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:
E [ R ] = D i v 1 P 0 + i + g − Δ S + Δ ( P / E ) {\displaystyle \mathbb {E} [R]={\frac {\mathrm {Div} _{1}}{P_{0}}}+i+g-\Delta S+\Delta (P/E)}
Where
E [ R ] {\displaystyle \mathbb {E} [R]} are the expected returns
D i v 1 {\displaystyle \mathrm {Div} _{1}} is the dividend in next period (period 1 assuming current t=0)
P 0 {\displaystyle P_{0}} is the current price (price at time 0)
i {\displaystyle i} is the expected inflation rate
g {\displaystyle 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)
Δ S {\displaystyle \Delta S} is the changes in shares outstanding (i.e. increases in shares outstanding decrease expected returns)
Δ ( P / E ) {\displaystyle \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).
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