**Calculating S&P 500 10-Yr Expected Annualized Equity Risk Premium (ERP) over 10-Year US Treasury Bonds**

**Four Key Premises:**

(1) The expected S&P 500 ERP over 10-Year Treasury Bonds is more important and relevant to a long-term investor than the expected ERP over 3-Month T-Bills.

(2) Because earnings are so volatile and cyclical from year to year, PE10 is more important and relevant to long-term investors than PE1 or any PE based on expected earnings. (Definition of PE10 from Wikipedia: "The cyclically adjusted price-to-earnings ratio, commonly known as CAPE or Shiller P/E, is a valuation measure usually applied to broad equity markets. It is defined as price divided by the average of ten years of earnings (Moving average), adjusted for inflation.")

(3)

(4) Real yield on 10-year TIPS = Expected real yield on 10-year treasury bonds = Expected annualized real return on 10-year treasury bondsUPenn Professor Jeremy Siegel wrote:...the earnings of a firm is based on real assets whose value will, over time, increase with the rate of inflation. Therefore the earnings yield is a real yield.

The historical data confirm this contention. In the United States, data of corporate profits go back to 1870 and the average P-E ratio during that period [from 1870 to April 2007] has been 14.4, leading to an average earnings yield of 6.9%. This is one-tenth percentage point above the average real return on equities, which is 6.8% over the period. [Source: https://web.archive.org/web/20080123071 ... vest/30733 ]

**The Variables:**

(A) Expected annualized real return on the S&P 500 (including dividends) over the next 10 years = Expected yearly earnings yield on S&P 500 = Inverse of PE10 = 3.9% currently (source: http://www.multpl.com/shiller-pe/ ).

(B) Real yield on 10-year TIPS = Expected annualized real return on 10-year treasury bonds = 0.6% currently (source: http://www.bloomberg.com/markets/rates- ... -bonds/us/ ).

**The Calculation:**

(A) - (B) =

**3.3%**= S&P 500 10-Yr Expected Annualized ERP over 10-Year Treasury Bonds.

**Historical Perspective:**

From 1928-2013 the annualized ERP for the S&P500 vs. 10-year treasury bonds has been 4.62%, whereas from 1962-2013 the annualized ERP for the S&P500 vs. 10-year treasury bonds was 3.33% (source: http://pages.stern.nyu.edu/~adamodar/Ne ... stret.html ). Best, Neil