FOR PROFESSIONAL INVESTORS
Multi-Alpha Equity Porfolios
R. Leote de Carvalho, X. Lu, P. Moulin
Inquire Europe – October 2013, Munich, Germany
I 08/04/2015 I
Smart Beta indexes
The buzz of the moment
● Smart Beta indexes have gained huge popularity
– Risk-based Indexes: Minimum Variance, Maximum Diversification, Risk Parity
– Fundamental Indexation: stock weights determined by company fundamental data
● Back-tests show that Smart Beta indexes would have performed better than market-cap
– More performance
– Less risk
– Or both
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What is new in Smart Beta indexes
Perhaps not that much new… clumsy approaches exposed to market anomalies?
● “Demystifying Equity Risk-Based Strategies: an alpha plus beta description”
Seminar Inquire Europe, Autumn 2012, 28 - 30 October, Pera Palace Hotel Istanbul, Turkey
– Risk-based Smart Beta indexation relies on alpha from Low Volatility and Small Cap stocks
● Others have since shown:
– Fundamental Indexation relies on alpha from Value stocks
Smart Beta indexes are a new form of systematic active strategies where stock selection
is based on a formula that determines how portfolios deviate from the market cap index.
Despite being transparent with the formula made public, many can be quite complex.
And finally, Smart Beta seems to rely on well known market anomalies but in a somewhat clumsy way.
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How to build a multi-alpha portfolio?
Let’s step back and reconsider the problem again
Objective:
Build an active portfolio invested in equities
Combine different sources of alpha
Make sure the portfolio complies with constraints
Make sure that constraints have the least possible impact on your alpha
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How to build a multi-alpha portfolio?
The steps required
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
R Leote de Carvalho, X. Lu, P. Moulin
Multi-Alpha Equity Portfolios: An Integrated Risk Budgeting Approach for Robust Constrained Portfolios.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230
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I 08/04/2015 I
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
6
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Identify sources of alpha
● Where to find sources of alpha?
– In any strategy that can generate returns higher than predicted by beta
● Examples of quantitative sources of alpha:
– 1972: Low Risk anomaly (Haugen & Stein, Wiscosin University)
– 1977: Value anomaly (Basu, Journal of Finance)
– 1979: Earnings Revisions anomaly (Lakonishok and Givoly, Journal of Acc. and Economics)
– 1981: Small Cap stocks anomaly (Banz, Journal of Financials Economics)
– 1990: Short-term reversal anomaly (Jagadeesh, Journal of Finance)
– 1993: Momentum anomaly (Jagadeesh and Titman, Journal of Finance)
– 1996: Accruals anomaly (Sloan, The Accounting Review)
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I 08/04/2015 I
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
8
I 08/04/2015 I
Allocate a risk budget to each source of alpha
How much do you know? How accurately?


Given expected information ratios and strategy variance-covariance matrix

Markowitz if correlations not too large

Re-sampling from history (bootstrapping optimisation)
Uncorrelated alpha strategies


Same expected Information Ratio for each alpha strategy but different correlations


Risk budget allocate to each alpha strategy is proportional to expected information ratio
Maximum diversification allocation of alpha strategies
No accurate forecast of returns or correlations

Equal risk budget allocation to each alpha strategy
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I 08/04/2015 I
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
10
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11
Build an unconstrained target portfolio
SC
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0%
-12%
-14%
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-7%
-20%
4%
-8%
-24%
9%
8%
18%
24%
9%
0%
16%
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7%
-4%
38%
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31%
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36%
26%
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37%
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58%
23%
29%
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39%
18%
36%
28%
38%
24%
29%
38%
28%
41%
19%
37%
35%
20%
29%
2%
-10%
6%
-15%
14%
-6%
27%
-11%
-1%
1%
2%
-25%
-6%
-10%
-1%
-15%
14%
-23%
3%
-9%
-11%
-3%
6%
-25%
9%
-23%
6%
-18%
9%
-1%
7%
-13%
-15%
-61%
8%
-7%
-1%
3%
2%
-17%
22%
2%
7%
0%
28%
13%
32%
7%
21%
14%
3%
-6%
7%
-19%
12%
-18%
19%
-17%
4%
9%
3%
-15%
2%
-26%
12%
-10%
29%
-2%
1%
1%
-7%
-15%
4%
-6%
-3%
-7%
-3%
-9%
-3%
-3%
-8%
-10%
-18%
-12%
-3%
-6%
-11%
-18%
-16%
-4%
8%
18%
17%
5%
11%
15%
13%
10%
14%
26%
46%
35%
26%
37%
28%
34%
45%
43%
21%
34%
60%
54%
47%
47%
43%
55%
38%
31%
47%
51%
53%
54%
38%
36%
25%
13%
55%
29%
12%
12%
6%
12%
19%
16%
20%
16%
20%
15%
14%
13%
18%
20%
17%
14%
6%
HML CONS DISC
HML CONS STAPLES
HML ENERGY
HML FINANCIALS
HML HEALTH CARE
HML INDUSTRIALS
HML INFO TECH
HML MATERIALS
HML TELECOM SCVS

ON
HM
LC
UT
ILI
TI
ES
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SC
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M
LV
MH
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CO
LV
MH
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MA
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LV
MH
V
FI
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LV
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EN
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LV
MH
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CO
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DI
SC
-4%
LVMHV CONS DISC
LVMHV CONS STAPLES
LVMHV ENERGY
LVMHV FINANCIALS
LVMHV HEALTH CARE
LVMHV INDUSTRIALS
LVMHV INFO TECH
LVMHV MATERIALS
LVMHV TELECOM SCVS
LVMHV UTILITIES
LV
MH
V
CO
NS
LV
MH
V
MSCI World - Rf
Sector Neutral
IN
D
Low Volatility and Value
CA
RE

HE
AL
TH
How much alpha?
ST
AP
LE
S

Correlation of low volatility and value alpha by sector
I 08/04/2015 I
12
Build an unconstrained target portfolio
SC
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LF
IN
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LC
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0%
-12%
-14%
-7%
-7%
-20%
4%
-8%
-24%
9%
8%
18%
24%
9%
0%
16%
14%
7%
-4%
38%
18%
31%
31%
36%
26%
25%
31%
27%
9%
52%
43%
27%
42%
26%
45%
20%
36%
24%
46%
27%
37%
28%
22%
18%
8%
58%
23%
29%
31%
39%
18%
36%
28%
38%
24%
29%
38%
28%
41%
19%
37%
35%
20%
29%
2%
-10%
6%
-15%
14%
-6%
27%
-11%
-1%
1%
2%
-25%
-6%
-10%
-1%
-15%
14%
-23%
3%
-9%
-11%
-3%
6%
-25%
9%
-23%
6%
-18%
9%
-1%
7%
-13%
-15%
-61%
8%
-7%
-1%
3%
2%
-17%
22%
2%
7%
0%
28%
13%
32%
7%
21%
14%
3%
-6%
7%
-19%
12%
-18%
19%
-17%
4%
9%
3%
-15%
2%
-26%
12%
-10%
29%
-2%
1%
1%
-7%
-15%
4%
-6%
-3%
-7%
-3%
-9%
-3%
-3%
-8%
-10%
-18%
-12%
-3%
-6%
-11%
-18%
-16%
-4%
8%
18%
17%
5%
11%
15%
13%
10%
14%
26%
46%
35%
26%
37%
28%
34%
45%
43%
21%
34%
60%
54%
47%
47%
43%
55%
38%
31%
47%
51%
53%
54%
38%
36%
25%
13%
55%
29%
12%
12%
6%
12%
19%
16%
20%
16%
20%
15%
14%
13%
18%
20%
17%
14%
6%
Average = 30%
HML CONS DISC
HML CONS STAPLES
HML ENERGY
HML FINANCIALS
HML HEALTH CARE
HML INDUSTRIALS
HML INFO TECH
HML MATERIALS
HML TELECOM SCVS

ON
HM
LC
UT
ILI
TI
ES
ES
SC
VS
M
LV
MH
V
TE
LE
CO
LV
MH
V
MA
TE
RI
AL
S
LV
MH
V
LV
MH
V
LV
MH
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IN
F
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CH
US
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LS
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LS
AN
C
LV
MH
V
FI
N
LV
MH
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EN
ER
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LV
MH
V
CO
NS
DI
SC
-4%
LVMHV CONS DISC
LVMHV CONS STAPLES
LVMHV ENERGY
LVMHV FINANCIALS
LVMHV HEALTH CARE
LVMHV INDUSTRIALS
LVMHV INFO TECH
LVMHV MATERIALS
LVMHV TELECOM SCVS
LVMHV UTILITIES
LV
MH
V
CO
NS
LV
MH
V
MSCI World - Rf
Sector Neutral
IN
D
Low Volatility and Value
CA
RE

HE
AL
TH
How much alpha?
ST
AP
LE
S

Correlation of low volatility and value alpha by sector
Average = 0%
Average = 30%
I 08/04/2015 I
Build an unconstrained target portfolio


Alpha Capture strategy based on long-short portfolios

long stocks with expected positive alpha

short stocks with expected negative alpha
Quantitative sources of alpha:

Exposure to factors predicts stock alpha

Value

Low Volatility

Momentum

Small cap

Etc
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Build an unconstrained target portfolio
Target portfolio = Benchmark Market Capitalisation Index + Long-Short factor tilts
● Quantitative alpha can be captured using the set of selected of factors:
– Each factor contributes to the final stock tilts via a long/short portfolio.
● Long-short factor tilts = active stock deviations from benchmark:
– Leverage to each long-short factor tilt to meet assigned risk budget
– Leverage to combination of long-short factor tilts to meet target tracking error risk budget
● Add tilts to Benchmark Market Capitalisation Index
– Target constant level of ex-ante portfolio tracking error risk
– Keep constant he contribution of each alpha factor to portfolio tracking error
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15
Build an unconstrained active target portfolio
Combine the different systematic alpha portfolios
Market
Portfolio
Target active deviations from market capitalization portfolio
cheap
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
expensive
Value
low risk
high Risk
Low
Volatility
positive
trend
negative
trend
Momentum
small cap
large cap
30%
20%
10%
-10%
-20%
-30%
Small
Cap
Tilts in favour of Cheap, Low Volatility, Trending and Small Cap stocks
Tilts away from Expensive, High Volatility, Negative Trending and Large Cap stocks
Size of tils is determined by the allocated risk budget to each source of alpha
80%
70%
60%
50%
40%
30%
20%
10%
-10%
-20%
-30%
-40%
-50%
-60%
-70%
-80%
small cap
positive
trend
low risk
cheap
expensive
high Risk
negative
trend
large cap
Combined target deviations from
market capitalization portfolio
I 08/04/2015 I
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
16
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Get implied returns for unconstrained active target portfolio
What are implied returns?

The implied return of each stock are return which renders the portfolio efficient

Implied returns are obtained through reverse optimisation of the unconstrained portfolio
small cap
positive
trend
Reverse optimization
low risk
cheap
expensive
high Risk
negative
trend
large cap
Combined target deviations from
market capitalization portfolio
Optimization
Implied stock returns
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I 08/04/2015 I
Identify your sources of alpha
Allocate a risk budget to each source of alpha
Build an unconstrained target portfolio
Get implied returns for unconstrained target portfolio
Optimise from implied returns applying constraints
18
I 08/04/2015 I
Optimise from implied returns applying constraints
Robust optimisation

The efficient portfolio obtained from the implied returns using constrained optimisation will:
 respect the constraints while minimizing their impact!
 represent as much as possible the views in the original unconstrained portfolio
Implied stock returns
Constraints
Optimisation
Constrained Porftolio
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Robust framework for model portfolio construction
How are constraints handled?
Starting
unconstrained portfolio
Do not apply
constraints
Implied
returns
Apply
constraints
Target same TE as in
unconstrained portfolio
Target same risk aversion as in
unconstrained portfolio
Target same TE as in
unconstrained portfolio
Starting
unconstrained portfolio
Portfolio with the lowest
tracking error against
unconstrained portfolio
Portfolio with the largest
correlation against
unconstrained portfolio
Constraints impact specific risk exposures. Exposures to risk factors are mimicked as much as possible.
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1. Combine Value, Low Volatility, Momentum and Small Cap
Build a benchmarked long-only constrained portfolio
Small
Value
Momentum
Low Volatility
Information
Ratio
0.43
0.25
0.79
0.47
Value
75
Correlation (%)
Momentum Low Volatility
0
-4
-26
4
-7
Jan-95 through Dec-11. USD.
MSCI World index stock universe.
Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230
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1. Combine Value, Low Volatility, Momentum and Small Cap
Build a benchmarked long-only constrained portfolio
900
Cumulated returns of unconstrained and constrained portfolios
compared to the MSCI World Index benchmark
800
700
600
500
400
300
200
100
0
MSCI World Index
Unconstrained
Long-only + Liquidity Constrained
Long-only + Liquidity + # of stocks Constrained
Jan-95 through Dec-11. USD.
MSCI World index stock universe.
Almost indistinguishable performance for different portfolios,
whether constrained or unconstrained!
Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230
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1. Combine Value, Low Volatility, Momentum and Small Cap
Build a benchmarked long-only constrained portfolio
Small
Value
Momentum
Low Volatility
Target Risk Budget (%)
Mean
Maximum
Equal
Variance Diversification Risk Budget
0.19
0.05
0.45
0.30
0.64
0.45
0.85
0.72
0.45
0.49
0.53
0.45
Intercept
Small
Value
Momentum
Low Volatility
R-square
Unconstrained
Factor exposures from regression
Mean
Maximum
Equal
Variance Diversification Risk Budget
0.00
0.00
0.00
0.21
0.08
0.43
0.22
0.52
0.39
0.70
0.57
0.36
0.40
0.43
0.38
96%
96%
98%
3 approaches to ex-ante risk budgeting
Ex-post, risk budgets are in line with ex-ante,
even with constraints.
First achievement of the framework!
Long-only + Liquidity constraints
Long-only + Liquidity + # stocks constraints
Factor exposures from regression
Factor exposures from regression
Mean
Maximum
Equal
Mean
Maximum
Equal
Variance Diversification Risk Budget
Variance Diversification Risk Budget
0.00
0.00
0.00
0.00
0.00
0.00
0.14
-0.02
0.28
-0.05
-0.11
0.04
0.21
0.50
0.38
0.18
0.41
0.37
0.73
0.59
0.39
0.78
0.63
0.45
0.45
0.49
0.45
0.48
0.42
0.55
91%
90%
89%
73%
66%
70%
Jan-95 through Dec-11. USD.
MSCI World index stock universe.
Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230
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24
1. Combine Value, Low Volatility, Momentum and Small Cap
Build a benchmarked long-only constrained portfolio
Mean-Variance Risk Budget
Maximum Diversification Risk Budget
Equal-Risk Budget
Long-only
Long-only
Long-only
Long-only Liquidity #
Long-only Liquidity #
Long-only Liquidity #
MSCI World
Liquidity
Liquidity
Liquidity
Unconstrained Liquidity
Unconstrained Liquidity
Unconstrained Liquidity
index
# of Stocks
# of Stocks
# of Stocks
constraints
constraints
constraints
constraints
constraints
constraints
Average return (%)
6.1
11.4
11.7
12.0
10.9
11.1
11.6
10.6
10.9
11.0
Volatility (%)
16.0
15.2
15.1
14.7
15.4
15.2
15.2
16.0
15.6
14.9
Sharpe ratio
0.15
0.51
0.53
0.56
0.47
0.49
0.52
0.43
0.46
0.49
Excess return (%)
5.3
5.6
5.9
4.8
5.0
5.5
4.5
4.8
4.8
Tracking error risk (%)
4.7
5.1
5.6
4.9
5.0
5.2
5.1
5.1
5.0
Information ratio
1.13
1.09
1.04
0.98
1.00
1.07
0.87
0.95
0.97
Average number of stocks (long / short) 839 / 883
1008 / 0
216 / 0
837 / 885
954 / 0
226 / 0
825 / 897
1083 / 0
220 / 0
Benchmark
Performance and risk are little impacted by constraints.
Long only implementation with much smaller number of stocks still achieves comparable results.
Second achievement of the framework!
Capturing alpha around constraints is possible if the portfolio is constructed thoughtfully.
Jan-95 through Dec-11. USD.
MSCI World index stock universe.
Source http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2173230
I 08/04/2015 I
2. Combine Value, Low Volatility, Momentum and Profitability
Build a benchmarked long-only constrained portfolio
● Long-only
● Max 200 stocks
● Max 2% weight for each stock
● 5% tracking error risk against the benchmark index
● Turnover constrained to max 150% annual
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2. Combine Value, Low Volatility, Momentum and Profitability
Build a benchmarked long-only constrained portfolio
Backtest - 2002-2013
35% LowVol - 30% Momentum - 20% Value - 15% Profitability
12
Without Constraint
Constrained except Turn-Over
10
All Constraints
MSCI
8
6
4
2
0
Source: Theam, BNP Paribas Investment Partners
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2. Combine Value, Low Volatility, Momentum and Profitability
Attribution analysis
U.S. Dollars
Since 1995 Since 2002 Since 2008
MSCI (World reconstructed)
Absolute return
6.9%
5.9%
0.9%
Absolute volatility (ex-post)
15.7%
16.4%
20.5%
Absolute return
12.0%
10.4%
3.8%
Absolute volatility (ex-post)
14.6%
16.0%
20.0%
0.59
0.52
0.14
+5.1%
+4.5%
+2.9%
Low Vol contribution
+2.0%
+3.0%
+1.9%
Momentum contribution
+1.8%
+1.1%
+0.0%
Value contribution
+2.5%
+2.2%
+1.7%
Profitability contribution
+1.2%
+0.6%
+0.6%
ex-TO constraint impact
-1.2%
-1.3%
-0.4%
Turnover impact
-1.1%
-1.0%
-1.0%
Turnover
150%
150%
157%
Tracking error (ex-post)
4.6%
3.7%
3.6%
Information ratio
1.13
1.22
0.79
Beta
0.89
0.95
0.96
Alpha
5.5%
4.7%
2.9%
Final Portfolio
Sharpe ratio
Excess return over BM
Source: Theam, BNP Paribas Investment Partners
Based on
monthly
returns
27
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2. Combine Value, Low Volatility, Momentum and Profitability
Performance breakdown of 1995-2013: contributions to excess returns
140%
120%
Profitability
100%
80%
Value
60%
Momentum
40%
20%
Low Volatility
0%
-20%
-40%
-60%
ex-To Constraints Impact
Turnover impact
Profitability
Source: Theam, BNP Paribas Investment Partners
Value
Momentum
Low Vol
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2. Combine Value, Low Volatility, Momentum and Profitability
Decomposition of ex-post active risk allocation compared to ex-ante target
100%
90%
Constraints
Profitability (15% ex-ante unconstrained target)
80%
70%
Value (20% ex-ante unconstrained target)
60%
50%
Momentum (30% ex-ante unconstrained target)
40%
30%
20%
Low Volatility (35% ex-ante unconstrained target)
10%
0%
Low Volconstraints
Momentum Value including
Profitability Constraints
Impact
Final portfolio, all
turnover
constraint
Source: Theam, BNP Paribas Investment Partners
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Conclusions
Intuitive but robust approach to portfolio construction

Separates the process of mixing unconstrained views from managing of constraints

Different approaches to mixing unconstrained views depending of information available

In any case, at stock level, all boils down to


weighted average of portfolios representing views to form unconstrained target portfolio
Back-test results show application to real portfolios

Intuition confirmed

Large correlation between unconstrained and constrained results

Management of portfolio constraints and risk while keeping simplicity

Achieves similar results to “Index + Long-Short hedge fund” while staying long-only
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Disclaimer
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