b&l factor model jan 2017

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

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


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.


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.


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.


6

Equity Valuation: CAPE Ratio & Fed-ModelLikely 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.

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CAPE Ratio 1987-2016

Average

+1 St. Dev.

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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

Equity: Return DecompositionConsiderable 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

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

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-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

IEF

-ET

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thly

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turn

(%

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10Y Monthly Rate Change (%)

Monthly L-T Bond Returns vs L-T Rate Change (2002-16)

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IEF (ETF): 12 Month Rolling Return

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

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Yie

ld (

%)

Maturity

Average Yield Curve Shapes and Forward Returns

Lower than -1% -1% to 1% Above 1% Current

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6 Month Actual Returns (%)

Forecasting Returns: Yield Curve Predicatbility

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

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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

• 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).


DBLCI Analysis: Mid-Term Returns Above Inflation

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133 168 203 238 273 308 343 378 413 448 483 518 553 588 623 658 693 728 763 798

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Commodity DBLCI Mid-Bin Index Price (real terms)

DBLCI Real Price Distribution (1989-2016)

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DBLCI Real Price Index (1989-2016)

Real DBLCI (LH) Average Index (LH) 3Y Forward Returns (RH)

Current level

12

Black–Litterman (BL) FrameworkA 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


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.


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

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

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

Revised Asset Allocation: Incorporating ViewsLarge 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

Dynamic Factors and their RisksAlso 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.


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)

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Long Value (Short Growth) Strategy

12 Month Rolling (r) RH Strategy Index (LH)

Average annualized return RH

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3 Year Rolling Beta & Average

Annualized Return Characteristics

Mean Premium St. Dev. Kurt. Skew.

0.4% 3.5% 4.7 -0.4

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)



1.1% 5.6% 3.7 -0.01

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Momentum Strategy

12 Month Rolling (r) RH Momentum Index (LH)

Average annualized return (RH)-0.8

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3 Year Rolling Beta & Average Beta

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)

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Volatility Portfolios

Return Next Month St Dev (hist) SR (RH)

21

Low-Risk Factor: Characteristics & RisksBy 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.



7.7% 9.3% 4.2 0.5

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Low

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Low Volatility Strategy

12 Month Rolling Return (RH) Low Volatility Index

Average Annualized Return-0.8

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3 Year Rolling Beta & Average Beta

22

Incorporating Dynamic Factors into BLStart 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.


23

BL Dynamic Factor: Momentum ExampleImplementation 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%

XLYConsumer

Discretionary13% 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

BL Dynamic Factor: Low-Volatility ExampleImplementation 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%

: : : : : :

XLYConsumer

Discretionary10.7% 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

Appendix: Covariance Matrix Inputs

• Detail construction of the variance-covariance matrix

• Correlations among factors

• Standard deviation forecast (GARCH and GJR)


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-Littermanapproach) 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-9

8

N-9

9

O-0

0

S-0

1

A-0

2

J-0

3

J-0

4

M-0

5

A-0

6

M-0

7

F-0

8

J-0

9

D-0

9

N-1

0

O-1

1

S-1

2

A-1

3

J-1

4

J-1

5

M-1

6

Co

rre

lati

on

Co

eff

icie

nt

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

• There has been a positive and increasing correlation between the S&P500 (SPY) and commodities (DBC) since 2009.


• 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-9

8

N-9

9

O-0

0

S-0

1

A-0

2

J-0

3

J-0

4

M-0

5

A-0

6

M-0

7

F-0

8

J-0

9

D-0

9

N-1

0

O-1

1

S-1

2

A-1

3

J-1

4

J-1

5

M-1

6

Co

rre

lati

on

Co

eff

icie

nt

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

• There has been a positive and increasing correlation between the S&P500 (SPY) and commodities (DBC) since 2009.


• 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-9

8

N-9

9

O-0

0

S-0

1

A-0

2

J-0

3

J-0

4

M-0

5

A-0

6

M-0

7

F-0

8

J-0

9

D-0

9

N-1

0

O-1

1

S-1

2

A-1

3

J-1

4

J-1

5

M-1

6

Co

rre

lati

on

Co

efi

cie

nt

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

• 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

Au

g-0

6

Feb

-07

Au

g-0

7

Feb

-08

Au

g-0

8

Feb

-09

Au

g-0

9

Feb

-10

Au

g-1

0

Feb

-11

Au

g-1

1

Feb

-12

Au

g-1

2

Feb

-13

Au

g-1

3

Feb

-14

Au

g-1

4

Feb

-15

Au

g-1

5

Feb

-16

Au

g-1

6

An

nu

ali

zed

Sta

nd

ard

De

via

tio

n (

%)

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

• 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



BL Vol. Input 15.0%

Min 8.0%

Max 51.4%0

10

20

30

40

50

60

Feb

-06

Au

g-0

6

Feb

-07

Au

g-0

7

Feb

-08

Au

g-0

8

Feb

-09

Au

g-0

9

Feb

-10

Au

g-1

0

Feb

-11

Au

g-1

1

Feb

-12

Au

g-1

2

Feb

-13

Au

g-1

3

Feb

-14

Au

g-1

4

Feb

-15

Au

g-1

5

Feb

-16

Au

g-1

6

Sta

nd

ard

De

via

tio

n (

%)


GARCH(1,1) Realized-Last 30 days

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



BL Vol. Input 5.5%

Min 3.9%

Max 14.6%0

2

4

6

8

10

12

14

16

18

Feb

-06

Au

g-0

6

Feb

-07

Au

g-0

7

Feb

-08

Au

g-0

8

Feb

-09

Au

g-0

9

Feb

-10

Au

g-1

0

Feb

-11

Au

g-1

1

Feb

-12

Au

g-1

2

Feb

-13

Au

g-1

3

Feb

-14

Au

g-1

4

Feb

-15

Au

g-1

5

Feb

-16

Au

g-1

6

Sta

nd

ard

De

via

tio

n (

%)


GARCH(1,1) Realized-Last 30 days

A Scalable ETF Factor Model Under the Black-Litterman Approach to Portfolio Optimization

Manuel Zapata, CFA & CQF

January 31, 2017


Detail Methodology

b&l factor model jan 2017

Documents