30% Value Gap in S&P 500 Closed by Rise in Treasury Yields, Price

Includes: SPY, TLT
by: Steve Hassett

When I first wrote about the RPF Valuation Model in Seeking Alpha on September 28, 2010, I described how the S&P 500 appeared to be undervalued by about 30% based on expected 2010 earnings and current yield on 30-year Treasury bonds. The S&P 500 was at 1,142 and the 30-year Treasury was yielding 3.73%.

Since lower Treasury yields result in a higher predicted price in the model, I calculated the predicted level of the S&P 500 at 1,505 using a 4% yield to be more conservative. This still resulted in a large valuation gap, suggesting that the S&P 500 was undervalued by about 30%. I cautioned that in addition to a change in the price of the index, the gap could be closed by a changed in interest rates or earnings. The gap has closed - today at 1,329 it looks like the S&P 500 is fairly valued with an intrinsic value suggested by the RPF Model of 1,315.

How did the gap close?
The RPF Model bases predicted value on the risk free rate as measured by Treasury yields and trailing operating earnings. The formula is: P = E / (Rf x (1+RPF) – (Rf – 2%) – 2.6%), where:

  • P = Predicted Price (Value of S&P 500 Index)
  • E = Actual Earnings (Annualize operating earnings for the prior four quarters as reported by S&P). Earnings, while not ideal, are used as a proxy for cash flow and seem to work very well
  • Rf = Risk Free Rate as measured using 10 or 30 Year Treasury yields
  • RPF = Risk Premium Factor, 1.24 for 1960 – 1980; 0.90 for 1981 – 2001; and 1.48 for 2002 – present. (You can read more about the model in the link to the September 28 article above.)

Since September 28, the S&P 500 is up about 16%. Earnings are also up 5% to $83.94 and the yield on the 30-year has jumped to 4.72%. As you can see from the formula above, when Treasury yields rise, the predicted value of the S&P 500 falls. The table below summarizes the impact of each factor that caused the predicted and actual values to converge.

Change in Predicted Due to Treasury Yields


Change Due to Earnings


Total Change in Predicted


Actual Change in Index (9/28/10 - 2/11/11)


Click to enlarge

As shown above, the biggest since factor was the rise in Treasury yields that caused the predicted value of the index to fall by 21%, followed by a 15% rise in the S&P 500 Index which accounted for the remainder of the convergence.

Developing Your Own Forecast
Since the index is highly sensitive to Treasury yields and earnings, future performance is dependent these two factors. In order to develop your own set of expectations for the S&P 500 Index, you need to apply your view on these two factors to the model. You can use the formula above to calculate predicted value of the S&P 500 based on your expectations or download my RPF Value iPhone app to perform the calculation based on your own inputs.

Based on expected earnings for 2011 of $92.00, the analyst average in my December 16, 2010 article, and a Treasury yield of 4.7%, the S&P would end 2011 at about 1,441, falling to 1,353 if the 30-year rises to 5.0%. You can use the calculator to perform these and other sensitivities to develop your own view of the market.

Disclosure: I am long SPY.

Additional disclosure: Short 30 year and 10 year Treasuries