This article posits that at the current price to book value of the S&P 500 (INDEXSP:.INX), Mr. Market is taking an optimistic view based on fundamentals. We support our thesis by reverse engineering the P/BV for the S&P 500 (INDEXSP:.INX) based on current and historical values for the market ROE, as well as other market fundamentals.

In 1977, Warren Buffett presented his “How inflation swindles the equity investor” article in Fortune that presented data regarding the stickiness of the return on equity at 12 % for the market during the post war period through the mid 1970’s. Mr. Buffett indicated that this 12 % threshold could be pierced through items such as cheaper leverage, lower income taxes, or wider operating margins. Reviewing S&P 500 (INDEXSP:.INX) data since the turn of this century, income taxes are lower than during the period studied by Mr. Buffett; leverage, particularly post financial crisis, is cheaper that at any point in the last 50 years (as a proxy, the median t bond rate from 1962 to 1975 was 5.8%, versus 4.1 % from 2000 through 2013; source Yahoo), while SP500 profit margins are well above average (see the attached article by Hussman, also note that Q1, 2013 S&P 500 (INDEXSP:.INX) net margin at 9.5%, source Howard Silverblatt).

The tailwinds described above, amongst others, have likely served as tools to pierce the 12% return on equity ceiling identified by Mr. Buffett for the SP500, since the median trailing twelve month (TTM) return of equity for the S&P 500 (INDEXSP:.INX) from 2000 to 2013, measured at 14.4 %. We should also note that the median TTM P/BV for SP500 during the same period was 2.7, while the median S&P 500 (INDEXSP:.INX) TTM net margin was 7.3 % (raw data courtesy of Howard Silverblatt).

### Is the S&P 500 fairly valued today?

At the current price of 1650, the S&P 500 (INDEXSP:.INX) P/BV is 2.4, with a risk free rate, as of 10/9/13 of 2.6%. We ask the question: is the S&P 500 (INDEXSP:.INX) fairly valued today?

To answer this question, we conduct a fundamental relative valuation analysis, as follows:

As shown by NYU’s Professor Damodaran,

P/BV = (ROE – g)/(r-g)

where: ROE= return on equity; g= growth; r= discount rate

The formula above holds as we value the S&P 500 (INDEXSP:.INX), since it is reasonable to assume that the SP500 is in stable growth. Reviewing the formula, as ROE increases, P/BV increases. Also, the higher the discount rate (interest rate), the lower the PBV should be.

Understanding that in the long run the market’s growth rate converges with the risk free rate, let’s assume today’s 10 year US treasury bond of 2.6% as the growth rate for the market in the long run. Regarding risk, let’s assume adding the risk free rate to the the current S&P 500 (INDEXSP:.INX) implied equity risk premium (ERP) of 5.8% (note the increase in the ERP since October 1, 2013, since the market is pricing the S&P 500 (INDEXSP:.INX) 40 points lower) provides a proxy for the discount rate for the market. We should note that the equity risk premium is the return that Mr. Market demands for investing in stocks, above and beyond the risk free rate.

### Mr. Market is being optimistic as it prices the S&P 500 circa 1650

If we assume that the median ROE for the S&P 500 (INDEXSP:.INX) during this century will remain at 14.4% over the long term, inserting the assumptions shown above into our equation, the P/BV for the market today should be priced around 2. As mentioned above, the current P/BV for the S&P 500 (INDEXSP:.INX) is approximately 2.4. Furthermore, recognizing that interest rates for the market are at historic lows after the financial crisis of 2008, and the median return on equity for the market this century has remained high relative to post World War II standards, we are concerned that reversion to the mean (generally works like gravity for markets) could represent further headwinds. As such, we conclude that Mr. Market is being optimistic as it prices the S&P 500 (INDEXSP:.INX) circa 1650. Buyers beware, particularly should headwinds appear.

*By Pedro Zuloaga*

Pedro is a self taught intrinsic value investor that has benefited from the extraordinary generosity of his finance mentors Aswath Damodaran and Whitney Tilson, as well as the teachings of Buffett, Munger, Greenwald, Pabrai, Greenblatt, Muhlenkamp, Dalio, Gross, Rodriguez, Berkowitz, Klarman, Ackman, Athanassakos, Kahneman, and Whitman, amongst many others. He writes with the intent to educate and try give back a tiny amount of what he has received.

*Note: this article is for educational purposes only*