Logistic Regression
Dependent variable: ValueGrowthVariable
The final version of our model included the following lagged variables:
Estimated Regression Model (Maximum Likelihood)
Parameter 
Standard Estimate 
Estimated Error 
Odds Ratio 
CONSTANT 
1.85029 
0.457137 

ChangeinEPSGrowth 
2.65823 
3.16751 
0.0700723 
ChangeinTbAAA 
0.326701 
0.23539 
0.721299 
LGChginAAABAA 
8.13943 
3.43402 
3426.95 
SPMovementLagged 
1.38466 
0.50167 
0.250408 
Analysis of Deviance
Source 
Deviance 
Df 
PValue 
Model 
16.9748 
4 
0.0020 
Residual 
156.491 
132 
0.0716 
Total (corr.) 
173.466 
136 
Percentage of deviance explained by model = 9.78567
Adjusted percentage = 4.02086
Likelihood Ratio Tests
Factor 
ChiSquare 
Df 
PValue 
ChangeinEPSGrowth 
0.707832 
1 
0.4002 
ChangeinTbAAA 
3. 14034 
1 
0.0764 
LGChginAAABAA 
6.34278 
1 
0.0118 
SPMovementLagged 
9.02818 
1 
0.0027 
Residual Analysis
Estimation 
Validation 
N 
137 
MSE 
0.0414753 
MAE 
0.418012 
MAPE 

ME 
0.00691168 
MPE 
The StatAdvisor
The output shows the results of fitting a logistic regression model o describe the relationship between ValueGrowthVariable and 4 independent variable(s).
The equation of the fitted model is:
ValueGrowthVariable = exp(eta)/(1+exp(eta))
where
eta = 1.85029  2.65823*ChangeinEPSGrowth  0.326701*ChangeinTbAAA +
8.13943*LGChginAAABAA  1.38466*SPMovementLagged
Because the Pvalue for the model in the Analysis of Deviance table is less than 0.01, there is a statistically significant relationship between the variables at the 99% confidence level. In addition, the Pvalue for the residuals is less than 0.10, indicating that the model is significantly worse than the best possible model for this data at the 90% confidence level.
The pane also shows that the percentage of deviance in ValueGrowthVariable explained by the model equals 9.78567%. This statistic is similar to the usual RSquared statistic. The adjusted percentage, which is more suitable for comparing models with different numbers of independent variables, is 4.02086%.
Source: Statgraphics Plus.
Model Performance:
We looked at two scenarios for our switching portfolio strategy.
Scenario 1:
We used the following decision rule: If the predicted value was greater than 0.5 we selected the growth index and if it was below 0.5, we would go with value.
Our in sample analysis, run from February 1988 to May 1999, predicted the correct portfolio 47% percent of the time. The portfolio delivered the following results:
S&P500 
S&P Barra Growth 
S&P Barra Value 
Our Model 

Average Monthly Return 
1.4958% 
1.65% 
1.39% 
1.69% 
Standard deviation 
3.7981% 
4.11% 
3.69% 
4.14% 
Our model generated a slightly higher monthly return than the S&P 500 Index and both the S&P/BARRA Growth and Valuation Indexes. The standard deviation is a bit higher (4.14%) than those of the indexes. These results are somewhat disappointing given that our regression yields an Rsquare of 9.78%, which is quite good for a predictive model.
In an effort to determine whether the model is better at predicting the outperformance of one strategy over the other, we looked the accuracy of the prediction when the magnitude of outperformance was greater than one percent.
Growth outperformed 
Value outperformed 
Total 

No of observations 
68 
69 
137 
Correctly Predicted 
57 
8 
65 
Incorrect predictions 
11 
61 
72 
No of observations with a 1% outperformance. 
44 
30 
74 
Number of times correctly predicted when the outperfomance was greater than 1% 
37 
5 
42 
Number of times incorrectly predicted when the outperfomance was greater than 1% 
7 
25 
32 
Our model clearly predicts growth better than value. It was right 87.7% of the time growth outperformed and only 15.3% of the time that value outperformed. When we include a constraint in the return spread (1%) our model accuracy increases from 47% to 57%.
Scenario 2:
We used the following decision rule: If the predicted value was greater than 0.6 we selected the growth index and if it was below 0.4, we would go with value.
Our in sample analysis, run from February 1988 to May 1999, predicted the correct portfolio 67% percent of the time. The portfolio delivered the following results:
S&P500 
S&P Barra Growth 
S&P Barra Value 
Our Model 

Average Monthly Return 
1.4958% 
1.65% 
1.39% 
1.7% 
Standard deviation 
3.7981% 
4.11% 
3.69% 
4.04% 
Our model generated a slightly higher monthly return than the S&P 500 Index and both the S&P/BARRA Growth and Valuation Indexes with a lower standard deviation (4.04%) than the Barra Growth index.
In an effort to determine whether the model is better at predicting the outperformance of one strategy over the other, we looked the accuracy of the prediction when the magnitude of outperformance was greater than one percent.
Growth outperformed 
Value outperformed 
Total 

No of observations 
68 
69 
137 
Correctly Predicted 
43 
3 
46 
Incorrect predictions 
1 
44 
45 
Inconclusive (invested in S&P) 
24 
22 
46 
Our model clearly predicts growth better than value. It was right 97.7% of the time growth outperformed and only 36.3% of the time that value outperformed.
We obtained a better result with strategy 2 which can be explained by the fact that we only adopt a strategy if we get a strong enough signal (0.6 instead of 0.5 and 0.4 instead of 0.5). The model does quite poorly in predicting value, this can be partially explained by the distribution of our insample prediction (see appendix 1). The distribution is skewed toward growth.