GMO Forecasting

GMO Forecasting#

Case: Grantham, Mayo, and Van Otterloo, 2012: Estimating the Equity Risk Premium [9-211-051].

# Output from previous execution
GMWAX (Start-2011) GMGEX (Start-2011) GMWAX (2012-Present) GMGEX (2012-Present) GMWAX (Start-Present) GMGEX (Start-Present)
Annualized Return 0.046422 -0.003823 0.043423 0.001311 0.045043 -0.001463
Annualized Volatility 0.110499 0.147253 0.094949 0.235554 0.10349 0.192622
Annualized Sharpe Ratio 0.42011 -0.025963 0.457326 0.005566 0.43524 -0.007595
Annualized Sortino Ratio 0.52979 -0.035968 0.658023 0.004641 0.573957 -0.007213
Skewness -0.891709 -0.509564 -0.507077 -6.028372 -0.758222 -5.131245
Excess Kurtosis 3.058298 0.672829 1.945528 57.473216 2.771186 58.272763
VaR (0.05) -0.044003 -0.082292 -0.040854 -0.068027 -0.041368 -0.076213
CVaR (0.05) -0.074072 -0.09856 -0.058858 -0.162657 -0.068849 -0.130719
Min -0.14915 -0.151592 -0.115018 -0.658863 -0.14915 -0.658863
Max 0.081877 0.096042 0.074458 0.124668 0.081877 0.124668
Max Drawdown -0.293614 -0.55563 -0.216795 -0.737364 -0.293614 -0.761812
Bottom 2009-02-27 00:00:00 2009-02-27 00:00:00 2022-09-30 00:00:00 2016-11-30 00:00:00 2009-02-27 00:00:00 2016-11-30 00:00:00
Peak 2011-04-29 00:00:00 2007-10-31 00:00:00 2024-09-30 00:00:00 2014-06-30 00:00:00 2024-09-30 00:00:00 2007-10-31 00:00:00
Recovery 2010-10-29 00:00:00 - 2024-02-29 00:00:00 - 2010-10-29 00:00:00 -
Duration (days) 609 - 517 - 609 -
Calmar Ratio 0.151448 -0.006779 0.192465 0.001776 0.14695 -0.001905 
# Output from previous execution
SPY Beta SPY Alpha R2
GMWAX (Start-2011) 0.542128 0.027000 0.648686
GMGEX (Start-2011) 0.764237 -0.031201 0.725898
GMWAX (2012-Present) 0.581793 -0.033960 0.748747
GMGEX (2012-Present) 0.838118 -0.110164 0.252468
GMWAX (Start-Present) 0.552608 0.000558 0.680167
GMGEX (Start-Present) 0.786683 -0.064790 0.397891 
# Output from previous execution
OLS Regression Results
Dep. Variable: SPY R-squared: 0.014
Model: OLS Adj. R-squared: 0.011
Method: Least Squares F-statistic: 4.727
Date: Mon, 17 Nov 2025 Prob (F-statistic): 0.0304
Time: 05:04:12 Log-Likelihood: 567.58
No. Observations: 334 AIC: -1131.
Df Residuals: 332 BIC: -1124.
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -0.0171 0.011 -1.519 0.130 -0.039 0.005
SPX D/P 1.3187 0.607 2.174 0.030 0.126 2.512
Omnibus: 27.416 Durbin-Watson: 1.957
Prob(Omnibus): 0.000 Jarque-Bera (JB): 35.086
Skew: -0.627 Prob(JB): 2.40e-08
Kurtosis: 3.975 Cond. No. 250.


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
# Output from previous execution
OLS Regression Results
Dep. Variable: SPY R-squared: 0.007
Model: OLS Adj. R-squared: 0.004
Method: Least Squares F-statistic: 2.418
Date: Mon, 17 Nov 2025 Prob (F-statistic): 0.121
Time: 05:04:12 Log-Likelihood: 566.44
No. Observations: 334 AIC: -1129.
Df Residuals: 332 BIC: -1121.
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -0.0095 0.011 -0.881 0.379 -0.031 0.012
SPX E/P 0.2991 0.192 1.555 0.121 -0.079 0.678
Omnibus: 24.617 Durbin-Watson: 1.960
Prob(Omnibus): 0.000 Jarque-Bera (JB): 30.294
Skew: -0.594 Prob(JB): 2.64e-07
Kurtosis: 3.874 Cond. No. 79.2


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
# Output from previous execution
OLS Regression Results
Dep. Variable: SPY R-squared: 0.017
Model: OLS Adj. R-squared: 0.008
Method: Least Squares F-statistic: 1.944
Date: Mon, 17 Nov 2025 Prob (F-statistic): 0.122
Time: 05:04:12 Log-Likelihood: 568.15
No. Observations: 334 AIC: -1128.
Df Residuals: 330 BIC: -1113.
Df Model: 3
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -0.0069 0.016 -0.417 0.677 -0.039 0.026
SPX D/P 0.6594 0.937 0.704 0.482 -1.183 2.502
SPX E/P 0.1630 0.265 0.616 0.538 -0.358 0.684
T-Note 10YR -0.2034 0.198 -1.026 0.306 -0.593 0.187
Omnibus: 26.366 Durbin-Watson: 1.967
Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.195
Skew: -0.616 Prob(JB): 6.19e-08
Kurtosis: 3.932 Cond. No. 396.


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
# Output from previous execution
All Three D/P Only E/P Only
Annualized Return 0.097024 0.089093 0.072883
Annualized Volatility 0.163234 0.165365 0.133875
Annualized Sharpe Ratio 0.594384 0.538765 0.544407
Max Drawdown -0.665389 -0.724389 -0.588043 
# Output from previous execution
Beta Alpha (Annualized) Information Ratio (Annualized)
All Three 0.769932 0.034096 0.305119
D/P Only 0.787617 0.024719 0.220838
E/P Only 0.748304 0.011722 0.173812 
# Output from previous execution
GMWAX (Start-2011) GMGEX (Start-2011) GMWAX (2012-Present) GMGEX (2012-Present) GMWAX (Start-Present) GMGEX (Start-Present) All Three D/P Only E/P Only
Annualized Return 0.046422 -0.003823 0.043423 0.001311 0.045043 -0.001463 0.097024 0.089093 0.072883
VaR (0.05) -0.044003 -0.082292 -0.040854 -0.068027 -0.041368 -0.076213 -0.051822 -0.049193 -0.048823 
# Output from previous execution

All Three    0.060268
D/P Only     0.051386
E/P Only     0.026740
dtype: float64

# Output from previous execution
All D/P E/P
Negative Risk Premium (%) 0.137725 0.101796 0.002994
Negative Risk Premium Count 46.000000 34.000000 1.000000 
# Output from previous execution

np.float64(-0.11416969570045854)

# Output from previous execution
All Three D/P Only E/P Only
Annualized Return 0.02676 0.075904 0.04398
Annualized Volatility 0.354236 0.337267 0.206451
Annualized Sharpe Ratio 0.075543 0.225057 0.21303
Max Drawdown -0.956592 -0.909461 -0.689213 
# Output from previous execution
Beta Alpha (Annualized) Information Ratio (Annualized)
All Three -0.309545 0.052993 0.150888
D/P Only -0.028496 0.078319 0.232235
E/P Only 0.131885 0.032804 0.159621 
# Output from previous execution
All Three D/P Only E/P Only
Annualized Return 0.02676 0.075904 0.04398
VaR (0.05) -0.105682 -0.072005 -0.059274 
# Output from previous execution
All D/P E/P
Negative Risk Premium (%) 0.312727 0.258182 0.232727
Negative Risk Premium Count 86.000000 71.000000 64.000000