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/functi
  ons 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.
• SP 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 variable
• Book(t-1)/Price(t-1)
• Growth portfolio sorting variable
• Earnings 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 dont 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) Im 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,?(t)) stands for the logistic predictive
  regression model. ?(t) stands for information set
  available at time t (at the end of t-1, lagged
  predictors).
• F(t, ?(t)) takes on a probability between 0 and 1
  given the predictors of period t-1.
• F(t, ?(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)gtw(g,1), w(v,1)w(g,1)1
• w(v,0),w(g,0), w(v,0)ltw(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))gtthe upper threshold,
• TTRR(t)w(v,1)R(v,t)w(g,1)R(g,t)
• if F(t,f(t))ltthe 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 (wont 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
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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.
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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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Model Selection Process (2)

• 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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Model Selection Process (3)

• 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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Model Selection Process (4)

• 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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Model Selection Process (5)

• 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
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Selected Predictors and Coefficients in Logistic
Regression Model
Seemed not very significant statistically.
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Model Statistics (1)
R-squares looked good for a predictive model)
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Model Statistics (2)
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)
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Performance of Conditional Portfolio
(1)Annualized Return
Huge returns
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Performance of Conditional Portfolio
(2)Volatility
Huge volatility as well, but volatility doesnt
matter for well diversified investors
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Performance of Conditional Portfolio (4)Skewness
Unexpected positive skewness out-of-sample!
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Performance of Conditional Portfolio
(4)Correlation
Low correlation with the market
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Performance of Conditional Portfolio (5)Beta
Small Beta
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Performance of Conditional Portfolio (6)Sharpe
Ratio
The returns are so huge as to compensate for the
huge volatilities.
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Performance of Conditional Portfolio (7)Alpha
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

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Conclusion for base case analysis

• 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.

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Further Analysis

• 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.