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

P-Value

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

Chi-Square

Df

P-Value

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 P-value 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 P-value 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 R-Squared 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 R-square 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 in-sample prediction (see appendix 1). The distribution is skewed toward growth.

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