# Finance: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:

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

Where

- [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).

## References[edit]

- ↑ Richard Grinold and Kenneth Kroner, "The Equity Risk Premium,"
*Investment Insights*(Barclays Global Investors, July 2002). - ↑ 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.

*https://en.wikipedia.org/wiki/Grinold and Kroner Model was the original source. Read more*.