Despite stocks (NYSEARCA:SPY) nearing all-time highs that are coupled with what are, in our opinion, less than favorable broad market valuations, investor caution is largely absent. Junk bonds (NYSEARCA:JNK) are yielding the lowest rates on record, credit spreads are below average, and multiples of earnings are above average on the highest profits recorded from near-peak margins. The implied volatility of stocks (NYSEARCA:VXX) is the lowest since 2007.

There are certainly good reasons for bullishness. The Federal Reserve continues to provide both an accommodative liquidity environment and interest rates near historical lows. Over the last year, housing prices have risen 8% and housing starts are up over 25%. Employment continues to grow and initial claims for unemployment insurance are the lowest since the first week of 2008. At present, there aren't many signs of an impending U.S. recession.

You read a lot in the press today that the stock market is "cheap" and that we are on the cusp of a new bull market. After all, they say, the S&P 500 is trading for "just" 14.1x 2013 operating earnings estimates of $111 per share, compared to the historical average of over 15x. While that is true, it is also as misleading. A review of P/Es is therefore warranted.

Price earnings (P/E) multiples are a shorthand method of calculating the valuation of a security or a broad market. Since the 1900s, stock indices have averaged a P/E multiple of 15. There is a lot of logic in this figure, which is often missed by market participants. The historical average P/E of 15 is more than just the average that investors have been willing to pay for a $1 of earnings over time; it is also the result of an equation of discounted cash flows.

The Gordon Growth Model is one method used to calculate the fair valuation of a security or index, assuming a certain level of earnings, a constant level of growth, and a stable required return (called the discount rate).

The Gordon Growth Model equation is:

How does this all relate to the P/E discussion above?

The P/E tells us what investors are paying for each dollar of earnings. The Gordon Growth Model can therefore be altered to determine a fair value for $1 of earnings, that is, a P/E.

Since 1926, the S&P 500 has returned an average (arithmetic) 11.26% per year while nominal earnings growth has averaged 4.60% per year. What is a fair P/E under these assumptions?

So, you can see that the historical average multiple of 15 isn't something that has arisen by chance, but rather, is the result of long-term earnings growth estimates and investors' required return.

Implicit in using a historical average P/E multiple is that the future will mirror the past. Often, it doesn't. Growth rates change as do required returns. Also, a valuation is only as good as the earnings estimates that underlie it. Now back to today's stock market valuation.

In 2007, analysts assumed the S&P 500 would earn over $115 in 2008. Ultimately, the S&P 500 posted operating earnings below $50, a staggering difference from expectations. And that's the rub -- the P/E method as used by Wall Street simply fails to adequately capture inflection points in the business cycle.

Generally speaking, the stock market never looks expensive at the peak of the business cycle. Earnings are unusually and unsustainably high and analysts expect them to continue to rise indefinitely. That's why it is imperative to think in terms of multi-year averages instead of focusing on a single year figure. Analysts will be touting a "cheap" stock market based on wildly-incorrect forward earnings estimates all the way into the next recession.

Today's forward P/E of 14.1x is below the historical P/E of 15, but it depends on earnings growing 15% in 2013 (earnings growth has been flat for three straight quarters) to both the highest level of earnings as well as the highest profit margin in history.

If a company earns 4% profit margins in a recession and 8% profit margins in a boom but averages 6.5% over a complete business cycle, would you happily pay an above average P/E multiple on earnings from an 8.0% profit margin year? Investors that own an equity index fund like the SPY, IVV, or DIA of today are doing just that.

We, on the other hand, remain invested in world-class companies trading for below average multiples on earnings estimates that do not depend on ever-rising peak profit margins.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.