BrokerDealer Leverage and the CrossSection of Stock Returns 1


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1 BrokerDealer Leverage and the CrossSection of Stock Returns 1 Tobias Adrian, Erkko Etula and Tyler Muir Federal Reserve Bank of New York and Northwestern University Bank of England, January 5, 11 1 The views expressed in this paper are those of the authors and do not necessarily represent those of the Federal Reserve Bank of New York or the Federal Reserve System.
2 Aggregate mplications of Financial ntermediaries The nancial crisis of 79 suggests that nancial intermediary balance sheet management has aggregate consequence The expansion and contraction of nancial intermediaries is associated with the asset price boom and bust Systemic risk arises when asset price declines are associated with disorderly unwinding of intermediary balance sheets Contrast internet stock price crash to housing price decline We provide evidence that asset price valuations are systematically tied to the balance sheet behavior of intermediaries Asset pricing approach: Merton s (1973) CAPM ntermediary leverage key variable for systemic risk because it is tied to asset valuations
3 Adrian and Shin (1) Liquidity and Leverage
4 Adrian and Shin (1) Liquidity and Leverage
5 Adrian and Shin (1) Changing Nature of Financial ntermediation
6 Realized Mean Return Asset Pricing Anomalies Failure of the CAPM in the crosssection of stock returns Vast literature developed to address such failures: size, value, momentum, longterm reversal,... CAPM: Pricing the Cross Section of 5 Size and B/M Sorted Porfolios S1B5 S3B5 S1B SB5 SB SB5 SB3 S3B SB S1B3 S3B3 S3B S1B SB3 SB S5B5 S5B SB SB1 S5B S5B3 MktFac S5B1 S3B1 SB1.5 S1B
7 BrokerDealer Asset Pricing Premise is that nancial intermediaries matter for risk premium determination Several theories are presented in the literature Gromb and Vayanos (9), He and Krishnamurthy (9), Danielson, Shin and Zigrand (9), Gârleanu and Pedersen (1) We motivate our empirical investigation with an CAPM setup that is giving rise to a multifactor asset pricing model Multifactor asset pricing explanations of pricing anomalies have proven successful in the past What is new is the focus on the pricing variable: brokerdealer leverage
8 ntuition CAPM Premise: Shocks to investment opportunities a ect portfolio choice e.g. technology shocks, nancial shocks, demand shocks and hence, matter for the equilibrium pricing of risky assets
9 ntuition CAPM Premise: Shocks to investment opportunities a ect portfolio choice e.g. technology shocks, nancial shocks, demand shocks and hence, matter for the equilibrium pricing of risky assets Risk premia can uncover aggregate state variables Problem: most investors are passive, their portfolio choice is hard to understand
10 ntuition CAPM Premise: Shocks to investment opportunities a ect portfolio choice e.g. technology shocks, nancial shocks, demand shocks and hence, matter for the equilibrium pricing of risky assets Risk premia can uncover aggregate state variables Problem: most investors are passive, their portfolio choice is hard to understand We isolate a group of active [securities brokers and dealers]: Portfolio optimization easier to understand Aggressive, active adjustment of leverage High leverage low U W, low risk premia
11 ntertemporal Asset Pricing The equilibrium asset pricing implication of the CAPM is: E dr i = Cov dr i, dr M Γ + Cov dr i, dx F, where dr M is excess market return and Γ and F are prices of risk. There are two agents A and P. The model so far is a completely general twoagent CAPM x, Γ, F not pinned down
12 ntertemporal Asset Pricing The equilibrium asset pricing implication of the CAPM is: E dr i = Cov dr i, dr M Γ + Cov dr i, dx F, where dr M is excess market return and Γ and F are prices of risk. There are two agents A and P. The model so far is a completely general twoagent CAPM x, Γ, F not pinned down Next, consider a particular example with: 1. Active investors: Leveraged nancial intermediaries (brokerdealers); manage leverage procyclically Maximize expected equity return s.t. a VaR constraint E ective risk aversion γ A proportional to the Lagrange multiplier on the VaR constraint. Passive investors: Rest of the economy (rest of nancials, non nancial rms, households) Myopic meanvariance optimizers with constant γ P
13 Application: CAPM with Financial ntermediaries We show that, in equilibrium, the e ective risk aversion γ A : s proportional to the economy s generalized sharpe ratio Has the following representation: γ A = γ A x 1 + γ A 1 x
14 Application: CAPM with Financial ntermediaries We show that, in equilibrium, the e ective risk aversion γ A : s proportional to the economy s generalized sharpe ratio Has the following representation: γ A = γ A x 1 + γ A 1 x Constants γ A, γa 1 depend on the parameters of the model State variables x 1, x are: x 1 = 1 lev A, x = w A w P 1 lev A. Puts intermediary leverage in the pricing kernel: E t rt+1 i = Cov t r t+1, i rt+1 M Γ t Cov t rt+1, i x t+1 Ft
15 State Variables
16 mplications Shocks to brokerdealer leverage may be priced in the crosssection of stock returns:
17 mplications Shocks to brokerdealer leverage may be priced in the crosssection of stock returns: Motivates the crosssectional regression [FamaMacBeth]: Er i = α + β im λ M + β ix λ x + error i, β im is the market beta with risk premium λ M β ix are additional risk exposures with risk premia λ x Betas can be estimated from the timeseries regression: r i t+1 = a i + β im r M t+1 + β ix x t+1 + error i t+1, x t+1 = x t+1 E t x t+1 are innovations to the state variables: x 1 = 1 {z lev BD, x = w BD 1 } w NonBD lev BD. {z } Capital Ratio Scaled Wealth
18 Data (Q1/ Q/9) Aggregate Balance Sheet Variables: Total nancial assets and total nancial liabilities of U.S. securities brokerdealers and the rest of the U.S. economy From the Federal Reserve s Flow of Funds database (quarterly)
19 Data (Q1/ Q/9) Aggregate Balance Sheet Variables: Total nancial assets and total nancial liabilities of U.S. securities brokerdealers and the rest of the U.S. economy From the Federal Reserve s Flow of Funds database (quarterly) Equity Portfolios and Additional Factors: 3 ndustry, 5 Size and B/M, 5 Size and Momentum, 5 Size and LongTerm Reversal, 5 Size and ShortTerm Reversal MKT, HML, SMB, MOM, LTREV, STREV From Ken French s website
20 Data (Q1/ Q/9) Aggregate Balance Sheet Variables: Total nancial assets and total nancial liabilities of U.S. securities brokerdealers and the rest of the U.S. economy From the Federal Reserve s Flow of Funds database (quarterly) Equity Portfolios and Additional Factors: 3 ndustry, 5 Size and B/M, 5 Size and Momentum, 5 Size and LongTerm Reversal, 5 Size and ShortTerm Reversal MKT, HML, SMB, MOM, LTREV, STREV From Ken French s website Address the critique of Lewellen, Nagel, Shanken (1) Large set of test assets (not only Size and B/M) nclude priced factors as test assets Take crosssectional alphas seriously
21 5 Size and Book/Market Portfolios Benchmarks BrokerDealer Models (i) (ii) (iii) (iv) (v) (vi) Constant (3.18) (.681) (.733) (1.65) (1.78) (.97) Leverage (3.6) (3.766) (3.96) (3.57) Scaled Wealth (.888) (.36) Market (.) (.57) (1.73) (1.) SMB (1.395) (1.18) HML (.98) (1.815) RSquared 3% 6% 57% 67% 68% 73% Adj. RSquared 1% 57% 55% 6% 6% 68%
22 Realized Mean Return Realized Mean Return Realized Mean Return Realized Mean Return 5 Size and Book/Market Portfolios CAPM 1 Factor Broker Dealer Model Factor Benchmark Model Factor Broker Dealer Model
23 5 Size and Momentum Sorted Portfolios Benchmarks BrokerDealer Models (i) (ii) (iii) (iv) (v) (vi) Constant (.368) (1.9) (.355) (.71) (1.3) (1.5) Leverage (3.753) (3.1) (.761) (3.98) Scaled Wealth (1.86) (1.7) Market (.33) (1.967) (.53) (.398) SMB.1.17 (1.71) (1.575) Momentum (3.35) (3.8) RSquared 1% 8% 76% 76% 77% 89% Adj. RSquared 3% 77% 75% 7% 7% 87%
24 Realized Mean Return Realized Mean Return Realized Mean Return Realized Mean Return 5 Size and Momentum Sorted Portfolios 6 CAPM 1 Factor Broker Dealer Model 6 3 Factor Benchmark Model 6 3 Factor Broker Dealer Model 6
25 3 ndustry Portfolios Benchmarks BrokerDealer Models (i) (ii) (iii) (iv) (v) (vi) Constant (3.81) (.7) (1.588) (1.87) (3.51) (3.955) Leverage (1.67) (1.87) (1.81) (1.77) Scaled Wealth (1.81) (1.3) Market.... (.19) (.57) (.) (.53) SMB (.866) (.86) HML (.9) (.537) RSquared 1% 15% 7% 8% 57% 36% Adj. RSquared % 6% % % 5% 7%
26 Realized Mean Return Realized Mean Return Realized Mean Return Realized Mean Return 3 ndustry Portfolios CAPM 1 Factor Broker Dealer Model Factor Benchmark Model Factor Broker Dealer Model
27 5 Size and Book/Market and 1 Momentum, 3 ndustry Benchmarks BrokerDealer Models (i) (ii) (iii) (iv) (v) (vi) Constant (5.131) (6.91) (.53) (.89) (1.38) (3.6) Leverage (.17) (.19) (.71) Scaled Wealth (.799) (.73) Market (.7) (.53) (1.1) (.58) SMB.1.38 (.67) (.78) HML.3.87 (.73) (1.) Momentum.19 (.8) RSquared 1% 3% 5% 6% 5% 6% Adj. RSquared 1% % % 5% 8% %
28 Realized Mean Return Realized Mean Return Realized Mean Return Realized Mean Return 5 Size and Book/Market and 1 Momentum, 3 ndustry Portfolios CAPM 1 Factor Broker Dealer Model 3 Factor Benchmark Model 3 Factor Broker Dealer Model
29 Conclusion Our results suggest that the BrokerDealer pricing model may provide a common explanation for many asset pricing puzzles The brokerdealer pricing model ties asset price movements to the balance sheet management of nancial intermediaries Systemic risk arises when asset price declines are associated with disorderly unwinding of leverage The disorderly unwinding has been particularly important in the nancial crisis
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