Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 1 Ninth BIS CCA Research Conference Rio de Janeiro June 2018 1 Previously presented as Cross-Section Skewness, Business Cycle Fluctuations and the Financial Accelerator Channel. The views expressed in this paper are solely my responsibility and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 1
Business Cycles: Prediction and Explanation Fluctuations in economic uncertainty and business cycles focus on 2nd moments and aggregate (negative) tail risks I want to shift the discussion to skewness. Too nerdy? captures the comparison of tail risks: upside X downside often used in FOMC and ECB comunications More specifically, can cross-section skewness of asset prices help us predict and understand business cycle fluctuations? Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 2
Cross-Sectional Distribution of Stock Returns of Financial Firms 10 8 2006:Q2 2008:Q4 6 4 2 0 Downside Risks Upside Risks ( ) ( ) -60-40 -20 0 20 40 60 Log returns (percent) (a) Probability Density Function 2006:Q2 2008Q4 Median 0% 0% Skewness 0% -27% (b) Cross-Sectional Moments financial skewness t = ( ln rt 95th ln rt 50th ) ( ln rt 50th ln r 5th ) t. }{{}}{{} upside tail risks downside tail risks Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 3
Financial Skewness Tracks Business Cycles 13 Percent Percent 13 4 Financial Skewness (Left) 9-5 4-14 GDP Growth (Right) 0-23 Q1-1927 Q2-1933 Q4-1939 Q1-1946 Q2-1952 Q3-1958 Q4-1964 Q2-1971 Q3-1977 Q4-1983 Q1-1990 Q3-1996 Q4-2002 Q1-2009 Q2-2015 Financial vs Nonfinancial -4 Correlations Logit Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 4
3 main results: 1) Financial skewness is a powerful predictor of economic activity better than many well-known indicators 2) Financial skewness seem to signal future economic performance of financial firms borrowers 3) Financial skewness shocks are important cyclical drivers, with transmission channel consistent with financial frictions models Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 5
Literature Review X Results Business cycles drivers: cross-sectional skewness is important. Idiosyncratic firms behavior is important driver of BC. Focus on 2 nd moments: Bloom et al (2012), Arellano et al (2012), Christiano et al (2014), Chugh (2016), Schaal (2015), Panousi and Papanikolaou (2012), Gabaix (2011); Acemoglu et al (2011). Tail risks are important for BC. Most focus on aggregate downside risks: Barro (2006), Gabaix (2012), and Gorio (2012). Asset prices predict business cycles: financial skewness does particularly well. Despite importance in BC theory, CS risk is not important in forecasting: Lit reviews: Stock and Watson (2003) and Ng and Wright (2013). Bond markets may signal better than stocks about economic fundamentals: Philippon (2009), Gilchrist and Zakrajsek (2012), and Lopez-Salido et al. (2017). Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 6
Data Evidence Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 7
1 st : Financial Skewness Predicts Economic Activity better than: well-known bond spreads (e.g., GZ (2012)) measures of uncertainty (e.g., Jurado et al (2015)) other cross-section moments (fin + nfin) both in expansions and recessions using in-sample and out-of-sample regressions several measures of economic activity Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 8
Financial Skewness Predicts Economic Activity, In-Sample Dependent Variable: Mean 4Q Ahead GDP Growth Sample: 1973Q1-2015Q2 Regressions Specifications Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) Mean + 1.19*** 0.73* Dispersion + -0.15* 1.07** Skewness + 1.20*** 1.60** 1.00*** Left Kurtosis + 0.71** 0.26 Right Kurtosis + 0.46** -1.06*** Uncertainty -0.46** 0.24 Real Fed Funds -0.44 0.18 Term Spread 0.92*** 1.03*** GZ Spread -0.55** -0.49 R 2 0.08 0.29 0.11 0.28 0.17 0.11 0.19 0.12 0.28 0.23 0.40 0.54 + Moments of the cross-section distribution of returns are for returns from financial firms All regressors are standardized, so we can compare the magnitude of their coefficients. For each regressor, I include its current and one-period lagged value, with reported coefficients being the sum of current and lagged effect. Coefficients measure the effect in GDP-growth (in percentage) of a sustained increase of 1 std in the regressor. Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 9
Financial Skewness Predicts Economic Activity, In-Sample 1) is one of the variables that single-handedly most explain future GDP growth Comparing R 2 s and columns (2)-(10) 2) has predictive power robust to the inclusion of many other variables. Such as other moments, financial uncertainty, GZ spread: columns (11)-(12) In all regressions, financial skewness is stat-sig and has intuitive effects. 3) is specially informative about the cycle In regressions (11)-(12) for un/weighted measures: one of largest coefficients 1 std in financial skewness: of 1%-1.6% in mean GDP growth over next 4Q s 4) is powerful predictor of many other variables: not shown (Consumption, Investment, Hours, U-rate) Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 10
Financial Skewness Predicts GDP t+h t 1, Out-of-Sample Sample: 1973Q1 - [1986Q1... 2015Q2] For each variable X t, I forecast GDP growth using regressions: p q GDP Xt t+h t 1 = α + ρ i GDP t i t i 1 + θ j X t j + u t+h. i=1 j=0 Performance of financial skewness relative to variable X t is: R-RMSFE of Variable X t = RMSFE of Financial Skewness RMSGE of Variable X t (in decimals) Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 11
Financial Skewness Predicts GDP t+h t 1, Out-of-Sample R-RMSFE = RMSE of Financial Skewness RMSE of Other Variable (in decimals) Term spread Baa-10y spread GZ spread Financial uncertainty h=2 h=4 h=6 pval<0.1 pval<0.1 pval<0.1 Baa-Aaa spread Macro uncertainty GDP-AR Consensus 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R-RMSFE in decimals (c) Full Sample 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R-RMSFE in decimals (d) Recessions 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 R-RMSFE in decimals (e) Expansions Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 12
Financial Skewness Predicts GDP t+h t 1, Out-of-Sample Financial skewness has highest predictive power for GDP growth Lowest RMSEs with most results stat. significant Differences economically significant: up to 38% of improvement Also, better than other distribution measures Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 13
Rolling RMSE Ratios: financial skewness predicts well most of the time R-RMSFE in decimals 3.5 3 2.5 2 1.5 R-RMSFE in decimals 3.5 3 2.5 2 1.5 1 0.5 0 Q4-1990 Q3-1993 Q1-1996 Q4-1998 Q2-2001 Q4-2003 Q3-2006 Q1-2009 Q4-2011 Q2-2014 (f) Macro Uncertainty Other Rolling RMSE ratios tell similar story. 1 0.5 0 Q4-1990 Q3-1993 Q1-1996 Q4-1998 Q2-2001 Q4-2003 Q3-2006 Q1-2009 Q4-2011 Q2-2014 (g) GZ-Spread Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 14
Interpreting Financial Skewness Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 15
2 nd : Financial Skewness is informative because......reflects future economic performance of financial firms borrowers Financial firms focus on specific loan markets, diversifying some CS distributions of returns of financial firms have less dispersion and thinner tails than those of nonfinancial firms. Stock markets price future economic performance of borrowers Data on asset quality (ROA and LSSF) explain about 75% of financial skewness ROA and LSSF released between 1 and 1.5 months after the reference quarter Financial skewness also lead credit conditions especially loan growth Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 16
Financial sector holds smaller cross-section risks Sample 1927-2015 Sample 1947-2015 financial nonfinancial difference financial nonfinancial difference Mean 3.3 3.7-0.5 2.9 3.4-0.5 Dispersion 36.5 49.2-12.7*** 35.8 58.8-23.0*** Skewness -0.4-0.1-0.3-1.1-2.0 0.9** Left kurtosis -7.1-9.0 1.9*** -7.9-12.1 4.3*** Right kurtosis 7.2 9.1-1.9*** 7.0 11.0-4.0*** Mean: Dispersion: Financial Skewness: Left tail: Right tail: stat the same smaller somewhat higher than Nonfinancial thinner thinner Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 17
Financial skewness reflects future performance of borrowers Data on asset quality of financial firms (ROA and LSSF) explain 76% of financial skewness... ROA and LSSF released 1-1.5 months after the reference quarter... while data measuring financial stresses and private sector GDP forecasts add little. AFCI EBP VIX Term GDP Consensus GDP t t 1 Consensus Spread t+2 t 1 ROA 3.7*** 3.5*** 3.6*** 3.5*** 4.0*** 3.4*** 3.4*** LSSF -2.1*** -1.6*** -1.6*** -1.4*** -1.9*** -1.8*** -1.8*** Variable -0.8* -0.7* -1.3*** 0.6** 0.8** 0.7* R 2 0.76 0.76 0.76 0.79 0.76 0.76 0.76 Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 18
What explain financial skewness? Part II Percent 10 5 0-5 -10-15 -20-25 Q1-1989 Q1-1992 Q4-1994 Financial Skewness Fitted Values Q4-1997 Q4-2000 Q3-2003 Q3-2006 Q3-2009 Q2-2012 (h) Fitted Values from Return on Assets and Lending Standards Q2-2015 Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 19
Structural Analysis: DSGE Model and BVARs Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 20
3 nd : Structural Analysis - BVAR and DSGE Models 14 variables: macro, financial and stock market cross-sectional moments. In both BVAR and DSGE model, financial skewness shocks: have a transmission channel consistent with financial frictions models are important business cycle drivers and have sizable economic effects account for most of the fluctuations in financial skewness drive out other shocks, including dispersion ones Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 21
NK-DSGE with financial accelerator channel Similar to Christiano et al (2014) in its bells and whistles Why this model? cross-section shocks generates business cycles endogenous cross-section distribution compare widely used DSGE model against BVAR Re-interpretation of the model: Households Loan Contracts Bank + Entrepreneur Bank+Entrepreneur Cross-section risk { nonfin CS risk after some diversification (e.g, dotcom) fin CS risk (e.g, Lehman) Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 22
Distribution of Returns and the Financial Accelerator Define gross realized equity return of entrepreneur i at period t: Xt i = ωt i Rc t Q t 1K i t Z t i Bi t Nt i, if ωt i Rc t Q t 1K i t Z t i Bi t 0, otherwise { [ ] ω i = t ω t R c t L t, if ωt i ωt 0, otherwise. endogenous distribution of X i t : ω t, R c t ω i t follows a mixture of two log-normal distributions and L t are endogenous variables E(ω i t) = 1, Std(ω i t) = sd t and m 1 t proxies skewness For instance, cross-section skewness of the model is: ( x 95 t x 50 t ) ( x 50 t x 5 t ), where x v t = log( ω v t ω t) and ω v t is the v th percentile of cdf F t( ω t > ω t). Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 23
NK-DSGE with financial accelerator channel: 1964-2015 1 st Step: 1964-2006, Taylor Rule; 2 nd Step: 2002-2015, Taylor Rule with news; re-estimate shocks autocorr and std; Observable variables GDP Consumption Investment Hours worked Real wage Fed Funds rate OIS 1Y-ahead (2002-2015) Shocks permanent TFP-growth inter-temporal discount capital adjustment cost (IS-shock) transitory TFP price-markup monetary policy news on monetary policy PCE core inflation inflation trend/target Relative price of Investment investment price Real credit government/nx residual Equity (Meant nfin ) equity and meas-error Baa - US 10y Dispt nfin and Skewt fin sd t and mt 1 news about them up to 4Q in advance Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 24
Primacy of Skewness Shocks: Hist + Var Decomp s 6 15 4 10 2 5 Percentage 0-2 Percentage 0-5 -10-4 -15-6 Data Anticipated and Unanticipated Skewness Shocks -20 Data Anticipated and Unanticipated Skewness Shocks -8 Q1-1964 Q4-1969 Q3-1975 Q1-1981 Q4-1986 Q3-1992 Q2-1998 Q1-2004 Q3-2009 Q2-2015 -25 Q1-1964 Q4-1969 Q3-1975 Q1-1981 Q4-1986 Q3-1992 Q2-1998 Q1-2004 Q3-2009 Q2-2015 (i) GDP (7 41 %) (j) Investment (9 51%) 8 6 Data Anticipated and Unanticipated Skewness Shocks 4 3 Data Anticipated and Unanticipated Skewness Shocks 4 2 2 Percentage 0-2 Percentage 1-4 0-6 -1-8 -10 Q1-1964 Q4-1969 Q3-1975 Q1-1981 Q4-1986 Q3-1992 Q2-1998 Q1-2004 Q3-2009 Q2-2015 -2 Q1-1964 Q4-1969 Q3-1975 Q1-1981 Q4-1986 Q3-1992 Q2-1998 Q1-2004 Q3-2009 Q2-2015 (k) Credit (6 35%) (l) Baa spread (16 50%) Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 25
Skewness shocks: FEVD: GDP = 5-20% IRF: GDP falls 0.3-0.75% FEVD: majority of FinSkew Fin-friction transmission: IRFs: general picture Baa-10y Larger IRFs DSGE IRFs BVAR IRFs Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 26
Introduction Data Evidence Interpretation DSGE Model Conclusion Dispersion shocks: FEVD of GDP = 0-3% IRF 0 Thiago Ferreira Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations Federal Reserve Board 27
Conclusion: Financial skewness is a powerful predictor of economic activity Financial skewness seem to signal future economic performance of financial firms borrowers Financial skewness shocks are important cyclical drivers Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 28
Percentage Introduction Data Evidence Interpretation DSGE Model Conclusion Percentage Percentage Percentage Cross-Section Skewness: Financial X Nonfinancial Back 13 Skew fin t 4Q-ave (left axis) GDP 4Q-growth (right axis) 13 4 9-5 4-14 0-23 Q1-1927 Q4-1931 Q2-1936 Q1-1941 Q3-1945 Q2-1950 Q1-1955 Q3-1959 Q2-1964 Q4-1968 Q3-1973 Q2-1978 Q4-1982 Q3-1987 Q1-1992 Q4-1996 Q2-2001 Q1-2006 Q4-2010 Q2-2015 -4 21 10 Skew nfin t 4Q-ave(left axis) GDP 4Q-growth (right axis) 13 9-0 4-11 0-22 Q1-1927 Q4-1931 Q2-1936 Q1-1941 Q3-1945 Q2-1950 Q1-1955 Q3-1959 Q2-1964 Q4-1968 Q3-1973 Q2-1978 Q4-1982 Q3-1987 Q1-1992 Q4-1996 Q2-2001 Q1-2006 Q4-2010 Q2-2015 -4 Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 29
Correlations Back Sample Financial Skewness Nonfinancial Skewness 1926-2015 0.34 0.31 1985-2015 0.58 0.48 (a) Correlations with Expansion Indicator Sample Financial Skewness Nonfinancial Skewness 1947-2015 0.40 0.36 1985-2015 0.69 0.41 (b) Correlations with GDP 4Q-growth Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 30
1926-2015: Financial Skewness Tracks Business Cycles Back Logit Regression Dependent Variable: NBER Expansion Indicator Regressions with Unweighted Distribution Measures Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) Constant -1.26*** -1.55*** -1.11*** -1.36*** -1.24*** -1.35*** -1.22*** -1.73*** -1.77*** Expansion Lag 4.12 4.55 3.93 4.38 4.11 4.23 4.04 5.02 5.05 Mean + 1.17*** 1.33*** 1.23** Dispersion + -0.34-0.44-0.68 Skewness + 1.17*** 1.71** 1.68** Left Kurtosis + 0.43-0.92* -0.98* Right Kurtosis + 0.20-0.69-0.64 Baa-Aaa -0.24** 0.23 Pseudo R 2 0.53 0.58 0.54 0.57 0.54 0.53 0.55 0.62 0.63 + Moments of the cross-section distribution of returns are for returns from financial firms All regressors are standardized, so we can compare the magnitude of their coefficients. For each regressor, I include its current and one-period lagged value, with reported coefficients being the sum of current and lagged effect. Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 31
1926-2015: Financial Skewness Tracks Business Cycles Back Financial Skewness: 1) is one of the variables that single-handedly most explain NBER-indicator. Comparing R 2 s of columns (2)-(7) 2) has explanatory power robust to the inclusion of many other variables. Such as other moments and credit spreads in columns (8)-(10). In all regressions, financial skewness is stat-sig and has intuitive effects. 3) is specially informative about the cycle In regressions (9)-(10) for un/weighted measures: one of largest coefficients 2 std decrease in financial skewness: 52% prob of recession Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 32
Financial Skewness Predicts GDP t+h t 1,Out-of-Sample Back Sample: 1973Q1 - [1986Q1... 2015Q2] RMSE of Financial Skewness Relative to other Variables (in decimals) Mean Dispersion Financial Skewness Left Kurtosis Right Kurtosis - Mean Dispersion Nonfinancial Skewness Left Kurtosis Right Kurtosis 0.6 0.8 1 1.2 (m) Nonweighted Measures 0.6 0.8 1 1.2 (n) Weighted Measures Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 33
What explain Financial skewness? Part II Back 8 Percent Percent 1.5 8 Percent Percent 25 0 1.1 0-0 -7 0.7-7 -25-15 -23 Q1-1989 Financial Skewness Return on Assets Q1-1992 Q4-1994 Q4-1997 Q4-2000 Q3-2003 Q3-2006 Q3-2009 Q2-2012 Q2-2015 (o) Return on Assets 0.3-0.1-15 -23 Q1-1989 Financial Skewness (Minus) Lending Standards Q1-1992 Q4-1994 Q4-1997 Q4-2000 Q3-2003 Q3-2006 Q3-2009 Q2-2012 Q2-2015 (p) Lending Standards -50-75 Stock Market Cross-Sectional Skewness and Business Cycle Fluctuations 34