The document presents an asset allocation model that incorporates both static factors (equities, bonds, commodities) and dynamic factors (value, momentum, low-volatility) using a Black-Litterman framework. Equity valuations appear rich based on CAPE ratios, but equity yields relative to bond yields suggest valuations are not unusually high if interest rates rise modestly. Expected returns are lower across asset classes compared to the last 30 years. The model suggests overweighting equities and commodities relative to long-term bonds, and incorporating dynamic factors can enhance returns, with low-volatility providing the greatest return premium at relatively low risk.

1. A Scalable ETF Factor Model Under
the Black-Litterman Approach to
Portfolio Optimization
Manuel Zapata, CFA & CQF
January 31, 2017
Presentation for discussion purposes
Detail Methodology

2. 2
Table of Contents
Objective 3
Summary 4
Valuation: Equity, L-T Bonds & Commodities 5
Black–Litterman (BL) Approach & Asset Allocation 12
Dynamic Factors and their Risks 17
Revised Asset Allocation: Incorporating Dynamic Factors 22
Appendix 25
Presentation for discussion purposes

3. 3
Objective
• The robust Black-Litterman (BL) approach to portfolio optimization allows to design a
well diversified portfolio in which views on factor (or asset classes) returns can be
incorporated. BL approach avoids corner solutions (extreme long or short positions).
• Factors (static and dynamic) are investment styles that deliver attractive returns
over the long-term. These return premiums have risks (periods of
underperformance); analyzing the historical record (at least 10 years) is a good
place to start understanding these risks.
• The example presented here can be extended to incorporate additional “static
factors” (i.e. non-US equities or bonds in developed or emerging markets).
• The framework allows to incorporate dynamic factors (also called smart beta or style
factors) to enhance equity returns. Here the following dynamic factors are used:
value, momentum and low-volatility.
• The framework can be used in an international context (through ETF’s) and in
particular markets (the example here uses the US market). For markets with few
ETF’s factor portfolios will need to be built from scratch.
• In addition, the approach allows to analyze alternative scenarios (higher or lower
correlations) and their impact in prior (or required) returns.
Presentation for discussion purposes

4. 4
Summary
• Three “static factors” (equity’s, bonds, and commodities) and three “dynamic factors”
(value, momentum and volatility) are used.
• Rich valuations under the BL framework suggest a larger than usual allocation to the
Risk Free Asset.
• The static factor allocation overweights equities and commodities (relative to long-
term bonds) despite the negative correlation of long-term bonds with equities and
commodities.
• In the absence of changes in the asset allocation (driven by changes in prior returns
and/or return expectations), trading will be limited to rebalancing allocations to the
pre-determined percentages (bands can be used to avoid unnecessary trading).
– Rebalancing is a key driver of long-term investment success (buys low & sales
high).
• Dynamic factors can enhance returns but understanding their risks is a prerequisite.
– The low-risk factor will likely deliver the greatest return premium with relative
low risk.
Presentation for discussion purposes

5. 5
Valuations: Equity, L-T Bonds & Commodities
This sections reviews valuations of broad indices (using ETF) as well as the historical
return performance.
• Despite high price-to-earnings valuation ratios (as measured by the CAPE ratio),
equity valuation levels relative to bonds (using the yield ratio often called FED
model) suggests equity valuation levels are not high even assuming interest rate
levels will rise.
• The likely increase in short-term interest rates will affect the long-end of the yield
curve. It will take a relative modest increase in long-term rates to translate into
negative returns of fixed income portfolios with long-term maturities.
• Over long periods of time commodities should provide returns in line with inflation;
however current commodity values (when measured in real terms) suggest real
returns are likely over the next few years.
Presentation for discussion purposes

6. 6
Equity Valuation: CAPE Ratio & Fed-Model
Likely Adjustment in Valuations going forward
• Using the last 30 years, Cambell & Shiller’s Cyclically Adjusted P/E Ratio (CAPE)
suggests valuation levels are likely to decline going forward.
• However, the yield ratio (often called “FED model”) shows that it will take an increase
of 150bps in long-term rates to take the yield ratio differential to its 30 year historical
average.
• At best valuation levels are likely to stay the same and will likely decline going forward.
0
5
10
15
20
25
30
35
40
45
50
Jan-87
Jun-88
Nov-89
Apr-91
Sep-92
Feb-94
Jul-95
Dec-96
May-98
Oct-99
Mar-01
Aug-02
Jan-04
Jun-05
Nov-06
Apr-08
Sep-09
Feb-11
Jul-12
Dec-13
May-15
Oct-16
CAPE Ratio 1987-2016
Average
+1 St. Dev.
-1 St. Dev.
-6%
-4%
-2%
0%
2%
4%
6%
Jan-87
Aug-88
Mar-90
Oct-91
May-93
Dec-94
Jul-96
Feb-98
Sep-99
Apr-01
Nov-02
Jun-04
Jan-06
Aug-07
Mar-09
Oct-10
May-12
Dec-13
Jul-15
Feb-17
YieldDifference
Treasury Bond Yield Minus Cyclically Adjusted
Earnings Yield
Treasury Minus (1/CAPE) 30Y Average
Cheap Bonds
Cheap Stocks
10 year yield
+150bps
Source: Shiller (http://www.econ.yale.edu/~shiller/data.htm), author calculations

7. 7
Equity: Return Decomposition
Considerable Lower Expected Returns (vs. the last 30 years)
• Throughout this exercise a 5% annual expected return from broad equities will be used
(RG refers to Real Earnings Growth).
• SPY ETF (which tracks the S&P 500) will be used as proxy for equities.
Source: Shiller, author calculations
2.6% 2.0%
2.2%
2.1%
3.1%
1.5%
1.4%
-0.8%
-2%
0%
2%
4%
6%
8%
10%
Last 30Y Next 10Y
Nominal Return Decomposition
CPI D/P RG Val. Change
9.3%
4.8%
to
5.6%

8. 8
L-T Fixed Income: Returns Affected by Rate
Increments going Forward
• The relation between changes in long-term rates (i.e. 10 year rates) and the value of
fixed income portfolios with long durations (i.e. 7 to 10 years) is extremely high as can
be appreciated in above chart (left).
• In 2017 between two and three interest rate increments are expected from the FED,
taking the FED funds rate to 1% or 1.25% (50 to 75 bps more than today).
• The decline in interest rates since the mid 2000’s translated into mostly positive returns
in long-term bonds. That trend will reverse in the next few years.
Source: IEF ETF and 10-year Government bond rate changes
-8
-6
-4
-2
0
2
4
6
8
10
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
IEF-ETFMonthlyReturn(%)
10Y Monthly Rate Change (%)
Monthly L-T Bond Returns vs L-T Rate Change (2002-16)
-10%
-5%
0%
5%
10%
15%
20%
Jul-03
Jun-04
May-05
Apr-06
Mar-07
Feb-08
Jan-09
Dec-09
Nov-10
Oct-11
Sep-12
Aug-13
Jul-14
Jun-15
May-16
12MonthRollingReturn
IEF (ETF): 12 Month Rolling Return

9. 9
• The valuation model uses the yield-curve shape (through implied forward rates) to
forecast returns over the next six months of IEF-ETF. This model suggests a modest
positive return over the next 6 months (less than 0.5%). The relationship is positive but
not extremely strong.
• Despite the positive expected return hinted by the model over the next 6 moths; for the
purpose of this exercise the return expectation used will be negative (i.e. -1.0%). This
is based on an expected increase in 10-year rates of 50bps over the next 12 months.
Source: IEF ETF and historical yield curves
L-T Fixed Income: Valuation Using the Yield
Curve
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
1 3 5 7 10 20
Yield(%)
Maturity
Average Yield Curve Shapes and Forward Returns
Lower than -1% -1% to 1% Above 1% Current
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
-10.0 -5.0 0.0 5.0 10.0 15.0
6MonthReturnForecast(%)
6 Month Actual Returns (%)
Forecasting Returns: Yield Curve Predicatbility

10. 10
• Although all three index ETF’s (DJP, GSG, and DBC) have different exposures to energy,
agriculture their return performance over the long term is highly correlated.
• The main objective of commodities, within this factor portfolio, is to provide
diversification benefits.
• I will use DBC ETF (which tracks Deutsche Bank Liquid Commodity Index) since it
shows the highest correlation with the other two indices and a better mean return over
the period.
Source: DJP, GSG, and DBC ETF data
Commodity ETF’s: Energy, Agriculture, Metals
-40%
-30%
-20%
-10%
0%
10%
20%
30%
1-Feb-07
1-Aug-07
1-Feb-08
1-Aug-08
1-Feb-09
1-Aug-09
1-Feb-10
1-Aug-10
1-Feb-11
1-Aug-11
1-Feb-12
1-Aug-12
1-Feb-13
1-Aug-13
1-Feb-14
1-Aug-14
1-Feb-15
1-Aug-15
1-Feb-16
1-Aug-16
MonthlyReturns
Commodity Index ETFs (2007-2016)
DJP GSG DBC
Commodity ETF Correlation of Monthly Returns
(2007-2016)
DJP GSG DBC
DJP 100% 91.3% 95.2%
GSG 91.3% 100% 96.4%
DBC 95.2% 96.4% 100%
Mean (r)
annualized
-4.9% -6.0% -1.5%

11. 11
• DBC ETF closely tracks the performance of Deutsche Bank Liquid Commodity Index
(DBLCI). Their correlation of monthly returns (2007-2016) is 97.4%.
• The current low price level suggest positive real returns are possible over the next few
years. Using monthly data since 1989, the real price level has been 10 times within 5%
of its current level of 192.7 (as of the YE2016 setting YE 1988 @ 100). From that level
range the average annual real return over the next three years has averaged 12% with a
minimum of 7%.
• For the purpose of this exercise, and given lower expected future returns in most other
asset classes, we will assume 4% real annual return (6% nominal return) in commodities
over the next few years (given current valuation levels).
Source: DJP, GSG, and DBC ETF data
DBLCI Analysis: Mid-Term Returns Above
Inflation
0
10
20
30
40
50
60
70
133 168 203 238 273 308 343 378 413 448 483 518 553 588 623 658 693 728 763 798
#ofObservations(monthlydata)
Commodity DBLCI Mid-Bin Index Price (real terms)
DBLCI Real Price Distribution (1989-2016)
-30%
-20%
-10%
0%
10%
20%
30%
0
100
200
300
400
500
600
700
800
900
Dec-88
May-90
Oct-91
Mar-93
Aug-94
Jan-96
Jun-97
Nov-98
Apr-00
Sep-01
Feb-03
Jul-04
Dec-05
May-07
Oct-08
Mar-10
Aug-11
Jan-13
Jun-14
Nov-15
RealReturn
RealIndexLevel
DBLCI Real Price Index (1989-2016)
Real DBLCI (LH) Average Index (LH) 3Y Forward Returns (RH)
Current level

12. 12
Black–Litterman (BL) Framework
A Very Brief Overview*
B&L framework overcomes the problems of implementing portfolio optimization using
historical return data (i.e. corner solutions or highly concentrated portfolios). The
following is a brief overview*:
Benchmark portfolio weights are first assumed to be optimal and prior (or market)
returns are derived using a covariance matrix. In other words, the derived returns
(together with the covariance matrix) will produce the benchmark portfolio weights.
Expectations on assets (or factors) returns are then incorporated which together
with the covariance matrix produces a different set of factor (or assets) weights
(relative to the market benchmark weights).
The Black-Litterman framework works with excess returns, as a result the final
allocation includes an allocation to the risk-free asset.
* For a detail explanation review: A Step-by-Step guide to the Black-Litterman Model by Thomas Idzorek.
* For a simplified review: Ch13 “The Black-Litterman Approcah”, Financial Modeling by Simon Benninga
Presentation for discussion purposes

13. 13
The tables above uses the base case scenario (correlations and volatilities) to derive the
base case covariance matrix. In addition, the appendix derived the inputs for two additional
correlation scenarios:
• Low (absolute) correlations. The increase in interest rates is slow and gradual resulting in
a marginal negative impact in the valuation of L-T bonds while at the same time there is
a positive performance in equities and commodities.
• High (absolute) correlations: i) The increase in interest rates takes place over a shorter
period of time. Valuations of L-T bonds affected to a larger extent translating into a
relative underperformance (vs. equities and commodities); ii) A scenario similar to that
of the GFC will result in increase absolute correlations; however in this case the
performance of equities will be negatively affected relative to bonds and commodities.
Source: DJP, GSG, and DBC ETF data
Covariance Scenario(s)
Refer to the Appendix for Details (correlations and volatility inputs)
Correlations
Base case SPY DBC IEF
SPY 1.0 0.4 -0.3
DBC 0.4 1.0 -0.2
IEF -0.3 -0.2 1.0
Covariance Matrix
Base case SPY DBC IEF
SPY 0.010 0.006 -0.002
DBC 0.006 0.023 -0.002
IEF -0.002 -0.002 0.004
St. Dev
Last Fcst
10.0%
15.0%
5.5%

14. 14
The following assumptions are made to derive the “equilibrium excess returns”:
1. Market weights for each of the asset classes are derived from ETF’s total market
capitalizations for those asset classes.
2. The 3 different scenarios (covariance matrices) mentioned in the previous slide are
used (for details please refer to the appendix).
3. The risk free rate is assumed to be the short-term (1 month) government rate over the
next twelve months (0.75% assumed).
4. To derive Lambda (market risk aversion) a Sharpe Ratio of 0.5 is used. This is
equivalent to expecting an average equilibrium excess return from the proposed
portfolio of 3.7%.
BL Prior (Market) Returns Under Different
Scenarios
Prior (Market) Annualized Returns
SPY DBC IEF Scenario
5.7% 4.3% 0.3% Base
5.7% 3.2% 0.9% Low (abs)
5.7% 5.4% -0.3% High (abs)
Asset Weight (%)
SPY 75.0%
DBC 3.5%
IEF 21.5%
Total 100.0%
Covariance Matrix
Scenario
Base
Low (abs)
High (Abs)

15. 15
IEF. The long-term (10 years) interest rate increment that will likely produce the annual
prior (market) returns over the next three years under each scenario is:
― Base case: An increase in the 10Y rate of around 30 bps per year will produce a similar
annual return (0.3%).
― Low (abs): An increase in the 10Y rate of around 20 to 25 bps per year will produce a
similar annual return (0.9%).
― High (abs): An increase in the 10Y rate of around 40 bps per year will produce a similar
annual return (-0.3%).
SPY. The 5.9% prior (market) return seems achievable assuming no change in market
valuation multiples (refer to slides 6 and 7).
DBC. The range of prior (market) returns seems achievable (refer to slides 10 and 11)
Prior (Market) Returns: Implied Expectations
SPY DBC IEF
5.7% 5.7% 5.7% 4.3% 3.2% 5.4% 0.3% 0.9% -0.3%
B L H B L H B L H
Prior (Market) Annualized Returns
Return level
Correl. scenario: Base (B), Low (L), High (H)

16. 16
Revised Asset Allocation: Incorporating Views
Large Allocation to the Risk Free Asset (RFA)
Asset Mkt. Cap
Weight
(%) (A)
Prior (Market)
Return (Base
Case)
Forecasted
Returns
B&L Revised
Allocation*
B&L Revised
Allocation no
Short Selling*
Base 100
Allocation (B) no
short positions
Difference vs
Market
Weights (B-A)
SPY 75.0% 5.7% 5.0% 58% 53% 87% +12.3%
DBC 3.5% 4.3% 6.0% 8% 8% 13% +9.2%
IEF 21.5% 0.3% -1.0% -6% 0% 0% -21.5%
Total 100.0% 60% 60% 100% 0%
RFA 40% 40%
*Assuming S-T risk free rate goes to 0.75% over the next twelve months
• The table above shows the change in asset allocations after return expectations
(forecasted returns) are incorporated.
• The large allocation to the risk-free asset (RFA) is driven by the low forecasted returns in
equity and fixed income (relative to prior-market returns)
• Among risky assets (SPY, DBC and IEF) equities and commodities are overweighted while
long-term bonds are underweighted.

17. 17
Dynamic Factors and their Risks
Also Called: Smart Beta, Style Factors or Investment Factors
Dynamic factors become an integral part of the overall allocation to equities, which
under the base case scenario is 53% (please refer to the previous slide).
Value factor. Long Value (IVE ETF) and Short Growth (IVW ETF).
Momentum factor (Up Minus Down). Uses SPDR sector ETF’s to go long (short)
ETF’s with positive (negative) momentum.
Low-Volatility factor. Uses SPDR sector ETF’s to go long (short) ETF’s with low (high)
volatility.
Presentation for discussion purposes

18. 18
Value Factor: Characteristics & Risks
• Characteristics. The strategy is Long (IVE S&P500 Value ETF) and Short (IVW S&P 500
Growth ETF). The average annualized return is modest (40 bps per year). The average
beta is close to zero but positive (0.08 on average) and fluctuates slightly over time.
• Risk. Since 2001 the minimum return (over a period of 12 months) has been -11%
(which reversed back to zero over the next 12 months)
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
85
90
95
100
105
110
115
120
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
Jan-08
Jan-09
Jan-10
Jan-11
Jan-12
Jan-13
Jan-14
Jan-15
Jan-16
12MonthRollingReturn
ValueIndexStrategy
Long Value (Short Growth) Strategy
12 Month Rolling (r) RH Strategy Index (LH)
Average annualized return RH
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
3YearBeta
3 Year Rolling Beta & Average
Annualized Return Characteristics
Mean Premium St. Dev. Kurt. Skew.
0.4% 3.5% 4.7 -0.4

19. 19
Momentum Factor: Characteristics & Risks
• Characteristics. The strategy uses 9 sector ETF’s and computes their return over the last 6
months. It goes long ETF’s with positive momentum (past 6 month returns above the
median) and short ETF with negative momentum. The average annualized return is 1.1%.
The average beta is close to zero (-0.07 on average) and fluctuates slightly over time.
• Risk. Since 2001 the minimum return (over a period of 12 months) has been -8% (which
reverse back to zero over the next 5 months)
Annualized Return Characteristics
Mean Premium St. Dev. Kurt. Skew.
1.1% 5.6% 3.7 -0.01
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
90
95
100
105
110
115
Nov-06
Jun-07
Jan-08
Aug-08
Mar-09
Oct-09
May-10
Dec-10
Jul-11
Feb-12
Sep-12
Apr-13
Nov-13
Jun-14
Jan-15
Aug-15
Mar-16
Oct-16
12MonthRollingreturn
StrategyIndex
Momentum Strategy
12 Month Rolling (r) RH Momentum Index (LH)
Average annualized return (RH)
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Oct-09
Mar-10
Aug-10
Jan-11
Jun-11
Nov-11
Apr-12
Sep-12
Feb-13
Jul-13
Dec-13
May-14
Oct-14
Mar-15
Aug-15
Jan-16
Jun-16
Nov-16
Beta(3YearRolling)
3 Year Rolling Beta & Average Beta

20. 20
Low-Risk Factor: Rationale
• The chart above uses 7 sector ETF and ranks them by historical volatility. The mean return
(over the next month) is showed along the Sharpe ratio. There is a large difference in
Sharpe ratios
• The low-risk anomaly takes advantage of the negative relation of realized volatility and
future returns. Despite the theoretical framework which suggests expected returns are
driven by how returns co-vary among assets (and not by their volatility levels).
• This behavior may be explained by leverage constrain investors, which are pushed to take
additional risks by overweighting stocks with built in leverage (higher volatility and/or
higher beta)
-
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-5%
0%
5%
10%
15%
20%
25%
30%
35%
7 Low 6 5 4 3 2 1 High
RawSharpeRatio
Mean&StandardDeviation
Volatility Portfolios
Return Next Month St Dev (hist) SR (RH)

21. 21
Low-Risk Factor: Characteristics & Risks
By Far the Largest Risk-Adjusted Premium with + skewness
• Characteristic: Relative to the historical median volatility level, long (short) positions are
taken in those ETF’s with lower (higher) volatility. The relative weight (in the long and
short positions) is scaled by the volatility ratio of each ETF to the median volatility level.
• The low volatility strategy is not market neutral (and its beta is different from zero); long
and short weights do not add to zero (in the time period analyzed, 2006-2016, the market
weight averaged 50%). This shortcoming will be addressed in the next section.
Annualized Return Characteristics
Mean Premium St. Dev. Kurt. Skew.
7.7% 9.3% 4.2 0.5
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
35%
0
50
100
150
200
250
300
May-06
Dec-06
Jul-07
Feb-08
Sep-08
Apr-09
Nov-09
Jun-10
Jan-11
Aug-11
Mar-12
Oct-12
May-13
Dec-13
Jul-14
Feb-15
Sep-15
Apr-16
Nov-16
12MonthRollingReturn
LowRiskFactorIndex
Low Volatility Strategy
12 Month Rolling Return (RH) Low Volatility Index
Average Annualized Return
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Jun-08
Dec-08
Jun-09
Dec-09
Jun-10
Dec-10
Jun-11
Dec-11
Jun-12
Dec-12
Jun-13
Dec-13
Jun-14
Dec-14
Jun-15
Dec-15
Jun-16
Dec-16
Beta(3yearRolling)
3 Year Rolling Beta & Average Beta

22. 22
Incorporating Dynamic Factors into BL
Start From Static Factor Allocation with Views (same as slide 16)
Asset Mkt. Cap
Weight
(%) (A)
Prior (Market)
Return (Base
Case)
Forecasted
Returns
B&L Revised
Allocation*
B&L Revised
Allocation no
Short Selling*
Base 100
Allocation (B) no
short positions
Difference vs
Market
Weights (B-A)
SPY 75.0% 5.7% 5.0% 58% 53% 87% +12.3%
DBC 3.5% 4.3% 6.0% 8% 8% 13% +9.2%
IEF 21.5% 0.3% -1.0% -6% 0% 0% -21.5%
Total 100.0% 60% 60% 100% 0%
RFA 40% 40%
*Assuming S-T risk free rate goes to 0.75% over the next twelve months
• Start from the asset allocation with no short-selling, which assigns a 53% allocation to
equities.
• Then complement the equity allocation with the dynamic factors (momentum, value and
volatility) as explained in the next few slides.
Presentation for discussion purposes

23. 23
BL Dynamic Factor: Momentum Example
Implementation using SPY Sector ETF’s
• The table above shows how to implement a 20% tilt (or loading) to the momentum
strategy.
• The different sector ETF’s (appropriately weighted) will make a 100% exposure to SPY.
The resulting allocation overweights (underweights) ETF’s with positive (negative)
momentum.
• The resulting allocation has the same weight to equities (and the same beta) and will
capture the momentum premium over the long-term.
• A similar approach used to incorporate value factor exposure
ETF ETF Sector Weight* Momentum (long-
short position)
Momentum
Tilt
Revised
Allocation
Equity Allocation
@53%
XLY
Consumer
Discretionary 13% Short (-) momentum
20%
6% 3%
: : : : : :
XLF Financials 18% Long (+) momentum 27% 14%
: : : : : :
XLK Technology 18% Short (-) momentum 9% 5%
Total 100% 100% 53%
*The weight of each sector ETF can be derived from the SPY sector breakdown or from a regression of returns vs SPY

24. 24
BL Dynamic Factor: Low-Volatility Example
Implementation using SPY Sector ETF’s
• The table above shows the mechanics of a 20% tilt (or loading) to the low-volatility
strategy.
• The different sector ETF’s (appropriately weighted) make a 100% exposure to SPY. The
resulting allocation overweights (underweights) ETF’s with low (high) volatility (relative
to the median volatility).
• Unfortunately, this strategy usually produces allocations that are not market neutral, in
this case the revised equity allocation increases to 58.8% (vs. the 53% initially allocated
to equities).
ETF ETF Sector Weight* Standard Deviation
(annualized)
Low-Vol.
Tilt
Revised
Allocation
Equity Allocation
@53%
XLE Energy 13.0% 24.2% (short)
20%
10.0% 5.3%
: : : : : :
XLF Financials 12.7% 10.9% (median value) 12.7% 6.7%
: : : : : :
XLY
Consumer
Discretionary 10.7% 8.8% (long) 19.0% 10.1%
Total 100% 100% 58.8%
*The weight of each sector ETF used in this strategy was derived from a regression of returns vs SPY

25. 25
Appendix: Covariance Matrix Inputs
• Detail construction of the variance-covariance matrix
• Correlations among factors
• Standard deviation forecast (GARCH and GJR)
Presentation for discussion purposes

26. 26
• There has been a negative correlation between the S&P500 (SPY) and L-T government
bonds (IEF) since the early 2000’s. The relation is not particularly strong however.
• For the purpose of building the variance-covariance matrix (under the Black-Litterman
approach) three scenarios are suggested: base case, a low (absolute) correlation
scenario and a high (absolute) correlation scenario.
• Correlation scenarios: base (-30%), low-absolute (-13%) and high-absolute (-48%)
Correlations: Pearson vs Spearman (Rank)
SPY – IEF Analysis
-50%
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
D-98
N-99
O-00
S-01
A-02
J-03
J-04
M-05
A-06
M-07
F-08
J-09
D-09
N-10
O-11
S-12
A-13
J-14
J-15
M-16
CorrelationCoefficient
10Y Rolling Correlations: SPY - IEF
Pearson Correl Spearman (Rank)
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Last 10Y Rank Correlation SPY-IEF

27. 27
• There has been a positive and increasing correlation between the S&P500 (SPY) and
commodities (DBC) since 2009.
• For the purpose of building the variance-covariance matrix (under the Black-Litterman
approach) three scenarios are suggested: base case, a low (absolute) correlation
scenario and a high (absolute) correlation scenario.
• Correlation scenarios: base (43%), low-absolute (26%) and high-absolute (59%)
Correlations: Pearson vs Spearman (Rank)
SPY – DBC Analysis
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
60%
D-98
N-99
O-00
S-01
A-02
J-03
J-04
M-05
A-06
M-07
F-08
J-09
D-09
N-10
O-11
S-12
A-13
J-14
J-15
M-16
CorrelationCoefficient
10Y Rolling Correlations: SPY - DBC
Pearson Spearman
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Last 10Y Rank Correlation SPY-DBC

28. 28
• There has been a positive and increasing correlation between the S&P500 (SPY) and
commodities (DBC) since 2009.
• For the purpose of building the variance-covariance matrix (under the Black-Litterman
approach) three scenarios are suggested: base case, a low (absolute) correlation
scenario and a high (absolute) correlation scenario.
• Correlation scenarios: base (-19%), low-absolute (-2%) and high-absolute (-37%)
Correlations: Pearson vs Spearman (Rank)
IEF – DBC Analysis
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
D-98
N-99
O-00
S-01
A-02
J-03
J-04
M-05
A-06
M-07
F-08
J-09
D-09
N-10
O-11
S-12
A-13
J-14
J-15
M-16
CorrelationCoeficient
10Y Rolling Correlations: IEF - DBC
Pearson Speraman
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Last 10Y Rank Correlation IEF-DBC

29. 29
• The correlation between the forecasted volatility at the beginning of the period and the
realized volatility (using daily returns over the last 30 days) is 78% for the S&P 500
(SPY).
• GJR incorporates the asymmetric behavior of investors (losses trigger higher volatility
levels than equal magnitude gains).
• The high variability in volatility could translate into excessive trading (under the Black-
Litterman framework), as a result a confidence volatility range (if volatility remains
between 8% - 11% use a 10% level) can be used.
SPY Volatility Forecast: GJR (1,1)
0
20
40
60
80
100
120
Feb-06
Aug-06
Feb-07
Aug-07
Feb-08
Aug-08
Feb-09
Aug-09
Feb-10
Aug-10
Feb-11
Aug-11
Feb-12
Aug-12
Feb-13
Aug-13
Feb-14
Aug-14
Feb-15
Aug-15
Feb-16
Aug-16
AnnualizedStandardDeviation(%)
Forecast vs Realized Vol. (Standard Deviation)
GJR-GARCH(1,1) Realized-Last 30 days
Variable Level
Current Vol. Forecast 8.8%
Average since 2006 16.8%
BL Vol. Input 10.0%
Min 7.7%
Max 101.2%

30. 30
• The correlation between the forecasted volatility at the beginning of the period and the
realized volatility (using daily returns over the last 30 days) is also 78% for
commodities.
• The GJR framework does not provide evidence of asymmetric behavior and therefore a
GARCH (1,1) is used instead.
• The high variability in volatility could translate into excessive trading (under the Black-
Litterman framework), as a result a confidence volatility range (if volatility remains
between 13% - 17% use a 15% level) can be used.
DBC Volatility Forecast: GARCH (1,1)
Variable Level
Current Vol. Forecast 15.2%
Average since 2006 19.2%
BL Vol. Input 15.0%
Min 8.0%
Max 51.4%0
10
20
30
40
50
60
Feb-06
Aug-06
Feb-07
Aug-07
Feb-08
Aug-08
Feb-09
Aug-09
Feb-10
Aug-10
Feb-11
Aug-11
Feb-12
Aug-12
Feb-13
Aug-13
Feb-14
Aug-14
Feb-15
Aug-15
Feb-16
Aug-16
StandardDeviation(%)
Forecast vs Realized Vol. (Standard Deviation)
GARCH(1,1) Realized-Last 30 days

31. 31
• The correlation between the forecasted volatility at the beginning of the period and the
realized volatility (using daily returns over the last 30 days) is 68% for L-T government
bonds. Is lower than for the S&P 500 (SPY) and commodities (DBC) but also significant.
• Here too the GJR framework does not provide evidence of asymmetric behavior and
therefore a GARCH (1,1) is used instead. IEF has a considerable lower average level of
volatility.
• The high variability in volatility could translate into excessive trading (under the Black-
Litterman framework), as a result a confidence volatility range (if volatility remains
between 4.0% - 7.0% use a 5.5% level) can be used.
IEF Volatility Forecast: GARCH (1,1)
Variable Level
Current Vol. Forecast 5.5%
Average since 2006 6.7%
BL Vol. Input 5.5%
Min 3.9%
Max 14.6%0
2
4
6
8
10
12
14
16
18
Feb-06
Aug-06
Feb-07
Aug-07
Feb-08
Aug-08
Feb-09
Aug-09
Feb-10
Aug-10
Feb-11
Aug-11
Feb-12
Aug-12
Feb-13
Aug-13
Feb-14
Aug-14
Feb-15
Aug-15
Feb-16
Aug-16
StandardDeviation(%)
Forecast vs Realized Vol. (Standard Deviation)
GARCH(1,1) Realized-Last 30 days

32. A Scalable ETF Factor Model Under
the Black-Litterman Approach to
Portfolio Optimization
Manuel Zapata, CFA & CQF
January 31, 2017
Presentation for discussion purposes
Detail Methodology