The Risk Premium Factor Model shows that S&P 500 is fairly valued relative to earnings and longterm interest rates. They are not in a bubble and priced for continued growth.
I have heard it say that you can't see a bubble when you are in it. The Risk Premium Factor Model can help you spot a bubble. A few days ago, Andrew Ross Sorkin on CNBC said something to the effect that it is safe to come on air and say the market is overvalued since those people look like geniuses if the market corrects. This may be true, but if you're managing money that safe approach is a recipe for disaster.
On April 9, 2011, the WSJ ran an article asking, "Is The Market Overvalued?" with arguments on both sides from David Bianco who is now chief U.S. equity strategist at Deutsche Bank AG and Yale Professor Robert Shiller who is now a Nobel Laureate. The market is up over 36% since then, so going with the safe call would have been very costly.
If you have followed my articles over the past three or so years, you might think that I am a permabull, since I've consistently said that the market is under or fairly valued. The truth is, I am looking forward to the day when I can make the bold call and say the market is overvalued. Unfortunately, today is not that day.
Determining whether the market is fairly valued is simple matter of looking at its price relative to earnings and the P/E ratio. The Risk Premium Factor (RPF for short) Model shows that the fair value P/E ratio at any point in time is determined relative to longterm interest rates and not based on a simple historical longterm average as some would argue.
Today the RPF Model shows that the S&P 500 is currently fairly valued with higher longterm bond rates already factored in. Fairly valued means that investors can expect annual equity returns of about 11%. This is a long way from a bubble.
The RPF Model is used to determine the intrinsic value of the market and understand the implied value of the components that drive the market: earnings and longterm interest rates, which drive cost of capital and embody inflation.
In short the model says that:
Intrinsic Value of the S&P 500 Index =
S&P Operating Earnings / (LongTerm Treasury Yield x 1.48  0.6%)
The model shows that equity prices (NYSEARCA:SPY) move inverse to yield. In this simplified version of equation, 1.48 is the Risk Premium Factor and 0.6% is the difference between longterm expected growth and real interest rates. I've written about the model numerous times, so rather than repeat my entire overview of the model, you can read about it in my book or on Seeking Alpha where you can find the expanded equation as well.
Using a rough estimate of normalized longterm interest rate of 4.5% (2% real plus 2.5% inflation) to adjust for the Federal Reserve's artificially depressing longterm rates by keeping shortterm rates near zero, the model shows the S&P 500 is fairly valued. (If you care to read my past articles, until recently they indicated that the S&P 500 was undervalued.)
If the market is fairly valued with a 4.5% yield, this must also imply that the fair value yield on the 10year Treasury is also about 4.5%.
The chart below shows predicted versus actual levels of the S&P 500 Index since 1986. Bubbles are indicated by periods where there is a large gap between predicted and actual levels. This also illustrates the strong historical performance of the model compared to actual continuing to revert to predicted levels.
This chart uses normalized yields on Treasuries of 4.5% (2% real plus 2.5% inflation) from August 2011 through the present. It shows the recent several year period where the S&P 500 was significantly undervalued.
Today the market is slightly overvalued based on trailing earnings and the estimated 4.5% 10year yield. Given 4.5% is a very rough estimate, I would not use it to make a granular valuation call and consider the market fairly valued today.
From both perspectives, the model tells the same story  while the market often deviates, it regresses back to predicted values. The implication for holders of longterm bonds is an expected loss when the Fed allows interest rates to return to market but no downside. Equity prices have already factored in higher longterm yields.
What does this mean for equities long term?
The model calculates expected returns (cost of equity) as LongTerm Treasury yield + Equity Risk Premium, where the Equity Risk Premium equals LongTerm Treasury yield times the Risk Premium Factor. That is, 4.5% + 4.5% x 1.48 = 11.6%. At fair value, the market can be expected to yield at total return of 11.6%.
Using S&P's forward estimates for operating earnings and assuming longterm rates stay at 4.5% or less, the RPF models show considerable upside for yearend 2014.
S&P 500 Operating Earnings 
Index Actual 
Index Predicted 

22Nov13 
102.20 
1,805 
1,686 
31Dec13 
107.20 
Estimated 
1,769 
31Dec14 
120.80 
Estimated 
1,993 
Of course, this is completely contingent on both earnings meeting projections and interest rates remaining 4.5% or less.
The model is very sensitive to interest rates. If we believed that 4% was a better estimate, the implied value of the S&P 500 would increase to 1921 today. If you want to do these calculations yourself, you can download my free iPhone or Android app from my profile page.
(SPY, IEF, DSTJ, PST, TBF, TBT, TLH, TLT)
Disclosure: I am long SPY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.
Additional disclosure: Short longterm treasuries.