Can someone explain the Grinold–Kroner model step by step with numbers?

The Grinold–Kroner model breaks the expected return on equity into three intuitive building blocks:

E(R) = Income Return + Earnings Growth Return + Repricing Return

Or more precisely:

E(R) = (D/P − ΔS) + (i + g + Δ(P/E))

Where:

• D/P = Dividend yield
• ΔS = Expected change in shares outstanding (negative = buybacks, positive = dilution)
• i = Expected inflation
• g = Expected real earnings growth
• Δ(P/E) = Expected change in the P/E ratio (repricing)

Worked Example: Suppose you're forecasting returns for a broad US equity index:

Component	Estimate
Current dividend yield (D/P)	1.8%
Expected share buybacks (−ΔS)	+1.0%
Expected inflation (i)	2.5%
Expected real earnings growth (g)	2.0%
Expected P/E expansion Δ(P/E)	+0.5%

Calculation:

• Income return = 1.8% + 1.0% = 2.8%
• Nominal earnings growth = 2.5% + 2.0% = 4.5%
• Repricing = 0.5%
• Total expected return = 2.8% + 4.5% + 0.5% = 7.8%

Common Pitfalls:

1. Share buybacks are added, not subtracted. Buybacks reduce shares outstanding, so ΔS is negative and −ΔS is positive. This reflects that each remaining share claims a larger slice of earnings.
2. Repricing is subjective. If you believe current valuations are stretched, you might assign a negative Δ(P/E), which drags down the expected return.
3. Don't double-count inflation. Real growth (g) is already stripped of inflation, so you add inflation separately.

This model is testable in both item sets and constructed response on the CFA Level III exam. Practice decomposing different market scenarios into these three components.

For more practice with equity return models, check out our question bank for CFA Level III.