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The Risk Premium Factor Model shows that equity prices have already factored in higher bond yields with upside based on projected earnings through 2014.

Federal Reserve actions to keep short-term rates near zero continue to artificially depress long-term yields. The RPF Model quantifies the Fed's impact and implies that holders of long-term bonds, but not equity investors, will face a significant loss once the Federal Reserve allows rates to rise to market levels.

The Risk Premium Factor Model (RPF for short) is used to determine the intrinsic value of the market and understand the implied value of the components that drive the market: earnings and long-term 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 / (Long-Term Treasury Yield x 1.48 - 0.6%)

The model shows that equity prices (SPY) move inverse to yield. In the equation, 1.48 is the Risk Premium Factor and 0.6% is the difference between long-term 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.

Using a rough estimate of normalized long-term interest rate of 4.5% (2% real plus 2.5% inflation) to adjust for the Federal Reserve's artificially depressing long-term rates by keeping short-term rates near zero, the model shows the S&P 500 is fairly valued. (If you care to read my past articles, 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 10-year Treasury is also about 4.5%.

The chart below shows how actual yield has compared to the implied yield since 1986.

When I wrote about this in May, the convergence from the bond side had not begun but is now readily apparent. The current period is unprecedented. Actual and implied have differed significantly since the start of the financial crisis, clearly showing the effectiveness of Federal Reserve actions. Today the implied fair value yield of the 10-year Treasury is 4.35% compared with the actual yield of 2.49%.

It will be very painful for holders of these bonds when the yield returns to normal levels.

The chart below illustrates how the model behaves from an equity perspective:

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 implied 4.5% 10-year 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.

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 long-term bonds is an expected loss when the Fed allows interest rates to return to market but no downside for equities unless yields rise the implied rate of 4.35%. Equity prices have already factored in higher long-term yields.

What does this mean for equities long term?

Using S&P's forward estimates for operating earnings and assuming long-term rates stay at 4.5% or less, the RPF models show considerable upside for year-end 2014.

S&P 500 Operating Earnings

Index Actual

Index Predicted

23-Oct-13

102.00

1,746

1,683

31-Dec-13

107.52

Estimated

1,774

31-Dec-14

121.46

Estimated

2,004

Of course, this is completely contingent on both earnings meeting projections and interest rates remaining 4.5% or less.

(SPY, IEF, DSTJ, PST, TBF, TBT, TLH, TLT)

Source: S&P 500 Fairly Valued At Record High With Higher Interest Rates Already Factored In

Additional disclosure: and short long-term Treasuries