EDHEC
Edhec Risk and Asset Management Research Centre
Tactical Style Allocation (TSA)
A New Form of Market Neutral Strategy
Professor Noël Amenc
noel.amenc@edhec.edu
1 - GAIM 2003
Overview
• Investment Philosophy
• Forecasting Style Returns
• Econometric Model
• Portfolio Process
• Implementation
• Portfolio Performance
• Next Step
• References
2 - GAIM 2003
Investment Philosophy
Timing and Picking
•
Stock (excess) returns can be decomposed into a systematic
and a specific components (Sharpe’s (1963) market model)
Ri ,t - r f ,t = b i[R M ,t - r f ,t ]+ e i ,t
14
4244
3 {
systematic
•
specific
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
3 - 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 – 0.17b – 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.
4 - GAIM 2003
Investment Philosophy
TAA, TSA and Stock Picking
•
Extension of the market model
Ri ,t - r f ,t = b i , M [RM ,t - r f ,t
]
1442443
systematic - market
+ b i , B/M [RB/M ,t - r f ,t]+ b i , size[Rsize,t - r f ,t ]+ e i ,t
144444424444443 {
systematic - style
•
specific
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
5 - GAIM 2003
Investment Philosophy
TAA, 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 “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
6 - GAIM 2003
Investment Philosophy
TAA, TSA and Stock Picking
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
X
(discretionary)
X
(discretionary)
X
(discretionary)
0
X
X
(systematic)
0
Hedge fund – Stock picking
long short
Hedge fund – Stock picking
equity market neutral
0
Mutual fund – Market timing
X
(discretionary or
systematic)
0
TSA – Market Neutral
7 - GAIM 2003
X
X
0
Investment Philosophy
Performance 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
8 - GAIM 2003
Investment Philosophy
Performance of TSA Strategies
TAA: Stocks Versus Bonds
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
Timer with perfect forecast ability switches to bonds in 2000
No negative returns or losses
Average Ret. = 20.88%
S.D. Ret. = 10.66%
TAA increases return and decreases risk
9 - GAIM 2003
Investment Philosophy
Performance of TSA Strategies
TSA rivals TAA
S&P Small
Cap
31.82
S&P 500
33.38
S&P Mid
Cap
29.59
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
Year
S&P Growth
S&P Value
1995
34.79
1996
34.10
Perfect timer gets a 27.10% average return with a 7.51% volatility, and no losses.
10 - 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
200.00%
Relative Return
150.00%
100.00%
50.00%
0.00%
-50.00%
-100.00%
-150.00%
Month
S&P 500 GROWTH - S&P 500 VALUE
11 - 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
250.00%
200.00%
Relative Return
150.00%
100.00%
50.00%
0.00%
-50.00%
-100.00%
-150.00%
-200.00%
Month
12 - GAIM 2003
S&P 600 SMALL CAP - S&P 500
Forecasting Style Returns
Contemporaneous 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
13 - GAIM 2003
Forecasting Style Returns
Contemporaneous Economic Conditions – Example of
Growth versus Value and the Term Spread
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
Difference between
Conditional Values and Unconditional Values
Unconditional Values
–
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
14 - GAIM 2003
Forecasting Style Returns
Contemporaneous 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
15 - GAIM 2003
Forecasting Style Returns
Contemporaneous Economic Conditions – Example of
Growth versus Value and the Business Cycle
Real Quarterly GDP
Low
Medium
High
Minimum
Maximum
Minimum
Maximum
Minimum
Maximum
-0.34%
0.55%
0.56%
1.07%
1.07%
2.01%
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Correlation
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
Difference between
Conditionnal Values and Unconditionnal Values
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
16 - GAIM 2003
Forecasting Style Returns
Contemporaneous 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
17 - GAIM 2003
Forecasting Style Returns
Contemporaneous Economic Conditions – Example of
Growth versus Value and the Default Spread
Default Spread
Low
Medium
High
Minimum
Maximum
Minimum
Maximum
Minimum
Maximum
0.53%
0.66%
0.66%
0.80%
0.80%
1.38%
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Correlation
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
Difference between
Conditionnal Values and Unconditionnal Values
Unconditionnal Values
– The default spread has been proxied by differences between AAA and Baa long term bonds
– 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
18 - GAIM 2003
Forecasting Style Returns
Lagged (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
19 - 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
Minimum
Maximum
Minimum
Maximum
Minimum
Maximum
-14.58%
-0.63%
-0.53%
2.79%
2.80%
11.16%
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Correlation
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
Difference between
Conditionnal Values and Unconditionnal Values
Unconditionnal Values
– 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
20 - GAIM 2003
Forecasting Style Returns
Lagged (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
21 - 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
Minimum
Maximum
Minimum
Maximum
Minimum
Maximum
-0.61%
0.99%
1.03%
2.35%
2.40%
3.91%
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Correlation
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
Difference between
Conditionnal Values and Unconditionnal Values
Unconditionnal Values
– 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
– 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
22 - GAIM 2003
Forecasting Style Returns
Contemporaneous 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)
23 - GAIM 2003
Forecasting Style Returns
Contemporaneous 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))
24 - 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
–
–
We prefer financial variables, more forward-looking than economic variables
However, we also consider economic variables while controlling for the risk of backfilling and posterior adjustment
• Principle 2: Financial versus Economic Variables
• 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
–
–
25 - GAIM 2003
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
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 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.
26 - GAIM 2003
Econometric Model
Selecting 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
–
–
–
–
•
27 - GAIM 2003
Interest rates
Risk
Relative cheapness of stock prices
Stock returns
Other variables include liquidity indicators, commodity
prices, currency rates, etc.
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
28 - 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
29 - 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
30 - 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
–
–
–
–
31 - GAIM 2003
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
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
–
–
–
–
32 - GAIM 2003
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
Econometric Model
Improving the Model – Regression Tuning
•
•
•
Autocorrelation
– Test for autocorrelation: Durbin-Watson, the Q-statistic and the BreuschGodfrey 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))
33 - GAIM 2003
Econometric Model
Improving 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
34 - GAIM 2003
Econometric Model
Updating 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 tstat 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
35 - GAIM 2003
Portfolio Process
Turning 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
Bet 2 : S C - L C > 0 Bet 2 : S C – LC < 0
Bet 1 : Growth - Value > 0
Long SC / Short LC Short SC / Long LC
Short V / Long G
Short V / Long G
Bet 1 : Growth - Value < 0
Long SC / Short LC Short SC / Long LC
Short G / Long V
Short G / Long V
• 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
36 - GAIM 2003
Portfolio Process
Confidence in Model versus Confidence in Prediction
•
•
•
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%)
37 - GAIM 2003
Portfolio Process
Relative Weighting Rule
•
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
–
–
–
–
–
38 - GAIM 2003
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 Process
Relative Weighting of the Bets and Portfolio Decisions
• 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
39 - GAIM 2003
Portfolio Process
Absolute Weighting Rule
•
•
•
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
40 - GAIM 2003
Portfolio Process
Beta 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)
 1 b1 +  2 b 2 +  3 b 3 +  4 b 4 = 0 (beta - neutrality constraint )

 0 +  1 +  2 +  3 +  4 = 1 (portfolio constraint )
  +  +  +  +  = l (leverage constraint )
1
2
3
4
 0
41 - GAIM 2003
Implementation
Investible 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
42 - GAIM 2003
Portfolio Performance
Back Test with ETFs
Monthly Allocation
from June 2000 to
December 2002
43 - GAIM 2003
Recommendations
June 2000
July 2000
August 2000
September 2000
October 2000
November 2000
December 2000
January 2001
February 2001
March 2001
April 2001
May 2001
June 2001
July 2001
August 2001
September 2001
October 2001
November 2001
December 2001
January 2002
February 2002
March 2002
April 2002
May 2002
June 2002
July 2002
August 2002
September 2002
October 2002
November 2002
December 2002
Large Cap Growth Large Cap Value Large Cap
-23.43%
24.86%
21.72%
-23.40%
24.62%
21.42%
25.20%
-26.77%
-23.23%
-36.29%
38.35%
11.17%
22.20%
-24.56%
21.31%
-37.85%
41.85%
-12.15%
-25.21%
28.78%
-24.79%
-25.05%
30.02%
-24.95%
-24.91%
29.70%
-25.09%
-22.65%
27.87%
23.18%
-24.60%
30.46%
-25.40%
-24.43%
30.53%
-25.57%
-24.47%
30.71%
-25.53%
-24.47%
30.63%
-25.53%
-24.50%
30.79%
-25.50%
-12.30%
15.15%
44.66%
-12.28%
15.16%
-37.72%
-24.60%
30.80%
-25.40%
-24.35%
30.52%
-25.65%
-12.01%
15.08%
-37.99%
-50.00%
60.63%
0.00%
-36.08%
42.69%
12.33%
0.00%
0.00%
0.00%
-50.00%
60.09%
0.00%
31.43%
-37.69%
10.73%
37.25%
-44.31%
-12.75%
-11.38%
13.00%
34.52%
-11.02%
12.90%
32.77%
-23.34%
26.27%
22.96%
-13.62%
14.70%
-36.38%
-35.91%
38.42%
10.69%
Small Cap
-26.57%
-26.60%
28.75%
-13.71%
-25.44%
14.41%
29.20%
30.12%
29.53%
-27.35%
29.66%
29.38%
29.65%
29.57%
29.80%
-37.70%
44.62%
29.99%
29.22%
43.27%
0.00%
-13.92%
0.00%
0.00%
-12.31%
14.44%
-38.62%
-38.98%
-26.66%
48.56%
-14.09%
Portfolio Performance
Back Test with ETFs
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
44 - GAIM 2003
Portfolio Performance
Back Test with ETFs
Significant Returns whatever the market’s conditions
Up months in up market: 91.67%
Up months in down market: 68.42%
Up market outperformance: 41.67%
Down market outperformance: 89.47%
TSA Return Distribution
Cumulative Net Return TSA vs S&P500
Returns > 0
77.5 %
12
35.00%
10.00%
30.00%
10
8
6
4
2
25.00%
-10.00%
20.00%
15.00%
-20.00%
10.00%
-30.00%
5.00%
-40.00%
0.00%
45 - GAIM 2003
rdt > 2%
1%< rdt < 2%
0%< rdt < 1%
-1%< rdt < 0%
-2%< rdt < -1%
rdt < -2%
0
-5.00%
-50.00%
TSA Fund
S&P 500
S&P 500 cumulative return
TSA Cumulative Return
0.00%
Portfolio Performance
Back Test with ETFs
January February March
2000
2001
2002
1.32%
-0.16%
June
July August September October November December
-1.56% 1.93%
3.97%
1.30%
0.72%
0.22%
4.32%
1.84% 1.20% 0.33% 0.74% 0.95% -1.54%
0.90%
-0.90%
1.83%
-0.25%
1.99%
0.90% 1.38% 0.41% 0.80% -1.08% 2.40%
0.59%
-0.56%
1.87%
1.99%
0.30%
Cumulative Return
Annualised Return
Annualised Std Deviation
Downside Deviation (3.0%)
Sortino (3.0%)
Sharpe
1st Centile
% Negative Returns
Worst Monthly Drawdown
Peak to Valley
Months in Max Drawdown
Months to recover
Beta
Alpha
April
May
TSA Fund
32.00%
10.90%
4.71%
2.26%
3.50
1.84
-1.55%
22.58%
-1.56%
-1.56%
1
1
0.075
0.099
S&P 500
-40.20%
-18.03%
18.72%
11.49%
-1.83
-1.10
-10.47%
61.29%
-11.00%
-46.28%
25
no recovery
=> Excess Return +72.20%
=> TSA Volatility 4 X lower than S&P500's
=> Few losing months with TSA Strategy
=> No outliers with TSA Strategy
=> TSA Strategy uncorrelated with stocks indices
=> Significant Alpha
=> The risk / return and correlation characteristics of the TSA Strategy are fairly stable
and therefore can be extrapolated into the future
46 - GAIM 2003
Next Step
Eurex research project
• Implementing an econometric process for
•
managing a European Equity long/short fund
This process relies on Eurex derivatives
–
–
–
–
47 - GAIM 2003
DJ EuroStoxx 50 Index Futures
DJ EuroStoxx 50 Options
DJ EuroStoxxSM Banks Index Futures and Options
DJ EuroStoxxSM Telecom Index Futures and Options
Next Step
Eurex 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
48 - GAIM 2003
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•
•
•
•
•
•
•
•
49 - GAIM 2003
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