Hedging Risk Factors - Wild Apricot Risk Factors.pdfHedging Risk Factors Bernard Herskovic Alan Moreira Tyler Muir UCLA Anderson Rochester UCLA Anderson NBER Q Group October, 2020

Hedging Risk Factors

Bernard Herskovic Alan Moreira Tyler MuirUCLA Anderson Rochester UCLA Anderson

NBER

Q GroupOctober, 2020

Hedging Risk Factors October 2020 0 / 28

COVID-19 recession1$ invested in January 2020 and market volatility


Cumulative returns around selected recessions1$ invested in December 2007 and market volatility


Recession Risk

I COVID-19 recessionI 34% drawdown in the S&P 500I VIX peaking above 80%

I Great Recession of 2008I 57% drawdown in the S&P 500I VIX peaking above 80%

I NBER recessions: market drops 20% on average

I Strong relation between market crashes and recessions

I Recessions are risky investment periods

Can we hedge recession risk?

At what reduction in expected returns?


Recession Risk









Recession Risk









Recession Risk









Recession Risk









Recession Risk









Recession Risk









Risk Factors

I Which macro factors to hedge?

I Indicators of macroeconomic conditions- e.g. consumption, GDP, unemployment, ...)

- Macro-finance literature: Parker-Julliard factor, Q4consumption growth, unfiltered consumption growth.

I Also some reduced-from asset pricing factors

- e.g. Mkt., SMB, HML, Momentum, ...- Similar analysis (and results) for traded factors- Not in today’s talk: see annex slides at the end


Asset Pricing Models

Our Approach

I Portfolios based on exposures

I Compute beta relative to macro indicatorsI Construct beta-sorted portfolios

I This provides a good and natural methodology tobuild macro-sensitive portfolios

I Intuitive long-short portfolios as hedges


Our Findings

I Build (good!) hedge portfolios against risk factors

I Hedge portfolios perform well in “bad” timesI negative exposure to Consumption, GDP, Recessions

I Our macro-hedged market portfolio avoided themarket crash of associated with COVID-19 pandemicI Out-of-sample!

I Surprising result: hedge portfolios are cheapI macro-sensitive portfolios have similar average returns

regardless of exposure


Why are these findings surprising?I Weak relationship between macro economy and returns

- but market crashes on the eve of recessions

I No free lunch argument: assets that pay well in bad states of theworld ought to have negative risk premia

I Standard consumption amply rejected, yet several new models

provided more hopeful view for the macro view of asset pricesScaled consumption-based models: Campbell and Cochrane (1999), Menzly etal. (2004), Lettau and Ludvigson (2001), Bansal et al. (2005), Lustig and VanNieuwerburgh (2005), Santos and Veronesi (2006), etc.Long-run risk models: Bansal and Yaron (2004), Parker and Julliard(2004),Hansen et al. (2008), Koijen, Lustig, and Van Nieuwerburgh (2010), etc.Measurement: Jagannathan and Wang (2007), Kroencke (2017), etc.

“assets are risky in these models [...] because they are more highlycorrelated with consumption in bad times, when the economy is doing poorlyand risk premia are already high.” (Ludvigson, 2013, p. 824)

Our paper

I We use cross-section of assets to hedge macro riskI Finding: mkt crashes associated with macro risks are hedgeable

– especially in bad times (economic recession)– tradeable and well-diversified portfolios

I Hedge portfolios as tools for future consumption-based models








Our paper











Our paper











Our paper





Building Hedge portfolios

Data

I Macro series (log changes)

- Industrial production- Initial claims (unemployment), flip sign- Moody’s BaaAaa spread, flip sign- Slope of term structure (5-year yield minus 3-month)- Combined macro series

EW average of standardized macro monthly series

- NBER recessions, GDP and consumption growth



1. For each factor construct beta-sorted portfolios

βfi,t = ρ(Rei,τ , fτ )

σ(fτ )

σ(Rei,τ )

I Daily returns: 24-month windowI Monthly factors: 120-month windowI Value weight within quintiles

2. Long low-beta quintile and short high-beta quintile

What to expect?

I Hedge portfolios carry negative premium

From the data

I They don’t. Premium ≈ 0

I Despite large negative post-formation exposure





σ(fτ )

σ(Rei,τ )



What to expect?


From the data







σ(fτ )

σ(Rei,τ )



What to expect?


From the data




Macro Hedged Portfolio: Individual Factors

Focus on 3 portfolios

1. Market Portfolio

2. Hedge Portfolio

3. Market + Hedge

Individual Factors

I industrial production

I unemployment

I credit spreads

I term premium


















Macro Hedged Portfolio: Combined-Macro Factor

Focus on 3 portfolios

1. Market Portfolio

2. Hedge Portfolio

3. Market + Hedge

Combined-macro factor

I industrial production

I unemployment

I credit spreads

I term premium

















Cumulative returns around selected recessions1$ invested in January 2020




Cumulative returns around selected recessions1$ invested in December 2007


Cumulative returns around selected recessions1$ invested in December 2007


Cumulative returns around selected recessions1$ invested in February 2001


Cumulative returns around selected recessions1$ invested in February 2001


Cumulative returns around selected recessions1$ invested in May 1990


Cumulative returns around selected recessions1$ invested in May 1990






Just hedge for market downturn overall?1$ invested in June 1987


Just hedge for market downturn overall?1$ invested in June 1987


Macro-hedge portfolios as new test assets

I Now, macro-hedge portfolios as test assets:

I Parker and Julliard (2005) Factor

I Q4 Consumption Growth (Jagannathan Wang 2007)

I Unfiltered Consumption Growth (Kroencke 2017)

I Estimate factor slopes :

E[Ri] = λ0 + λ1βi,f

I Contrast our test assets with standard FF25








Revisiting prices of risk of macro factors

1. Literature arguing macro risk explains cross-section

2. Typical approach: FF25 to estimate price of macro risk

3. Several critiques to traditional approach:I strong factor structure of these portfolios

(Lewellen Nagel Shanken 2010, Daniel Titman 2012),I weak spread in betas on the macro factors Bryzgalova 2017

(e.g., first stage of estimating beta is weak)

4. Our portfoliosI New test assets to evaluate modelsI Spread in betas directly related to macro risk

5. ConclusionI Very different price of risk estimatesI Point estimate always lower, close to zero


How much of SDF volatility is macro risk?

I So far: inconsistent w/ existing factors as single factors

I Our hedge portfolio might load on unobserved factors

I Can we say anything about these omitted factors?

Contribution of macro risk once we allow omitted factors?

Our approach:

1. SR bound implied by reduced form model (e.g. FF3)

2. Use hedged portfolio to eliminate macro exposure ofmodel-implied MVE portfolio

3. SR difference bounds macro contribution to sdf



I So far: inconsistent w/ existing factors as single factors

I Our hedge portfolio might load on unobserved factors

I Can we say anything about these omitted factors?

Contribution of macro risk once we allow omitted factors?

Our approach:

1. SR bound implied by reduced form model (e.g. FF3)

2. Use hedged portfolio to eliminate macro exposure ofmodel-implied MVE portfolio

3. SR difference bounds macro contribution to sdf



Our approach

mt = 1− bzzt + bfft (SDF: ft is unobserved)

Rzt = −zt + εz,t︸︷︷︸

≡βz,fft+εzt

(hedge portfolio)

Market-macro-hedged portfolio:

Ri,−zt = Ri

t + βi,zRzt (e.g. market w/ zero macro exp.)



Our approach

Euler equation and SR bounds

E[mtR

i,−zt

]= 0∣∣∣∣∣E

[Ri,−zt

]σ(Ri,−z

t )

∣∣∣∣∣ ≤ |bf |σ(ft)

SDF volatility decomposition:

b2zσ2z

σ2m︸︷︷︸

% SDF Vol from Macro

= 1− b2fσ

2f

σ2m≤ 1−

(E[Ri,−zt ]σ(R

i,−zt )

)2

σ2m

≈ 1−(SRMVE-Macro-Hedge

SRMVE

)2



Application: Hedging recession exposure

Sharpe ratio Upper bound

Factor Models Original (MVE) Recession Hedged Variance share

CAPM 0.49 0.40 0.59FF3 0.62 0.58 0.60FF3+UMD 0.98 0.91 0.32FF5 1.04 0.99 0.19FF5+UMD 1.21 1.14 0.13

1. Recession risk explains at most 60% of overall SDF vol

2. Substantially less for richer factor models: 13%–32 %


Final RemarksI Portfolios based on exposures are natural test assetsI Construct portfolios with strong spread in exposures

⇒ Exposure vs expected return relation is flat

⇒ Even in recessions (bad times)

I Pattern holds for macro and reduced-form factors

Important implications:

1. Build hedges against macro risk

Good hedges against recession-led financial crashes

2. New test assets to evaluate models- Price of risk estimates always lower, close to zero

3. Limits contribution of economic fluctuations andrecessions to SDF

4. Large α’s for traded factors


Annex


Traded Factors

I Look at leading factors/multi-factor combinations

I Same analysis, similar findings: hedges are too cheap

I Tradable factors: cheap hedges ⇒ α > 0


Traded Factors

I Look at leading factors/multi-factor combinations

I Same analysis, similar findings: hedges are too cheap

I Tradable factors: cheap hedges ⇒ α > 0


Form 10 portfolios sorted by beta of traded factor

Same finding: low beta have high alpha, hedges are cheapHedging Risk Factors October 2020 28 / 28

Hedge portfolios on individual factors
























Hedge portfolios on MVE combinations




















Hedge portfolios on EW combinations




















Minimum Variance PortfolioAssume constant expected returns:

1. Regress stock returns on asset pricing factor F(36-mth windows)

Ri,τ = ai,t + β′i,tFτ + εi,τ

2. Build proxy for var-cov matrix of all returns

Σt ≡ BtΩtB′t + St

3. Compute the mean-variance efficient portfolio weights

ωt =1

1′Σ−1t 1

1′Σ−1t

4. Form our low risk portfolio using monthly data

RLow Riskt =

∑i

ωi,tRi,t


Minimum Variance Portfolio

I Low-risk portfolio

RLow Riskt =

∑i

ωi,tRi,t

Avg. excess return t-statistic Sharpe ratioMkt 8.19 10.07 0.81Car 7.89 9.59 0.82FF5 7.80 9.61 0.81

I High Sharpe ratios

I Exploits cross-sectional variation in volatility


Minimum Variance Portfolio

CAPM 3FF 3FF 5FF 5FF 5FF+MOM +MOM +MOM

+BABMkt Alpha 6.36 6.36 5.98 4.13 4.25 2.77

t-stat. 6.73 6.72 6.17 3.40 3.45 2.49Info. ratio 0.70 0.70 0.66 0.47 0.48 0.35

Car Alpha 6.16 6.19 5.82 4.33 4.45 3.19t-stat. 6.83 6.86 6.28 3.66 3.71 2.86Info. ratio 0.71 0.72 0.67 0.51 0.52 0.40

FF5 Alpha 6.14 6.20 5.72 4.45 4.57 3.29t-stat. 6.73 6.81 6.13 3.73 3.77 2.92Info. ratio 0.70 0.71 0.66 0.52 0.53 0.41


Hedging Risk Factors - Wild Apricot Risk Factors.pdfHedging Risk Factors Bernard Herskovic Alan Moreira Tyler Muir UCLA Anderson Rochester UCLA Anderson NBER Q Group October, 2020

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