Below is a chart of just that going back to 1950 and the corresponding 60 year average.

Step 2) Take that 60 year average (8.2184%) to normalize the first year of your 'Fair Value S&P 500' "FV" Index by taking nominal GDP at the starting date (in this case June 1950 = $284.5 billion) and multiplying by the percent (x 8.2184% = 23.83). In this case 23.83 = the FV Index level.
Step 3) Using that 23.83 (or calculated value using a different time frame) as the FV Index starting value, at each interval increase the index by the change in nominal GDP (note... in the chart below, I estimated the S&P value for Q2 end at today's closing level and Q2 GDP at 4.0% annualized). Why nominal GDP? Go here.
The below chart shows this FV Index against the actual S&P 500 index.

Step 4) Calculate the percent the S&P 500 Index is over or under valued relative to the FV Index.

Proof....

Note 1: under this methodology, the S&P 500 is currently slightly below fair value
Note 2: a change in the starting value of the FV Index would simply shift the x-axis to the right or left (i.e. it would not change the relationship between the two)
Source: Irrational Exuberance
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