Grinold and Kroner Model

The Grinold and Kroner Model is used to calculate expected returns for a stock, stock index or the market as whole.

Description
The model states that:

$$ \mathbb{E}[R] = \frac{\mathrm{Div}_1}{P_0} + i + g  - \Delta S  + \Delta (P/E) $$

Where $$ \mathbb{E}[R] $$ are the expected returns
 * $$\mathrm{Div}_1$$ is the dividend in next period (period 1 assuming current t=0)
 * $$P_0$$ is the current price (price at time 0)
 * $$i$$ is the expected inflation rate
 * $$g$$ is the real growth rate in earnings (note that by adding real growth and inflation, this is basically identical to just adding nominal growth)
 * $$ \Delta S $$ is the changes in shares outstanding (i.e. increases in shares outstanding decrease expected returns)
 * $$ \Delta (P/E) $$ is the changes in P/E ratio (positive relationship between changes in P/e and expected returns)

One offshoot of this discounted cash flow analysis is the disputed Fed model, which compares the earnings yield to the nominal 10-year Treasury bond yield.

Grinold, Kroner, and Siegel (2011) estimated the inputs to the Grinold and Kroner model and arrived at a then-current equity risk premium estimate between 3.5% and 4%. The equity risk premium is the difference between the expected total return on a capitalization-weighted stock market index and the yield on a riskless government bond (in this case one with 10 years to maturity).