value and growth regime switching

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Value and Growth Regime Switching

Improved Version

Bo Jiang

May 02, 2005

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Part 1: Background:

the Bigger Context and the Data

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The Bigger Context for this Forecasting Task (1)

Forecasting whether next period Value Investing Style will outperform Growth Investing Style is at the core of Regime Switching, viewed by many as the ‘crown jewel’ of active asset management.

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The Bigger Context for this Forecasting Task (2)

After we have forecasted which investing style will perform better next period, we will try to optimize weights between value and growth trading styles periodically (monthly), so that the total returns and/or risk adjusted returns of our dynamic trading rule beat those of the benchmark portfolios and/or other selected benchmarks.

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The Sources of Data

First we construct a value portfolio (representing value investing style) and a growth portfolio each month in FACTSET (a financial mega-database); the Alpha Testing tool of FACTSET will produce returns for both portfolios.

As for the potential predictors, they have two sources:(1)The first group is macroeconomic variables collected by Professor Campbell

Harvey. (2)The second group is the transformations/functions of the macroeconomic variables and the return time series.

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Security Universe

In FACTSET

We select the top 5,000 U.S. stocks in market capitalization as the universe.

S&P 500: universe size too small

Russell 2000: only small- to mid cap.

We select 01/1983 to 08/1996 (164 months) as in sample, and 09/1996 to 11/2004 (99 months) as out of sample.

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Value and Growth Portfolio (a)

In FACTSET:

Value portfolio sorting variableBook(t-1)/Price(t-1)

Growth portfolio sorting variableEarnings growth per price dollar

[E(t-1)-E(t-13)]/[│E(t-13) │*P(t-1)]

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Value and Growth Portfolio (b)

In FACTSET

• For each period, long F(1) stocks and short F(10) stocks in our universe.

• Within the two groups, equally value weighted.

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The Data Files

Raw Data From Factset are contained in 6 Excel files zipped together.

In the “DataProcessing” Excel file, we incorporated Factset data and macroeconomic data, and also did something transformation of the data using Excel functions.

In the “Pastedasvalue-fromdataprocessing” Excel file, data of “DataProcessing” are pasted as values here.

In “Final Data” Excel file, data are sorted by date and truncated. The data are ready to be transported to SPSS (Since so many bugs are revealed about SG, I don’t want to take the risk of trusting SG in logistic regression.)

Note: In this Final Data” file, there are 7 created variables (colored) which is prefixed by Pre or Lag, they can used directly as predictors since they are created by variables of previous periods. Other than these 7 variables, variables must be lagged before they become predictors (cannot use information that is not available on the decision making date to make decision.)

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Appendix to Part 1

The Methodology used to Construct the Conditional Portfolio

Note: the construction of Conditional Portfolio is the purpose of the forecasts (after-forecasting); I’m including its construction and later its in-the-sample and out-of-sample performance as a check for the effectiveness of the forecasting.

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Logistic Predictive Regression

F(t,ω(t)) stands for the logistic predictive regression model. ω(t) stands for information set available at time t (at the end of t-1, lagged predictors).

F(t, ω(t)) takes on a probability between 0 and 1 given the predictors of period t-1.

F(t, ω(t)) conditions the Conditional Portfolio.

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Conditional Weighted Trading Rule (1)

For each period, assign w(v,t) to the value portfolio and w(g,t) to the growth portfolio.

w(v,t)+w(g,t)=1 Total trading rule return (TTRR), this is also

called the return of the “conditional portfolio”.

TTRR(t)=w(v,t)*Rv(t)+w(g,t)*Rg(t)

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Conditional Weighted Trading Rule (2)

We use two sets of weights, one for prediction that value will out-perform growth), one for prediction that growth will outperform value. And then we use in-the-sample R(v,t) and R(g,t) data, and optimizer to maximize the return of the Conditional Portfolio.

Suppose two sets of weights are {w(v,1),w(g,1)}, w(v,1)>=w(g,1), w(v,1)+w(g,1)=1{w(v,0),w(g,0)}, w(v,0)<=w(g,0), w(v,0)+w(g,0)=1

Also, a threshold is used to deal with the gray area (where we are not sure about the forecast), Then, if F(t,f(t))>the upper threshold,

TTRR(t)=w(v,1)*R(v,t)+w(g,1)*R(g,t)if F(t,f(t))<the lower threshold,

TTRR(t)=w(v,0)*R(v,t)+w(g,0)*R(g,t)If F(t,f(t)) is between the lower and upper threshold, the weights of last period will be maintained (to save

transaction costs.)

F(t,f(t)) stands for the logistic predictive regression. f(t) stands for information set available at time t (at the end of t-1)

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Objective Function to Solve for Weights

Objective function for Optimizer (solve for optimal conditional weights)

Maximize Conditional Portfolio holding period return over the whole in-the-sample period.

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The Reason for Using the Thresholds

Use the upper and lower thresholds to minimize between-portfolio turnover (won’t switch between value and growth investing style too frequently, unless the forecast ‘strongly’ suggests so).

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Map it out: the big picture of the steps

Total Trading Rule Return = if(C4=1,w(v,1)*G4+w(g,1)*H4, w(v,0)*G4+w(g,0)*H4)

Regression Sorting and portfolio construction Trading/Benchmarking

Periods Step : TTRR(t)Value Growth

Dec-04 F(t,ω(t)): 0/1 Predictor 1 (t-1) Predictor n (t-1) Rb(v,t) Rb(g,t) Provide conditional info TTRR(t)

Out-of SampleTest F(t)

Dec-94

Feedback: change sorting variables, weights?

Feedback: change predictors, model?

Step: F(t,ω(t)) Step: Rb(v/g,t)

Out of sample

test

In the sample

data

Challenge: predictorsChallenge: Sorting variables

Challenge: WeightsTransaction costs

each row is sorted long short return for that period for value or growth.

Optimizer to find out w(v,1), w(g,1) w(v,0), w(g,0)

Generate 0/1

Forecast 0/1

Starting Point

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Part 2: Explore the Data and Run the Logistic Regression

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Overall, Growth outperformed Value slightly (in terms of periods)

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The Difference between Value return and Growth return is

positively correlated at lag 1, suggesting momentum.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Lag Number

-1.0

-0.5

0.0

0.5

1.0

AC

F

Coefficient

Upper Confidence Limit

Lower Confidence Limit

ValLessGrow

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Model Selection Process (1)

Left side: ValueBetter (1 means value outperforms growth)

The challenge is the right side variables (no wonder asset management firms regard regressors as top secret!)

Arbitrarily selected the in-sample and out-of-sample [01/1983 to 08/1996 (164 months) as in sample, and 09/1996 to 11/2004 (99 months) as out of sample]

The key is out-of-sample predictive performance.

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Created time-series of variables in SPSS. Tried Backward and Forward regression on the

numerous variables. What I found out for these stepwise schemes are:

• It is easy to do well in in-sample periods, with significant coefficients, high R squares (up to 30%) and correct predictions (up to 80%).

• However, it is totally a different story for out-of-sample periods, with correct prediction rate of consistently less than 50%!

• Probably over-fitting the in-sample periods!

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Decided that I have to base the prediction model on ‘theory’ to avoid over-fitting and get consistent performance across in-sample and out-of-sample.

Then what drives the disparity of the performances of value investing and growth investing?

The only driver I can think of is the market psychology: so when the economy is doing well, people lean towards growth; when the economy is not doing well, people prefer value.

So I need to select the proxies of market psychology and macroeconomic situation as the predictors.

Other variables, such as the Oil Price, seem to me would have similar and undistinguishable effect on the two investing style!

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Decided to focus on momentum (lags of left side variables), yield spread and credit spread, which I believe represent the market psychology in the economy state. Also tried to create transformations of the right side variables to ‘make the signal stronger’.

As for how to make the signal stronger (filter out some of the noises in the predictors)? Honestly I have no theory except intuition. My method is trial-and-error.

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Created finaldata_v2_truncated.sav and focus on this data file.

The backward regression intended for model selection was tried in “output_backward.spo”

I selected one model that makes the most sense to me in “output_final.spo.” (Step 12: sensible variables, consistent and good performance both in-sample and out-of-sample).

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In-sample and Out-of-sample

Case Processing Summary

164 62.4

0 .0

164 62.4

99 37.6

263 100.0

Unweighted Casesa

Included in Analysis

Missing Cases

Total

Selected Cases

Unselected Cases

Total

N Percent

If weight is in effect, see classification table for the totalnumber of cases.

a.

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Selected Predictors and Coefficients in Logistic Regression Model

Variables in the Equation

-.671 .535 1.575 1 .210 .511

-.156 .095 2.724 1 .099 .855

.040 .035 1.336 1 .248 1.041

.453 .364 1.551 1 .213 1.574

-.089 .291 .093 1 .760 .915

Pre3ContMonGroBetter

PrePELessMA

lagValueTotRtn1

lagValueBetter2

Constant

Step1

a

B S.E. Wald df Sig. Exp(B)

Variable(s) entered on step 1: Pre3ContMonGroBetter, PrePELessMA, lagValueTotRtn1,lagValueBetter2.

a.

Seemed not very significant statistically.

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Model Summary

214.907a .073 .097Step1

-2 Loglikelihood

Cox & SnellR Square

NagelkerkeR Square

Estimation terminated at iteration number 4 becauseparameter estimates changed by less than .001.

a.

Model Statistics (1)

R-squares looked good for a predictive model)

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Model Statistics (2)

Classification Tablec

47 35 57.3 31 23 57.4

27 55 67.1 16 29 64.4

62.2 60.6

Observed0

1

ValueBetter

Overall Percentage

Step 10 1

ValueBetter PercentageCorrect

Selected Casesa

0 1

ValueBetter PercentageCorrect

Unselected Casesb

Predicted

Selected cases InorOut EQ 1a.

Unselected cases InorOut NE 1b.

The cut value is .500c.

More importantly, the predictors did well both in-sample and out-of-sample.

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Part 3: Check the Effectiveness the Predictive Model

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Conditioning & Weight Optimization

Conditioning and optimization were done in Excel file: “final_analysis_forecasting”.

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Performance of Conditional Portfolio (Base Case: weights adding to 1, no other constraints on weights)

In the sampleOut of sample

Value portfolio Growth portfolio Midas Conditional Market T-bill

Annualized return2.9% 6.8% 32.4% 15.8% 6.2%1.3% 2.2% 54.6% 8.9% 3.6%

Volatility17.5% 16.4% 62.2% 14.1% 0.6%27.2% 25.1% 88.4% 17.0% 0.5%

skewness0.267852777 -0.224029575 -0.204555395 -0.947330467 0.121644780.325153705 -0.903974044 1.668352058 -0.44332867 -0.26165161

Correlation0.18015612 -0.064764674 0.057640054 1 0.020920404

0.231625625 -0.14891185 0.04664383 1 0.04701875Beta

0.223959466 -0.075261526 0.254731216 1 0.0008656830.370174598 -0.219414786 0.242251389 1 0.001496022

Alpha-5.49% 1.29% 23.69% 0.00% -0.01%-4.23% -0.25% 49.70% 0.00% -0.01%

Sharpe Ratio-0.191648659 0.034701059 0.420019376 0.678891568 0-0.084078342 -0.055893274 0.576306017 0.307982992 0

Midas conditional portfolio turnover times16 10.25 average months per turn over8 12.375 one turnover average month

HPRv HPRg HPRconditional HPRmarket T-bill147.4% 245.8% 4614.2% 741.6% 228.5%111.5% 119.8% 3636.0% 201.5% 134.1%

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Performance of Conditional Portfolio (1)

Annualized Return

Annualised Return

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%


Per

cent

age

In the sample

Out of sample

Huge returns

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Volatility

Volatility

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%


In the sample

Out of sample

Huge volatility as well, but volatility doesn’t matter for well diversified investors

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Skewness

Skewness

-1.5

-1

-0.5

0

0.5

1

1.5

2


In the sample

Out of sample

Unexpected positive skewness out-of-sample!

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Correlation

Correlation

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2


In the sample

Out of sample

Low correlation with the market

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Beta

Beta

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2


In the sample

Out of sample

Small Beta

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Sharpe Ratio

Sharpe Ratio

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


In the sample

Out of sample

The returns are so huge as to compensate for the huge volatilities.

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Performance of Conditional Portfolio (7)Alpha

Alpha

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%


In the sample

Out of sample

Unbelievably huge risk adjusted returns, beating not only the two benchmark portfolios but also the market portfolio big big time!

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The concern of transaction costs

Partially addressed

Turnover

0

2

4

6

8

10

12

14

average months per turn over

In the sample

Out of sample

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The forecasting model (and the conditioning and optimization scheme) seems to be very successful.

Before this assignment, we were using 7 predictors and got an out-of-sample alpha of 13%; now I am using 4 predictors and get an out-of-sample alpha of 49%.

Conclusion for base case analysis

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Please refer to the accompanying Excel file for analyses for other scenarios, such as

disallowing short; Short weights greater than -0.5 using regression results directly as weights; other weighing schemes for the ‘gray area’ (within

the low-high thresholds) Self-financed base case, no-short, short-weights-

greater than -0.5.

Further Analysis:

value and growth regime switching

Documents

factset data

data filesraw data

macroeconomic data

data of dataprocessing

growth investing style

growth portfolio ain

final data file

final data excel file