Financial Intermediaries and the Cross-Section of Asset Returns

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1 Financial Intermediaries and the Cross-Section of Asset Returns Tobias Adrian - Federal Reserve Bank of New York 1 Erkko Etula - Goldman Sachs Tyler Muir - Kellogg School of Management May, The views expressed in this presentation are not necessarily those of the Federal Reserve Bank of New York or the Federal Reserve System.

2 What do we nd? Factor Pricing Model: Cross-Section of Expected Returns I E [R i ] r = β i,f λ f = risk x risk premium I Single factor, broker-dealer leverage, explains expected returns across assets I Factor prices size, book-to-market, momentum, bonds, as well / better than Fama-French + momentum I Motivation: theories of intermediaries and asset pricing I De-leveraging measures bad times for intermediaries

3 Realized Mean Return Single leverage factor and the cross-section of returns Size & Book-to-Market, Momentum, Bonds, estimated simultaneously S1B5 S3B5 Mom10 S1B4 S2B3 S2B4 S3B4 S1B3 S1B2 S3B2 S3B3 S4B4 S4B5 Mom S4B3 S2B2 9 Mom 8 S5B5 S4B1S5B2 S4B2 S5B4 S5B3 S5B1 S3B1Mom Mom Mom 3 Mom 4 76 S2B1 Mom 5 Mom y 2 3yr 3 4yr 4 5yr 1 2yr S1B1 0 1yr S2B5 2 4 Mom Predicted Expected Return

4 Realized Mean Return Fama-French Three Factors (Mkt, SMB, HML) yr 5 10y 2 3yr 3 4yr 1 2yr 0 1yr S1B5 S3B5 Mom10 S1B4 S2B5 S2B4 S2B3 S3B4 S4B4 S1B3 S4B5 S3B3 S1B2 S3B2 Mom 9 S4B3 S2B2 Mom 8 S5B5 S4B1 S5B2S4B2 S5B4 Mom S5B3 Mom 7 Mom 6 S5B1 S3B1 Mom 4 3 Mom S2B1 5 Mom 2 S1B1 2 4 Mom Predicted Expected Return

5 Traditional Asset Pricing: Prices determined by risk faced by representative household I Classic theory: SDF is proportional to aggregate consumption risk (CCAPM) or aggregate market risk (CAPM) I Assumptions: everyone participates in all markets, no transactions costs, agents can compute dynamic portfolio strategies, optimize continuously, know return moments I But: I there is lots of evidence of frictions in trading; market segmentation; ine cient household behavior

6 This Paper: Intermediaries t classic assumptions Prices determined by risk faced by representative intermediary I Assumptions about intermediaries: participate in all markets, no transactions costs, can follow dynamic complicated strategy, optimize continuously, know return moments I Expect focusing on intermediaries will price large class of assets (He and Krishnamurthy (2010)) I Leverage of broker-dealers measures risk faced by intermediary: consistent w/ theory of intermediaries and asset prices

7 Intermediary Asset Pricing Leverage of broker-dealers measures risk faced by intermediary: High leverage = good times for intermediary I Brunnermeier Pedersen (2009) I Intermediaries face funding constraints I E t [R t+1 ] R f = cov t (φ t+1, R t+1 ), where φ =funding / margin constraint. Funding liquidity risk. I I φ is inversely related to leverage: High leverage implies low φ Leverage measures marginal value of wealth I Literature: Gromb Vayanos (2002), Brunnermeier Pedersen (2009), Geanakoplos (2010), He and Krishnamurthy (2010), Garleanu Pedersen (2010), Danielson, Shin, Zigrand (2010)

8 Data (Q1/ Q4/2009) Flow of Funds (Quarterly) I Total assets, Total liabilities of U.S. securities broker-dealers I Lev=(Total Assets)/(Total assets -Total liabilities) Leverage factor: shocks to log leverage (seasonally adjusted)

9 Broker-Dealer Leverage and Leverage Factor 3 2 Oil '87 Crash Peso 911 LTCM Lehman Iraq/ Enron Lev Fac LogLev

10 The Flow of Funds Assets from Flow of Funds (billions) Liabilities from Flow of Funds (billions) Cash (including segregated cash) $96.9 Net repo $404.7 Credit market instruments $557.6 Corporate and foreign bonds $129.7 Commercial paper $36.2 Trade payables $18.1 Treasury securities (net of shorts) $94.5 Security credit $936.6 Agencies $149.8 Taxes payable $3.6 Municipal securities $40.0 Miscellaneous liabilities* $480.7 Corporate and foreign bonds $185.6 Payables to brokers and dealers Other (syndicated loans etc) $51.4 Securities sold not yet purchased Corporate Equities $117.2 Payables Security credit $278.2 Subordinated liabilities Miscellaneous assets* $1,025.3 Receivables Reverse repos Property, furniture, equipment, etc. TOTAL $2,075.1 TOTAL $1,973.4 *Sub-categories implicit in FOCUS Reports

11 Growth of Broker-Dealer Balance Sheets

12 Lev Growth Lev Growth Procyclical Leverage of Dealers 5 Household 3 BrokerDealer Asset Growth Asset Growth

13 Correlation of Broker-Dealer Leverage Factor with Aggregate Variables Correlation of Broker-Dealer Leverage Factor with: Log Broker-Dealer Market Baa-Aaa Financials Asset Growth Volatility Spread Stock Return ρ p-value

14 Asset Pricing Test Cross-Section of Expected Returns: I Time-series regression (β i,lev exposure to risk): R e i,t = a i + β i,lev Lev t + η i t t = 1,..., T, i = 1,.., N I Cross-sectional regression (λ lev price of risk): E [R e i ] = α + β i,lev λ lev + ɛ i, i = 1,..., N I Intuition/Theory: λ lev >0, signi cant I Want: α=0, R 2 high I Report the results from the cross-sectional regression

15 25 Size and Book/Market, 10 Momentum, 6 Treasury Portfolios Panel A: Prices of Risk CAPM FF FF,Mom FF,Mom,PC1 LevFac Intercept t-shanken LevFac t-shanken 3.12 Mkt t-shanken SMB t-shanken HML t-shanken MOM t-shanken PC t-shanken 0.93

16 25 Size and Book/Market, 10 Momentum, 6 Treasury Portfolios Panel B: Test Diagnostics MAPE E[R E ] CAPM FF FF,Mom FF,Mom,PC1 LevFac Size B/M MOM Bond Intercept Total AdjR C.I.AdjR2 [0.02, 0.30] [0.02, 0.36] [0.74, 0.88] [0.72, 0.88] [0.82, 1] Chi P-Value 0.0% 0.0% 0.0% 0.0% 0.3%

17 Realized Mean Return Treasury Bonds by Maturity 0.65 Leverage and the Cross Section of Bond Returns y R Square=94% 2 3yr 3 4yr 4 5yr yr yr Predicted Expected Return

18 Robustness Checks: I We show pricing results for the individual cross sections: 25 size and book-to-market, 25 size and momentum, and Treasury bonds I Prices of risk are very stable, pricing better than the benchmark models in each of the cross sections I The ndings are robust to varying the starting date I Works well excluding nancial crisis

19 Simulation Randomly draw from leverage factor and attempt to price large cross section of returns This factor is purely noise should have no power I Alpha: prob of absolute pricing error as low as we nd I R 2 : prob of R 2 as high as we nd P-value Number of Occurrences Replications Alpha ,000 R ,000 Alpha, R 2 Jointly ,000

20 Leverage Sorted Portfolios I Rank all CRSP stocks by leverage betas and decile sort. I Large spread in returns increase mechanically in beta. Leverage Sorted Portfolios Low Medium High High-Low E [R e ] σ[r e ] E [R e ]/σ[r e ] Leverage Beta

21 The Leverage Mimicking Portfolio Project factor onto 6 FF Benchmarks & Momentum Traded return: allows new tests/insights Panel A: Time-Series Alphas MAPE Mean LMP FF,MOM FF SBM MOM Bond Total Model Fit LMP FF,MOM FF GRS P-value 0 0 0

22 E(R e ) Mean-Variance Analysis P=max(Sharpe(amkt + bsmb + chml + dmom)) 1.2 Mean Standard Dev iation Frontier 1 P 0.8 LMP 0.6 Mom Mkt 0.4 HML 0.2 SMB Sigma(R e )

23 Mean-Variance Analysis E [R e ] σ[r e ] Sharpe Ratio Annualized Sharpe Market SMB HML Mom LMP Max Sharpe

24 Betting Against Beta BAB1-10 portfolios sorted by betas, scaled to have unit beta, following Frazzini and Pedersen (2011) Time-Series Regressions: Ri,t e = c i + β Lev,i LevFac t + ɛ i,t E[R E ] Sharpe Leverage Betas (x10-2 ) T-stat R 2 BAB % BAB % BAB % BAB % BAB % BAB % BAB % BAB % BAB % BAB % %

25 Adrian, Moench, Shin (2010): Dynamic Asset Pricing λ 0 ybdlevg qsbag CAY dy CP W Λ1 Rxs 2 BD Leverage Growth ybdlevg (7.12) Intermediary Model ybdlevg (6.38) (-5.31) (-0.63) (0.00) Benchmark Factor Model ybdlevg (7.54) (5.33) (3.88) (-3.57) (0.00) Combined Model ybdlevg (7.87) (-6.16) (-2.50) (6.49) (3.07) (-3.42) (0.00)

26 Adrian, Moench, Shin (2010): Broker-Dealer Leverage and Fama-MacBeth Price of Risk 3 Price of BD Leverage Growth Risk and lagged Broker Dealer Leverage Growth Price of BDlevg risk (MA(4)) 4 qtr lagged ( ybdlevg)

27 Conclusion A single factor, broker-dealer leverage, can explain a large set of asset returns I Single factor competes with leading 4 factor equity pricing model and bond pricing model I Economically meaningful: measures intermediary risk I Think about risks faced by intermediaries for asset pricing. Lot more to do here!

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