BA 453 - Global Asset Allocation & Stock Selection Assignment 1 Growth vs. Value Trading Strategies

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 e

BA 453 - Global Asset Allocation & Stock Selection

Assignment 1: Growth vs Value Trading Strategies

CONSISTENT PERFORMANCE ASSET MANAGEMENT

Table of Content

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:

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 arethen 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 forthis given hypothetical trading strategy

Optimum

Large Growth

Large Value

Small Growth

Small Value

Mid Value

Mid Growth

All Value

All Growth Tbill Allocation All Assets 13.71% 6.69% 20.74% 6.02% 3.34% 4.01% 12.71% 26.42% 7.02% Trading Strategy Hypothetical Annualized Return 6.27% 7.32% 5.12% 8.00% 3.55% 6.93% 5.77% 4.80% 6.02%

Volatility 16.15% 11.67% 10.99% 12.41% 6.27% 14.71% 11.73% 10.43% 11.07% Actual Annualized Return 1.23% 1.15% 1.25% 1.35% 1.32% 1.22% 1.14% 1.10%

Volatility 18.03% 14.23% 22.56% 13.94% 14.93% 20.45% 14.79% 18.39%

Optimum Trading Strategy - No Short Selling - Tbill

Large Growth Large Value Small Growth Small Value Mid Value Mid Growth All Value All Growth

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

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:

Predictive Model Variables

The following variables were considered in developing the predictive models

Independent Variable

Risk free rate

Positive, Negative, squared

Expectation

Positive, Negative, squared

Economic activity10yrs-3months Government

A total of 15 raw 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

 Separation according Terms 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 againstthe 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:

Wilshire MidCap Growth TR (%Total Return)

Wilshire MidCap Value TR (%Total Return)

Wilshire MidCap Growth- Value TR (%Total Return)

Wilshire AllCap Growth TR (%Total Return)

Wilshire AllCap Value TR (%Total Return)

Wilshire AllCap Growth- Value TR (%Total Return)

Wilshire LargeCap Growth TR (%Total Return)

Wilshire LargeCap Value TR (%Total Return)

Wilshire LargeCap Growth- Value TR (%Total Return)

Wilshire SmallCap Growth TR (%Total Return)

Wilshire SmallCap Value TR (%Total Return)

Wilshire SmallCap Growth- Value TR (%Total Return)

Cap Type Positive Return Negative Return

AllCap Growth- Value

MidCap Growth- Value

LargeCap Growth- Value Positive Return Negative Return

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

*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 wewould 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

Actual vs Predicted Returns for the In Sample Wilshire 5000 Value Index

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%

Predicted vs Actual Returns for Our Out of Sample Wilshire 5000 Value Index

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

*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 wewould 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 Change lagged 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

Predicted vs Actual Returns for our In Sample Wilshire 5000 Growth Index

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%.

Predicted vs Actual Returns for our Out of Sample Wilshire 5000 Growth Index

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

In Sample Actual Growth vs Predicted Growth

In Sample Actual vs Predicted Value

Out of Sample Growth Actual vs Predicted

Out of Sample Actual vs Predicted Growth

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 Inother 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

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

Large Cap Value

*All variables lagged 1 month, except Growth, which is lagged 2 months

Large Cap Growth

*All variables lagged 1 month, except Growth, which is lagged 2 months

Both predictive models had significant statistics for the Dividend Yield We tried to have 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

t-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:

Large Cap Value

Large Cap Growth max(V-G)

Large Cap Value

Large Cap Growth max(V-G)

% of Returns' Direction

In sample, our model seems quite unappealing While it seems that we can predict the

direction of the value and growth portfolios, we are unable to predict the direction of the short portfolio It is surprising then that out of sample, our model predicts correctly the

long-direction of the long-short portfolio 75% of the time, while at the same time it does worse with the growth and value portfolios We were even more surprised to find out, after we did a simple analysis of the gains and losses, it turns out that in-sample our gains are about 68% of our losses, in other words, our losses were 1.5 times our gains At the same time, out out-of-sample gains were about 3.5 times larger than our losses

We then looked at the in-sample predicted returns vs actual returns for the growth stocks:

Growth Ret Predicted Growth

As you can see from the chart, our model often times follows closely the trend of the actual

returns The same is true for the in-sample predicted returns vs actual returns for the value

Value Ret Predicted Value

An analysis of our predictions reveals that we predict a positive skew of the value returns,

and a very slight negative one for the growth ones