Value and Growth Regime Switching

1. Value and Growth Regime Switching Improved Version Bo Jiang May 02, 2005

2. Part 1: Background: the Bigger Context and the Data

3. 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.

4. 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.

5. 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.

6. 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.

7. 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)]

8. 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.

9. 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.)

10. 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.

11. 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.

12. 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)

13. 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)

14. 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.

15. 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).

16. Map it out: the big picture of the steps

17. Part 2: Explore the Data and Run the Logistic Regression

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

19. The Difference between Value return and Growth return is positively correlated at lag 1, suggesting momentum.

20. 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.

21. 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!

22. 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!

23. 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.

24. 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).

25. In-sample and Out-of-sample

26. Selected Predictors and Coefficients in Logistic Regression Model Seemed not very significant statistically.

27. Model Statistics (1) R-squares looked good for a predictive model)

28. Model Statistics (2) More importantly, the predictors did well both in-sample and out-of-sample.

29. Part 3: Check the Effectiveness the Predictive Model

30. Conditioning & Weight Optimization • Conditioning and optimization were done in Excel file: “final_analysis_forecasting”.

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

32. Performance of Conditional Portfolio (1)Annualized Return Huge returns

33. Performance of Conditional Portfolio (2)Volatility Huge volatility as well, but volatility doesn’t matter for well diversified investors

34. Performance of Conditional Portfolio (4)Skewness Unexpected positive skewness out-of-sample!

35. Performance of Conditional Portfolio (4)Correlation Low correlation with the market

36. Performance of Conditional Portfolio (5)Beta Small Beta

37. Performance of Conditional Portfolio (6)Sharpe Ratio The returns are so huge as to compensate for the huge volatilities.

38. 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!

39. The concern of transaction costs • Partially addressed

40. 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%.

41. 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.