Solution - Forecasting with Linear Factor Pricing Models

Solution - Forecasting with Linear Factor Pricing Models#

# Output from previous execution

Loaded 25 size/value portfolios (FF 25)
Date range: 1980-01-31 to 2025-08-31
Number of monthly observations: 548

# Output from previous execution

Built forecasts using expanding factor premia
Factor model: ['MKT', 'HML', 'RMW', 'UMD']
Rolling window: 60 months (5.0 years)

# Output from previous execution
Forecast Evaluation: Summary Across Securities
  OOS R-squared IC
Mean -0.4% -5.9%
Median -0.4% -5.3%
Min -1.1% -11.7%
Max 0.2% 0.2%
% Positive 16.0% 4.0% 
# Output from previous execution
Top 5 Portfolios by IC
  OOS R-squared IC
ME5 BM4 -0.0% 0.2%
BIG LoBM 0.2% -0.8%
SMALL LoBM 0.1% -1.0%
ME4 BM5 0.2% -2.7%
ME3 BM5 -0.0% -3.3%
Bottom 5 Portfolios by IC
  OOS R-squared IC
ME4 BM3 -0.5% -11.7%
ME4 BM1 -0.6% -11.7%
ME5 BM2 0.0% -11.4%
ME4 BM2 -0.4% -9.5%
ME3 BM3 -0.3% -9.2% 
# Output from previous execution

  CAPM / expanding...

  CAPM / constant...

  AQR 4-Factor / expanding...

  AQR 4-Factor / constant...

  FF 5-Factor / expanding...

  FF 5-Factor / constant...
Table A: Forecast Quality — Factor Model × Lambda Method
    Mean OOS R-squared Mean IC
Factor Model Lambda Method    
CAPM expanding -0.0% -7.3%
constant 0.3% 0.2%
AQR 4-Factor expanding -0.4% -5.9%
constant 0.1% -0.1%
FF 5-Factor expanding -0.1% -7.5%
constant 0.3% -0.7% 
# Output from previous execution

  CAPM / 36 months...

  CAPM / 48 months...

  CAPM / 60 months...

  CAPM / 120 months...

  CAPM / 180 months...

  CAPM / 240 months...

  AQR 4-Factor / 36 months...

  AQR 4-Factor / 48 months...

  AQR 4-Factor / 60 months...

  AQR 4-Factor / 120 months...

  AQR 4-Factor / 180 months...

  AQR 4-Factor / 240 months...
Table B: Forecast Quality — Beta Window (Constant Lambda)
    Mean OOS R-squared Mean IC
Factor Model Beta Window (months)    
CAPM 36 0.4% 1.8%
48 0.4% 1.0%
60 0.3% 0.2%
120 0.3% 2.7%
180 0.2% 1.4%
240 0.2% 1.9%
AQR 4-Factor 36 0.2% 1.4%
48 0.1% -0.8%
60 0.1% -0.1%
120 0.2% 1.3%
180 0.1% 0.3%
240 0.2% 1.4% 
# Output from previous execution
Performance: Long-Short vs MKT
  Mean Vol Sharpe
Long-Short 1.3% 14.4% 8.7%
MKT 8.8% 15.6% 56.1% 
# Output from previous execution
MKT Attribution: Long-Short Strategy
  alpha MKT r-squared Info Ratio
Long-Short 2.85% -18.27% 3.94% 20.22% 
# Output from previous execution
../_images/69d39bc7429fef09ace7efacac7bd32cffe02494efeaf09e0bb4f9e3fb13e480.png 
# Output from previous execution
Forecast Quality by Factor Model
  Mean OOS R-squared Mean IC
CAPM -0.0% -7.3%
AQR 4-Factor -0.4% -5.9%
FF 5-Factor -0.1% -7.5%
Strategy Performance by Factor Model
  Mean Vol Sharpe
CAPM -2.6% 12.0% -21.5%
AQR 4-Factor 1.3% 14.4% 8.7%
FF 5-Factor 0.9% 13.4% 6.7%
MKT Attribution by Factor Model
  alpha MKT r-squared Info Ratio
CAPM -5.17% 29.69% 15.04% -46.88%
AQR 4-Factor 2.85% -18.27% 3.94% 20.22%
FF 5-Factor 2.39% -17.08% 3.94% 18.15% 
# Output from previous execution
../_images/ea8d4c982084710a2e8b23fd9fdcd42ac411c9933b4f89ed3d8297886bf618ff.png