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Federal Reserve actions to keep short-term rates near zero and purchase long-term bonds have resulted in artificially depressed long-term yields. The RPF Model quantifies the Fed's impact and implies that holders of long-term bonds will face a significant loss once the Federal Reserve allows rates to rise.

The Risk Premium Factor Model (RPF for short) is typically used to determine the intrinsic value of the market but it can also be used to 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 (NYSEARCA: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 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 (finally) 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.

(click to enlarge) 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 aimed to keep long-term rates low by keeping short-term rates near zero and buying long-term securities. Today the implied fair value yield of the 10-year Treasury is 4.41% compared with the actual yield of 1.94%.

It will be very painful for holders of these bonds when the yield returns to normal levels. Since price moves inversely to yield, the price of the 10-year Treasury would fall about 20% if yields reverted to the implied fair value yield of 4.4%.

The chart below illustrates how the model behaves from an equity perspective using normalized bond yields.

(click to enlarge)

This chart uses normalized yields on Treasuries of 4.5% (2% real plus 2.5% inflation) from August 2011, through the present. You can clearly see the several year period where the S&P 500 was significantly undervalued.

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.

Note that since the RPF Model implies an inverse relationship between bond yields and equity prices. This means that if the S&P is actually overvalued, as some contend, then the implied bond yield would actually be higher than 4.4% and the downside risk to bond holders would be greater.

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

Source: Bond Bubble: Risk Premium Factor Model Suggests Fair Value Yield On 10-Year Treasury Is 4.4%

Additional disclosure: and short long-term treasuries