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NEW TECHNIQUES INPORTFOLIO MANAGEMENT

FEBRUARY 7, 2018

QUANTIFYING MACRO RISKIN PORTFOLIO ANALYTICS

NEW TECHNIQUES IN PORTFOLIO MANAGEMENT

DIETER VANDENBUSSCHEHEAD OF EQUITY RESEARCH

Confidential – Not for Redistribution – Copyright © 2018 Axioma, Inc. 3

DEFINING AND QUANTIFYING MACRO RISK

• We define Macro Risk as sensitivity to drivers in the Macro Economy

• Fluctuations in commodity prices like Oil, Metals, and Gas• Changes in interest rates, yield curve shape, credit spreads• Movements in FX markets• Changes in inflation expectations• (unexpected) Changes in macro statistics like industrial production, consumer confidence, and

unemployment

• Today’s focus is only a few of these macro risks on equity portfolios

• How do we quantify Macro Risk? We will quantify it through the lens of Stress Testing (could also do Risk Decomposition, etc.)


STRESS TESTING AND MACRO RISK

We will shock a macro factor and use a “model” of some kind to explore the effect on your portfolio

• Historical Model: run portfolio through a historical period• Pro: No need to construct correlations across factors• Con: Historical period may not reflect expected dynamics

• Granular Resolution: Establish a direct statistical relationship between portfolio or assets and macro factor• Pro: Simple to compute• Con: Requires long history of portfolio or asset returns, estimation error

• Risk (Model) Resolution: Establish a relationship between macro factor and risk/pricing factors for portfolio• Pro: Can evaluate portfolio based on current factor exposures, no portfolio history required• Con: Introduces possible specification error


RISK RESOLUTION

Granular Risk Resolution:

• Pricing factors for equities are the equities themselves

• Estimating relationships directly means the risk factors are also the equities

Factor Model Resolution:

• We use fundamental factor models as the source of risk factors

• We map the individual equities to the factors via exposures

Risk Resolution provides the user the flexibility to select Risk Factors that drive the Pricing Factors.


QUANTIFYING MACRO RISK: STRESS TESTING

During the presentation, we will illustrate two main themes:

• The benefits of using a well-understood pricing model, in this case a fundamental risk model in quantifying macro risks in an equity portfolio

• The need for having a flexible mechanism that allows for • a deeper understanding of the implications of historical analysis, • alternative views on pricing models (i.e. alternative risk models),• the possibility to introduce economic expectations and views to override historical analysis.


US EQUITY MARKET AND 10 YEAR YIELD FOR GOVERNMENT BONDS

• 𝑓𝑓𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝛽𝛽 𝑓𝑓10𝑦𝑦𝑚𝑚 + 𝜖𝜖 (market = Broad index, alla R3k)

• How do we find 𝛽𝛽 ?

• Estimate via 5 years of weekly returns as of end of 2017: 𝛽𝛽 = 5.3, correlation of 𝜌𝜌 = 0.31. (no decay, no special weighting of historical data).

• This implies that a 50 basis point increase in 10 year yield would give an expected return of ~ 2.5% in the market (5 x 50bps).

• The results of this “stress test” may run counter to the usual expectation that equity markets go down when yields go up.

• Same exercise at the end of 1996: 𝛽𝛽 = −4.10 and 𝜌𝜌 = −0.37!


CORRELATION BETWEEN US EQUITY MARKET AND 10 YEAR YIELD CHANGES


WHY THE CHANGE IN CORRELATIONS?

• Traditional expectations are that equities as a whole would be negatively correlated to interest rates• Asset pricing via discounted dividend model• This interpretation has broken down recently

• Some suggest that level of the interest rates is key:• During low rate regimes, the market is much more concerned about deflation than inflation, so increases

in rates (and hence inflation expectations) are considered a plus• During high rate regimes, the threat of inflation is a danger sign

• For short term stress tests with small shifts in the yield curve, using a more recent correlation may be more appropriate.

• For long term stress tests that bring rates significantly higher, use correlations from 1990s or earlier

10Confidential – Not for Redistribution – Copyright © 2018 Axioma, Inc.

ILLUSTRATIVE EXAMPLE:UTILITIES PORTFOLIO


ILLUSTRATIVE EXAMPLE: UTILITIES PORTFOLIO

• Sensitive to interest rate changes:• Reliance on long term debt• Usually significant dividends• Sensitive to inflation due to regulatory constraints: can’t raise prices when inputs become more expensive

• How will my utilities portfolio react to a 50 basis point increase in 10-year yield?

• Use Risk Resolution with a Fundamental Factor Model to answer:

• What equity factors are driving my interest rate sensitivity?

• What is my exposure to interest rate moves?

• What fraction of portfolio risk is driven by interest rate risk?


US UTILITIES PORTFOLIO - EXAMPLE

Cap weighted assets from Utilities sector in Axioma’s US Estimation Universe (~ 90 assets), Beta to the market: ~0.6

Top 10 NamesNEXTERA ENERGY INC

DUKE ENERGY CORP NEWDOMINION RESOURCES INC VA

SOUTHERN COEXELON CORP

AMERICAN ELEC PWR INCSEMPRA ENERGY

CONSOLIDATED EDISON INCPUBLIC SVC ENTERPRISE GROUP

XCEL ENERGY INC


CORRELATION WITH CHANGES IN YIELD


UTILITIES SENSITIVITY TO 10 YEAR YIELD

• Timeseries Risk resolution• 5 years of weekly history of utilities portfolio• 5 years of weekly changes in 10 yr yield• Compute beta and correlation

• Model Risk resolution• Compute covariance matrix between 10 year yield returns and fundamental model factor returns• Deduce beta and correlation from covariance matrix and current portfolio exposures

• Calculation as of end of 2017

Timeseries Model𝛽𝛽 -6.6 -6.3𝜌𝜌 -0.35 -0.34

Market𝛽𝛽 5.3𝜌𝜌 0.31


USING FUNDAMENTAL MODEL FOR RISK RESOLUTION

We establish a relationship between fundamental factors and macro factor of interest

• Fundamental model: 𝑟𝑟 = 𝑋𝑋𝑓𝑓 + 𝜖𝜖, where cov(𝑓𝑓)=Ω𝑓𝑓𝑓𝑓

• 𝑓𝑓 = 𝛽𝛽𝛽𝛽 + 𝛿𝛿, where 𝛽𝛽 is a macro factor (or factors) like yield, oil, etc…

• A shock to 𝛽𝛽 implies a shock to 𝑓𝑓: 𝐸𝐸 𝑓𝑓 𝛽𝛽 = 𝛽𝛽𝛽𝛽

• Translates into shock to equity returns: 𝐸𝐸 𝑟𝑟 𝛽𝛽 = 𝑋𝑋𝛽𝛽𝛽𝛽

• This transformation allows us to decompose the macro shock into contributions due to individual fundamental factors


10 YEAR YIELD UP 50 BPS: END OF 2017 • Market: 2.7%• Utilities: -3.2%

• Both portfolios get same contribution from market intercept (by construction)

• Certain Utility industries have significantly negative correlations with changes in yield

• Market Sensitivity factor has positive correlation, Utilities portfolio has strongly negative exposure to Market Sensitivity

• Contribution is determined by three components:• Correlation of factor with yield• Volatility of the factor• Exposure of portfolio to the factor


CORRELATION X EXPOSURE X FACTOR VOL CONTRIBUTION

Divide by Yield Vol

10 YEAR YIELD UP 50 BPS: END OF 2017



• Market: -2.2%• Utilities: -2.8%

• Negative contribution from market intercept

• Positive contribution from Market Sensitivity due to negative correlation with yield

• Significantly lower magnitude contributions from industry factors


CORRELATION X EXPOSURE X FACTOR VOL CONTRIBUTION

Divide by Yield Vol



USING FUNDAMENTAL MODEL FOR RISK RESOLUTION

• We can rewrite the risk model in terms of a different set of factors

• Start with covariance matrix on 𝑓𝑓 and 𝛽𝛽:

Ω =Ω𝑔𝑔𝑔𝑔 Ω𝑔𝑔𝑓𝑓Ω𝑔𝑔𝑓𝑓𝑇𝑇 Ω𝑓𝑓𝑓𝑓• 𝛽𝛽 = Ω𝑔𝑔𝑓𝑓𝑇𝑇 Ω𝑔𝑔𝑔𝑔−1

• Recast risk model to 𝑟𝑟 = 𝑋𝑋𝛽𝛽𝛽𝛽 + 𝑋𝑋𝛿𝛿 + 𝜖𝜖

• New factor covariance matrix on 𝛽𝛽 and 𝛿𝛿 is

Ω =Ω𝑔𝑔𝑔𝑔 0

0 Ω𝑓𝑓𝑓𝑓 − Ω𝑔𝑔𝑓𝑓𝑇𝑇 Ω𝑔𝑔𝑔𝑔−1Ω𝑔𝑔𝑓𝑓

• Allows for a different risk decomposition, changes the “focus” of the model

Fundamental Factors with the Macro factor projected out


ALTERNATIVE ACTIVE RISK DECOMPOSITION

• Risk decomposition of original fundamental model vs “projected” model

• More than 30% of the tracking error between the Utilities portfolio and the overall market can be explained by volatility in the 10-year yield

• 10-yr yield factor takes risk contribution away from the most correlated factors


ASSET LEVEL EXPOSURES TO 10 YEAR YIELD: END OF 2017

• Average asset exposure is positive because the market is positively correlated with yield

• The magnitude is much higher than usual because the factor has very low volatility

• Utilities assets have very low exposures to the 10 year yield, mostly in negative territory


EXPOSURES TO 10 YEAR YIELD: END OF 1996

• Average asset exposure is negative because the market was negatively correlated with yield

• Utility stocks are closer to the average due to lower correlation of Utility industry factors to yield


USING A FUNDAMENTAL MODEL FOR RISK RESOLUTION

Pros:

• Overall risk forecasts stay unchanged• No history of portfolio returns required• Can express individual asset exposures to macro factor (𝑋𝑋𝛽𝛽)• Decompose exposure into contributions from fundamental factors• No need to estimate asset level sensitivities to macro factor

Cons:

• Assumes that residuals do not contain any macro effect, i.e. specification error, i.e. 𝐸𝐸 𝛽𝛽𝜖𝜖𝑇𝑇 = 0

Use a risk analytics platform that can provide both model and granular views


ILLUSTRATIVE EXAMPLE:ENERGY ETF


ENERGY ETF: OIL SENSITIVITY STRESS TEST

• POWERSHARES DYNAMIC ENERGY SECTOR PORTFOLIO

• Effect of 10% drop in oil price:• Market: -1.1%• ETF: -4.7%

• Using data as of end of 2017

• ETF has high beta and volatility exposure, each of which is negatively correlated with oil


EXPOSURE TO OIL: END OF 2017

• Not surprisingly, model predicts that energy stocks have much higher betas to oil than most stocks.


END OF 1996

• Using correlations forecast with data ending in 1996

• Effect of 10% drop in oil price:• Market: 0.0%• ETF: -2.0%

• Negligible contributions from market and market sensitivity factors


ROLLING 5-YEAR CORRELATION BETWEEN MARKET AND OIL

• Correlation with market near zero in late 90s

• Correlation increased and stayed high since the financial crisis


ASSET EXPOSURES TO OIL

• Now exposure to oil is exclusively determined by exposure to the two Energy industry factors

• Most other assets have exposures to oil centered around zero


ROLLING 5-YEAR CORRELATION BETWEEN OIL RETURNS AND THE OIL, GAS AND CONSUMABLE FUELS FACTOR

• Correlation stays relatively high throughout

• Get contribution from this factor regardless of market correlation with oil


CUSTOM ENERGY MODEL

• Build an Energy model using a broad, liquid universe of Energy stocks as estimation universe

• Covers only energy stocks

• Custom factors• 2-year timeseries beta to oil returns• 2-year timeseries beta to sector returns,

orthogonalized to oil beta

• Remove several style factors that are only marginally significant (profitability, growth,…)

• Remaining factors are statistically significant

Fraction of days significant


OIL STRESSTEST WITH CUSTOM MODEL

• Oil down 10%:• US4 model forecasts drop of 4.7%• Custom model forecasts drop of 5.2%

• Provides more direct view on how certain stocks co-move with changes in oil prices


OVERRIDING CORRELATIONMATRICES


ESTIMATING THE MACRO BETAS

• 𝛽𝛽 = Ω𝑔𝑔𝑓𝑓𝑇𝑇 Ω𝑔𝑔𝑔𝑔−1

• Ω𝑔𝑔𝑓𝑓𝑇𝑇 is the covariances between the fundamental and macro factors

• To understand these, need to understand the underlying correlations and how to estimate them• What frequency?• How much history?• Which history?


ESTIMATION TECHNIQUES

• Daily frequency may be too granular to capture relationships between certain types of factors.

• On the other hand, already have a vetted covariance matrix on the fundamental factors (based on daily returns).

• May believe that a different time period better reflects the anticipated dynamics.

• How can we combine correlation estimates of different frequencies and different histories?

• How can we override historical correlation based on an analyst’s estimate or economic intuition?


CUSTOMIZING CORRELATION MATRIX

• Begin with a prior for the correlation matrix: 𝐶𝐶𝑝𝑝• Possibly based on different frequencies/histories for different pairs of factors• Partially based on vendor provided covariance matrix • Prior may not be positive semidefinite

• User can specify views• Expectation of correlation between given portfolios• Expectation of correlation between factors

• User can specify confidence of views

min 𝐶𝐶 − 𝐶𝐶𝑝𝑝 + 𝑠𝑠𝑇𝑇Σ−1𝑠𝑠

𝑑𝑑𝑑𝑑𝑑𝑑𝛽𝛽 𝐶𝐶 = 𝐼𝐼 𝐴𝐴𝑖𝑖 � 𝐶𝐶 = 𝑏𝑏𝑖𝑖 + 𝑠𝑠𝑖𝑖 𝐶𝐶 ≽ 0


CREDIT SPREAD ILLUSTRATION

• Credit spread comes from Moody's Seasoned Baa Corporate Bond Yield Relative to Yield on 10-Year Treasury Constant Maturity

• Construct two covariance matrices (correlations vary significantly with the frequency of the data)1. Based on weekly correlations2. Based on monthly correlations

• Block of equity factors matches off-the-shelf model

• Volatility of credit spread factor based on weekly returns

• Find correlation matrix whose equity to credit spread correlations most closely match weekly (monthly) correlations


ACTIVE SECTOR PORTFOLIOS CORRELATIONSWITH CREDIT SPREADS

• Compute correlation between active sector portfolio and credit spreads

• Measure with different covariance matrices that have different views of correlation imposed

• Daily numbers seem to understate longer-term correlation

• Traditionally defensive sectors have positive correlation with credit spread

• Expected to see cyclical sectors to show more negative correlation (will come back to this)


EXAMPLE: DEFENSIVE VS. CYCLICALS BETS

• Construct long-only, fully invested portfolio• Overweight

• Consumer Staples• Health Care• Telecom Services• Utilities

• Underweight• Consumer Discretionary• Industrials• Information Technology• Materials

• Neutral to• Energy• Financials


STRESS TEST: BUMP UP SPREADS 100BPS.

• Expected active return under stress:• Daily: 0.9%• Weekly: 2.5%• Monthly: 3.5%

• Portfolio outperforms the market under scenario

• Drastically different magnitudes from different covariance matrices


STRESSING THE CORRELATION MATRIX

• Correlation of various factors (especially industry factors) with macro factors may vary through different regimes

• Estimating correlation matrices at various points in time to evaluate portfolio reaction to different historical scenarios

• What if future scenario combines multiple stressed scenarios from the past?

• Try to compute correlation matrix that reflects most significant period of comovement for each factor• For factors, that usually have positive (negative) correlations with the macro factor, choose the most

positive (negative) correlation observed historically• Override current correlations with these extreme correlations• Find nearest correlation matrix consistent with current equity factor correlations


STRESSED CORRELATION MATRIX ILLUSTRATED

• Defensive vs Cyclical case

• Compute “Worst” correlation matrix and recompute stress test:• Daily: 0.9%• Weekly: 2.5%• Monthly: 3.5%• Worst: 5.0%

• IT and Cons. Disc drastically different• Current estimated correlations for industries are mild• Some historical periods show significantly negative

correlations• Stress test shows significant benefit from shorting

these industries should that historical behavior return


CONCLUSIONS


CONCLUSIONS

• Need a stress testing tool that is sufficiently flexible to• View historical correlations in the context of current macroeconomic assumptions and regimes.• View risk through various lenses:

• Granular• Factor Model• Custom Model

• Accommodate differing methodologies for estimating correlations (e.g. frequency)• Accommodate analysts expectations of future dynamics

• By leveraging an existing factor model, we can• Explain macro exposures based on factors everyone is used to• Eliminate the need for long histories of portfolio returns/holdings• Reduce the number of parameters that require estimation

WILL THE FUTURE RESEMBLETHE PAST?INSIGHTS FROM STRESS TESTING

NEW TECHNIQUES IN PORTFOLIO MANAGEMENT

MELISSA R. BROWN, CFA HEAD OF APPLIED RESEARCH


• Quant managers know the factors that drive their portfolios’ expected returns inside and out• But do they know the vulnerabilities that fall outside the likelihood of factor underperformance?• If funds tilt on one factor (like many “Smart Beta” products), how might a move in a different

factor impact returns?• Stress testing can help managers better understand the potential impact of economic, market

and factor events • In this presentation we will show results of stress tests on sample quantitatively-driven portfolios

• Examine how portfolios would have fared under various historical scenarios• Test the impact of big moves in selected economic and model variables• Compare results from two dates to show how vulnerabilities can differ through time• Highlight the impact of constraints on the expected outcomes

HOW WELL DO YOU KNOW YOUR PORTFOLIO?


• Stress tests can provide insight into a portfolio’s vulnerabilities to moves in variables that are not necessarily part of the investment process

• Quantitatively-driven portfolios may be vulnerable market events, changes in economic variables and factor shocks

• Even “single-factor” portfolios (such as many “Smart-Beta ETFs”) may be exposed to big shifts in other risk factors via correlations

• The impact of a given shock will vary over time, a function of the portfolio’s current exposures, a factor’s volatility and changing factor correlations

• “Belt-and-braces” constraints do not necessarily help avoid problems

KEY TAKEAWAYS


• Our test portfolios use various Axioma factors as alphas• We create long-only, US portfolios that maximize exposure to the factor while targeting 3%

tracking error• Benchmark and investment universe are the Russell 1000• One set of portfolios has no other constraints imposed• One set of portfolios zeroes out style and industry exposures• We also tested minimum variance strategies• No turnover, liquidity, maximum active weight or other constraints were imposed

SAMPLE FACTOR PORTFOLIOS: MIMICKING MANY SMART BETA STRATEGIES


We use the following factors as alphas

• Dividend Yield• Growth• Profitability• Medium-Term Momentum• Combination of Value and Earnings Yield• Total risk (minimized exposure)

And also created minimum variance portfolios

We then ran a series of stress tests, which we will describe in the next few slides

SAMPLE FACTOR PORTFOLIOS


STRESS-TESTING: REPLAYING HISTORY

“History doesn’t repeat itself, but it often rhymes” Mark Twain?

• What happens if we run a current portfolio through known historical periods

• Expected performance is based on portfolios’ current factor exposures, and how those factors performed

• Stress tests ignore specific returns

Historical periods *

• Black Monday 1987

• Bond Market Crash 1994

• Russian Debt Default/LTCM crisis 1998

• Dot-Com Bubble Burst 2000

• WorldCom Scandal 2002

• Subprime Crisis 2007

• Lehman Collapse 2008

• Oil Price Drop 2014

*See Appendix for exact dates


STRESS-TESTING: SHOCKING FUNDAMENTALFACTORS

Portfolios that tilt on just one factor may still be impacted by a big move in another risk factor

• Use Axioma US4 Fundamental Model for factor shocks

• Each factor is shocked by a move three standard deviations* above or below the long-term average, using volatility estimates and averages at the end of December 2017

• Positive or negative shock is based on sign of long-term average return

*Using monthly volatility and average monthly returns. Long-term average is calculated from 1999 through 2017

Fundamental Factor Shocks

• Market Intercept down 20%

• Growth down 1.1%

• Medium-Term Momentum down 2.5%

• Market Sensitivity up 2.8%

• Volatility up 3.3%

• Value down 1.4%

• Size up 2.8%

• Exchange Rate Sensitivity down 1%

• Earnings Yield down 1.7%


STRESS-TESTING: SHOCKING MACRO FACTORS

How will the portfolio react given shocks in economic variables?Returns are based on current factor exposures and how those factors are correlated with other factorsUse Axioma US Macro Model for factor shocksNote: These tests are useful if you are only interested in a quick assessment based the few factors that comprise the US Macro model. As Dieter described earlier, there are far more elegant and comprehensive ways to test macro factors

Macro Factor Shocks

• Inflation up 5%

• Term spread down 1%

• Credit spread up 50 basis points

• FX Basket up 10%

• Oil up 25%

Confidential – Not for Redistribution – Copyright © 2018 Axioma, Inc.

HISTORICAL STRESS TESTS

54


HISTORICAL STRESS TESTS RESULTS: RUSSELL 1000 RETURNS

-50% -40% -30% -20% -10% 0% 10%

Oil Price Drop 2014

Lehman Collapse 2008

Subprime Crisis 2007

WorldCom Scandal 2002

Dot-Com Bubble Burst 2000

Russian Default/LTCM 1998

Bond Market Crash 1994

Black Monday 1987

55


HISTORICAL STRESS TESTS RESULTS: ACTIVE PORTFOLIO RETURNS

-6% -4% -2% 0% 2% 4%

Oil Price Drop 2014







Black Monday 1987

Dividend Yield

-10% -5% 0% 5%

Value + Earnings Yield

-10% -5% 0% 5% 10%

Profitability

56



-6% -5% -4% -3% -2% -1% 0% 1%

Oil Price Drop 2014







Black Monday 1987

Medium-Term Momentum

-10% -5% 0% 5%

Growth

57



-2% 0% 2% 4% 6% 8% 10% 12%

Oil Price Drop 2014







Black Monday 1987

Minimum Variance

-10% -5% 0% 5%

Low Total Risk

58


RESULTS OF BIG MARKETDOWNTURN

59


STRESS TESTS RESULTS: ACTIVE RETURNS, MARKET DOWN 20%

-1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5%

Dividend Yield


Profitability

Medium-Term Momentum

Growth

0.0% 2.0% 4.0% 6.0% 8.0% 10.0%

Minimum Variance

Low Total Risk

60


GROWTH UNCONSTRAINED, ACTIVE RETURN, MARKET DOWN 20%

-0.5 0.0 0.5 1.0 1.5 2.0

Size

Equity REITs

Growth

Value

MidCap

Electric Utilities

Banks

Air Freight & Log

Market Sensitivity

Volatility

-10% -5% 0% 5% 10% 15% -0.8% -0.4% 0.0% 0.4% 0.8%

Exposure X Return = Contribution

Even small exposures can have big consequences

61


MINIMUM VARIANCE UNCONSTRAINED, ACTIVE RETURN, MARKET DOWN 20%


-0.8 -0.6 -0.4 -0.2 0.0 0.2

Machinery

Software

Beverages

Household Products

Size

Banks

Electric Utilities

Mortgage REITs

Volatility

Market Sensitivity

-10% -5% 0% 5% 10% 15% 0.0% 2.0% 4.0% 6.0%

Min Var seemed to be on the right side of many bets

62


MOMENTUM UNCONSTRAINED, ACTIVE RETURN, MARKET DOWN 20%


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

Volatility

Market Sensitivity

Capital Markets

Electronic Equipment

Equity REITs

Household Products

Personal Products

Semi & Semi Equip

Size

MT Momentum

-10% -5% 0% 5% 10% 15% -2.0% -1.0% 0.0% 1.0% 2.0%

The correlation between Momentum and Market Intercept has been negative

63


SHOCKING FUNDAMENTAL FACTORS

64


DECEMBER 2017 FACTOR STRESS TESTS RESULTS: RUSSELL 1000 RETURNS

-1% 0% 1% 2% 3% 4%

Earnings Yield Down 1.4%

Exch Rate Sens Down 0.9%

Size Up 3.5%

Value Down 1.2%

Volatility Up 2.3%

Market Sensitivity Up 2.8%

MT Momentum Down 2.6%

Growth Down 1.1%

65


CHANGE IN MODEL CORRELATION10/31/16 TO 12/31/17Correlations between many factors changed a lot

after the US election in 2016

These correlation changes meant the impact of factor moves on factor portfolios was likely to be large

Volatility also plummeted during this period

On the next few slides we test the impact of a 3-standard-deviation move in the opposite direction of the long-term average return for a given factor on our sample factor portfolios at two points in time: October 2016 and December 2017

As before, volatility is based on the monthly estimate at the beginning of the period, average return from 1999 through the beginning of the test period

Earnings Yield

ValueLeverage

GrowthProfita

bility

Dividend Yield

Size Liquidity

Mkt Sens

Volatility

MT Momentum

MidCap

Exch Rate Sens

Mkt Intercept

Earnings YieldValueLeverageGrowthProfitabilityDividend YieldSizeLiquidityMarket SensitivityVolatilityMedium-Term MomMidCapExchange Rate SensMarket Intercept

-0.23 0.23

66


EXPECT ACTIVE RETURN: FACTOR STRESS TESTS, OCTOBER 2016 VS. DECEMBER 2017

Shock Size

2016 2017

Earnings Yield -1.7% -1.4%

Exchange Rate Sensitivity -1.0% -0.9%

Size 2.8% 3.5%

Value -1.4% -1.2%

Volatility 3.3% 2.3%

Market Sensitivity 4.6% 2.8%

Medium Term Momentum -2.5% -2.6%

Growth -1.1% -1.1%

67



-0.7% -0.2% 0.3%

Dividend Yield

Value + EarningsYield

Profitability

Medium-TermMomentum

GrowthShock: Earnings Yield

-1.0% -0.5% 0.0% 0.5%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Value

-0.7% -0.5% -0.3% -0.1% 0.1% 0.3% 0.5%

Minimum Variance

Low Total Risk

Shock: Earnings Yield

-0.5% 0.0% 0.5% 1.0% 1.5%

Minimum Variance

Low Total Risk

Shock: Value

An Earnings Yield shortfall’s impact on Minimum Variance would be quite different from Value’s, and more variable

2016 2017

68



Exch Rate Sens shocks could have a surprisingly large impact; Most portfolios have a small cap bias

2016 2017

-0.5% -0.3% 0.0% 0.3%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Exch Rate Sens

-0.5% -0.3% -0.1% 0.1%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Size

-0.1% 0.0% 0.1% 0.2% 0.3%

Minimum Variance

Low Total Risk

Shock: Exch Rate Sens

-1.0% -0.8% -0.6% -0.4% -0.2% 0.0%

Minimum Variance

Low Total Risk

Shock: Size

69


EXAMPLE ATTRIBUTION: EXCHANGE RATE SENSITIVITY SHOCK ON GROWTH PORTFOLIO

-0.5 0.0 0.5 1.0 1.5

Pharmaceuticals Construction Materials

Metals & Mining Multi-Utilities

Exch Rate Sensitivity Dividend Yield

Oil, Gas Growth

Exposure X

-5% 0% 5% 10%

Return

-0.3% -0.2% -0.1% 0.0% 0.1%

= Contribution

-0.5 0.0 0.5 1.0 1.5 2.0

Size Banks

Energy Equip&Svs Air Freight & Logistics

LeverageGrowth

Exch Rate Sensitivity Value

Equity REITs

-5% 0% 5% 10% -0.2% -0.1% 0.0% 0.1% 0.2%

Oct 2016 (Active Return -0.43%)

Dec 2017 (Active Return ~ 0)

70


-0.5% -0.3% 0.0% 0.3%

Minimum Variance

Low Total Risk

Shock: Growth


Momentum’s correlation with Value-oriented factors was more negative in 2016, and shocking Growth had a very different impact on Minimum Variance than it did on Low Total Risk

2016 2017

-2.0% -1.0% 0.0% 1.0%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Momentum

-1.5% -1.0% -0.5% 0.0% 0.5%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Growth

-2.0% -1.5% -1.0% -0.5% 0.0%

Minimum Variance

Low Total Risk

Shock: Momentum

71


EXAMPLE ATTRIBUTION: 2016 GROWTH SHOCK, MIN VAR VS LOW RISK

Minimum Variance (-0.74%)

Low Total Risk(+0.26%)

-0.8 -0.6 -0.4 -0.2 0.0 0.2

Market Sensitivity Banks

PharmaceuticalsMortgage REITs

Food & Staples Retail Volatility

Equity REITs Internet Soft&SVC

Insurance Biotechnology

Growth

Exposure X

-4% -2% 0% 2% 4% 6%

Return

-1.0% -0.5% 0.0% 0.5%

= Contribution

-0.3 -0.2 -0.1 0.0 0.1 0.2

Market Sensitivity Banks

Health Care Equip&SupMortgage REITs Profitability

Div Fin'l SVcsEquity REITs

Pharmaceuticals Biotechnology

Insurance Growth

Conglomerates

-4% -2% 0% 2% 4% 6% -0.2% -0.1% 0.0% 0.1% 0.2%

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EXPECT ACTIVE RETURN: FACTOR STRESS TESTS, OCTOBER 2016 VS. DECEMBER 20172016 2017

-0.2% 0.0% 0.2% 0.4% 0.6%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Volatility

-0.2% 0.0% 0.2% 0.4% 0.6%

Dividend Yield


Profitability

Medium-TermMomentum

GrowthShock: Mkt Sens

-4.0% -3.0% -2.0% -1.0% 0.0%

Minimum Variance

Low Total Risk

Shock: Volatility

-5.0% -4.0% -3.0% -2.0% -1.0% 0.0%

Minimum Variance

Low Total Risk

Shock: Mkt Sens

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US MACRO MODEL

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MACRO MODEL STRESS TEST RESULTS: ACTIVE RETURNS

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

Dividend Yield Value +Earnings Yield

Profitability Medium-TermMomentum

Growth

Inflation Up 5% Term Spread Down 1% Credit Spread Up 1%

FX Basket Up 10% Oil Up 25%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

Inflation Up 5% Term Spread Down1%

Credit Spread Up1%

FX Basket Up 10% Oil Up 25%

Minimum Variance Low Total Risk

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• In our recent paper “When it Comes to Momentum, Don’t Cramp My Style” we noted that for a momentum strategy, imposing constraints only for purposes of a “belt and braces” approach resulted in less factor and more specific risk, more concentration of active weights and contribution to risk from individual names, and generally worse performance when compared with fewer constraints

• Below we examine if more constraints lead to a larger magnitude of expected returns, thereby providing justification for the additional constraints

• “Constrained” factor portfolios have zero exposure to style factors (other than the factor the portfolios tilts on) and industries

• “Constrained” Minimum Variance and Low Total Risk portfolios have zero exposure to risk factors other than Market Sensitivity and Volatility

IMPACT OF CONSTRAINTS


STRESS-TEST RESULTS, CONSTRAINED VS. UNCONSTRAINED PORTFOLIOS

SOMETIMES THE MOVE HAD A SMALLERIMPACT ON THE UNCONSTRAINED PORTFOLIO

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%Momentum

-1.2%-1.0%-0.8%-0.6%-0.4%-0.2%0.0%0.2%0.4%0.6%0.8%

Value & EY-0.5%

-0.3%

0.0%

0.3%

0.5%Profitability

-2.0%

-1.0%

0.0%

1.0%Growth

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0% Dividend Yield


STRESS-TEST RESULTS, CONSTRAINED VS. UNCONSTRAINED PORTFOLIOS

CONSTRAINTS HAD LITTLE IMPACT ONLOW/MINIMUM RISK DRAWDOWNS

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%Mininim Variance

-2.5%

0.0%

2.5%

5.0%Low Total Risk

78


CONCLUSIONS

• Quantitatively-driven portfolios may be vulnerable to big and not-so-big market events

• Even “single-factor” portfolios (such as many “Smart-Beta ETFs”) may be exposed to big shifts in other risk factors via correlations

• The impact of a given shock will vary over time, a function of the portfolio’s current exposures, a factor’s volatility and changing factor correlations

• “Belt-and-braces” constraints do not necessarily help avoid problems

• A good stress-testing tool, employed periodically, can help managers understand these vulnerabilities and take appropriate action where desired

• Even if no action is taken, understanding these relationships can be helpful in explaining performance

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APPENDIX: TIME PERIODS USED

• Black Monday 10/16 to 10/19 1987

• Bond Market Crash 1/31 to 7/12 1994

• Russian Debt Default/LTCM crisis 6/8 to 10/7/1998

• Dot-Com Bubble Burst 3/9 to 5/23/2000

• WorldCom Scandal 6/24 to 7/22/2002

• Subprime Crisis 7/13 to 8/16/2007

• Lehman Collapse 9/12 to 11/20/2008

• Oil Price Drop 9/29/2014 to 1/29/2015

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