Is the SP 500 Overvalued? Part I

Good Evening.

I was recently asked what is the fair value of the SP 500 and how could one value it? 

After digging into the SP 500 reported earnings for the past 5 years from here - http://us.spindices.com/indices/equity/sp-500 
I was able to correlate the TTM (trailing twelve months) GAAP Reported Earnings with the Index. As reported earnings = Income from continuing operations, also known as GAAP (Generally Accepted Accounting Principles).

Throughout the past 5 years, the SP 500 has had a positive correlation with the TTM GAAP Reported EPS. However, over the past year a divergence developed between the TTM GAAP Reported EPS (orange line) and the SP 500 (black line).

Here is the end of quarter 1) Reported TTM GAAP Earnings, 2) Closing Price of the SP 500 and 3) P/E Ratio. Highlighted you will notice that for 2011-2012, the Reported TTM GAAP EPS was between 86.50-88.54 & the SP 500 closing price by quarter was between 1253-1598.

The Reported TTM GAAP EPS for the most recent Q4'15 was 87.14 with 94.3% of the companies within the index reporting their earnings. 
So why is the SP 500 around 1940?  

If one thinks the future will be better than the present (China CAIXIN PMI missed forecasts, U.S. Services/Manufacturing PMI readings below 50, possible deflation, record low Oil prices, Shiller Housing Index declining, etc.) then perhaps it's possible to justify the 22.36 current P/E ratio. However, for most of the past 5 years, the Median P/E of the SP 500 has been ~18.  

With a P/E=18 and current EPS=87.14, the SP 500 would be ~1569. Does the index deserve to be valued this highly right now? 

Can TTM GAAP EPS rise to 105-110 (happened once in the past 5 years)? It's certainly possible, but based on weak economic readings and the Federal Reserve's rate normalization policy it appears very unlikely. Can the SP 500 rise to 2100+? If QE4 is enacted, yes, it's possible asset prices may once again divorce from reality.

Further, even with threats of QE4 and NIRP, what policymakers fail to recognize is that Monetary Policy is simply an illusion. Asset prices such as housing and equities were inflated as the money supply expanded, and a few lucky ones felt the positive wealth effect.

However, there must be organic economic fundamentals to support inflated asset prices once the monetary policy accommodation is removed. As the Federal Reserve attempts to normalize monetary policy, assets must reprice. Did the Federal Reserve leave rates low for too long? Did they enable malinvestment? Many signs point to yes. Will these opinions become facts? Time will tell. Based on the weak GAAP EPS readings today, the SP 500 appears to be overvalued.

Here is a chart of the SP 500 juxtaposed with the blue line (P/E=20) and the red line (P/E=15). Sometime in early 2015, the SP 500 surpassed the blue line and the index valuation became stretched. With earnings declining, does the current price of the index belong here? You decide.

Caveat Emptor.