Grinold and Kroner's 2002 paper decomposes an equity return into terms that can be forecast separately:
E(R_equity) = (D/P − ΔS) + (i + g) + ΔP/E
income earnings repricingD/P is the dividend yield. ΔS is the net change in shares outstanding, so a company issuing stock has a positive ΔS that subtracts from the return and a company buying back stock has a negative ΔS that adds to it. i is expected inflation and g is expected real earnings growth, so together they give nominal earnings growth. ΔP/E is the annualised percentage change in the multiple over the horizon.
Three sources, three separate arguments, and each one falsifiable on its own. The decomposition is worth its extra work for that reason alone.
Worked example: the Nifty 50 and the income term
For the Nifty 50 with a dividend yield of 1.15%, net share issuance of 0.55%, expected inflation of 4.50%, real earnings growth of 4.20% and a price-to-earnings ratio of 22.0 assumed to revert to 21.0 over five years, the repricing term is (21.0/22.0)^(1/5) − 1 = −0.9261% and the total comes to 8.3739% in rupees. All five inputs carry a September 2026 verify flag, and the P/E path is a view rather than a measurement.
The income line is where the two markets differ most and where the commonest error lives. India's income return is 1.15 − 0.55 = 0.60%, because Indian companies in aggregate issue more equity than they retire. The United States runs the other way: a gross buyback yield of 2.30% against gross issuance of 1.60%, mostly stock compensation and acquisition paper, gives a net ΔS of minus 0.70%, so the income return is 1.25 + 0.70 = 1.95% on a 1.25% dividend yield. Worked example 4 shows what happens when the gross buyback yield is used as the net figure: 7.00% instead of 5.40%, an overstatement of exactly the 1.60 points of issuance ignored.
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How does it compare with a risk-premium estimate?
Where a decomposition and a risk-premium build of the same index differ, attribute the difference rather than averaging it. A required-return route on the Indian index gives clean risk-free 4.50% + equity risk premium 5.60% = 10.10% against the decomposition's 8.3739%, a gap of 1.7261 points. Of that, 0.9261 points is the repricing term, which the required-return route does not contain because it prices risk rather than forecasting a multiple. The residual 0.80 points is a genuine disagreement about growth: the decomposition's 8.70% nominal earnings growth is top-down, while an implied premium backs out whatever growth sits in current analyst forecasts, which is higher.
Having attributed it, choose. Splitting the difference at 9.24% produces a number neither method supports and nobody can defend a component of. Taking 8.3739% and recording the disagreement produces a number with a falsification test attached: if the index P/E is at or above 22.0 in five years, the repricing view was wrong and 0.93 points of the shortfall is explained.