usually reacts to prices after the day's close, their trades are processed during the first hour of the next day. And since the professional traders watch the whole day unfold, they are the ones that take, or barrier, positions overnight, depending on the risk exposure they desire.... So by comparing what these two disparate groups are doing, we can attempt to gain some insight into where the market may be headed. For example, if over a period of time the fans are buying while the professionals are selling, this indicator will fall showing that distribution is taking place. Which is what we saw well before the infamous 1987 market crash. ...

For more on the origin of the indicator, read the Barrons interview of Don Hays on the Wallstreetcourier.com site (or here as a PDF document doc.1444). See also the site of Don Hays and the TechnicalAnalysis site .

The smart money indicator: market timing for the brave-hearted
 
The smart money indicator is not so much a technical indicator of the best time of day to trade, but rather a predictive tool used by traders to try to predict future price movements. Let’s look at  this indicator in more detail.

Without sharing its general approach to investing, a site that we find interesting is Minyanville .On this site we found an article (see also here as a PDF document doc.1446) by Greg Collins describing the smart money indicator, which it calculates by taking price changes for the last hour (which under this indicator is assumed to be by professionals) and subtracting the price changes of the first hour (which under this indicator is assumed to be by amateurs).

The 'Last Hour' is one of our favorite long-term timing indicators. It's calculated using the following formula ...
(today's close - today's 3:00 pm price) - (today's price 10:30 am --
yesterday's close.)

A positive number indicates the Dow's final hour outperformed the first
hour, while a negative number indicates the final hour was weaker than
the first hour.... The daily readings are plotted on a cumulative basis in order to display the underlying trend of vs. last hour- first hour performance. The idea behind the Last Hour is that the 'smart money' is most heavily involved during the last hour of the trading day, while the crowd is most heavily involved during the first hour of the day. By comparing the performance of the market during the first and last hours, we gain insight into smart money accumulation and distribution that would otherwise go unnoticed. ... The key point to keep in mind regarding the Last Hour is that it's a true lead indicator, Declining well in advance of sell offs in the market and rising well in advance of market rallies.

The site TradersNarrative.com (see also here as a PDF document doc.1443) gives its own formula for doing the above calculation:

The way we calculate the index is to subtract the performance of the S & P 500 cash index during the first half hour of trading and add to the performance of the S & P during the last hour.
For example, let's say the Smart Money Index closed yesterday at 800. During the first 1 / 2 hour of today's trading, the S & P 500 gained a total of 5 points. We then know what happens until the last hour of trading. Now suppose that during the final hour, the S & P lost 8 points. To get today's Smart Money Index reading, we take yesterday's number (800), subtract the opening gain or loss (5 points) and add the last hour exchange (minus 8 points). So today's SMI would be 800 to 5 - 8 = 800 to 13 = 787. Today's SMI would be 787. The following chart shows exactly the kind of action that would be very bearish ... Considered a market opening strongly, only to fade (fall) near the close.... Unlike most of our indicators, there are no hard-and-fast rules to go by with the SMI. There are no absolute or relative levels we can point to and say "yep, this is bullish." Instead, we need to look at the action in the SMI - when it is rising rapidly during a decline, that means the smart money is buying, and we should expect a bottom soon. Conversely, a rapidly falling SMI during an uptrend would tell us that the smart money is selling into rising prices, and a market decline is Likely ahead.

  See also the site Meta-formula.com (or here as a PDF document doc.1447).