Finance:Grinold and Kroner Model

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The Grinold and Kroner Model is used to calculate expected returns for a stock, stock index or the market as whole. It is a part of a larger framework for making forecasts about market expectations.

The model states that:

[math] \mathbb{E}[R] = \frac{\mathrm{Div}_1}{P_0} + i + g - \Delta S + \Delta (P/E) [/math][1]


  • [math] \mathbb{E}[R] [/math] are the expected returns
  • [math]\mathrm{Div}_1[/math] is the dividend in next period (period 1 assuming current t=0)
  • [math]P_0[/math] is the current price (price at time 0)
  • [math]i[/math] is the expected inflation rate
  • [math]g[/math] is the real growth rate in earnings (note that by adding real growth and inflation, this is basically identical to just adding nominal growth)
  • [math] \Delta S [/math] is the changes in shares outstanding (i.e. increases in shares outstanding decrease expected returns)
  • [math] \Delta (P/E) [/math] 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 Fed Model. Under the Fed model, the earnings yield is compared to the 10-year treasury bonds. If the earnings yield is lower than that of the bonds, the investor would shift their money into the less risky T-bonds.

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%.[2] 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).


  1. Richard Grinold and Kenneth Kroner, "The Equity Risk Premium," Investment Insights (Barclays Global Investors, July 2002).
  2. Richard Grinold, Kenneth Kroner, and Laurence Siegel, "A Supply Model of the Equity Premium," in B. Hammond, M. Leibowitz, and L. Siegel, eds., Rethinking the Equity Risk Premium, Charlottesville, VA: Research Foundation of CFA Institute, 2011. and Kroner Model was the original source. Read more.