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What Is the Fair Value of the S&P? Over 20% Higher


AAA corporate bonds suggest the bull has a long way to go.

MINYANVILLE ORIGINAL In my last article What Is the Fair Value of the S&P? Ask Baa Long-Term Corporate Bonds, I presented the case that the most appropriate discount rates to use in valuing stocks were corporate bond yields. My rationale for picking corporate bonds over Treasuries was that the government can print money and corporations can't. In that article, my firm examined Baa bonds and concluded that stocks were substantially undervalued. This article will now examine the relationship between AAA long-term corporate bonds and equities to calculate a fair value estimate for the S&P.

Courtesy of the Federal Reserve Bank of St. Louis, we have monthly data for AAA and Baa corporate bonds going back to January 31, 1919. Courtesy of Robert Shiller, we have earnings yields going back to January 31, 1871. Using the oldest common starting date of January 31, 1919 for all, the historical average yield has been 5.86% for AAA bonds, 7.06% for Baa bonds, and 7.43% for stocks' earnings yield. Therefore, stocks' earnings yield has historically been 1.57% more than AAA corporate bonds yields and 0.37% more than Baa corporate bonds yields.

As of the November 30, 2012 close, AAA corporate bonds were yielding 3.58%. If you add the 1.57% historical stocks premium yield over AAA bonds, you obtain 5.15% for a fair value earnings yield. The earnings of the S&P are $87.92 per share. Therefore, the calculation of the fair value of the S&P by use of AAA corporate bonds is: 87.92 / 0.515 = 1,707.

With the S&P in the low 1400s, this indicator suggests that the S&P is substantially undervalued.

Is this indicator effective?

The all-time indicator high was 15.17% on June 30, 1949. A 266% bull market started on June 13, 1949, and it lasted for over seven years.

The post-1970s indicator high was 3.73% on September 30, 2011. From that date, stocks went up by over 30% within one year's time.

The all-time indicator low was -5.48% on September 30, 1987. Stocks fell 32.6% over the next 20 calendar days.

Let's update our Baa calculation to compare apples to apples.

As of the November 30, 2012 close, Baa corporate bonds were yielding 4.57%. If you add the 0.37% historical stocks premium yield over Baa bonds, you obtain 4.94% for a fair value earnings yield. The earnings of the S&P are $87.92 per share. Therefore, the calculation of the fair value of the S&P by use of Baa corporate bonds is: 87.92 / 0.0494 = 1,779.

It is encouraging to see two different methodologies producing such similar results.

Which method is better?

Let's test to see which methodology has been more accurate in the past. To define accuracy, we will use the average absolute value of (projected earnings yield minus actual earnings yield). The answers were startlingly similar. The average absolute value error for the AAA bonds was 3.18%; for the Baa bonds, it was 3.17%. In my previous article, I hypothesized that using Baa corporates bonds to value stocks would make more sense than using AAA corporate bonds because there are only four AAA companies. While my hypothesis was proven correct by a hair, the fact of the matter is these two methodologies are practically indistinguishable with respect to accuracy.

The AAA corporate bond indicator is suggesting that stocks still have room to go up over 20% before even hitting fair value. Quantitative easing III has only just begun. The masses incorrectly believe in the fiscal cliff myth . There has been a massive inflow of money into bond funds. All evidence suggests that the stock market hitting new all-time highs in 2013 is merely but a stepping stone on the way to the 1700s and possibly the 1800s.
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