## S&P 500 Fair Value: ''Have it Your Way'' Q4 2012 Update

### March 27th, 2013

### by Chris Turner

With 99% of all S&P 500 companies reporting earnings for Q4 2012, let's update the previous post Fair Value Analysis for the Fair Value table for the 4th Quarter 2012.

There are many great methods for valuing the S&P 500. Doug Short posts monthly updates of multiple valuation metrics on this site, one of which uses a common valuation popularized by Yale Professor Robert Shiller. The chart below shows the monthly average of S&P 500 closing prices divided by 10 years average earnings and adjusted for inflation based on the Consumer Price Index (CPI) and earlier pricing data for the period before 1913, when the Bureau of Labor Statistics took on the task of creating this indicator.

Professor Shiller's latest chart (as of March 21st) puts the current P/E ratio at 22.79. The Long Term Interest Rate (red line) provides general information regarding historical values. Comparing the current value of 22.79 VS the long term mean at 16.47 represents an overvaluation. However, digging into these numbers a bit provides a bit more insight toward the "currency" of the calculation.

On the far right, readers may notice that the calculation is missing some numbers. Always wanting to be accurate – a couple quick entries into his fields will correct his data below:

After entering the earnings on the highlighted line, the far right boxed CAPE 10 value of 21.23 would be the most accurate "known" valuation. The bottom number depicts the future earnings of Q1-13 and will not be known until those earnings are final. His original chart showing 22.79 is just a bit off, but since it is within 5%, perhaps that is close enough.

While Prof. Shiller uses BLS CPI to "adjust" for inflation, what may be misunderstood is that simply calculating the nominal numbers produce a very similar outcome. Consider the following chart which uses Prof. Shiller's original data but removes the long term interest rate and replaces with just the nominal Price to Earnings ratio.

Since both methods use earnings averaged over 10 years – the results clearly show that nominal and CPI adjustment possess very high correlations.

Some may find futility in trying to determine exactness out of Shiller's Product, but by simply applying some math and placing his data on steroids, his chart has more meaning.

The red line now represents the S&P 500, the Blue line does the math for you to show exactly where "fair value" should be on a monthly basis (Equivalent Fair Value). For the chart-challenged, the box provides context toward the exactness we strive to find – which would be the exact fair value number that Prof. Shiller's data warrants (the corrected data anyway).

For comparison purposes, the following chart displays the nominal calculation. The scale looks different simply because back in 1881, the S&P Composite was actually around 6 rather than the CPI adjusted S&P composite of 130.

No surprise - both show the S&P 500 would be fairly valued around 1100. With nominal data producing a number so close to the CPI-adjusted Shiller data, readers must be baffled toward why Prof. Shiller uses CPI adjustment at all (I second that opinion). However, to be fair, many other questions popped into my head, such as the magic of 10 years versus other time periods. To alleviate all my concerns and answer all my questions, I calculated the following which produces both nominal and CPI adjusted (Shiller method) for many time periods.

The table presents time periods that should suit any individual's preference. In an effort to create the ultimate "fair value" indicator, the addition of three metrics seemed warranted, a monthly PE value, the use of Earnings Yield, and some sort of "sentiment" indicator.

Combining all the indicators within the table over an aggregation of various time periods produces the Combined Fair Market Value, shown below.

Based upon the averages of earnings over many time periods, the S&P 500 index remains overvalued by about 27%. Consider this data simply as information that provides a snapshot of historical relative valuation rather than "tradable" ideas. Investors should understand that knowing a "fair value" target provides an educated backdrop for making "investments" or "trades." But as the charts and tables above illustrate, the market can remain over- and under-valued for long periods of time. The full report with all the charts is located here (http://www.scribd.com/doc/132150996/CFMV-Q4-12-Rev). We can revisit this fair value table as earnings season progresses throughout the year.

**Note** : For readers unfamiliar with the S&P Composite Index (a splice of historical data different from the S&P Composite 1500), see this article for an explanation.