Two analysts estimate EM equity returns. One uses a 20-year historical average (11.2%). The other applies Singer-Terhaar (8.4%). The 280-bps gap shifts the recommended EM allocation from 18% to 7%. The choice of model is an allocation decision disguised as a methodology decision.
The CFA® Level III curriculum frames capital market expectations as a structured forecasting problem across every asset class. The rest of this lesson walks through each major class, then connects the forecasts to portfolio reweighting.
Historical averages are objective but fragile. The arithmetic mean overstates compound growth because volatility creates negative compounding drag: a 50% loss needs a 100% gain just to break even, so the realized growth rate is always below the simple average of period returns.
Geometric mean is approximately equal to arithmetic mean minus one-half times variance
For an asset with 10% arithmetic mean and 20% standard deviation: geometric mean = 10% - 0.5 x 0.04 = 8%.
HIGH-FREQUENCY: Arithmetic mean is correct for single-period mean-variance optimization. Geometric mean is correct for multi-period wealth accumulation and performance reporting. The exam tests this distinction directly.
Common mistakes
- Forgetting to remove correlation in the fully segmented Singer-Terhaar formula. The segmented premium uses total standard deviation times the global Sharpe ratio. Correlation does not appear, the asset is priced in isolation.
- Using the arithmetic mean for multi-year return projections. The geometric mean accounts for volatility drag. For volatile assets like EM equities (28% vol), the difference between arithmetic and geometric mean can exceed 300 bps.
- Treating the integration weight as a fixed number. Integration weights shift over time as capital markets liberalize or restrict. An EM market that opens to foreign capital flows becomes more integrated, lowering its equilibrium risk premium.
Bottom line
- Geometric mean ≈ arithmetic mean minus one-half variance; use geometric for compounding, arithmetic for single-period optimization.
- Shrinkage estimators pull extreme sample estimates toward a structured target to cut estimation error; weight the target more with smaller, noisier samples.
- Singer-Terhaar blends fully integrated and fully segmented ICAPM premiums by integration weight; the fully segmented premium is higher because correlation drops out.
- The building block approach sums risk premiums layer by layer: real rate + inflation + term + credit + liquidity.
Exam shortcut
For Singer-Terhaar calculations, set up two lines: integrated premium (vol x correlation x Sharpe) and segmented premium (vol x Sharpe). Blend with the integration weight. The integrated premium is always lower, if your blended number is higher than the segmented premium, you made a math error. Remember: More integrated = lower risk premium. More segmented = higher risk premium. Correlation drops out in the segmented case.
The full lesson (about 5,543 words, 37 min read) adds 2 worked examples, all 11 common mistakes, a self-check, free in the app.
Learning objectives
- cme part 2
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