Moody's AAA Curve

Linear model of Moody's AAA Curve at period t from the other tracked series and the LN_ / squared transforms described on the Regression Models index: Y(t) = Σ a_i X_i(t−6).

Integrated series (S&P 500, Dow, Home Price Index, Commercial RE) are fit as ΔY. Quarterly series use one row per quarter.

Terms are added one at a time to minimize training AIC, at most min(5, n/8) predictors, one transform per driver, and only when the term’s p-value is at most 0.1 and |coefficient| is greater than 1.0e-10. A candidate correlated above 0.8 with Y or with an already selected X is skipped.

LN_ and squared predictors are clamped to their training range. Coefficients smaller than 0.001 are shown in scientific notation.

Each section is labeled by the month after its 12-month test window; the fit uses the prior 48 months of Y. Independents are dated six months earlier than Y.

Charts start in January 2020 and plot published prints only (not carried-forward extra samples). Fitted (train), fitted (test), and forecast are joined at the window boundaries so the line is continuous through the label month. The OLS test/forecast is shown when its test MAE beats or matches a last-print (or zero-change) baseline.

An intercept-only heading (for example “Δ SP500 = 40.657”) means no lagged series improved training AIC by at least 2 after the intercept, so the model is the training-mean change (a random walk with drift).

Test MAE is omitted when every print in the test window is a CCAR extra sample rather than a published observation.

Sept 2026: Moody's AAA Curve = -3.702 + 0.266 × LN_3-month Treasury Yield − 0.023 × Nominal disposable income growth + 0.795 × LN_Dow Total Stock Market Index

Train: Sept 2021 – Aug 2025 (42 observations). Test: Sept 2025 – Aug 2026 (11 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	-3.702 (+/- 2.967)
	p = 0.220
LN_3-month Treasury Yield	0.266 (+/- 0.030)
	p = 0.000^***
Nominal disposable income growth	-0.023 (+/- 0.003)
	p = 0.000^***
LN_Dow Total Stock Market Index	0.795 (+/- 0.276)
	p = 0.007^***

Observations	42
R²	0.888
Adjusted R²	0.879
Residual Std. Error	0.253 (df = 38)
F Statistic	100.398^*** (df = 3; 38)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (Sept 2025 – Aug 2026)

MAE	0.123
Last-print MAE	0.103
RMSE	0.182
R²	-0.123

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
LN_3-month Treasury Yield	+0.6141	+6.9781
Nominal disposable income growth	+0.2494	-0.1446
LN_Dow Total Stock Market Index	+0.0245	+2623.2768

Aug 2026: Moody's AAA Curve = 4.419 + 0.385 × LN_Nominal disposable income growth + 2.363e-10 × Dow Total Stock Market Index² − 9.020e-4 × Real disposable income growth² − 0.497 × LN_CPI Inflation Rate

Train: Aug 2021 – July 2025 (41 observations). Test: Aug 2025 – July 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	4.419 (+/- 0.391)
	p = 0.000^***
LN_Nominal disposable income growth	0.385 (+/- 0.065)
	p = 0.00000^***
Dow Total Stock Market Index²	0.000 (+/- 0.000)
	p = 0.013^**
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.000^***
LN_CPI Inflation Rate	-0.497 (+/- 0.109)
	p = 0.0001^***

Observations	41
R²	0.912
Adjusted R²	0.903
Residual Std. Error	0.242 (df = 36)
F Statistic	93.840^*** (df = 4; 36)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (Aug 2025 – July 2026)

MAE	0.249
Last-print MAE	0.102
RMSE	0.298
R²	-2.264

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
LN_Nominal disposable income growth	+0.1522	+15.5866
Dow Total Stock Market Index²	+0.0505	+31.0354
Real disposable income growth²	+0.0668	-0.0114
LN_CPI Inflation Rate	+0.0117	+3.0088

July 2026: Moody's AAA Curve = 1.57 + 0.182 × 1-month Treasury Yield + 0.311 × LN_Nominal disposable income growth − 6.768e-4 × Real disposable income growth² + 4.693e-8 × SP500 Stock Price Index² + 0.574 × LN_Nominal GDP growth

Train: July 2021 – June 2025 (40 observations). Test: July 2025 – June 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	1.570 (+/- 0.593)
	p = 0.013^**
1-month Treasury Yield	0.182 (+/- 0.039)
	p = 0.00004^***
LN_Nominal disposable income growth	0.311 (+/- 0.086)
	p = 0.001^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.00000^***
SP500 Stock Price Index²	0.00000 (+/- 0.000)
	p = 0.00002^***
LN_Nominal GDP growth	0.574 (+/- 0.195)
	p = 0.006^***

Observations	40
R²	0.930
Adjusted R²	0.920
Residual Std. Error	0.219 (df = 34)
F Statistic	90.779^*** (df = 5; 34)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (July 2025 – June 2026)

MAE	0.147
Last-print MAE	0.083
RMSE	0.212
R²	-1.946

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
1-month Treasury Yield	+0.6284	+49.7901
LN_Nominal disposable income growth	+0.1831	+19.5352
Real disposable income growth²	+0.0658	-0.0310
SP500 Stock Price Index²	+0.0353	+169.2787
LN_Nominal GDP growth	+0.0178	+73.9971

June 2026: Moody's AAA Curve = 1.572 + 0.194 × 1-month Treasury Yield + 0.289 × LN_Nominal disposable income growth − 6.556e-4 × Real disposable income growth² + 4.329e-8 × SP500 Stock Price Index² + 0.603 × LN_Nominal GDP growth

Train: June 2021 – May 2025 (39 observations). Test: June 2025 – May 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	1.572 (+/- 0.594)
	p = 0.013^**
1-month Treasury Yield	0.194 (+/- 0.041)
	p = 0.00004^***
LN_Nominal disposable income growth	0.289 (+/- 0.089)
	p = 0.003^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.00000^***
SP500 Stock Price Index²	0.00000 (+/- 0.000)
	p = 0.0002^***
LN_Nominal GDP growth	0.603 (+/- 0.198)
	p = 0.005^***

Observations	39
R²	0.930
Adjusted R²	0.920
Residual Std. Error	0.220 (df = 33)
F Statistic	87.866^*** (df = 5; 33)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (June 2025 – May 2026)

MAE	0.15
Last-print MAE	0.087
RMSE	0.201
R²	-1.888

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
1-month Treasury Yield	+0.6367	+66.4241
LN_Nominal disposable income growth	+0.1783	+21.1470
Real disposable income growth²	+0.0699	-0.0508
SP500 Stock Price Index²	+0.0256	+163.4445
LN_Nominal GDP growth	+0.0196	+93.8525

May 2026: Moody's AAA Curve = 3.749 + 0.276 × 3-month Treasury Yield − 3.614e-4 × Real disposable income growth²

Train: May 2021 – Apr 2025 (48 observations). Test: May 2025 – Apr 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	3.749 (+/- 0.128)
	p = 0.000^***
3-month Treasury Yield	0.276 (+/- 0.034)
	p = 0.000^***
Real disposable income growth²	-0.0004 (+/- 0.0001)
	p = 0.0004^***

Observations	48
R²	0.722
Adjusted R²	0.710
Residual Std. Error	0.513 (df = 45)
F Statistic	58.472^*** (df = 2; 45)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (May 2025 – Apr 2026)

MAE	0.417
Last-print MAE	0.083
RMSE	0.428
R²	-12.761

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
3-month Treasury Yield	+0.6316	+180.5489
Real disposable income growth²	+0.0319	-0.0733

Apr 2026: Moody's AAA Curve = -26.001 + 0.431 × 3-month Treasury Yield + 0.012 × CPI Inflation Rate² + 4.504 × LN_Commercial Real Estate Price Index + 3.617e-10 × Dow Total Stock Market Index² + 0.649 × LN_Market Volatility Index

Train: Apr 2021 – Mar 2025 (48 observations). Test: Apr 2025 – Mar 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's AAA Curve**

	Dependent variable (+/- SE):

	Moody's AAA Curve

Constant	-26.001 (+/- 7.145)
	p = 0.001^***
3-month Treasury Yield	0.431 (+/- 0.042)
	p = 0.000^***
CPI Inflation Rate²	0.012 (+/- 0.003)
	p = 0.0001^***
LN_Commercial Real Estate Price Index	4.504 (+/- 1.225)
	p = 0.001^***
Dow Total Stock Market Index²	0.000 (+/- 0.000)
	p = 0.006^***
LN_Market Volatility Index	0.649 (+/- 0.267)
	p = 0.020^**

Observations	48
R²	0.899
Adjusted R²	0.887
Residual Std. Error	0.323 (df = 42)
F Statistic	75.065^*** (df = 5; 42)

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Test period (Apr 2025 – Mar 2026)

MAE	0.337
Last-print MAE	0.091
RMSE	0.378
R²	-9.416

Chart forecast uses the last-print baseline (OLS MAE is worse).

R² impact

Train ΔR² is the gain when the term was added. Test ΔR² is the drop if that term is omitted from the frozen coefficients and the reduced model is scored on the test window.

Variable	Train ΔR²	Test ΔR²
3-month Treasury Yield	+0.6322	+349.3193
CPI Inflation Rate²	+0.2207	+5.9664
LN_Commercial Real Estate Price Index	+0.0210	+49143.9228
Dow Total Stock Market Index²	+0.0112	+154.9396
LN_Market Volatility Index	+0.0142	+472.6862

Moody's AAA Curve

Sept 2026: Moody's AAA Curve = -3.702 + 0.266 × LN_3-month Treasury Yield − 0.023 × Nominal disposable income growth + 0.795 × LN_Dow Total Stock Market Index

Test period (Sept 2025 – Aug 2026)

R2 impact

Aug 2026: Moody's AAA Curve = 4.419 + 0.385 × LN_Nominal disposable income growth + 2.363e-10 × Dow Total Stock Market Index² − 9.020e-4 × Real disposable income growth² − 0.497 × LN_CPI Inflation Rate

Test period (Aug 2025 – July 2026)

R2 impact

July 2026: Moody's AAA Curve = 1.57 + 0.182 × 1-month Treasury Yield + 0.311 × LN_Nominal disposable income growth − 6.768e-4 × Real disposable income growth² + 4.693e-8 × SP500 Stock Price Index² + 0.574 × LN_Nominal GDP growth

Test period (July 2025 – June 2026)

R2 impact

June 2026: Moody's AAA Curve = 1.572 + 0.194 × 1-month Treasury Yield + 0.289 × LN_Nominal disposable income growth − 6.556e-4 × Real disposable income growth² + 4.329e-8 × SP500 Stock Price Index² + 0.603 × LN_Nominal GDP growth

Test period (June 2025 – May 2026)

R2 impact

May 2026: Moody's AAA Curve = 3.749 + 0.276 × 3-month Treasury Yield − 3.614e-4 × Real disposable income growth²

Test period (May 2025 – Apr 2026)

R2 impact

Apr 2026: Moody's AAA Curve = -26.001 + 0.431 × 3-month Treasury Yield + 0.012 × CPI Inflation Rate² + 4.504 × LN_Commercial Real Estate Price Index + 3.617e-10 × Dow Total Stock Market Index² + 0.649 × LN_Market Volatility Index

Test period (Apr 2025 – Mar 2026)

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