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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
Hedging Risk Factors October 2020 1 / 28
Cumulative returns around selected recessions1$ invested in December 2007 and market volatility
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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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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?
Hedging Risk Factors October 2020 3 / 28
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
Hedging Risk Factors October 2020 4 / 28
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
Hedging Risk Factors October 2020 5 / 28
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
Hedging Risk Factors October 2020 6 / 28
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
Hedging Risk Factors October 2020 7 / 28
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
Hedging Risk Factors October 2020 7 / 28
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
Hedging Risk Factors October 2020 7 / 28
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
Hedging Risk Factors October 2020 7 / 28
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
Hedging Risk Factors October 2020 8 / 28
Building Hedge portfolios
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
Hedging Risk Factors October 2020 9 / 28
Building Hedge portfolios
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
Hedging Risk Factors October 2020 9 / 28
Building Hedge portfolios
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
Hedging Risk Factors October 2020 9 / 28
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
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Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
Hedging Risk Factors October 2020 11 / 28
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
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Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 13 / 28
Hedging Risk Factors October 2020 14 / 28
Hedging Risk Factors October 2020 14 / 28
Hedging Risk Factors October 2020 14 / 28
Cumulative returns around selected recessions1$ invested in January 2020
Hedging Risk Factors October 2020 15 / 28
Cumulative returns around selected recessions1$ invested in January 2020
Hedging Risk Factors October 2020 15 / 28
Cumulative returns around selected recessions1$ invested in December 2007
Hedging Risk Factors October 2020 16 / 28
Cumulative returns around selected recessions1$ invested in December 2007
Hedging Risk Factors October 2020 16 / 28
Cumulative returns around selected recessions1$ invested in February 2001
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Cumulative returns around selected recessions1$ invested in February 2001
Hedging Risk Factors October 2020 17 / 28
Cumulative returns around selected recessions1$ invested in May 1990
Hedging Risk Factors October 2020 18 / 28
Cumulative returns around selected recessions1$ invested in May 1990
Hedging Risk Factors October 2020 18 / 28
Cumulative returns around selected recessions1$ invested in January 1980
Hedging Risk Factors October 2020 19 / 28
Cumulative returns around selected recessions1$ invested in January 1980
Hedging Risk Factors October 2020 19 / 28
Just hedge for market downturn overall?1$ invested in June 1987
Hedging Risk Factors October 2020 20 / 28
Just hedge for market downturn overall?1$ invested in June 1987
Hedging Risk Factors October 2020 20 / 28
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
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Hedging Risk Factors October 2020 22 / 28
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
Hedging Risk Factors October 2020 23 / 28
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
Hedging Risk Factors October 2020 24 / 28
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
Hedging Risk Factors October 2020 24 / 28
How much of SDF volatility is macro risk?
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.)
Hedging Risk Factors October 2020 25 / 28
How much of SDF volatility is macro risk?
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
Hedging Risk Factors October 2020 26 / 28
How much of SDF volatility is macro risk?
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 %
Hedging Risk Factors October 2020 27 / 28
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
Hedging Risk Factors October 2020 28 / 28
Annex
Hedging Risk Factors October 2020 28 / 28
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
Hedging Risk Factors October 2020 28 / 28
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
Hedging Risk Factors October 2020 28 / 28
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
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on individual factors
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on MVE combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
Hedge portfolios on EW combinations
Hedging Risk Factors October 2020 28 / 28
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
Hedging Risk Factors October 2020 28 / 28
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
Hedging Risk Factors October 2020 28 / 28
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 October 2020 28 / 28