Tactical Style Allocation TSA A New Form of Market Neutral Strategy Professor No l Amenc noel.amencedhec

1. Tactical Style Allocation (TSA) A New Form of Market Neutral Strategy Professor No�l Amenc noel.amenc@edhec.edu

2. Overview Investment Philosophy Forecasting Style Returns Econometric Model Portfolio Process Implementation Portfolio Performance Next Step References

3. Investment PhilosophyTiming and Picking Stock (excess) returns can be decomposed into a systematic and a specific components (Sharpe�s (1963) market model) Two forms of active strategies Market timing: aims at exploiting predictability in systematic return Stock picking: aims at exploiting predictability in specific return Academic evidence There is ample evidence of predictability in systematic component (Keim and Stambaugh (1986), Campbell (1987), Campbell and Shiller (1988), Fama and French (1989), Ferson and Harvey (1991), etc.) There is little evidence of predictability in specific component (more no�sy) in the absence of private information

4. Investment Philosophy Investment Styles - Size and B/M Factors Is the market portfolio the only rewarded systematic factor affecting asset returns? Specific term = approximately 70% of return Looking for other systematic factors in specific risk Fama and French (1992) Firm size and B/M capture the cross-sectional variation in average stock returns (size and B/M ratio are proxies for underlying risk factors) E(r) = 2.07 � 0.17b � 0.12(Size Factor) + 0.33(B/M Factor) (6.55) (-0.62) (-2.52) (4.80) CAPM may not be dead, but certainly needs to be generalized under the form of multi-factor models Academia: Merton�s ICAPM (1973), Ross�s APT (1976) Industry: BARRA, Aptimum, etc.

5. Investment PhilosophyTAA, TSA and Stock Picking Extension of the market model Three forms of active strategies Tactical Asset Allocation: exploits evidence of predictability in market factor Tactical Style Allocation: exploits evidence of predictability in style factors Stock picking: exploits evidence of predictability in specific risk

6. Investment PhilosophyTAA, TSA and Stock Picking TSA is not a new concept Most mutual fund managers make bets on styles as much as bets on stocks They perform TAA, TSA and stock picking at the same time in a somewhat confusing �m�lange des genres� As in many other contexts, we have evidence that specialization pays Daniel, Grinblatt, Titman and Wermers (Journal of Finance, 1997): �We find no evidence that funds are successful style timers. (�) Our application (�) suggests that, as a group, the funds showed some stock selection ability, but no discernable ability to time the different stock characteristics (e.g., buying high book-to-market stocks when those stocks have unusually high returns). We (�) find no convincing evidence of individual funds successfully timing the characteristics.� Stock picking is already challenging per say without adding the complexity of style timing We focus on style timing only

7. Investment PhilosophyTAA, TSA and Stock Picking

9. Investment PhilosophyPerformance of TSA Strategies

10. Investment Philosophy  Performance of TSA Strategies

13. Forecasting Style ReturnsContemporaneous Economic Conditions � Example of Growth versus Value and the Term Spread Economic intuition about differential growth versus value and the term spread Growth stocks, whose valuations typically rely on expected earnings growth farther into the future than value stock valuations, may be said to have a longer "duration" than value stocks, and, similarly to longer-duration bonds, rising or high future interest rates will disproportionately hurt the discounted value of a growth company's future earnings stream Thus, growth stocks tend to underperform in an environment of steep yield curves, which imply expectations of rising interest rates in the future Confirmation When changes in the term spread are low (i.e., when the yield curve is flattening), S&P growth outperfoms S&P value by an annualized 6.39% on average When changes in the term spread are high (i.e., when the yield curve is steepening), S&P growth underperforms S&P value by an annualized 7.46% on average

15. Forecasting Style ReturnsContemporaneous Economic Conditions � Example of Growth versus Value and the Business Cycle Economic intuition about the differential growth versus value and the business cycle Value stocks tend to be preferred as defensive investment vehicles in bad times On the other hand, growth stocks are preferred when the economy is booming Confirmation When economic growth is low, S&P growth underperfoms S&P value by an annualized 11.80% on average When the default spread is high, S&P growth outperforms S&P value by an annualized 10.35% on average

17. Forecasting Style ReturnsContemporaneous Economic Conditions � Example of Growth versus Value and the Default Spread Economic intuition about the differential growth versus value and the default spread In uncertain times, value stocks can become flight to quality vehicles; for this reason, growth stocks tend to underperform value stocks when concern about economic situation increases The default spread (measured in terms of the difference between the yield on long term Baa bonds and the yield on long term AAA bonds) can be regarded as a proxy for how uncertain investors are about economic prospects Confirmation When the default spread is low, S&P growth outperfoms S&P value by an annualized 8.55% on average When the default spread is high, S&P growth underperforms S&P value by an annualized 8.01% on average

19. Forecasting Style ReturnsLagged (1 Month) Economic Conditions � Example of Small versus Large Cap and Return on Large Cap Stocks Economic intuition about the differential small versus large cap and the lagged return on large cap stocks Equity market returns, essentially biased towards large-cap stocks, are correlated with future returns on small cap stocks This is consistent with the lead-lag pattern uncovered by Lo and MacKinlay (1990) For example, if Microsoft goes up dramatically and a few days later one may expect a price jump in other computer software manufacturers. Confirmation When the return on S&P500 is high, S&P 600 SC outperfoms S&P 500 one month later by an annualized 10.15% on average When the return on S&P500 is low, S&P 600 SC underperforms S&P 500 one month later by an annualized 6.30% on average

21. Forecasting Style ReturnsLagged (1 Month) Economic Conditions � Example of Small versus Large Cap and the Term Spread Economic intuition about the differential small versus large cap and the lagged value of the term spread A steeply upward (downward) slopping yield curve signals expectations of rising (decreasing) short-term interest rates in the future Increases in interest rates have a negative impact on large cap stock returns, and a subsequent similar impact on small cap stock return through the lead-lag effect Confirmation When the term spread is low (downward or slightly upward slopping yield curve), S&P 500 outperfoms S&P 600 SC one month later by an annualized 7.70% on average When the term spread is high (steeply upward slopping yield curve), S&P 500 underperforms S&P 600 SC one month later by an annualized 6.74% on average

23. Forecasting Style ReturnsContemporaneous Versus Lagged Variables We have just seen a series of examples illustrating that both contemporaneous and lagged economic and financial variables had an impact on style differentials (growth - value, large - small cap) Forecasting economic variables is a difficult art, with the failures often leading to all systematic tactical allocation processes being abandoned Two ways of considering tactical style allocation Forecasting returns is based on forecasting the values of economic variables (scenarios on the contemporaneous variables) Forecasting returns is based on anticipating market reactions to known economic variables (econometric model with lagged variables)

24. Forecasting Style ReturnsContemporaneous Versus Lagged Variables The anticipation of market reactions to known variables is easier It leads one to think that the performance does not result from privileged information but an analysis of the reactions of the market to its publication The market is guided by the information (informational efficiency) but certain players can hope to manage the consequences better than others (inefficiency or reactional asymmetry) This approach has given rise to numerous academic studies (cf. de Bondt and Thaler (1985), Thomas and Bernard (1989), McKinley and Lo (1990))

25. Econometric Model Our Approach : both Art and Science Principle 1: Parsimony Principle Other things equal, simple models are preferable to complex models KISS principle (�Keep It Sophisticatedly Simple�): simple model is not na�ve model Principle 2: Financial versus Economic Variables We prefer financial variables, more forward-looking than economic variables However, we also consider economic variables while controlling for the risk of back-filling and posterior adjustment Principle 3: Data Mining versus Economic Analysis? We prefer to select variables on the basis of their natural influence on returns rather than screening lots of variables through stepwise regression (leads to high in-sample R-squared but low out-of-sample R-squared: robustness problem) Roughly speaking, economic analysis is key in the variable selection process, while data mining and econometric analysis is more predominant for model selection Principle 4: Forecast Sign more than Magnitude Because we believe there is more robustness in forecasting signs than absolute values, our portfolio process focuses on pairs of returns differentials (see portfolio process) We make two types of econometric bets : Growth versus Value and Small Cap versus Large Cap differential

26. Econometric Model Setting Up the Data Base � The Data Statistical tools SAS mainly Other software for specific tests Dates Most financial data are available before the 7th of the month Therefore, monthly trading decisions take place on the 7th When a variable is available after the 7th of the month, it is regarded as being available before the 7th of the previous month Data Economic variables: Gross Domestic Product, Consumer Sector, Investment Spending, Foreign Sector, Government Sector, Inflation, Other Measures of Production, Survey, etc. Financial variables: Equity Index, Bond Index, Foreign Exchange, Commodities, Interest Rates, Liquidity, Volatility, Volume, BARRA Variables, etc.

27. Econometric ModelSelecting the Variables � Economic Analysis We know that some among the financial variables have a natural impact on stock returns For each style differential, we first generate a list of preferred variables based on an economic analysis These variables can be found within the following broad categories Interest rates Risk Relative cheapness of stock prices Stock returns Other variables include liquidity indicators, commodity prices, currency rates, etc.

28. Econometric Model Selecting the Variables � Econometric Analysis Econometric analysis is then used to help us decide What is the proxy for a given variable which is most useful for TSA decisions How should a given proxy enter an econometric model For each variable X(t), we duplicate the data 10 times Lag 1 month: X(t-1) Lag 2 months: X(t-2) Lag 3 months: X(t-3) Moving average: 1/3*(X(t-1)+ X(t-2)+ X(t-3)) Stochastic detrending: X(t-1)-(X(t-2)+X(t-3)+�+X(t-13))/12 Squared value: X(t-1)^2 (volatility indicator) Absolute change one lag: (X(t-1)-X(t-2)) Absolute change two lags: (X(t-2)-X(t-3)) Relative change one lag: (X(t-2)-X(t-3))/X(t-3) or lnX(t-2)-lnX(t-3) Relative change two lags: (X(t-2)-X(t-3)) We regress style differentials on all variables/declinations

29. Econometric Model Selecting the Variables � Decision Procedure Two types of indicators Indicator of type 1 (quality of fit): t-stats (and R-squared) Indicator of type 2 (forecasting power): hit ratio (sign) and prediction error (magnitude) Forecasting can only be tested on an out-of-sample basis Hit ratios are percentage of accurate sign prediction Prediction error is measured in terms of standard deviation of the realized errors Time-weighting: we want a model that works at the end of the test period, not at the beginning We use an exponentially-weighted average of values taken at different points in time so as to put more weight to more recent observations Associate to each variable a preference number It is the sum of the normalized R-squared, normalized t-stat and normalized hit ratio (normalized value = (value�mean)/std deviation) Rank variables/declinations in terms of preference number

30. Econometric Model Selecting the Variables � Final Selection For each style, we select a limited number (around 30) of useful variables based on economic and econometric analysis Econometric method for variable selection First sort in decreasing order of absolute value of t-stat (keep variables with It-statI > 2) Among remaining variables, select highest hit ratios (keep only higher than 60%) and lowest prediction errors Avoid non stationary variables (unit root tests) Two types of variables Type 1 (typically about 10): score high both on economic analysis and econometric performance (preference number) Type 2 (typically about 20): score high either on economic analysis or econometric performance (preference number) The list of variables for each style differential is (marginally) updated through time

31. Econometric Model Building the Model � The Approach We test for the performance of multi-variate linear models based on a limited number of variables (max 5), while systematically avoid multi-colinearity R-squared, significance of coefficients on the period January 1994 to December 1998, hit ratios on the period starting in January 1998 We use adjusted R-squared and Schwartz Information Criterion (SIC) to strongly penalize the different models for the number of degrees of freedom (the lower the SIC the better the model) Again exponentially-weighted averaging is performed Same decision rule as for variable selection More demanding in terms of t-stats Take a close look at a dozen among the best models Use economic analysis (favor models with type 1 variables) Select the best three to five models, i.e., models that score high both on economic analysis and econometric performance

32. Econometric Model Building the Model � Competing Models On-going test of out-of-sample performance Null hypothesis: hit ratio=50%, i.e., model has no predictive ability Test whether hit ratios are significantly greater than � (benchmark case of no model) In the case of 24 observations, a hit ratio of At least 63% can be regarded as is significantly greater than � at the 10% level At least 67% can be regarded as is significantly greater than � at the 5% level We maintain a set of 3 to 5 models for each style differential Allows us for a quicker switch in case a change of conditions occurs Need to re-do the analysis in case a change of paradigm See �updating the model� below Also used in the estimation of a confidence level

33. Econometric Model Improving the Model � Regression Tuning Autocorrelation Test for autocorrelation: Durbin-Watson, the Q-statistic and the Breusch-Godfrey LM test Correction for autocorrelation (regression analysis with ARMA disturbance) Heteroskedasticity Tests for detecting heteroskedasticity: White (1980) The correction for heteroskedasticity involves weighted (or generalized) least squares Cointegration Unit root test: Dickey-Fuller (1981) and Phillips and Perron (1987) test of cointegration (Johansen (1991, 1995))

34. Econometric ModelImproving the Model � Robustness Checks Checking the robustness of the model through time Models are dynamically calibrated We use Chow test as a parameter stability test When appropriate, we use Kalman filter analysis, where priors on model parameters are recursively updated in reaction to new information Conditional models are attractive but they involve additional parameters and often result in lower out-of-sample performance (Ghysels (1998)) Checking the robustness of the linear specification Estimate probability of positive sign differential through a logit regression Linear and logit models agree in most cases (when not, decrease model confidence - see portfolio process below) Checking the robustness of the distributional assumption Test for evidence of non-normality in the residuals When appropriate, we use bootstrapping as a non-parametric way of estimating confidence intervals

35. Econometric ModelUpdating the Model Models are used to generate predictions A model is regarded as satisfactory as long as The coefficients remain significant Hit ratios are good Decisions of updating the model are triggered by Two (one) consecutive months with (strongly) decreasing t-stats and/or t-stat below a reasonable confidence level And/or three consecutive errors on predicted sign of style differential Strong interconnection between these events: more often than not, decrease in t-stats precedes a decrease in hit ratio When this happens, and model 2 and 3 also fail, we take this an indication of a paradigm shift 100% of money is invested in cash until a satisfactory model is obtained We re-do all the analysis: we search for best declination of each variable in the selected set of 30, and best 3 models from permutations of these

36. Portfolio ProcessTurning Econometric Bets in Optimal Portfolio Decisions Because we believe there is more robustness in forecasting signs than absolute values, our portfolio process focuses on pairs of returns differentials Bet 1: bet on Growth versus Value differential Bet 2: bet on Small Cap versus Large Cap differential The following rule is applied We implement an optimal decision rule that makes Relative weighting of two bets a function of relative confidence in 2 models Level of leverage a function of absolute level of confidence in 2 models

37. Two aspects in the level of confidence Confidence in the model Confidence in the prediction These are different items: for example, a good trusted model can generate a prediction with low confidence (predicted sign differential close to zero) Confidence in the model As usual, it is a mix of economic analysis and econometric analysis (in particular, level and persistence of t-stats, agreement between linear model and competing models from the shortlist, Kalman, logit regression, etc.) Takes on the values 0%, 50%, 75% and 100% Confidence in the prediction For each model, assume actual value is normally distributed with a mean equal to forecasted value and standard deviation given by model�s standard error Use the Gaussian distribution function to compute the estimated probability that actual value has a sign different from forecasted value (less than 50%) Portfolio ProcessConfidence in Model versus Confidence in Prediction

38. Total confidence Confidence in model times confidence in prediction Call that number it x% for bet 1 and y% for bet 2 Introduce w=x%/(x%+y%) Relative weighting rule If 0% < w < 12.5%, take w = 0% (100% weight in bet 2) If 12.5% < w < 37.5%, take w = 25% (75% weight in bet 2) If 37.5% < w < 62.5%, take w = 50% (50% weight in bet 2) If 62.5% < w < 87.5%, take w = 75% (25% weight in bet 2) If 87.5% < w < 100%, take w = 100% (0% weight in bet 2) Portfolio ProcessRelative Weighting Rule

39. Weighting scheme 1: 50%-50% Equal-weighting of bets if same level of confidence in both models Example: -25% LC, 25% SC, -25% V, 25% G Weighting scheme 2: 75%-25% Over-weighting of bet for which higher confidence in model Example: -37.5% LC , 37.5% SC, -12.5% V, 12.5% G Weighting scheme 3: 100%-0% 100% of the portfolio invested in single bet with higher confidence Example: -50% LC , 50% SC Portfolio ProcessRelative Weighting of the Bets and Portfolio Decisions

40. The target leverage is 2 but the actual leverage can be lower than 2 In particular, 100% of the portfolio invested in cash if there is no satisfying model available for any of the two bets More generally, we make leverage a function of the absolute level of confidence in both models Take l = a(x% + y%) Choose a so as to reach level l=2 on average Impose that l can not be higher than 3 Portfolio ProcessAbsolute Weighting Rule

41. Portfolio ProcessBeta Neutrality Optimal allocation in 4 styles (SC, LC, G, V) + risk-free asset (0th style) is implemented so as to satisfy a number of constraints Constraints Beta-neutrality constraint Portfolio constraint (including risk-free asset) Leverage constraint (including risk-free asset)

42. ImplementationInvestible Indices What are the best instruments to implement the TSA strategy? 2 series of investable indices selected to apply our Tactical Style Allocation: S&P and Russell A choice of 2 corresponding types of instruments Index Futures (Chicago Mercantile Exchange) Exchange Traded Funds (American Stock Exchange) For US Equity Investment, we have a clear preference for the ETFs Better Liquidity Larger Range of Instruments Better Correlation with Style Indices

47. Next StepEurex research project Implementing an econometric process for managing a European Equity long/short fund This process relies on Eurex derivatives DJ EuroStoxx 50 Index Futures DJ EuroStoxx 50 Options DJ EuroStoxxSM Banks Index Futures and Options DJ EuroStoxxSM Telecom Index Futures and Options

48. Next StepEurex research project The investment strategy proposed is based on the following principles: The �long� bias is optimized through a TAA process We smooth TAA performance with DJ EuroStoxx 50 Options We generate alphas through a sector rotation strategy We implement truncated return strategies eliminating the worst (and best) returns for the fund track record using options or sector indexes This research is supported by Eurex

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51. References (3) Gerber, G.,. 1994, Equity style allocations: timing between growth and value, in Global Asset Allocation: Techniques for Optimizing Portfolio Management. New York: John Wiley & Sons. Ghysels, E., 1998, On stable factor structure in asset pricing: Do time-varying betas help or hurt? Journal of Finance, 53, 549-573. Ferson, W., and C. Harvey, 1991, Sources of predictability in portfolio returns, Financial Analysts Journal, May/June, 49-56. Kao, D.-L., and R. Shumaker, 1999, Equity style timing, Financial Analysts Journal, January/February, 37-48. Keim, D., 1983, Size related anomalies and stock return seasonality: further empirical evidence, Journal of Financial Economics, 1, 13-32. Keim, D., and R. Stambaugh, 1986, Predicting returns in the stock and bond markets, Journal of Financial Economics, 17, 357-390. Levis, M., and M., Liodakis, 1999, The profitability of style rotation strategies in the United Kingdom, Journal of Portfolio Management, 26 (Fall), 73-86. Lo, A., and Mackinlay, A., 1990, When are contrarian profits due to stock market overreaction?, Review of Financial Studies, 3, 175-205. Merton, R. C., 1973, An intertemporal capital asset pricing model, Econometrica, 41, 867-888.

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