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. It is a part of a larger framework for making forecasts about market expectations.

The model states that:

Expected Returns= Div₁ /P₀ + i + g - ΔS + Δ (P/E)^[1]

Div₁ = dividend in next period (period 1 assuming current t=0)
P₀ = current price (price at time 0)
i= expected inflation rate
g= real growth rate in earnings (note that by adding real growth and inflation, this is basically identical to just adding nominal growth)
ΔS= changes in shares outstanding (i.e. increases in shares outstanding decrease expected returns)
Δ(P/E)= 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).

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