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 / (R

_{f}x (1+RPF) – (R

_{f}– 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
- R
_{f }= 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 | -21% |

Change Due to Earnings | 6% |

Total Change in Predicted | -15% |

Actual Change in Index (9/28/10 - 2/11/11) | 16% |

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