Growth vs. Value Trading Strategies11/16/2018

BA 453 - Global Asset Allocation & Stock Selection

Assignment 1: Growth vs. Value Trading Strategies

Consistent performance Asset Management

John O’Reilly

Sebastian Otero Barba

Nikolay Pavlov

Franck Violette

Table of Content

1.Introduction

2.Methodology

General

Predictive Model Variables

Multivariate Linear Regression

3.Value & Growth Indexes Trends

4.Wilshire All Cap Indexes

Best Value and Growth Variables

Best Value Regression

Best Growth Regression

5.Wilshire Large Cap Indexes

Large Cap Value and Growth analysis:

Wilshire Large-Cap Growth historical

Wilshire Large-Cap Value historical

Growth-Value historical returns:

Large cap value predictions histogram:

Large cap growth predictions histogram

Out-of-sample predicted returns vs. actual returns for the growth stocks:

Out-of-sample predicted returns vs. actual returns for the value stocks:

6.Wilshire Mid Cap Indexes

Wilshire Mid Cap Value Index Predictive Model:

Out of Sample Forecast of Wilshire Mid Cap Value Index:

In-Sample Forecast of Wilshire Mid Cap Value Index:

Wilshire Mid Cap Growth Index Predictive Model:

Out of Sample Forecast of Wilshire Mid Cap Growth Index:

In-Sample Forecast of Wilshire Mid Cap Growth Index:

7.Wilshire Small Cap Indexes

Wilshire Small Cap Value Index Predictive Model:

Out of Sample Forecast of Wilshire Small Cap Value Index:

In-Sample Forecast of Wilshire Small Cap Value Index:

Wilshire Small Cap Growth Index Predictive Model:

Out of Sample Forecast of Wilshire Small Cap Growth Index:

In-Sample Forecast of Wilshire Small Cap Growth Index:

8.Summary of Directionality Performance

9.Simple Trading Strategy

10.A More Complex Trading Strategy

11.Summary & Conclusions

12.Appendix

Adjusted R^2 for all Predictive Models

1.Introduction

Growth and Value are two fundamental investment approaches that have been the subject of significant research by Sharpe, Fama & French, Harvey to name a few. In brief, growth and value are defined as follows

Growth stocks represent companies that have demonstrated better than average gains in earnings in recent years and are expected to continue delivering high levels of profit growth.

Value Stocks represent companies that are currently out of favor in the marketplace and are considered bargain priced. Value stocks are typically priced much lower than stocks of similar companies in the same industry and may include stocks of newer companies with unproven track records.

By combining the two styles, one can help to reduce portfolio volatility because each has outperformed the other at different phases of the business cycle. The characteristics that affect the valuation of a stock as a member of the growth or value asset class are as follows:

Valuation Measure / Value / Growth
Dividend Yield / Higher / Lower
Price/Earnings / Lower / Higher
Price/Book / Lower / Higher
Price/Net Tangible Assets / Lower / Higher
Price/Cash Flow / Lower / Higher

Historical trends are shown in the following figure and illustrate periods of growth/value dominance associated with the different phases of the business cycle.

In being able to forecast the switch between growth and value, one may expect a significant increase in returns. As an indicator of potential strategy performance, we investigated a strategy with no short selling and whereby under negative returns, the allocation is transferred into TBills. All value and growth indexes were considered for this strategy and it was assumed that if the predictive model were perfect then one could place 100% in the best performing asset class every month or if the return were negative then place it into TBills. From January 78 to November 82, the table below gives the percentage over which a certain asset class is selected e.g. 13.71% large cap growth, 20.74% Small Cap Growth, 7.02% Tbill. This trading strategy would yield 6.27% annualized returns and a volatility of 16.27%. The effective returns of each asset class are then shown for only the periods where they were selected. Obviously, it is observed a significant gain in returns and reduced volatility compared with the actual value that represents a 100% allocation in each separate asset class over the whole of the period. While this example may be hypothetical, it sets the scene for the potential tremendous benefits that could be gained from reliable predictive models for this family of value and growth indexes. The figure below also illustrates the allocation over the sample period for this given hypothetical trading strategy.

2.Methodology

General

To assess the performance of various trading strategies involving allocation between value and growth, multivariate predictive models of the value and growth indexes expected returns have been derived.

The selected set of variables for the predictive models represent variables which are expected to have an effect on the market as a whole as well as variables that are expected to influence the index directly. We also considered economic indicators such as the monthly consumer confidence index in our analysis.

The following Growth and Value indexes - independent variables - considered in this study are as follows:

  • Wilshire All Cap Growth
  • Wilshire Large Cap Growth
  • Wilshire Mid Cap Growth
  • Wilshire Small Cap Growth
/
  • Wilshire All Cap Value
  • Wilshire Large Cap Value
  • Wilshire Mid Cap Value
  • Wilshire Small Cap Value

The indexes’ data series commence in January 1978 and end in November 02. The data sample was divided into an in-sample dataset from January 1979 to November 00 and an out-of-sample dataset from December 00 to November 02.

The indexes’ predictive models were tested bout in- and out-of-sample, and the expected returns for December 02 were predicted as well as the volatility using an ARCH(1) model.

The predictive models were used to back test and define proposed asset allocations for each index capitalization class using the following trading strategies:

  • Growth Long/Hold
  • Value Long/Hold
  • Value/Growth Swap

Predictive Model Variables

The following variables were considered in developing the predictive models.

Independent Variable
- Change in - / Lag / Relationship to / Format
CPI / 1 / Interest rates
Economic activity / Positive, Negative
Aaa minus T-Bill / 1 / Market risk / Positive, Negative
Aaa minus Baa / 1 / Market risk / Positive, Negative
Dividend Yield / 1 / Market return / Positive, Negative
Treasury Bill rate / 1 / Economic activity
Risk free rate / Positive, Negative, squared
U Michigan Consumer Index / 1 / Economic activity
Expectation / Positive, Negative, squared
IT Govt. Treasury / 1 / Expectation
Economic activity
10yrs-3months Government Bond / 1 / Expectation
Economic activity / Positive, Negative, squared
Aaa Corporate Bond Yield / 1 / Economic activity / Positive, Negative
Disposable Personal Income / 1 / Economic activity / Positive, Negative
New Private Housing started / 1 / Economic activity
Expectation / Positive, Negative
Initial Claims of Unemployment / 1 / Economic activity
Expectation / Positive, Negative
Cons Credit Out / 1 / Economic activity
Expectation / Positive, Negative
Index Total Return / 1,2 / Momentum / Positive, Negative

A total of 15raw independent variables were considered for this analysis. The raw data was obtained from DataStream and transformed into suitable dependent variables using transformations such as:

  • Separation into positive and negative change
  • Square of the change
  • Separation accordingTerms Structure sign
  • Stochastic detrending

It is worth to note that other variables such as P/E, B/P would have provided enhanced regression models for the value-based indexes. However, we were unable to locate the data due to the short timescale, but consider that despite this, the validity of the model is still confirmed by their high R^2.

Multivariate Linear Regression

The Excel regression data analysis add-in has been used to determine the regression parameters. In performing the analysis, the correlation between the variables has been examined and closely correlated variables discarded. Significance tests using the t-statistics and p-value were applied to define the significant variables with threshold levels of >1.0~1.5 and <0.1. The Adjusted R squared was used as the criteria to assess the goodness of fit of the regression model.

The procedure also involved plotting scatter diagrams of the independent variable against the dependent variable to assess the level of relationship and define if significant higher order relationship might be considered in the analysis.

3.Value & Growth Indexes Trends

The following graphs illustrate the trends over the period investigated. A positive bar indicates a period where the growth index has a higher return than the value index and vice versa. It is worth to note that the end part of the sample exhibit higher returns and thus expected volatility that may bias the predictions. With the in-sample dataset extending till November 00, we expect this effect to be small but at the same time we expect the prediction out of sample to be affected and therefore of lower performance. Assuming that the latter period represents the effect of the .com bubble and there is a return to a more stable return variation representative of the earlier part of the data sample, our model should predict better than expected results. This is of course a trade off between using as much data as possible to do the predictive model. For completeness, the predictive models have also been computed over the whole length of the data sample and the results are given in the appendix.

The summary statistics of the indexes time series are summarized as follows:

It is observed from the table below that over the studied period the small cap value index has performed best with positive returns exceeding 70% frequency. In general, value dominates in terms of positive return frequency except for All Cap. However, the actual statistics in terms of mean and standard deviation do not give such a clear picture. For example, Large Cap Growth has 1.22% average return and 5.2 standard deviation versus Large Cap Value that has 1.15% average return and 4.10 standard deviation. It is also observed that all raw time series have negative skewness. However, when Growth is subtracted to value i.e. long growth – short value, the skewness is positive for All, Large and small Cap. The opposite applies for Mid Cap.

4.Wilshire All Cap Indexes

Best Value and Growth Variables

IT Government Treasuries-The intermediate government treasury is a proxy for intermediate expected interest rates. This variable outperformed either the short or long term government bonds for the in sample models.

University of Michigan Consumer Confidence Index-This index is selected as the best proxy for consumer spending based on scatter plots and regressions. Higher consumer spending will increase earnings.

Best Value Regression

All Cap Value
Variable / Coefficient / T-Stat
IT Govt Tres / 0.007 / 5.31
U Mich Concumer Confidence Index % Change Squared / -0.376 / -1.53
U Mich Concumer Confidence Index % Change / 0.141 / 3.66
Intercept / 0.009 / 3.20
*All variables lagged 1 month

In our best regression, the variable IT Government Treasuries lagged 1 month has a coefficient of 7.08E-03. The positive coefficient is actually contrary to our intuition as we would expect equity returns to be lower in times of higher interest rates. The variable is significant with a high T Statistic of 5.31. The University of Michigan Consumer Confidence Index Percentage Change squared lagged 1 month variable has a negative coefficient of -0.376. This coefficient is reasonable if you assume the market reacts more negatively to large percentage drops in the index. Since, the University of Michigan Consumer Confidence Index Percentage Change lagged 1 month variable has a T Statistic of 3.66 and its coefficient is positive, most large percentage changes must be negative. The T Statistic for the squared variable is -1.53. The unsquared variable has a coefficient of 0.141. When consumer confidence is high, consumer spending increases, as does earnings. The intercept has a coefficient of 0.141 and a T Statistic of 3.66.

Our all cap value prediction model has an adjusted R^2 of 0.1214. The model is based on the Wilshire 5000 Value Index for the period August,1978 to November, 2000. The relatively high adjusted R^2 is consistent with the high percentage of months, 69.0%, where the model correctly predicted whether the index’s returns would be positive or negative.

The in-sample graph shows our model correctly predicts the correct direction in 87% of the months where the return is greater than 5% or less than -5%.

The out of sample portion of the Wilshire 5000 Value Index includes the period December, 2000 to November, 2002. It is a good test period given the high volatility and large ranges of returns for the period. Unfortunately, our model does not correctly forecast either the direction or the magnitude of most of these returns. The out of sample graph shows our model correctly predicts the correct direction in only 12.5% of the months where the return is greater than 5% or less than -5%. Our model would be improved if we included this period when constructing our all cap value model.

Best Growth Regression

All Cap Growth
Variable / Coefficient / T-Stat
IT Govt Tres / 0.007 / 4.44
U Mich Concumer Confidence Index % Change / 0.146 / 3.21
Intercept / 0.008 / 2.64
*All variables lagged 1 month

In our best regression, the variable IT Government Treasuries lagged 1 month has a coefficient of 7.19E-03. The positive coefficient is actually contrary to our intuition as we would expect equity returns to be lower in times of higher interest rates. The variable is significant with a high T Statistic of 4.44. The University of Michigan Consumer Confidence Index Percentage Changelagged 1 month variable has a T Statistic of 3.21 and its coefficient is 3.21. The positive coefficient is expected because when consumer confidence is high, consumer spending increases, as does earnings. The intercept has a coefficient of 8.33E-03 and a T Statistic of 2.64.

Our all cap growth prediction model has an adjusted R^2 of 0.0888. The model is based on the Wilshire 5000 Growth Index for the period August,1978 to November, 2000. The relatively high adjusted R^2 is consistent with the high percentage of months, 67.2%, where the model correctly predicted whether the index’s returns would be positive or negative.

The in-sample graph shows our model correctly predicts the correct direction in 80% of the months where the return is greater than 5% or less than -5%.

The out of sample portion of the Wilshire 5000 Growth Index includes the period December, 2000 to November, 2002. It is a good test period given the high volatility and large ranges of returns for the period. Unfortunately, our model does not correctly forecast either the direction or the magnitude of most of these returns. The out of sample graph shows our model correctly predicts the correct direction in only 13.3% of the months where the return is greater than 5% or less than -5%. Our model would be improved if we included this period when constructing our all cap growth model.

5.Wilshire Large Cap Indexes

Large Cap Value and Growth analysis:

The returns of both value and growth stocks in the large capitalization category were approximately normally distributed, over the past 20+ years. While the growth stocks had better performance, they also had a larger standard deviation, or volatility, which makes them more risky. Both indexes displayed negative skewness. We compare the performance of buy and hold to a long-short trading strategy that is based on buying the outperformer and selling the underperformer or investing in 30-day T-bills displays, whichever is larger. As we can see, the long-short strategy has a higher mean return, and a lower standard deviation of results. We were somewhat disappointed by the negative skewness of all strategies. That can be explain by the fact that large capitalization stocks are reasonably valued and are sometimes perceived as a safe-haven equity investment. In other words, investors expect good news from these leading companies. As such, large capitalization stocks have less potential to surprise on the positive than on the negative side.

Wilshire Large-Cap Growth historical

Wilshire Large-Cap Value historical

Growth-Value historical returns:

We then ran multiple quadratic regressions to determine what would be the best predictive model. The best one had the following statistics:

Both predictive models had significant t-statistics for the Dividend Yield. We tried to have t-statistics of at least 1 for each predictive variable. That meant that our Adjusted R2 became smaller every time we removed a variable with a small t-statistic. Our final models had Adjusted R2’s of 1.18% for our Value model, and 2.02% for our Growth model.

We tested our models both in and out of sample. Both times our Adjusted R2 became negative, and our error rate increased. In order to assess the implications this had on our potential results, we checked to see whether our models could correctly predict the direction of the returns: