**Quick Summary**

1. Calculate implicit inflation forecast from treasury rates

2. Look up the IMF World Economic Outlook for GDP growth

3. Examine current and historical P/E ratios

4. Find the TTM dividend yield of the S&P 500

5. Estimate long-term forecast of equity risk premium

**1. Expected Inflation (EINFL)**

In Ibbotson and Chen’s supply-side equity risk premium model, equity returns are composed from supply-side variables that describe the aggregate equity market. These supply factors include inflation, earnings, the P/E, and dividends. Expected inflation can be derived from the market by referring to the yield curve rates on nominal and real US treasury securities. The implicit inflation forecast is calculated as follows.

(When calculating expected inflation, 10-year maturities are preferred over 20- or 30-year bonds since the latter are less liquid, which means higher premiums. Inflation-protected securities, however, suffer from illiquidity themselves. That means investors might demand higher returns to hold these bonds, thereby compressing the spread between the two securities).

At the time of writing this (12/29/2015), the 10-year treasury yield curve rate was 2.32% and the 10-year treasury real yield curve rate was 0.79%. This implied the market was forecasting annual inflation at 1.52% [= (1.0232 / 1.0079) – 1].

**2. Expected Growth in Real Earnings per Share (EGREPS)**

Expected growth in earnings should approximately track *real* GDP growth. In other words, investors should not expect returns much lower or higher than that produced by companies in the real economy. A good estimate for GDP growth can be found by looking at the International Monetary Fund’s (IMF) World Economic Outlook (WEO) database (here). Select the most recently published WEO database and follow the steps of the query until you have selected the country (or countries) of interest. Since we are interested in *real* GDP growth, refer to the variable *Gross domestic product, constant prices: Percent change*. The output of the report gives a 5-year forecast (and an estimate for the current or most recent year). At the time of writing this, the 5-year arithmetic and geometric averages were both 2.50%.

**3. Expected Growth Rate in P/E Ratio (EGPE)**

Growth in P/E reflects the market’s changing predictions of future earnings growth. The expected change in P/E, therefore, should only be adjusted when an analyst believes the current P/E ratio reflects a market that is over- or undervalued. In the majority of cases, the expected growth in P/E is assumed to be zero. Online resources are available to compare the current P/E relative to historic ratios (here).

**4. Expected Income Component (EINC)**

A good source for looking up the current dividend yield is the S&P 500 Dow Jones Indices website. Click the *Additional Info* drop-down and select *S&P 500 Stock Buybacks*. The downloaded spreadsheet will have a column named *Dividend Yield* that can be referred to for this information. At the time of writing this, the most recently reported dividend yield was 2.03%. To account for the return on reinvested dividends, add an additional 0.20%.

**5. Equity Risk Premium (ERP) Forecast**

The equity risk premium can now be forecasted using the following equation (per the Ibbotson and Chen earnings model):

In their paper *Long-Run Stock Returns*, Ibbotson and Chen decomposed historical equity returns from 1926 to 2000 using the factors outlined above. Annual inflation, represented by changes in the U.S. Consumer Price Index (CPI), was 3.08%. Growth in historical real earnings of U.S. equity was 1.75%. The annual increase of the P/E was 1.25%. The average income return was 4.28%, the reinvestment return averaged 0.20%, and the real risk-free rate was 2.05% (the analysis of the paper was done in real terms). This would mean the nominal risk-free rate was equal to 5.19% [=(1 + 2.05%) x (1 + 3.08%) – 1].

**Suggested Reading**

Roger Ibbotson and Peng Chen. *Long-Run Stock Returns: Participating in the Real Economy*.

** Since Ibbotson and Chen don’t explicitly show all of their work in the above article, you might be wondering, like I was, how they calculated an equity risk premium of 5.24%. Recall that their entire analysis is done in real terms and that this is a *real* (rather than nominal) premium. The return on equity (prior to subtracting the risk-free rate) is 10.70%. The *real *equity risk premium is therefore 5.24% [= (1 + 10.70%) / (1 + 3.08%) x (1+2.05%) – 1] (difference due to rounding).