How do I derive implied ERP directly from market prices?

Question

AcadiFi · Accepted Answer

Implied ERP derivation uses a full multi-stage DCF of aggregate equity cash flows to solve for the discount rate that equates PV to current market price.

Mechanics (Damodaran's approach):

1. Aggregate current cash flow
S&P 500 buybacks + dividends in latest 12 months. For early 2026: ~$178 per index unit.

2. Forecast horizon (Stage 1)
Use bottom-up analyst estimates for 5 years:
- Year 1: 6.0% cash flow growth
- Year 2: 5.5%
- Year 3: 5.0%
- Year 4: 4.5%
- Year 5: 4.25%

3. Terminal value (Stage 2)
At end of year 5, apply growth rate = risk-free rate (4.25%) in perpetuity.

4. Equation to solve
S&P_level = Σ[CF_t / (1+ke)^t] + [TV / (1+ke)^5]

Where TV = CF_6 / (ke − g_terminal)

5. Iterate for ke
At S&P = 5,840, solve numerically. Typical solution: ke ≈ 8.8%

6. Calculate implied ERP
ERP = ke − Rf = 8.8% − 4.25% = 4.55%

Spreadsheet template:
Year | CF | PV Factor | PV
1 | 188.7 | 1/(1+ke) | 
2 | 199.1 | 1/(1+ke)^2 | 
3 | 209.0 | 1/(1+ke)^3 | 
4 | 218.4 | 1/(1+ke)^4 | 
5 | 227.7 | 1/(1+ke)^5 | 
TV | 5,260 | 1/(1+ke)^5 | 
Sum PV = 5,840 → solve for ke

Excel Goal Seek: set PV total to 5,840 by changing ke.

Refinements:
- Use earnings + buyback-adjusted cash flow (not just dividends)
- Adjust for expected changes in payout ratio
- Apply sensitivity tables around growth assumptions and terminal rate
- Strip out companies with negative earnings

Comparison to other ERP methods (as of early 2026):
- Historical arithmetic: ~7.2%
- Historical geometric: ~6.5%
- Supply-side: ~5.5-6.0%
- Implied (full DCF): ~4.5%
- Gordon simplified: ~3.0-3.5%

Why use implied ERP:
- Forward-looking
- Reflects current valuation level (auto-adjusts when market crashes or rallies)
- Consistent with internal rate of return concept

Caveats:
- Extremely sensitive to growth assumption
- Assumes Gordon-style mean-reversion in terminal period
- Can give spurious precision — report with sensitivity range

How do I derive implied ERP directly from market prices?

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