Optimal Alpha Modeling
Q Group Conference
March 26, 2007
Eric Sorensen
Eddie Qian
Ronald Hua
Topics of Quantitative Equity Research
¾Statistical methodology – factor returns, IC, IR
y Fama, Eugene F and James D. MacBeth. 1973. “Risk, Return, and
Equilibrium: Empirical Tests.” Journal of Political Economy, 81, 607-636
y Grinold, R.C. 1989. “The Fundamental Law of Active Management.”
Journal of Portfolio Management, vol. 15, no. 3 (Spring): 30-37
y Grinold, Richard C. 1994, “Alpha is Volatility Times IC Times Score.”
Journal of Portfolio Management, vol. 20, no. 4, pp 9 – 16
y Grinold, Richard C. And Ronald N. Kahn, 1999. Active Portfolio
Management, McGraw-Hill, New York
y Goodwin, Thomas H. 1998. “The Information Ratio.” Financial Analysts
Journal, vol. 54, no. 4 (July/August) 34-43
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Topics of Quantitative Equity Research
¾Portfolio setting – long-short, constrained long-short
y Clarke, Roger, Harindra de Silva, and Steven Thorley, 2002. “Portfolio
Constraints and the Fundamental Law of Active Management,” Financial
Analysts Journal, vol. 58, no. 5 (Sept/Oct) 48-66
y Clarke Roger, Harindra de Silva, and Steven Thorley. 2004. “Toward
More Information Efficient Portfolios.” Journal of Portfolio Management.
vol. 31, no. 1 (Fall) 54-63
y Grinold, Richard C. and Ronald N. Kahn, 2000. “The Efficiency Gains of
Long-short Investing.” Financial Analysts Journal, vol. 56, no. 6
(November/December) 40-53
y Jacobs, Bruce I. And Kenneth N. Levy, 2006. “Enhanced Active Equity
Strategies.” Journal of Portfolio Management, vol. 32, no. 2 (Spring
2006) 45-55
y Sorensen, Eric, Ronald Hua and Edward Qian, “Aspects of Constrained
Long/short Equity Portfolios.” Journal of Portfolio Management, vol. 33,
no. 2, (Winter 2007), 12-22
Q Group Conference, March 26, 2007
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Topics of Quantitative Equity Research
¾Portfolio turnover and portfolio dynamics
y Kahn, Ronald N., And J. S. Shaffer. 2005. “The Surprising Small Impact
of Asset Growth on Expected Alpha.” Journal of Portfolio Management,
vol. 32, no. 1 (Fall 2005) 49-60
y Sneddon, Leigh, “The Dynamics of Active Portfolios.” Northfield
Research Conference Proceedings, 2005
y Grinold, Richard C. “A Dynamic Model of Portfolio Management.”
Journal of Investment Management, vol. 4, no. 2
y Coppejans, Mark and Ananth Madhavan, “Active Management and
Transactions Costs”, 2006, working paper, BGI
y Qian, Edward, Eric Sorensen and Ronald Hua, “Information Horizon,
Portfolio Turnover, and Optimal Alpha Models”. Forthcoming, JPM
Q Group Conference, March 26, 2007
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Optimal Alpha Modeling – An Outline
¾Optimal multi-factor models
y Single factor evaluation: risk-adjusted IC, strategy risk, turnover
y Multi-factor IR maximization: IC standard deviation, IC correlation (not
factor correlation), orthogonalized “factors”
y Qian, Edward and Ronald Hua, “Active Risk and Information Ratio”,
Journal of Investment Management, vol. 2., no. 3, (2004) 20-34
y Sorensen, Eric, Ronald Hua, Edward Qian and Robert Schoen,
“Multiple Alpha Sources and Active Management.” Journal of Portfolio
Management, vol. 30, no. 2 (Winter 2004) 39-45
¾Contextual models
y Moving away from one-size-fits-all: piecewise linear models
y Sorensen, Eric, Ronald Hua and Edward Qian, “Contextual
Fundamental, Models, and Active Management.” Journal of Portfolio
Management, vol. 32, no. 1 (Fall 2005) 23-36
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Optimal Alpha Modeling - Continued
¾Optimal models with turnover constraints
y Turnover endogenous not exogenous
y Integrated modeling approach
y Qian, Edward, Ronald Hua and John Tilney, “Portfolio Turnover of
Quantitatively Managed Portfolios.” 2004, Proceeding of the 2nd
IASTED International Conference, Financial Engineering and
Applications, Cambridge, MA
y Qian, Edward, Eric Sorensen and Ronald Hua, “Information Horizon,
Portfolio Turnover, and Optimal Alpha Models”. Forthcoming, JPM
y Qian, Edward, Ronald Hua and Eric Sorensen, Quantitative Equity
Portfolio Management: Modern Techniques and Applications,
Forthcoming, CRC press, 2007
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The Analytical Framework of Measuring Investment Skill
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Skill Measures
¾Goal: Hit rate → IC → IR → α
¾Hit rate is a basic measure of skill
y Play well
y Play often
y Play a worthwhile game (dispersion)
¾IC is a statistical measure of skill
y Correlation of forecast residual return with ex post residual return
y Based on well-accepted statistical methods
¾IR is the reward to risk in residual space
y Like Sharpe ratio in total risk space
y Relates skill directly to Capital Market Theory, assuming specific IC properties
and investor decision process
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FLAM
¾The fundamental law of active management (Grinold, 1989)
y IR ≈ skill applied to breadth
y Gives insight, rather than operational
y Requires several assumptions
IR = IC N
¾Investor behavior assumptions
y Manager knows the metric of skill
y Manager applies (optimizes) skill, according to CAPM
¾Security behavior assumptions
y Same skill level applies to all asset choices
y Sources of information are independent
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Optimal Multi-Factor Models: Maximizing IR
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IR Definition
¾Fundamental law of active management IR = IC N
y Do we then maximizing expected IC?
y What about IC volatility?
y What defines IC?
Time Series of IC
0.25
0.20
Avg IC
Stdev IC
IR
0.15
0.10
CFO2EV
0.055
0.053
1.04
0.05
Corr
0.00
-0.05
-0.10
-0.15
CFO2EV
Ret9
D
ec
-8
6
D
ec
-8
7
D
ec
-8
8
D
ec
-8
9
D
ec
-9
0
D
ec
-9
1
D
ec
-9
2
D
ec
-9
3
D
ec
-9
4
D
ec
-9
5
D
ec
-9
6
D
ec
-9
7
D
ec
-9
8
D
ec
-9
9
D
ec
-0
0
D
ec
-0
1
D
ec
-0
2
D
ec
-0
3
-0.20
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-0.50
Ret9
0.051
0.092
0.55
IC Definitions
ICraw = corr ( f , r )
¾Raw IC
ICrisk-adjusted = corr ( Ft ,R t )
¾Risk-adjusted IC
¾There could be a big difference
Raw IC and Risk-adjusted IC
0.30
IC.raw
0.25
IC.refine
Fi =
σi
r − m0 − m1β1i − L − mK β Ki
Ri = i
σi
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
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Dec-02
Dec-01
Dec-00
Dec-99
Dec-98
Dec-97
Dec-96
Dec-95
Dec-94
Dec-93
Dec-92
Dec-91
Dec-90
Dec-89
Dec-88
Dec-87
-0.20
Dec-86
GP2EV
f i − l0 − l1β1i − L − lK β Ki
IR Derivation
Single Period Analysis
Multi Period Analysis
N
α t = ∑ wi ri
α t = ICt N σ model
i =1
wi = λ −1
N
fi − l0 − l1β1i − L − lK β Ki
α t = ∑ wi ri = λ
i =1
σ
−1
σ = std ( ICt ) N σ model
2
i
N
∑FR
i =1
i
i
ICt
IR ≈
std ( ICt )
α t = ( N − 1) λt−1corr ( Ft ,R t ) dis ( Ft ) dis(R t )
α t = ICt N − 1σ model dis(R t ) ≈ ICt N σ model
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IR Results
¾Information ratio is approximately average IC/standard
deviation of IC
¾True active risk consists of
σ = std(IC) N σ model
y Risk-model target tracking error
y Strategy risk std(IC)
y The strategy risk is different for different factors
¾The fundamental law of active management is true only if
std(IC) =
1
N
y It is only due to the sampling error, implying IC is time invariant
y This is not likely to be true in reality
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IR Maximization of Multifactor Models
¾A quantitative framework for combing multiple factors
y Similar to optimal allocation problem for multiple active managers
¾Individual factor (one manager)
y Average IC (expected alpha), standard deviation of IC (active risk)
¾Multi factors (managers)
y IC correlation: time series correlations between different IC’s is key
y Analogous to correlations between excess returns of different managers
y The correlations between different factors are much less important
y Factor correlation is not the same as IC correlation
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IC Correlation – Indication of Diversification
Factor Correlation
IC Correlation
0.40
0.30
0.20
average = -0.04
stdev = 0.10
Avg IC
Stdev IC
IR
0.10
CFO2EV
0.055
0.053
1.04
Ret9
0.051
0.092
0.55
0.00
Corr
-0.10
-0.50
-0.20
-0.30
CFO2EV/RET9
IC Correlation
D
D
ec
-8
6
ec
-8
D 7
ec
-8
D 8
ec
-8
D 9
ec
-9
D 0
ec
-9
D 1
ec
-9
D 2
ec
-9
D 3
ec
-9
D 4
ec
-9
D 5
ec
-9
D 6
ec
-9
D 7
ec
-9
D 8
ec
-9
D 9
ec
-0
D 0
ec
-0
D 1
ec
-0
D 2
ec
-0
D 3
ec
-0
4
-0.40
¾In many cases, IC correlations are significantly different from average
factor correlations
¾IC correlations are crucial to maximize multi-period IR
¾Factor correlations are useful for single-period composite scores
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IR Maximization of Multifactor Models
Problem
Maximize
avg(ICt )
IR =
std (ICt )
Q Group Conference, March 26, 2007
Solution
(
IC = IC1 , IC2 ,L, ICM
)
w* ∝ Σ −IC1 IC
19
(
′ Σ = ρ
IC
ij ,IC
)
M
i , j =1
Correlated Factors
¾Correlated factors in general leads to correlated ICs
y High IC correlation can lead to unstable factor weights
¾Correlated factors also present a problem in return attribution
¾Fama-MacBeth formulation leads to information loss
r = α + β1f1 + β2f 2 + ε,
Coefficient should be interpreted as the residual f2
influence netting out other factors.
f1
r = α + β1ε f1 + ε1 ,
r = α + β2ε f 2 + ε 2 ,
εf2
where
ε f1 : is the residual portion of f1 uncorrelated with f 2 , i.e. f 2 = ρf1 + ε f 2 , and
ε f 2 : is the residual portion of f 2 uncorrelated with f1 , i.e. f1 = ρf 2 + ε f 2 .
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εf1
Sequential Orthogonalization
¾Utilize full information set for the alpha model
¾Make factor correlations stable – always zero
Identical estimations in one single regression.
f2
f1
r = α + β1*f1 + β2*ε f 2 + ε,
r = α + β1*f1 + ε1 ,
r = α + β2*ε f 2 + ε 2 ,
εf2
f1
where
r : is the vector of cross - sectional security returns,
f1 , f 2 : are vectors of cross - sectional factor scores,
ε ,ε1 ,ε 2 : are vectors of regression residuals, and
ε f 2 : is the residual portion of f 2 uncorrelated with f1 , i.e. f 2 = ρf1 + ε f 2 .
Q Group Conference, March 26, 2007
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Contextual Models – A Unique Model for Every Stock
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Contextual Models
¾Theoretical advances
y Conditional asset pricing
¾Practical approaches
y Style investing
y Sector models
¾Contextual modeling
y A piecewise linear model
y Partitioning the security universe according to risk / attributes
y It follows business cycle of individual stocks
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Contextual Model – A Two Dimensional Example
High Value
Stock
Stock on
valuation
spectrum
Low Growth Model
High Growth Model
Stock on
growth
spectrum
Low Value
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Contextual Alpha Modeling – Factor Weights
20 models
universe
large
large
large
large
large
large
large
large
large
large
small
small
small
small
small
small
small
small
small
small
high/low
high
low
high
low
high
low
high
low
high
low
high
low
high
low
high
low
high
low
high
low
riskfactor
growth
growth
value
value
earnyld
earnyld
earnvar
earnvar
predBeta
predBeta
growth
growth
value
value
earnyld
earnyld
earnvar
earnvar
predBeta
predBeta
d2p
4.4%
7.1%
13.0%
2.4%
22.5%
1.5%
12.4%
0.6%
5.0%
3.7%
9.1%
5.1%
8.2%
3.4%
4.8%
7.1%
7.8%
1.2%
7.0%
2.1%
b2p
-0.2%
10.9%
2.7%
2.2%
0.2%
2.1%
1.0%
0.3%
-1.4%
3.1%
1.5%
4.0%
3.0%
1.5%
3.1%
2.7%
1.9%
1.5%
1.7%
2.6%
Value
e2p
-0.3%
5.0%
1.1%
1.3%
4.0%
-3.3%
-0.2%
1.4%
0.5%
2.1%
2.0%
3.5%
1.1%
1.9%
6.2%
4.4%
1.3%
2.1%
1.0%
3.4%
c2p
6.2%
13.8%
10.1%
9.2%
17.2%
9.9%
7.3%
10.2%
6.5%
7.7%
8.9%
12.5%
8.9%
8.3%
17.7%
10.6%
6.4%
13.6%
8.0%
11.3%
holt
3.0%
11.3%
7.0%
6.2%
8.5%
11.6%
2.5%
12.5%
3.3%
7.8%
2.9%
4.3%
1.3%
2.0%
1.5%
3.6%
0.3%
3.0%
1.4%
5.8%
oe
20.5%
4.2%
5.2%
24.4%
4.5%
16.0%
14.3%
27.5%
25.2%
14.6%
14.1%
9.6%
8.4%
15.9%
11.5%
13.7%
8.9%
15.6%
19.7%
10.6%
Fundamental
fs
eq
capx
14.7% 17.1%
4.1%
-1.6% 16.1%
7.2%
6.8% 12.5%
8.7%
9.0% 15.1%
2.2%
1.8% 11.0%
6.3%
3.7% 17.6%
6.1%
12.6% 13.9% 10.4%
5.8% 16.3%
2.8%
11.1% 20.8%
4.2%
1.7% 27.1%
3.0%
9.7% 13.6%
7.0%
7.2% 13.7%
8.6%
12.0% 14.9%
8.9%
9.4% 21.7%
3.4%
8.6% 18.2%
7.8%
5.9% 13.2%
3.7%
7.8% 24.9%
9.1%
12.8% 17.7%
9.0%
16.2% 16.2%
5.3%
13.7% 13.8%
8.6%
noag
8.7%
9.8%
20.6%
6.7%
15.2%
5.7%
18.7%
5.4%
8.4%
10.7%
18.1%
10.9%
15.3%
15.0%
7.0%
16.9%
15.8%
14.1%
16.9%
6.3%
Factor Weights
Source: PanAgora Asset Management
Q Group Conference, March 26, 2007
Table is shown for illustrative purposes only.
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Momentum
pm
em
7.5% 13.2%
1.7% 11.2%
3.4%
8.9%
8.7% 12.6%
3.9%
4.8%
9.1% 13.2%
2.9%
3.8%
5.5% 11.5%
5.0%
8.6%
4.0% 14.4%
6.5%
6.7%
9.7% 10.9%
7.8% 10.2%
8.7%
8.8%
6.7%
6.8%
8.4%
9.9%
7.3%
8.5%
4.6%
4.7%
4.0%
2.6%
8.1% 13.8%
Company’s Contextual Dimensions
B: Model Weights
Category
Growth
Value
Large
Earnings
Yield
Earnings
Variability
Beta
Growth
Value
Small
Earnings
Yield
Earnings
Variability
Beta
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
High
Low
IBM
1%
4%
1%
10%
2%
83%
-
GM
1%
48%
50%
1%
-
TYC VSAT
94%
0%
0%
5%
0%
95%
1%
2%
-
IBM : large, stable earnings
GM : large, cheap
TYC : large, high growth
VSAT : small, high growth
Source: PanAgora Asset Management
Table is shown for illustrative purposes only.
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Unique Factor Weights for Each Stock
Factor Values
Stock
IBM
GM
TYC
VSAT
b2p
0.00
1.39
-0.74
-0.45
e2p
1.45
1.29
0.00
-0.35
Factor Weights
Stock
d2p b2p
IBM
2%
1%
GM
18% 2%
TYC
4%
0%
VSAT
9%
1%
e2p
2%
3%
0%
2%
Scores
Stock
IBM
GM
TYC
VSAT
d2p
1.62
-0.55
1.17
0.80
Score
0.75
-0.84
0.88
0.93
Source: PanAgora Asset Management
Q Group Conference, March 26, 2007
c2p
1.31
-1.33
0.35
-0.08
holt
0.07
-1.34
-0.58
0.06
c2p holt
10% 12%
14% 8%
6%
3%
9%
3%
oe
1.52
-1.70
0.89
1.35
fs
0.91
-1.66
0.23
1.35
oe
fs
26% 6%
5%
4%
20% 14%
14% 10%
eq
0.83
-1.25
1.08
1.33
capx
-0.92
0.23
1.29
1.15
noag
1.45
-1.56
1.36
1.23
eq capx noag
16% 3%
6%
12% 8% 18%
17% 4%
9%
13% 7% 18%
pm
-0.69
-0.35
1.40
0.37
em
-0.41
1.01
1.18
1.02
pm
6%
4%
7%
6%
em
12%
7%
13%
6%
Factor weightings are unique for each stock
to provide the best return forecast.
IBM : efficiency of operations and positive earnings revisions
GM : share buybacks (debt pay-downs), and cash flow yield
TYC : efficiency of operations, high earnings quality, and
momentum (very little valuation)
VSAT : same as TYC, except valuation
Table is shown for illustrative purposes only.
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Optimal Alpha Models with Turnover Constraints: Maximize Net IR
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Portfolio Turnover of Quantitative Factors
1 N t +1
T = ∑ wi − wit
2 i =1
T=
N
π
⎛1⎞
⎟
⎝σ ⎠
σ model 1 − ρ f E ⎜
ρ f = corr ( F% t +1 , F% t )
σ model - targeted risk ⇑
T ↑
N the number of stocks ⇑
T ↑
ρ f factor autocorrelation ⇓
T ↑
σ specific risk ⇓
T ↑
¾Turnover is a function of the targeted risk, the number of stocks, the
forecast autocorrelation, and the average specific risk
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Portfolio Turnover of Quantitative Factors
Category
Factors
Avg( ρ f )
Momentum
EarnRev9
0.64
Ret9Monx1
0.60
LtgRev9
0.37
E2PFY0
0.96
B2P
0.93
CFO2EV
0.84
RNOA
0.89
XF
0.76
NCOinc
0.80
Value
Quality
¾Momentum factors have a lowest autocorrelation (highest turnover)
¾Value factors have a highest autocorrelation (lowest turnover)
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Reducing Turnover
¾Brute force – turnover constraint in portfolio optimization
¾Integrated approach – optimal models with turnover targets
y More value, less momentum
y Use moving average of factors
¾Do the lagged factors forecast future return?
y Lower turnover at the cost of alpha?
y What is the right tradeoff?
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Reducing Turnover
Figure 8.2 Serial autocorrelation of forecast moving average with L = 2 , and
ρ f (1) = 0.90, ρ f ( 2 ) = 0.81 .
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
v1
t
¾Moving average – MA(2) Fma
= v0 F t + v1F t −1
¾Reduction rate – 70%
Q Group Conference, March 26, 2007
1 − 0.95 ≈ 71% 1 − 0.9
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0.9
1
Lagged Information Coefficients
¾Conventional IC
y Factors known at time t
y Subsequent return from t to t+1
ICt ,t = corr ( Ft , R t )
¾Lagged IC
y Factors known at time t-l
y Subsequent return from t to t+1
y Information decay
ICt −l ,t = corr ( Ft −l , R t )
¾Horizon IC
ICth = corr ( Ft , R t ,t + h ) , h = 0,1,L , H
y Factors known at time t
y Subsequent return from t to t+h
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ICs
ICt ,t = corr ( Ft , R t )
Ft −l
L
Ft
t
ICt −l ,t = corr ( Ft −l , R t )
t
Rt
L
Rt +h
ICth = corr ( Ft , R t ,t + h )
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Lagged IC and Horizon IC
¾ Relationship between ICs
ICth ≈
ICt ,t + ICt ,t +1 + L + ICt ,t + h
h +1
= avg ( IC ) h + 1
¾ Horizon IC typically increases with horizon
0.20
0.15
0.10
0.05
0.00
0
-0.05
1
2
Lagged IC
Horizon IC
3
4
5
-0.10
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6
7
8
9
Different Decay Rates
¾Two factors: E2P, PM (Ret9x1)
Standard Deviation of IC
Average IC
0.12
0.08
Avg(IC_PM)
Avg(IC_E2P)
0.06
0.09
0.04
0.06
0.02
0.03
0.00
Std(IC_PM)
Std(IC_E2P)
0.00
0
1
Lag
2
3
0
1
Lag
Information Ratio
1.50
1.20
0.90
0.60
IR_PM
0.30
IR_E2P
0.00
0
Q Group Conference, March 26, 2007
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Lag
36
2
3
2
3
Optimal Alpha Models With Lagged Factors
¾Objective: maximize model IR utilizing current and lagged
factors while controlling portfolio turnover
Fct,ma = v01F1t + v02F2t + v11F1t −1 + v12F2t −1 + L +
¾Constrained optimization to find the optimal weights
Maximize: IR =
v′ ⋅ IC
v′ ⋅ Σ IC ⋅ v
IC Covariance Matrix
subject to: ρ fc ,ma = ρ target ( v, Σ F )
Average Factor Covariance
Matrix
Q Group Conference, March 26, 2007
37
IC Correlation Matrix
¾Two factor example: Σ IC
Table 8.2 The IC correlation matrix of current and lagged values for the price
momentum and earning yield factor
PM_0
E2P_0
PM_1
E2P_1
PM_2
E2P_2
PM_3
E2P_3
PM_0
E2P_0
PM_1
E2P_1
PM_2
E2P_2
PM_3
E2P_3
1.00
-0.42
0.86
-0.37
0.78
-0.26
0.61
-0.19
-0.42
1.00
-0.44
0.92
-0.31
0.84
-0.29
0.78
0.86
-0.44
1.00
-0.45
0.88
-0.36
0.71
-0.30
-0.37
0.92
-0.45
1.00
-0.33
0.94
-0.30
0.86
0.78
-0.31
0.88
-0.33
1.00
-0.28
0.83
-0.22
-0.26
0.84
-0.36
0.94
-0.28
1.00
-0.28
0.94
0.61
-0.29
0.71
-0.30
0.83
-0.28
1.00
-0.30
-0.19
0.78
-0.30
0.86
-0.22
0.94
-0.30
1.00
Q Group Conference, March 26, 2007
38
Average Factor Correlation Matrix
¾Two factor example Σ F
Table 8.3 The factor correlation matrix of current and lagged values for the price
momentum and earning yield factor
PM_0
E2P_0
PM_1
E2P_1
PM_2
E2P_2
PM_3
E2P_3
PM_4
E2P_4
PM_0
E2P_0
PM_1
E2P_1
PM_2
E2P_2
PM_3
E2P_3
PM_4
E2P_4
1.00
-0.08
0.68
0.00
0.40
0.05
0.09
0.08
0.07
0.09
-0.08
1.00
-0.09
0.94
-0.06
0.84
0.01
0.73
0.03
0.61
0.68
-0.09
1.00
-0.08
0.68
0.00
0.40
0.05
0.09
0.08
0.00
0.94
-0.08
1.00
-0.09
0.94
-0.06
0.84
0.01
0.73
0.40
-0.06
0.68
-0.09
1.00
-0.08
0.68
0.00
0.40
0.05
0.05
0.84
0.00
0.94
-0.08
1.00
-0.09
0.94
-0.06
0.84
0.09
0.01
0.40
-0.06
0.68
-0.09
1.00
-0.08
0.68
0.00
0.08
0.73
0.05
0.84
0.00
0.94
-0.08
1.00
-0.09
0.94
0.07
0.03
0.09
0.01
0.40
-0.06
0.68
-0.09
1.00
-0.08
0.09
0.61
0.08
0.73
0.05
0.84
0.00
0.94
-0.08
1.00
Q Group Conference, March 26, 2007
39
Optimal Alpha Model Weights
¾Maximize IR while targeting model autocorrelation
ρf
IR
PM_0
E2P_0
PM_1
E2P_1
PM_2
E2P_2
PM_3
E2P_3
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
2.30
2.33
2.36
2.38
2.39
2.38
2.37
2.36
2.33
2.28
2.21
2.09
1.88
45%
43%
41%
39%
36%
34%
31%
28%
24%
21%
18%
15%
11%
55%
57%
59%
61%
64%
65%
65%
65%
65%
58%
50%
42%
32%
0%
0%
0%
0%
0%
2%
4%
7%
10%
12%
12%
11%
8%
0%
0%
0%
0%
0%
0%
0%
0%
0%
4%
8%
10%
14%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
2%
5%
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
4%
7%
12%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
2%
5%
0%
0%
0%
0%
0%
0%
0%
0%
1%
4%
8%
10%
14%
Highest IR
Lagged Factor Weights
Q Group Conference, March 26, 2007
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Optimal Alpha Model Weights
¾Optimal weights - aggregated
ρf
IR
PM
E2P
w0
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
2.30
2.33
2.36
2.38
2.39
2.38
2.37
2.36
2.33
2.28
2.21
2.09
1.88
45%
43%
41%
39%
36%
35%
35%
35%
34%
33%
30%
30%
28%
55%
57%
59%
61%
64%
65%
65%
65%
66%
67%
70%
70%
72%
100%
100%
100%
100%
100%
98%
96%
93%
88%
79%
68%
57%
42%
Q Group Conference, March 26, 2007
41
w1
0%
0%
0%
0%
0%
2%
4%
7%
10%
15%
20%
21%
23%
w2
w3
0%
0%
0%
0%
0%
0%
0%
0%
0%
1%
4%
9%
16%
0%
0%
0%
0%
0%
0%
0%
0%
1%
4%
8%
13%
19%
IR and Turnover Tradeoff
¾IR declines slowly while turnover decreases more rapidly
2.5
650%
2.4
600%
2.3
550%
2.2
500%
2.1
450%
IR
2.0
400%
IR
Turnover
1.9
350%
Forecast Autocorrelation
Q Group Conference, March 26, 2007
42
0.
97
0.
96
0.
95
0.
94
0.
93
0.
92
0.
91
0.
90
0.
89
0.
88
250%
0.
87
1.7
0.
86
300%
0.
85
1.8
T
Optimal Alpha Models of Net Returns
¾They have higher forecast autocorrelations and utilize lagged factors
Figure 8.7 The gross excess return and net excess returns under different
transaction cost assumption for portfolios with N = 3000 , target riskσ model = 4% ,
and stock specific risk σ 0 = 30% .
10.0%
9.0%
Gross
Return
8.0%
7.0%
Net
Return
(0.5%)
Net
Return
(1.0%)
Net
Return
(1.5%)
6.0%
5.0%
4.0%
3.0%
2.0%
Forecast Autocorrelation
Q Group Conference, March 26, 2007
43
0.
97
0.
96
0.
95
0.
94
0.
93
0.
92
0.
91
0.
90
0.
89
0.
88
0.
87
0.
86
0.
85
1.0%
Summary - Advances in Multifactor Models
¾Correct skill measure – risk adjusted IC
y Bridge the gap between model and actual performance
¾Optimal modeling framework – maximizing IR
y Maximize IR not IC
y Incorporate IC volatility and IC correlation
¾Contextual modeling – not one-size-fits-all
y Increase the depth of quant model
y Know where the market efficiency is
¾Optimal models with costs constraints – maximizing net IR
y Integrate alpha model with implementation
Q Group Conference, March 26, 2007
44
This presentation is provided for limited purposes, is not definitive investment
advice, and should not be relied on as such. The information presented in this
report has been developed internally and/or obtained from sources believed to be
reliable; however, PanAgora does not guarantee the accuracy, adequacy or
completeness of such information. References to specific securities, asset classes,
and/or financial markets are for illustrative purposes only and are not intended to be
recommendations. All investments involve risk, and investment recommendations
will not always be profitable. PanAgora does not guarantee any minimum level of
investment performance or the success of any investment strategy. As with any
investment, there is a potential for profit as well as the possibility of loss.
This material is for institutional investors, intermediate customers, and market
counterparties. It is for one-on-one use only and may not be distributed to
the public.
PanAgora Asset Management, Inc. ("PanAgora") is a majority-owned subsidiary of
Putnam Investments, LLC and an affiliated company of Putnam Advisory Company
(PAC). PAC provides certain marketing, client service, and distribution services for
PanAgora. PanAgora advisory services are offered through The Putnam Advisory
Company, LLC.
Q Group Conference, March 26, 2007
45