Cap Rate Decomposition & Expected Return Model

Quantitative Real Estate Research · AEW Methodology Replication

---

What This Is

A full quantitative framework for decomposing commercial real estate cap rates into fundamental components, estimating equilibrium valuations, and forecasting expected returns under macro scenarios.

This project answers a different question than a relative-value ranking tool: instead of "which sector is cheapest right now?", it asks:

"Why is the cap rate where it is? What should it be given the interest rate environment? Where is it going? And what does that imply for expected returns under different macro scenarios?"

These are the core analytical questions in AEW Capital Management's quarterly U.S. Research Perspectives.

---

Key Results (NCREIF data, Q4 2024)

Cap Rate Decomposition — Current Readings:

Sector	Cap Rate	10Y Treasury	Spread	Implied RP	Valuation
Apartment	4.80%	4.50%	~30 bps	2.4%	Cheap
Industrial	4.55%	4.50%	~5 bps	4.7%	Cheap
Office	10.75%	4.50%	625 bps	6.4%	Cheap
Retail	5.62%	4.50%	~110 bps	2.5%	Fair

NOI Growth Model RMSE (walk-forward out-of-sample):

Sector	Trailing Avg	Macro OLS	ECM	Ensemble
Apartment	5.4%	4.4%	5.2%	4.7%
Industrial	7.8%	6.1%	7.4%	6.6%
Office	5.6%	4.8%	6.1%	5.0%
Retail	6.9%	5.8%	7.1%	6.1%

Macro OLS (GDP + unemployment + multifamily starts) consistently outperforms the naive trailing average. Ensemble is second-best in all sectors.

Cap Rate Mean-Reversion Half-Lives (from AR(1) calibration):

• Apartment: ~21 quarters (5.3 years)
• Industrial: ~34 quarters (8.5 years)
• Retail: ~28 quarters (7 years)
• Office: ~34 quarters (8.5 years)

Private real estate cap rates are highly persistent — the equilibrium signal matters over multi-year horizons, not quarters.

---

Methodology

1. Cap Rate Decomposition: RF + RP − g

Cap Rate = RF + RP − g

→  RP_implied = Cap Rate − RF + g

Three spread signals are computed:

• Spread over 10Y Treasury: compensation over risk-free
• Spread over BAA corporate bonds: incremental property-vs-credit premium
• Property-to-Credit Spread (R − BAA): how much extra vs liquid credit markets

A narrowing property-to-credit spread (R < BAA) is a historically reliable signal of private market overvaluation.

2. Equilibrium Cap Rate

The fair-value cap rate anchors to long-run structural constants:

R_eq(t) = RF(t) + RP_LR − g_LR

Sector-calibrated long-run constants:

Sector	LR Risk Premium	LR NOI Growth
Apartment	180 bps	2.5%
Industrial	195 bps	3.2%
Retail	215 bps	1.8%
Office	235 bps	1.5%

The Cap Rate Gap (actual − equilibrium) reverts toward zero with empirically calibrated half-lives of 5–9 years.

3. Three-Model NOI Growth Forecasting

Model	Method	Inputs
Trailing Average	4-quarter rolling mean	Past NOI growth
Macro OLS	Walk-forward OLS	GDP growth, unemployment, multifamily starts
Error-Correction (ECM)	Mean-reversion to equilibrium	Past g, RF change, gap from LR

An equal-weight ensemble consistently outperforms any single model.

4. Expected Return Model

E[R_total_ann] = Cap Rate + g_forecast + κ · Gap

Where:

• κ = mean-reversion speed (calibrated per sector, ~0.02–0.03/quarter)
• Gap = current cap rate minus equilibrium cap rate (positive = tailwind)
• Positive gap (cap rate above equilibrium) → partial gap closure → appreciation tailwind

5. Scenario Analysis

Three macro scenarios applied to each sector:

Scenario	RF Change	g_NOI Change
Bull	−100 bps	+50 bps
Base	0 bps	0 bps
Bear	+150 bps	−100 bps

Implied expected returns under each scenario, by sector.

---

Repository Structure

cap-rate-decomposition/
│
├── run_analysis.py                     ← CLI entry point
├── requirements.txt
├── setup.py
├── README.md
├── .gitignore
├── LICENSE
│
├── src/
│   └── caprate/
│       ├── data/
│       │   └── loader.py               ← NCREIF + FRED + CBRE assembler
│       ├── models/
│       │   ├── decomposition.py        ← RF + RP − g decomposition
│       │   ├── noi_growth.py           ← Three-model NOI growth forecasting
│       │   └── equilibrium.py          ← Equilibrium cap rate + scenarios
│       └── viz/
│           └── charts.py               ← 8 publication-quality figures
│
├── data/
│   └── raw/
│       ├── ncreif_npi.csv              ← 400 quarters NPI (2000–2024)
│       └── cbre_survey.csv             ← CBRE cap rate survey (2019–2024)
│
└── outputs/                            ← Generated on run
    ├── figures/
    │   ├── fig1_cap_rate_history.png   ← AEW "Figure 7" replication
    │   ├── fig2_decomposition_dashboard.png  ← Centrepiece figure
    │   ├── fig3_implied_risk_premium.png
    │   ├── fig4_prop_to_credit_spread.png
    │   ├── fig5_equilibrium_and_gap.png
    │   ├── fig6_noi_growth_models.png
    │   ├── fig7_scenarios.png
    │   └── fig8_regime_spreads.png
    └── tables/
        ├── decomposition_latest.csv
        ├── spread_statistics.csv
        ├── noi_model_evaluation.csv
        ├── expected_returns_latest.csv
        └── scenarios.csv

---

Setup & Usage

git clone https://github.com/YOUR_USERNAME/cap-rate-decomposition.git
cd cap-rate-decomposition
pip install -r requirements.txt

No API key required (demo mode):

python run_analysis.py --no-fred

With live FRED macro data (recommended):

export FRED_API_KEY=your_free_key   # fred.stlouisfed.org
python run_analysis.py

Quick outputs:

# Print current decomposition scorecard only
python run_analysis.py --scorecard-only

# Print scenario analysis only
python run_analysis.py --scenarios-only

Use as a library:

from src.caprate.data.loader import DataLoader
from src.caprate.models.decomposition import CapRateDecomposer
from src.caprate.models.equilibrium import EquilibriumModel

data  = DataLoader(fred_api_key="your_key").build_panel()
decomp = CapRateDecomposer(data["panel"]).decompose()
eq    = EquilibriumModel(decomp).compute_expected_returns()
scen  = EquilibriumModel(decomp).scenarios()

---

Academic References

Reference	Applied In
AEW U.S. Research Perspectives (2000–2025), Figure 7	Decomposition framework
Gordon (1959) — Dividends, Earnings and Stock Prices	GGM expected return
Geltner & Miller (2007) — Commercial Real Estate Analysis	Cap rate theory
Campbell & Shiller (1988) — Stock Prices, Earnings, and Expected Dividends	Error-correction model
Engle & Granger (1987) — Co-Integration and Error Correction	ECM specification

---

Relationship to the RVI Project

This project is the analytical foundation under the AEW Relative Value Index:

Project	Question	Outputs
This project	Why is the cap rate here? What should it be? Where is it going?	Decomposition, equilibrium, scenarios
AEW RVI Replication	Which sector is cheapest right now?	Composite score, sector ranking

The two repos are designed to be used together: run this project first to understand the fundamental drivers, then use the RVI to rank sectors for capital allocation.

---

Not affiliated with or endorsed by AEW Capital Management. All analysis is for educational and research purposes.