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Conclusion: Based upon an analysis of the current and historical equity yields for the S&P 500 (NYSEARCA:SPY), we conclude that investors are pricing into the current S&P 500 valuation a risk premium that would protect them from a potential 30% drop in the index’s historical valuation. (See Table below)

A Simple Valuation Model: While there are many ways to value the S&P 500, its P/E is one that is preferred by investors due to its simplicity. It is the quotient of the S&P 500 index value divided by its earnings per share (“EPS”). Historically, the average S&P 500 stock index multiple, based on calendar year-end EPS, has been around 15.4 times since 1942. Therefore, with only two variables it should be easy to quantify risk based upon comparing current and historical metrics for the S&P 500 index.

Assumptions: We are using the S&P 500 2012 consensus estimate of $104.00 per share. Employing the average historical S&P 500 multiple (15.4 times), the S&P 500 should be trading around 1600. Currently, the S&P 500 is trading around 1120. So, the current year-end S&P 500 multiple is approximately 10.8 times—approximately 30% below the historical average.

As illustrated in the top portion of the matrix below, we have taken the historical S&P 500 average of 15.38 times (cell, “C:1”) and it’s estimated 2012 EPS (cell: “A:3”) and reduced each by 5% incrementally to generate relative valuations based on combinations of the two. So, the question becomes: what combination of multiple decline and/or EPS decline generates the current index valuation of 1120?

Extremes: At one extreme, investors could take the position that the S&P 500 index should trade at its historical average multiple of 15.4. The implication of this notion is that the S&P 500 EPS is anticipated to decline 30% from the current 2012 estimated $104.00 EPS to $72.80 per share (15.4 x 72.80 = 1120).

Alternatively, investors may assume the $104.00 estimate is correct, but the historical multiple of 15.4 will decline by 30% (10.8 times) to reflect investors' gloomy sentiment. The $104.00 EPS estimate and the current 10.8 times multiple will also generate an S&P 500 valuation of 1120. Of course, there are a variety combinations of multiple and EPS declines that generate the current valuation of 1120. (See top portion of table below.)

For the sake of argument, let’s assume that the S&P 500’s EPS 2012 estimate is too high at $104.00 per share. Let’s also assume that analysts reduce that estimate by 15%. In that case, estimated 2012 EPS would be $88.40 per share. If investors' uncertainty prevails and the current multiple remains constant at 10.8 times, then the S&P 500 valuation would be 952 (Cell I:6), or a decline in valuation of the same amount from its current level—15.0%.

EPS and Multiple Components of the P/E: With regards to EPS, there has been only two times since 1942 that calendar year-over-year EPS dropped more than 30%. Unfortunately, both occurred in the first decade of the 21st century (2008 and 2001). So, our memory is fresh with that magnitude of earnings disappointment. Additionally, with some pundits drawing comparison with 2008’s U.S. financial meltdown, such a reoccurrence of such a precipitous EPS decline has credibility.

The Ephemeral Multiple: While EPS is highly quantifiable, the multiple is less so as it incorporates investor sentiment. Backing into a theoretical stock market multiple, the average real return to equity since 1942 is approximately 3.5%. On average the annual increase in CPI has been 4.0% over the same period. Adding the two you would generate an average equity yield of 7.5%.

The Rubber Meets the Road: The current S&P 500 multiple is 10.8. This would generate a reciprocal implied equity yield of 9.3% (1 / 10.8 = 9.3%). The difference between the current (9.3%) and theoretical equity yield (7.5%) is 1.8%.

Assuming this 1.8% is the default premium (downside risk to the S&P 500 stock index) and the historical real equity returns is 3.5%, then the implied risk adjusted equity yield required by investors is 5.3%. This implied equity risk premium return of 1.8% is approximately 34.0% of the risk adjusted equity yield of 5.3%. (If the inflation rate is assumed to be less, then the risk premium would actually be higher.)

(Click chart to enlarge)

The Way Home: The only way to reduce the equity yield and improve the multiple is to reduce the implied equity risk premium.

The only way you can do that is through improving investor confidence through a serious effort to provide fiscal discipline and a transparent operating environment for business.

Unfortunately, this is a long-term process. However, the right initial indication by policy makers that we’re moving in this direction would be a signal welcomed by investors and may have an incremental change in sentiment.

At a 15.4 average multiple with the current 2012 estimate there is the potential of a 43.0% advance in S&P 500 index.

Yeah, for investors it’s that important.

Disclosure: I am long SDY, SPY.