Moody's BAA Curve

Linear model of Moody's BAA 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 BAA Curve = 4.716 − 0.001 × Real disposable income growth² + 0.369 × LN_Nominal disposable income growth − 0.455 × LN_CPI Inflation Rate + 0.326 × LN_Market Volatility 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 BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	4.716 (+/- 0.485)
	p = 0.000^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.000^***
LN_Nominal disposable income growth	0.369 (+/- 0.054)
	p = 0.00000^***
LN_CPI Inflation Rate	-0.455 (+/- 0.078)
	p = 0.00000^***
LN_Market Volatility Index	0.326 (+/- 0.146)
	p = 0.032^**

Observations	42
R²	0.913
Adjusted R²	0.904
Residual Std. Error	0.236 (df = 37)
F Statistic	97.665^*** (df = 4; 37)

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

Test period (Sept 2025 – Aug 2026)

MAE	0.289
Last-print MAE	0.101
RMSE	0.339
R²	-5.648

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
Real disposable income growth²	+0.1557	+0.0091
LN_Nominal disposable income growth	+0.0807	+18.5636
LN_CPI Inflation Rate	+0.0303	+5.0647
LN_Market Volatility Index	+0.0142	+75.9072

Aug 2026: Moody's BAA Curve = 4.994 + 0.433 × LN_Nominal disposable income growth − 0.001 × Real disposable income growth² − 0.676 × LN_CPI Inflation Rate + 0.512 × LN_Nominal GDP growth

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 BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	4.994 (+/- 0.304)
	p = 0.000^***
LN_Nominal disposable income growth	0.433 (+/- 0.058)
	p = 0.000^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.000^***
LN_CPI Inflation Rate	-0.676 (+/- 0.119)
	p = 0.00001^***
LN_Nominal GDP growth	0.512 (+/- 0.184)
	p = 0.009^***

Observations	41
R²	0.920
Adjusted R²	0.911
Residual Std. Error	0.230 (df = 36)
F Statistic	102.948^*** (df = 4; 36)

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

Test period (Aug 2025 – July 2026)

MAE	0.333
Last-print MAE	0.101
RMSE	0.346
R²	-6.455

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	+0.1722	+36.0039
Real disposable income growth²	+0.0728	-0.0552
LN_CPI Inflation Rate	+0.0201	+10.2628
LN_Nominal GDP growth	+0.0194	+63.4953

July 2026: Moody's BAA Curve = -59.096 + 1.679 × LN_20-year Treasury Yield + 10.316 × LN_Commercial Real Estate Price Index + 6.956e-10 × Dow Total Stock Market Index² − 0.075 × Real GDP growth + 0.509 × LN_Market Volatility Index

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

**Regression for Moody's BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	-59.096 (+/- 6.554)
	p = 0.000^***
LN_20-year Treasury Yield	1.679 (+/- 0.178)
	p = 0.000^***
LN_Commercial Real Estate Price Index	10.316 (+/- 1.096)
	p = 0.000^***
Dow Total Stock Market Index²	0.000 (+/- 0.000)
	p = 0.00000^***
Real GDP growth	-0.075 (+/- 0.026)
	p = 0.006^***
LN_Market Volatility Index	0.509 (+/- 0.197)
	p = 0.014^**

Observations	48
R²	0.904
Adjusted R²	0.892
Residual Std. Error	0.319 (df = 42)
F Statistic	78.796^*** (df = 5; 42)

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

Test period (July 2025 – June 2026)

MAE	0.27
Last-print MAE	0.089
RMSE	0.309
R²	-6.293

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_20-year Treasury Yield	+0.6398	+426.7736
LN_Commercial Real Estate Price Index	+0.1297	+262063.6921
Dow Total Stock Market Index²	+0.0897	+321.7215
Real GDP growth	+0.0293	+8.6071
LN_Market Volatility Index	+0.0153	+154.4975

June 2026: Moody's BAA Curve = -61.614 + 0.534 × Moody's AAA Curve + 10.658 × LN_Commercial Real Estate Price Index + 7.543e-10 × Dow Total Stock Market Index² − 0.014 × Real GDP growth² + 0.566 × LN_Market Volatility Index

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

**Regression for Moody's BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	-61.614 (+/- 6.273)
	p = 0.000^***
Moody's AAA Curve	0.534 (+/- 0.070)
	p = 0.000^***
LN_Commercial Real Estate Price Index	10.658 (+/- 1.055)
	p = 0.000^***
Dow Total Stock Market Index²	0.000 (+/- 0.000)
	p = 0.000^***
Real GDP growth²	-0.014 (+/- 0.004)
	p = 0.002^***
LN_Market Volatility Index	0.566 (+/- 0.201)
	p = 0.008^***

Observations	48
R²	0.907
Adjusted R²	0.896
Residual Std. Error	0.322 (df = 42)
F Statistic	82.151^*** (df = 5; 42)

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

Test period (June 2025 – May 2026)

MAE	0.275
Last-print MAE	0.092
RMSE	0.303
R²	-4.629

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
Moody's AAA Curve	+0.6360	+418.8743
LN_Commercial Real Estate Price Index	+0.1429	+224914.7137
Dow Total Stock Market Index²	+0.0763	+291.6985
Real GDP growth²	+0.0346	+3.7793
LN_Market Volatility Index	+0.0175	+164.8387

May 2026: Moody's BAA Curve = 4.972 − 0.001 × Real disposable income growth² + 0.444 × LN_Nominal disposable income growth

Train: May 2021 – Apr 2025 (38 observations). Test: May 2025 – Apr 2026 (12 observations). Independents are dated six months before each Y period.

**Regression for Moody's BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	4.972 (+/- 0.116)
	p = 0.000^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.000^***
LN_Nominal disposable income growth	0.444 (+/- 0.064)
	p = 0.00000^***

Observations	38
R²	0.870
Adjusted R²	0.862
Residual Std. Error	0.288 (df = 35)
F Statistic	116.838^*** (df = 2; 35)

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

Test period (May 2025 – Apr 2026)

MAE	0.367
Last-print MAE	0.096
RMSE	0.436
R²	-7.014

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
Real disposable income growth²	+0.0255	-0.0848
LN_Nominal disposable income growth	+0.0415	+35.2750

Apr 2026: Moody's BAA Curve = 4.707 − 0.001 × Real disposable income growth² + 0.504 × LN_Nominal disposable income growth + 0.151 × LN_Real GDP growth

Train: Apr 2021 – Mar 2025 (37 observations). Test: Apr 2025 – Mar 2026 (9 observations). Independents are dated six months before each Y period.

**Regression for Moody's BAA Curve**

	Dependent variable (+/- SE):

	Moody's BAA Curve

Constant	4.707 (+/- 0.138)
	p = 0.000^***
Real disposable income growth²	-0.001 (+/- 0.0001)
	p = 0.000^***
LN_Nominal disposable income growth	0.504 (+/- 0.059)
	p = 0.000^***
LN_Real GDP growth	0.151 (+/- 0.066)
	p = 0.030^**

Observations	37
R²	0.906
Adjusted R²	0.898
Residual Std. Error	0.249 (df = 33)
F Statistic	106.462^*** (df = 3; 33)

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

Test period (Apr 2025 – Mar 2026)

MAE	0.502
Last-print MAE	0.116
RMSE	0.542
R²	-12.387

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
Real disposable income growth²	+0.0398	-0.1304
LN_Nominal disposable income growth	+0.0625	+50.4790
LN_Real GDP growth	+0.0169	+8.6726

Moody's BAA Curve

Sept 2026: Moody's BAA Curve = 4.716 − 0.001 × Real disposable income growth² + 0.369 × LN_Nominal disposable income growth − 0.455 × LN_CPI Inflation Rate + 0.326 × LN_Market Volatility Index

Test period (Sept 2025 – Aug 2026)

R2 impact

Aug 2026: Moody's BAA Curve = 4.994 + 0.433 × LN_Nominal disposable income growth − 0.001 × Real disposable income growth² − 0.676 × LN_CPI Inflation Rate + 0.512 × LN_Nominal GDP growth

Test period (Aug 2025 – July 2026)

R2 impact

July 2026: Moody's BAA Curve = -59.096 + 1.679 × LN_20-year Treasury Yield + 10.316 × LN_Commercial Real Estate Price Index + 6.956e-10 × Dow Total Stock Market Index² − 0.075 × Real GDP growth + 0.509 × LN_Market Volatility Index

Test period (July 2025 – June 2026)

R2 impact

June 2026: Moody's BAA Curve = -61.614 + 0.534 × Moody's AAA Curve + 10.658 × LN_Commercial Real Estate Price Index + 7.543e-10 × Dow Total Stock Market Index² − 0.014 × Real GDP growth² + 0.566 × LN_Market Volatility Index

Test period (June 2025 – May 2026)

R2 impact

May 2026: Moody's BAA Curve = 4.972 − 0.001 × Real disposable income growth² + 0.444 × LN_Nominal disposable income growth

Test period (May 2025 – Apr 2026)

R2 impact

Apr 2026: Moody's BAA Curve = 4.707 − 0.001 × Real disposable income growth² + 0.504 × LN_Nominal disposable income growth + 0.151 × LN_Real GDP growth

Test period (Apr 2025 – Mar 2026)

R2 impact

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