Jeff Miller asked the question, "Why does a Shiller disciple care about profit margins?" David Merkel answered it in the same vein I would, by saying they expect mean reversion, but margins are unlikely to fully revert to the mean. The question may be asked in a different form: Where do Shiller's disciples go wrong?

**The Basic Argument**

Shiller developed the Cyclically Adjusted P/E, or CAPE, which uses 10 year average EPS as the E in P/E. His book "Irrational Exuberance" applied the concept to the S&P 500 (NYSEARCA:SPY), and CAPE is usually used to refer to the P/E on that index, computed on the basis of 10 year average earnings.

Noting that CAPE currently stands at 20.87, the typical Shiller disciple remarks that the historical average since 1871 is 16.42, and declares that stocks are overvalued. Unless one buys at or below the long-term average CAPE, one has no reason invest. As of this moment, 1,005 would be a buy point on the S&P 500, by that line of thinking. Perhaps this typical Shillerite is a straw-man. I don't think so. Many fundamentalists take exactly this approach.

Where this goes wrong is that it refuses to think intelligently about risk, reward and growth. Before proceeding further, it's important to have the thought tools available to relate P/E to growth.

**Ben Graham's Formula updated**

Graham, when asked to explain what an investor should be willing to pay for growth, offered a formula: P/E = 8 +(2 X Growth). That is, if growth is 5%, the proper PE by his formula would be 8 + (2 X 5) = 18.

David Merkel did some good work on the question, using a linear regression on current data to develop the following version:

P/E = 11.7 +(0.7 X Growth)

By Merkel's formula, 5% growth would call for a PE of 15.2; 7% would call for 16.6. These values are very close to the 15 and 17 I've used as a rule of thumb for many years, based on my own experience of what works.

It's not realistic to project growth more than 5 years in advance. In an effort to quantify the value of growth, I took the present value of 5 years projected additional earnings, plus a residual for maintaining the increased level of earnings indefinitely into the future, and discounted at various rates.

Discounting future earnings increases at 6.7%, I arrived at Merkel's 0.7X. In order to match Graham's 2X, I discounted at 2%. I think Graham offered the advice he gave as a way of focusing on the importance of growth. If you're not growing, you're shrinking. In any event, I like Merkel's approach, and I use it for the remainder of this article.

That leaves the question, what return should an investor require for the no growth portion of this equation? Graham's 8X inverts to 12.5%. 11.7X inverts to 8.5%. What is the proper return on Shiller's E10 (10 year average inflation adjusted earnings for the S&P 500), before considering growth?

**Rate of Return vs. Risk**

The point of using a 10 year average is to compensate for the business cycle, since it is normal to experience a recession at some point during a period that long. When considering the aggregate performance of 500 stocks over a 10 year period, almost all risks are already averaged into the computation. Companies going bankrupt, management incompetence, inflation, deflation, obsolescence, financial crises, etc. are already in the mix.

Comparing the current E10 to TTM earnings is instructive. E10 is 62.53, while TTM earnings were 89.72 as of 12/31/2012. The difference quantifies all historically known risks to earnings.

The one risk that isn't included is market volatility and its effect on share prices. What risk premium would a prudent investor need to cover volatility? To some extent, that depends on his time frame. If it is as long as 10 years, he can reasonably expect that prices will be above average at some point during that decade.

In any event, the 10 year treasury yields 1.7%. Subtracting 2% for inflation, I get a real risk-free rate of return of -0.3%. Subtracting that from a 5% risk premium, I arrive at a desired real rate of return of 4.7%, to be applied to Shiller's E10, and then augmented by a provision for expected growth, along the lines discussed above. I round 4.7% up to 5%.

**A Graham Formula for CAPE**

Without further ado:

CAPE = 20 + (0.7 X Growth)

I can hear the purists screaming in indignation. Postulating 4% real growth, I get a CAPE of 22.8. From there, $62.53 (E10) X 22.8 (NYSEARCA:CAPE) = 1,425 for the S&P 500, as of today.

**Risk Aversion and the Fed Model**

Analysis has shown that when treasury rates are low (usually during times of financial stress), investors prefer the safety of bonds, creating a risk premium for equities. When treasury rates are high, over 5% from the modern perspective, investors prefer equities, and the risk premium frequently goes negative.

I published an article on the topic, here on Seeking Alpha. In it, I developed a formula for E/P10 (CAPE inverted), which fit the data available then. Expected future growth is the missing dimension in that study. Briefly, that study suggests that the risk premium is likely to go negative if and when treasury rates increase toward more normal levels.

As clarity on the numerous issues facing the markets emerges, favorable resolutions-- in the context of historically low interest rates-- would create considerable potential for multiple expansion in the event that the risk premium is reduced or actually reverses. When fear subsides, rational thinking will cut in, and the Fed model will become operative.

**Growth**

What will E10 be a year from now? Assuming the coming year has earnings of $90, equal to the TTM, an approximation would be (($62.53 x 9) +$90)/10. This assumes an average year drops off the back of the 10 year rolling computation, to be replaced by a $90 year, increasing E10 to $65.28. From $62.53 to $65.28 amounts to growth of 4.4%.

So, at the end of 2012, $65.28 X 23.08 = 1,506 for the S&P 500. Bad things happen sometimes, in which case new estimates will be needed.

**A Longer Term View**

Here's a chart of 10 year average real returns as a function of CAPE, using data from 1957 to 2002. It ends at 2002 because of the 10 year look forward to determine the real rate of return. The return is calculated by considering the beginning and ending real index level and the accumulated dividends.

The linear regression formula provides a tool for predicting future returns. Plugging the current CAPE of 20.87 into formula, an investor could realistically expect a 10 year real rate of return of 3.98%. That could be compared to the -0.3% real return on 10 year treasuries, or the approximate 3% real rate of return on Moody's Baa bonds.

A similar exercise, conducted using Shiller's data back to 1871, predicts a 10 year real rate of return of 3.25%, investing at today's prices. Using data from 1987 forward, 10 year real returns would be 7.86%. That would require that the risk premium go negative, entirely possible if economic catastrophe is avoided and interest rates remain low.

**Investment Implications**

The biggest criticism of the simplistic use of CAPE is that it keeps you out of the market almost all the time. After bypassing the 1990's huge run, a 16.42 CAPE would have had the investor finally entering the market in October 2008 and exiting in September 2009 with no gains. Admittedly, looking at CAPE's over 40 in late 1999, a classic Shillerite would have been far away. But you have to get back in sometime, or find an alternative to equity investing.

Shiller didn't intend the CAPE concept as a market timer. It's about assessing the long-term investment outlook. Any logical approach of the type discussed in this article is extremely sensitive to assumptions with regard to long time frames. 1% a year is a lot over 10 years, whether it is about growth or return requirements.

About 4% real rate of return on S&P 500 constituents looks good compared to the alternatives available in fixed income securities of comparable quality, particularly when interest rate and inflation risk are considered.

I don't want to be on the sidelines if the risk premium reverses.

**A Market of Stocks**

Many stocks are trading at attractive valuations. The overall level of geopolitical and financial concerns in the markets has them moving in unison and on beta. Apprehension about overall market level has to be balanced against compelling metrics on many individual names.

**Disclosure: **I am long SPY.