Variations on Minimum Variance
Ruben Falk, Capital IQ Quantitative Research
March 2011
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Agenda
• Quick overview of the tools employed in constructing the Minimum
Variance (MinVar) Portfolio
• Features of a basic unconstrained MinVar Portfolio and comparative
performance against the main benchmarks
• Impact on performance of imposing constraints such as style or sector
neutrality
• Alternative methods for imposing style tilts within the minimum
variance framework
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The Tools
• Capital IQ US Fundamental Risk Model
› 140 Alphaworks factors aggregated into 8 style factors: Value, Momentum,
Earnings Quality, Analyst Expectations, Historical Growth, Capital Efficiency,
Volatility, Size
› Other factors: Market factor and 24 industry factors based on GICS
› Responsiveness: Based on daily returns with serial correlation adjustment
• Capital IQ ClariFI Mean-Variance Optimizer
› State of the art solver for Mixed Integer Quadratically Constrained
Quadratic Programming problems
• Capital IQ ClariFI Portfolio Attribution Framework: Classic side-by-side
factor based risk and return attribution
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Historical Evidence
• Early work from HAUGEN/BAKER (1991). For the period covering the years
1972 to 1989 the authors found that a MinVar portfolio would outperform
the Wilshire 5000 at lower risk
• Many studies followed the original paper. For the US stock market
CHAN/KARCESKI/LAKONISHOK (1999), SCHWARTZ (2000) and
JAGANNATHAN/MA (2003) and CLARKE/SILVA/THORLEY (2006) found both
higher returns and lower realized risks for the MinVar portfolio versus a
capitalization weighted benchmark
• For global equity markets GEIGER/PLAGGE (2007), POULLAOUEC (2008) and
NIELSEN/AYLURSUBRAMANIAN (2008) all find similar results
• SCHERER (2010) shows that 79% of the variation of the MinVar portfolio’s
excess return can be attributed to exposure to low market beta and low stock
specific risk. Value and size are other characteristics noted
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The Anomaly
Return
Security Market Line
Empirical MinVar
Portfolio
Efficient Frontier
Market Portfolio
Theoretical MinVar Portfolio
Risk
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Base Case Minimum Variance Portfolio
• Portfolio size $1.5BN (initial), long only
• Monthly rebalancing, Apr. 1998 to Oct. 2010
• Objective: Minimum Variance at each rebalancing
• Risk Model: Capital IQ US Fundamental Medium Term
• Universe: S&P 1500
• Max 100 Holdings (not always binding)
• Max trade size: 10% of ADV
• Trade costs: 25bps
• Max holding size: 3% of portfolio per name
• Threshold holding and trade size: $50k
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Capital IQ, A Standard & Poor’s Business
10/31/2010
4/30/2010
10/31/2009
4/30/2009
10/31/2008
4/30/2008
10/31/2007
4/30/2007
10/31/2006
4/30/2006
10/31/2005
4/30/2005
10/31/2004
4/30/2004
10/31/2003
4/30/2003
10/31/2002
4/30/2002
10/31/2001
4/30/2001
10/31/2000
4/30/2000
10/31/1999
4/30/1999
10/31/1998
4/30/1998
Base Case MinVar Performance
Cumulative Performance (Pre Transaction Cost)
250%
200%
150%
100%
Min Var
S&P 500
S&P 400
50%
S&P 600
S&P 1500
0%
-50%
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Base Case MinVar Performance
Apr. 1998 –
Oct. 2010
Compound
Ann Return
Compound Arith. Avg.
Return/Risk Return/Risk
Ratio
Ratio
Ann Risk
MinVar (Pre Tcosts)
6.0%
11.4%
0.53
0.61
MinVar (Post Tcosts)
5.1%
11.4%
0.45
0.52
S&P 500
2.8%
16.5%
0.17
0.26
S&P 400
8.7%
19.3%
0.45
0.58
S&P 600
6.9%
20.7%
0.33
0.47
S&P 1500
3.4%
16.6%
0.20
0.30
Note: The annualized risk numbers in this presentation are based on monthly returns. Using daily
returns, the risk of the Base Case MinVar portfolio is 13.4% and the S&P 500 is 21.8%
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Base Case MinVar Portfolio Factor Attribution
Apr. 1998 – Oct. 2010
Factor
Market
Styles
Valuation
Size
Analyst Expectation
Historical Growth
Capital Efficiency
Price Momentum
Earnings Quality
Volatility
Industries
Stock Specific
Grand Total
Portfolio
Exposure
0.48
-0.08
-0.17
0.01
-0.03
-0.21
-0.12
0.93
-0.27
0.02
0.000
Forecast
Forecast
Realized
Realized
Annualized
Realized
Contribution Percent of Contribution Percent of
Portfolio
Return/Risk
to Portfolio Portfolio to Portfolio Portfolio
Return
Ratio
Risk
Risk
Risk
Risk
1.96%
10.16%
89.67%
9.63%
72.09%
0.20
2.11%
9.09%
70.37%
8.44%
55.35%
0.25
-0.58%
3.04%
9.21%
3.11%
7.49%
-0.19
0.82%
-0.58%
-0.79%
-0.98%
-0.74%
-0.84
0.18%
0.41%
-0.30%
1.04%
0.84%
0.17
-0.28%
0.58%
0.35%
0.94%
0.68%
-0.30
0.07%
0.94%
1.24%
-0.46%
-0.16%
-0.15
-0.18%
1.15%
0.81%
2.27%
4.01%
-0.08
0.46%
-0.30%
-0.24%
2.03%
3.19%
0.23
-0.94%
2.27%
5.11%
0.85%
0.56%
-1.11
-0.71%
1.34%
3.03%
-1.07%
-0.89%
0.66
0.43%
3.36%
10.10%
3.45%
9.25%
0.12
4.07%
3.06%
10.33%
5.99%
27.91%
0.68
6.02%
10.61%
100.00%
11.35%
100.00%
0.53
The Base Case MinVar portfolio has a low average beta of 0.48 and derives most of
its return from stock specific sources
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Base Case MinVar Sector Attribution against S&P 1500
The Base Case MinVar portfolio on average overweights traditionally defensive sectors such as
Consumer Staples and Utilities while underweighting IT and Financials
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Base Case MinVar Cap. Group Attribution against
S&P 1500
The unconstrained MinVar portfolio heavily underweights the top market cap. decile while, on
average, overweighting decile 2-5 and staying neutral to the bottom half market cap names in the
S&P 1500. However on average, the top Market cap. decile still represents 34% of the MinVar
portfolio by value
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Base Case MinVar v. Fama-French 3 Factor Model Returns
Dependent
Variable
Beta
Std Error
P-value
Constant
0.130
0.175
0.459
Market Excess
Return
0.500***
0.035
0.000
SMB (Size)
0.052
0.047
0.271
HML (Value)
0.215***
0.049
0.000
R-squared
0.597
Market and Value (but not Size) loadings were statistically significant at the 95% level in
explaining the returns of the Base Case MinVar portfolio. The Market beta was about the
same as when using the CIQ risk model at 0.5 while the exposure to Value was positive
which is consistent with the results of Scherer (2010)
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Optimal Turnover & Holding Period (Base Case)
Turnover vs. Return
Turnover vs. Risk
8.0%
13.2%
13.0%
12.8%
6.0%
12.6%
Rebalancing
5.0%
Monthly
4.0%
Quarterly
3.0%
Semi-Annual
Annual
2.0%
Annual Risk
Annual Return (after T-Costs)
7.0%
12.4%
12.2%
12.0%
11.8%
11.6%
1.0%
11.4%
0.0%
11.2%
0%
50%
100%
150%
Annual 2-Way Turnover
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200%
250%
0%
50%
100%
150%
200%
250%
Annual 2-Way Turnover
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Implementing Sector & Style Neutrality & Style Tilts
• Imposing sector neutrality on the Base Case with respect to the S&P
1500 (+/-2%) has the effect of pushing up the market exposure which
increases risk while return suffers as we can’t achieve a defensive
sector allocation
• Imposing strict style neutrality on the Base Case shows some
promise in terms of providing higher returns and return/risk ratio
but the problem often isn’t feasible
• Three scenarios for style neutrality with flexible tilts (lower bound of
the style exposure is zero but no upper bound)
› Earnings Quality tilt
› Value Tilt
› Both Value & Price Momentum Tilt
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Performance of MinVar Portfolios with Value Style Tilts
Factor Contribution
to Ann. Return
Apr. 1998 – Oct. 2010
Base Case
MinVar
Earnings
Quality Tilt
MinVar
Value Tilt
MinVar
Value & Price
Momentum Tilt
MinVar
2.1%
2.9%
2.8%
2.6%
Market Exposure
0.48
0.58
0.60
0.58
Return/Risk Ratio
0.25
0.29
0.26
0.25
Value
0.8%
0.2%
-0.2%
-0.2%
Earnings Quality
-0.9%
-0.7%
-0.1%
-0.1%
Price Momentum
0.5%
0.1%
0.1%
0.3%
Other Styles
-1.0%
-0.3%
-0.2%
-0.2%
Industries
0.4%
0.7%
1.0%
0.6%
Stock Specific
4.1%
4.5%
4.6%
4.5%
TOTAL (Pre-Tcosts)
6.0%
7.4%
8.0%
7.5%
0.53
0.58
0.60
0.58
5.1%
6.3%
6.9%
6.3%
0.45
0.50
0.51
0.48
Market
Total Return/Risk Ratio
TOTAL (Post-Tcosts)
Total Return/Risk Ratio
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› The tilted MinVar portfolios
generally outperform both on
absolute and risk adjusted
return
› The sources of
outperformance are: more
efficient market exposure,
higher stock and industry
specific returns, and the fact
the style contributions to
return are mostly negative
when not constrained
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Market & Style Exposures: Base Case v. Single Tilts
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Style Exposures: Price Momentum & Value Tilt
0.6
0.4
0.2
Price
Momentum Exp.
Value Exp.
0
Val-PM Cum. Rtn Spread
-0.2
6/1/2010
1/1/2010
8/1/2009
3/1/2009
10/1/2008
5/1/2008
12/1/2007
7/1/2007
2/1/2007
9/1/2006
4/1/2006
11/1/2005
6/1/2005
1/1/2005
8/1/2004
3/1/2004
10/1/2003
5/1/2003
12/1/2002
7/1/2002
2/1/2002
9/1/2001
4/1/2001
11/1/2000
6/1/2000
1/1/2000
8/1/1999
3/1/1999
10/1/1998
5/1/1998
-0.4
The style factor exposures have ICs of 0.08 and 0.13 with respect to 1-month forward factor
returns of Price Momentum and Value respectively. The Value exposure IC is statistically
significant at the 95% while the Price Momentum exposure IC is only statistically significant at
the 84% level
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MinVar with Flexible Style Tilts Spreads
Cumulative Active Return vs. S&P 500
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Global MinVar Performance
• Base Case and Value tilted global MinVar portfolios constructed using the
same parameters as for the US portfolios except drawn from the S&P
1200 universe
Cumulative Performance (Pre T-Costs)
160%
Apr. 1998 –
Oct. 2010
Ann
Return/Risk
Return Ann Risk
Ratio
Global Base Case*
6.2%
9.8%
0.63
Global Value Tilt*
6.9%
10.7%
0.65
140%
120%
100%
80%
60%
S&P 1200**
4.2%
18.7%
0.22
Global Value Tilt
20%
S&P 1200
0%
-20%
-40%
04/30/1998
12/31/1998
08/31/1999
04/30/2000
12/31/2000
08/31/2001
04/30/2002
12/31/2002
08/31/2003
04/30/2004
12/31/2004
08/31/2005
04/30/2006
12/31/2006
08/31/2007
04/30/2008
12/31/2008
08/31/2009
04/30/2010
*Pre transaction costs. Transaction costs impact annual
returns by 0.7% in the Base Case
**Capitalization weighted
Note: Returns are compounded
Global Base Case
40%
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Capital IQ, A Standard & Poor’s Business
5/1/2010
12/1/2009
Hong Kong
7/1/2009
USA
2/1/2009
9/1/2008
4/1/2008
11/1/2007
6/1/2007
1/1/2007
UK
8/1/2006
3/1/2006
10/1/2005
5/1/2005
12/1/2004
7/1/2004
2/1/2004
9/1/2003
4/1/2003
11/1/2002
6/1/2002
-0.1
1/1/2002
8/1/2001
3/1/2001
10/1/2000
5/1/2000
0.1
12/1/1999
7/1/1999
2/1/1999
9/1/1998
4/1/1998
MinVar Active Weight
Base Case Global MinVar Country Attribution vs. S&P 1200
0.4
0.3
USA
0.2
GBR
DEU
Japan
FRA
HKG
Canada
0
JPN
PRT
NLD
USA
CAN
TWN
-0.2
SWE
ITA
-0.3
BRA
KOR
-0.4
FIN
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Summary
• From Apr. 1998 to Oct. 2010, our MinVar portfolio without sector or style
constraints easily outperforms the S&P 500 and S&P 1500 with much lower risk
• Portfolio construction with a minimum variance objective naturally lends itself to a
large cap. but not mega-cap. bias
• During this period, the minimum variance objective has the effect of over
allocating to traditionally defensive sectors such as Consumer Staple and Utilities
while under allocating to Financials and Technology
• Imposing sector constraints has the effect of lowering returns and increasing risk
• Style constraints, however, when combined with certain specific style tilts,
enhance the performance of the MinVar portfolio
• As a side effect, the style factor exposures that are generated from minimum
variance portfolio construction provide useful input for factor switching strategies,
at least in the case of Value and Price Momentum
• The results are quite robust for different style tilts which suggests that many
existing strategies could use minimum variance as a performance enhancing
overlay
• Initial results appear generally consistent for global portfolios
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