1 - GAIM 2003 Tactical Style Allocation (TSA) A New Form of Market Neutral Strategy Professor Noël Amenc [email protected] EDHEC Edhec Risk and Asset

1 - GAIM 2003

Tactical Style Allocation (TSA)

A New Form of Market Neutral Strategy

Professor Noël [email protected]

EDHECEdhec Risk and Asset Management Research Centre

2 - GAIM 2003

Overview

• Investment Philosophy• Forecasting Style Returns• Econometric Model• Portfolio Process• Implementation• Portfolio Performance• Next Step• References

3 - GAIM 2003

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 noïsy) in the absence of private information

specific

,

systematic

,,,, titftMitfti rRrR

4 - GAIM 2003

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 – 0.17 – 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 - GAIM 2003

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

specific

,

style - systematic

,,,,,//,

market - systematic

,,,,,

titftsizesizeitftMBMBi

tftMMitfti

rRrR

rRrR

6 - GAIM 2003


• 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 “mélange 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 - GAIM 2003


Classification of Active Portfolio Strategies Systematic – Market Systematic – Style Specific Form of active strategy Tactical Asset

Allocation Tactical Style

Allocation Stock Picking

Mutual fund – Stock picking X (discretionary)

X (discretionary)

X

Hedge fund – Stock picking long short

X X (discretionary)

X

Hedge fund – Stock picking equity market neutral

0 X (discretionary)

X

Mutual fund – Market timing X (discretionary or

systematic)

0 0

TSA – Market Neutral 0 X (systematic)

0

8 - GAIM 2003

Investment PhilosophyPerformance of TSA Strategies

• Kao and Shumaker (1999) and Amenc, Malaise, Martellini and Sfeir (2003) have formalized the concept of style timing or tactical style allocation

– Involves dynamic trading in various investment styles (growth, value, large cap, small cap)

– They build on seminal work by Fama and French (1992)

• Related papers include – Case and Cusimano (1995), Fan (1995), Fisher, Toms and Blount (1995),

Mott and Condon (1995), Sorensen and Lazzara (1995), Levis and Liodakis (1999), Oertmann (1999), Reiganum (1999), Avramov (2000), Ahmed, Lockwood and Nanda (2002), Amenc and Martellini (2001), Amenc, El Bied and Martellini (2002)

• The industry has started to look into TSA strategies– In 1993, Salomon Brothers developed a fact-based forecasting model for

the Growth/Value relative with monthly categorical forecasts– See Kao and Schumaker (1999) for discussion of practical implementation

of TSA strategy in the industry

9 - GAIM 2003

Investment PhilosophyPerformance of TSA Strategies

Timer with perfect forecast ability switches to bonds in 2000No negative returns or lossesAverage Ret. = 20.88%S.D. Ret. = 10.66%TAA increases return and decreases risk

Year S&P 500 Return Global Bond Index Return

1995 34.10 10.07

1996 18.91 -2.29

1997 25.52 2.07

1998 27.17 1.29

1999 16.19 -6.91

2000 -4.30 3.38

Average 19.60 1.27

St. Dev. 13.31 5.70

TAA: Stocks Versus Bonds

10 - GAIM 2003

Investment Philosophy Performance of TSA Strategies

Perfect timer gets a 27.10% average return with a 7.51% volatility, and no losses.

Year S&P Growth S&P Value S&P MidCap

S&P SmallCap

S&P 500

1995 34.79 33.38 29.59 31.82 34.10

1996 19.41 18.46 17.50 21.06 18.91

1997 26.61 24.25 27.47 23.53 25.52

1998 37.54 16.11 21.43 0.66 27.17

1999 20.87 10.49 19.37 13.83 16.19

2000 -16.52 9.57 20.91 15.38 -4.30

Average 20.45 18.71 22.71 17.71 19.60

St. Dev. 19.51 8.99 4.76 10.54 13.31

TSA rivals TAA

11 - GAIM 2003

Forecasting Style Returns The Dynamics of Style Differentials: Growth - Value

• Equity styles have contrasted performance under different economic conditions

Style Differential (annualized returns): S&P 500 Growth-Value

-150.00%

-100.00%

-50.00%

0.00%

50.00%

100.00%

150.00%

200.00%

01/9

7

05/9

7

09/9

7

01/9

8

05/9

8

09/9

8

01/9

9

05/9

9

09/9

9

01/0

0

05/0

0

09/0

0

01/0

1

05/0

1

09/0

1

01/0

2

05/0

2

Month

Rel

ativ

e R

etu

rn

S&P 500 GROWTH - S&P 500 VALUE

12 - GAIM 2003

Forecasting Style Returns The Dynamics of Style Differentials: Small Cap - Large Cap

• Equity styles have contrasted performance under different economic conditions

Size Differential (annualized returns): S&P 600 Small - S&P 500

-200.00%

-150.00%

-100.00%

-50.00%

0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

01/9

7

05/9

7

09/9

7

01/9

8

05/9

8

09/9

8

01/9

9

05/9

9

09/9

9

01/0

0

05/0

0

09/0

0

01/0

1

05/0

1

09/0

1

01/0

2

05/0

2

Month

Rel

ativ

e R

etu

rn

S&P 600 SMALL CAP - S&P 500

13 - GAIM 2003

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

14 - GAIM 2003

Forecasting Style Returns Contemporaneous Economic Conditions – Example of

Growth versus Value and the Term Spread

– The term spread has been proxied by differences between a 10Y T-Bond and a 3 month T-Bill rates

– These numbers have been generated from monthly data on the period ranging from September 1991 to May 2002 – Yellow signals difference between conditional and unconditional average returns greater than 5% or lower than -5% annualized – Pale blue signals difference between conditional and unconditional average returns between 2 and 5% or between –5 and –2% annualized

Percentage Change in Term Spread Low Medium High

Minimum Maximum Minimum Maximum Minimum Maximum

-4100.00% -6.59% -6.38% 5.98% 6.36% 284.21%

Mean Stdev Mean Stdev Mean Stdev Mean Stdev Correlation

S&P 500 7.04% 3.09% -0.32% -3.94% -6.72% 0.03% 10.28% 14.22% -0.13

S&P 500 GROWTH 10.09% 3.46% 0.30% -4.79% -10.39% 0.11% 10.64% 16.41% -0.11

S&P 500 VALUE 3.70% 3.12% -0.78% -3.08% -2.93% -0.48% 9.75% 13.81% -0.13

S&P 600 SMALL CAP -5.23% 1.56% 4.08% -4.95% 1.15% 2.71% 13.75% 17.47% -0.14

S&P 500 - S&P 600 SMALL CAP 12.27% 1.60% -4.40% -3.77% -7.87% 1.06% -3.47% 13.23% 0.05

S&P 500 GROWTH - S&P 500 VALUE 6.39% 2.33% 1.08% -1.92% -7.46% -1.01% 0.89% 10.74% 0.01

Unconditional ValuesDifference between Conditional Values and Unconditional Values

15 - GAIM 2003


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

16 - GAIM 2003


Growth versus Value and the Business Cycle

Real Quarterly GDP Low Medium High


-0.34% 0.55% 0.56% 1.07% 1.07% 2.01%


S&P 500 -4.28% 1.36% -1.91% 0.56% 6.19% -1.96% 10.28% 14.22% 0.17

S&P 500 GROWTH -9.94% 2.42% -1.20% -0.78% 11.14% -2.18% 10.64% 16.41% 0.22

S&P 500 VALUE 1.87% 0.55% -2.66% 1.44% 0.79% -1.91% 9.75% 13.81% 0.08

S&P 600 SMALL CAP 6.50% 0.66% -12.73% 1.58% 6.23% -2.71% 13.75% 17.47% 0.10

S&P 500 - S&P 600 SMALL CAP -10.78% -2.34% 10.82% 3.09% -0.04% -1.89% -3.47% 13.23% 0.06

S&P 500 GROWTH - S&P 500 VALUE -11.80% 1.66% 1.46% -1.83% 10.35% -0.89% 0.89% 10.74% 0.24

Unconditionnal ValuesDifference between Conditionnal Values and Unconditionnal Values

– The business cycle has been proxied by the growth in the real quarterly GDP

– These numbers have been generated from monthly data on the period ranging from September 1991 to May 2002

– Dark blue signals difference between conditional and unconditional average returns greater than 5% or lower than -5% annualized

– Pale blue signals difference between conditional and unconditional average returns between 2 and 5% or between –5 and –2% annualized

17 - GAIM 2003


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

18 - GAIM 2003


Growth versus Value and the Default Spread

Default Spread Low Medium High


0.53% 0.66% 0.66% 0.80% 0.80% 1.38%


S&P 500 5.44% 0.50% 4.61% -3.08% -10.05% 1.98% 10.28% 14.22% -0.12

S&P 500 GROWTH 9.54% -0.85% 4.44% -2.88% -13.99% 2.81% 10.64% 16.41% -0.14

S&P 500 VALUE 0.99% 1.20% 4.98% -2.53% -5.98% 1.14% 9.75% 13.81% -0.08

S&P 600 SMALL CAP -1.80% 2.21% 3.12% -4.39% -1.32% 1.78% 13.75% 17.47% 0.01

S&P 500 - S&P 600 SMALL CAP 7.24% 0.54% 1.49% -2.28% -8.73% 1.36% -3.47% 13.23% -0.14

S&P 500 GROWTH - S&P 500 VALUE 8.55% -2.46% -0.54% 0.73% -8.01% 1.08% 0.89% 10.74% -0.11


– The default spread has been proxied by differences between AAA and Baa long term bonds




19 - GAIM 2003

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

20 - GAIM 2003

Forecasting Style Returns Lagged (1 Month) Economic Conditions – Example of

Small versus Large Cap and Return on Large Cap Stocks

S&P 500 Index Return Low Medium High


-14.58% -0.63% -0.53% 2.79% 2.80% 11.16%


S&P 500 6.50% 2.55% 0.77% -2.44% -7.27% -0.50% 11.01% 14.27% -0.10

S&P 500 GROWTH 10.75% 2.38% -0.86% -2.77% -9.89% -0.17% 11.28% 16.53% -0.12

S&P 500 VALUE 1.77% 3.42% 2.48% -2.73% -4.25% -1.18% 10.57% 13.80% -0.06

S&P 600 SMALL CAP 0.20% 3.74% -3.08% -1.50% 2.88% -2.49% 14.12% 17.57% 0.00

S&P 500 - S&P 600 SMALL CAP 6.30% 3.42% 3.85% -4.15% -10.15% -0.54% -3.11% 13.35% -0.10

S&P 500 GROWTH - S&P 500 VALUE 8.98% 2.24% -3.34% -2.41% -5.64% -0.56% 0.71% 10.82% -0.11





21 - GAIM 2003

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

22 - GAIM 2003

Forecasting Style Returns Lagged (1 Month) Economic Conditions – Example of

Small versus Large Cap and the Term Spread

Term Spread Low Medium High


-0.61% 0.99% 1.03% 2.35% 2.40% 3.91%


S&P 500 1.66% 3.31% 5.28% -0.24% -6.94% -3.87% 11.01% 14.27% -0.04

S&P 500 GROWTH -1.67% 4.52% 11.09% -1.49% -9.43% -4.47% 11.28% 16.53% -0.01

S&P 500 VALUE 5.28% 2.91% -0.89% 0.18% -4.38% -3.70% 10.57% 13.80% -0.06

S&P 600 SMALL CAP -6.05% 3.48% 6.24% -0.33% -0.19% -3.63% 14.12% 17.57% 0.03

S&P 500 - S&P 600 SMALL CAP 7.70% 1.48% -0.96% 0.14% -6.74% -1.84% -3.11% 13.35% -0.07

S&P 500 GROWTH - S&P 500 VALUE -6.94% 3.80% 11.99% -2.97% -5.04% -2.88% 0.71% 10.82% 0.05


– The term spread has been proxied by differences between a 10Y T-Bond and a 3 month T-Bill rates




23 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 naïve 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 - GAIM 2003

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 7 th of the month– Therefore, monthly trading decisions take place on the 7th– When a variable is available after the 7 th 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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 ½ (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 ½ at the 10%

level– At least 67% can be regarded as is significantly greater than ½ 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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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 - GAIM 2003

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

Bet 2 : S C - L C > 0 Bet 2 : S C – LC < 0

Long SC / Short LC Short SC / Long LCShort V / Long G

Bet 1 : Growth - Value > 0

Bet 1 : Growth - Value < 0 Long SC / Short LCShort G / Long V Short G / Long V

Short SC / Long LC

Short V / Long G

37 - GAIM 2003

• 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 - GAIM 2003

• 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 87.5% < w < 100%, take w = 100% (0% weight in bet 2)

Portfolio ProcessRelative Weighting Rule

39 - GAIM 2003

• 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 - GAIM 2003

• 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 - GAIM 2003

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)

)constraint (leverage

)constraint (portfolio 1

)constraint neutrality-(beta 0

43210

43210

44332211

l

42 - GAIM 2003

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

43 - GAIM 2003

Monthly Allocation from June 2000 to December 2002

Portfolio PerformanceBack Test with ETFs

Recommendations Large Cap Growth Large Cap Value Large Cap Small CapJune 2000 -23.43% 24.86% 21.72% -26.57%July 2000 -23.40% 24.62% 21.42% -26.60%August 2000 25.20% -26.77% -23.23% 28.75%September 2000 -36.29% 38.35% 11.17% -13.71%October 2000 22.20% -24.56% 21.31% -25.44%November 2000 -37.85% 41.85% -12.15% 14.41%December 2000 -25.21% 28.78% -24.79% 29.20%January 2001 -25.05% 30.02% -24.95% 30.12%February 2001 -24.91% 29.70% -25.09% 29.53%March 2001 -22.65% 27.87% 23.18% -27.35%April 2001 -24.60% 30.46% -25.40% 29.66%May 2001 -24.43% 30.53% -25.57% 29.38%June 2001 -24.47% 30.71% -25.53% 29.65%July 2001 -24.47% 30.63% -25.53% 29.57%August 2001 -24.50% 30.79% -25.50% 29.80%September 2001 -12.30% 15.15% 44.66% -37.70%October 2001 -12.28% 15.16% -37.72% 44.62%November 2001 -24.60% 30.80% -25.40% 29.99%December 2001 -24.35% 30.52% -25.65% 29.22%January 2002 -12.01% 15.08% -37.99% 43.27%February 2002 -50.00% 60.63% 0.00% 0.00%March 2002 -36.08% 42.69% 12.33% -13.92%April 2002 0.00% 0.00% 0.00% 0.00%May 2002 -50.00% 60.09% 0.00% 0.00%June 2002 31.43% -37.69% 10.73% -12.31%July 2002 37.25% -44.31% -12.75% 14.44%August 2002 -11.38% 13.00% 34.52% -38.62%September 2002 -11.02% 12.90% 32.77% -38.98%October 2002 -23.34% 26.27% 22.96% -26.66%November 2002 -13.62% 14.70% -36.38% 48.56%December 2002 -35.91% 38.42% 10.69% -14.09%

44 - GAIM 2003

Results from investing in ETFs traded on the AMEX (from June 2000 to December 2002)

• Selected ETFs : iShares & Spiders

• Working Assumptions– executed prices = last trade prices– transaction fees: 1.8 cent/share (pair trade)– stock loan fees: 40 bps– administration costs: USD 4,000 a month– initial capital: USD 2 million investment– risk free rate: LIBOR 1 month


45 - GAIM 2003

Up months in up market: 91.67% Up market outperformance: 41.67%Up months in down market: 68.42% Down market outperformance:

89.47%


Significant Returns whatever the market’s conditions

TSA Return Distribution

0

2

4

6

8

10

12

rdt <

-2%

-2%

< rd

t < -

1%

-1%

< rd

t < 0

%

0%<

rdt <

1%

1%<

rdt <

2%

rdt >

2%

Returns > 077.5 %

Cumulative Net Return TSA vs S&P500

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

TS

A C

um

ula

tiv

e R

etu

rn

-50.00%

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

S&

P 5

00

cu

mu

lati

ve

re

turn

TSA Fund S&P 500

46 - GAIM 2003


January February March April May June July August September October November December2000 -1.56% 1.93% 3.97% 1.30% 0.72% 0.22% 4.32%2001 1.32% 1.84% 1.20% 0.33% 0.74% 0.95% -1.54% 0.90% -0.90% 1.83% -0.25% 1.99%2002 -0.16% 0.90% 1.38% 0.41% 0.80% -1.08% 2.40% 0.59% -0.56% 1.87% 1.99% 0.30%

TSA Fund S&P 500 Cumulative Return 32.00% -40.20% => Excess Return +72.20%Annualised Return 10.90% -18.03%Annualised Std Deviation 4.71% 18.72% => TSA Volatility 4 X lower than S&P500'sDownside Deviation (3.0%) 2.26% 11.49%Sortino (3.0%) 3.50 -1.83Sharpe 1.84 -1.101st Centile -1.55% -10.47%% Negative Returns 22.58% 61.29% => Few losing months with TSA StrategyWorst Monthly Drawdown -1.56% -11.00%

Peak to Valley -1.56% -46.28% => No outliers with TSA StrategyMonths in Max Drawdown 1 25

Months to recover 1 no recovery

Beta 0.075 => TSA Strategy uncorrelated with stocks indicesAlpha 0.099 => Significant Alpha

The risk / return and correlation characteristics of the TSA Strategy are fairly stable and therefore can be extrapolated into the future

47 - GAIM 2003

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 - GAIM 2003

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

49 - GAIM 2003

References (1)

• Ahmed, P., L. Lockwood, and S. Nanda, 2002, Multistyle rotation strategies, Journal of Portfolio Management, Spring, 17-29.

• Amenc, N., S. El Bied and L. Martellini, 2002, Evidence of predictability in hedge fund returns and multi-style multi-class style allocation decisions, Financial Analysts Journal, forthcoming

• Amenc, N., and L. Martellini, 2001, It’s time for asset allocation, Journal of Financial Transformation, 3, 77-88.

• Amenc, N., P. Malaise, L. Martellini and D. Sfeir, 2003, Tactical style allocation: a new form of market neutral strategy, Journal of Alternative Investments, forthcoming.

• Avramov, D., 2002, Stock return predictability and model uncertainty, Journal of Financial Economics, forthcoming.

• Campbell, J., 1987, Stock returns and the term structure, Journal of Financial Economics, 18, 373-399.

• Campbell, J., and R. Shiller, 1988, Stock prices, earnings, and expected dividends, Journal of Finance, 43, 661-676.

• Case, D., and S., Cusimano, 1995, Historical tendencies of equity style returns and the prospects for tactical style allocation, chapter 12 from Equity Style Management, Irwin Publishing.

50 - GAIM 2003

References (2)

• Chow, G, 1960, Tests of equality between sets of coefficients in two linear regressions, Econometrica, 28, 591-605.

• Daniel, K., Grinblatt, M., Titman S., and Wermers, S., 1997, Measuring mutual fund performance with characteristic based benchmarks, Journal of Finance, 52, 3, 1035-1058.

• Fama, E., 1981, Stock returns, real activity, inflation, and money, American Economic Review, 545-565.

• Fama, E., and K. French, 1992, The cross-section of expected stock returns, Journal of Finance, 442-465.

• Fama, E., and K. French, 1998, Value versus growth: the international evidence, Journal of Finance, 53, 6, 1975-2000.

• Fama, E., and W. Schwert, 1977, Asset returns and inflation, Journal of Financial Economics, 115-46.

• Fan, S., 1995, Equity style timing and allocation, chapter 14 from Equity Style Management, Irwin Publishing.

• Ferson, W., and C. Harvey, 1991, Sources of predictability in portfolio returns, Financial Analysts Journal, May/June, 49-56.

• Fisher, K., J., Toms, and K., Blount, 1995, Driving factors behind style-based investing, chapter 22 from Equity Style Management, Irwin Publishing.

51 - GAIM 2003

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.

52 - GAIM 2003

References (4)

• Mott, C., and K., Condon, 1995, Exploring the cycles of small-cap style performance, chapter 9 from Equity Style Management, Irwin Publishing.

• Oertmann, P., 1999, Why do value stocks earn higher returns than growth stocks, and vice-versa?, working paper, Investment Consulting Group Inc. and University of St. Gallen.

• Reignaum, M., 1999, The significance of market capitalization in portfolio management over time, Journal of Portfolio Management, 25 (Summer), 39-50.

• Ross, S., 1976, The arbitrage theory of capital asset pricing, Journal of Economic Theory, December, 341-360.

• Sharpe, W., 1963, A simplified model for portfolio analysis, Management Science, 277-293.

• Sorensen, E., and C. Lazzara, 1995, Equity style management: the case of growth and value, chapter 4 from Equity Style Management, Irwin Publishing.

• White, H., 1980, A heteroskedasticity-consistent covariance matrix and a direct test for heteroskedasticity, Econometrica, 48, 817–838.

Documents

1 - GAIM 2003 Tactical Style Allocation (TSA) A New Form of Market Neutral Strategy Professor Noël Amenc [email protected] EDHEC Edhec Risk and Asset