What is the forward earnings yield, and how is it used to estimate the equity risk premium in the Fed Model?

Question

AcadiFi · Accepted Answer

The forward earnings yield is simply the inverse of the forward P/E ratio. When compared to bond yields, it provides a rough gauge of equity attractiveness — though the theoretical foundations are debated.

**Definition**

Forward Earnings Yield = Forward EPS / Current Price = 1 / Forward P/E

If the S&P 500 trades at 20x forward earnings, the forward earnings yield is 5.0%.

**The Fed Model**

The so-called Fed Model (named by Ed Yardeni, not endorsed by the Federal Reserve) compares:
- **Forward earnings yield of equities** vs. **10-year Treasury yield**

| Signal | Condition |
|---|---|
| Stocks cheap | Earnings yield > Treasury yield (wide gap) |
| Stocks fair | Earnings yield ≈ Treasury yield |
| Stocks expensive | Earnings yield < Treasury yield (inverted) |

**Worked Example — Current Market Assessment:**

| Metric | Value |
|---|---|
| S&P 500 forward P/E | 19.5x |
| Forward earnings yield | 5.13% |
| 10-year Treasury yield | 4.35% |
| **Yield gap** | **+0.78%** |

The positive gap suggests stocks offer a modest premium over bonds, historically narrower than the long-run average spread of 2-3%.

**Why the Fed Model Is Problematic**

Despite its popularity, the Fed Model has serious theoretical flaws:

1. **Comparing real to nominal:** Earnings grow with inflation (real asset), but Treasury yields are nominal. During high inflation, Treasury yields rise while earnings yields don't need to — making stocks look falsely cheap.

2. **Ignores growth:** The earnings yield is a static snapshot. A 5% earnings yield with 6% growth is very different from one with 0% growth, but the model treats them identically.

3. **No risk adjustment:** Equities are riskier than Treasuries. A proper comparison requires adding an equity risk premium, not equating the two yields.

4. **Empirically unreliable:** Backtests show the Fed Model has poor predictive power for subsequent equity returns compared to simple valuation measures like CAPE.

**A Better Framework — Building Block ERP:**

Equity Risk Premium = Forward Earnings Yield - Real Risk-Free Rate + Expected Real Earnings Growth - Expected Dilution

This is more theoretically sound but requires more assumptions.

**When Earnings Yield Is Useful:**

1. Quick cross-asset comparison when yields are in the same inflation regime
2. Screening across markets (comparing earnings yields of different country indices)
3. Communicating with non-specialists who understand yield concepts
4. As one input among many in a multi-factor valuation framework

**Exam Guidance:**

The CFA curriculum acknowledges the Fed Model but emphasizes its limitations. Know both the calculation and the criticisms — expect a question testing whether the Fed Model is theoretically justified (it is not).

Explore equity risk premium estimation in our CFA Level II course.

What is the forward earnings yield, and how is it used to estimate the equity risk premium in the Fed Model?

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