Asset Pricing Models with Financial Intermediaries

Transcription

1 Asset Pricing Models with Financial ntermediaries Zhiguo He University of Chicago Booth School of Business June 2018, MFM Summer School

2 ntroduction (1) Financial intermediaries are huge and playing important roles in asset pricing and real economy Separation between ownership and control is ubiquitous Financial crisis reveals rst-order importance of studying nancial intermediaries Especially for those sophisticated assets which NPA households will no way be marginal investors! Recent events: high spreads in debt markets Aug 2007 to Oct 2008 n contrast, S&P or Dow Jones near all time high in Aug 2008 n general, debt markets are more sophisticated Role of distressed intermediary capital in the crises of market with complex asset classes (e.g. MBS) Narrative: intermediaries get in trouble, drive up required risk premium in intermediated asset

3 ntroduction (2)

4 Nonlinearity Paper Overview Comments Missing part: Housing Conclusion Bank equity vs aggregate stock market 1.4 Bank Equity and Aggregate Stock Market Bank Equity S&P Financial sector turmoils start early 2007, due to subprime mortgage losses (Bear Stearn)

5 Nonlinearity Paper Overview Comments Missing part: Housing Conclusion Bank equity, aggregate stock market, Case-Shiller 1.4 Bank Equity, Aggregate Stock Market, and Case-Shiller Bank Equity S&P500 Case-Shiller Housing leads bank equity, which leads S&P 500 At 2007Q3, both bank equity and case-shiller index hit back to 2005Q1 level!

6 Nonlinearity Paper Overview Comments Missing part: Housing Conclusion Residential investment 6.00% nvestment Growth: Residential Vs Nonresidential, BEA data 4.00% 2.00% 0.00% -2.00% -4.00% -6.00% -8.00% % % Nonresidential nvestment Residential nvestment % He-Krishnamurthy (2014) have housing sector, but it is one-to-one to the production sector

7 Nonlinearity Paper Overview Comments Missing part: Housing Conclusion nvestment of large public firms % S&P500 nvestment Growth, Compustat 6.00% 4.00% 2.00% 0.00% -2.00% -4.00% -6.00% -8.00% % % % Nonresidential nvestment Residential nvestment S&P500 investment Large public firms tend to draw down existing credit lines (vashina-schafstein), which shields the negative shocks during 2008

8 Annual Review Paper on ntermediary Asset Pricing There are more and more empirical papers in the topic of intermediary asset pricing Our annual review paper has a model section and empirical literature review section Goal: build a simple model as the framework to Understand the essence and connections between these results Clarify what the empirical results are able and unable to claim n our view, the essence of intermediary asset pricing is that "intermediary is not a veil"

9 Simple CARA-Normal Model Draw the essence from He-Krishnamurthy (2012, Restud) Two period model, risky asset with exogenous supply θ, dividend payout ed N µ, σ 2 CARA (exponential utility) agents, households with constant risk tolerance ρ H and managers with constant risk tolerance ρ M ui (W i ) = e 1 ρ i W i, mean-variance preference Risk-free rate is exogenous 0; we derive time-0 asset price p Frictionless benchmark. Given P Agent i s demand of risky asset Equilibrium x H + x M = θ so µ p x i = ρ i σ 2 p = µ {z} expected return θσ 2 ρ H + ρ M {z } risk premium

10 Market Segmentation and Agency Friction Say households cannot directly get access to invest in risky asset As in reality, a manager can set up an intermediary, which essentially o ers households access to risky asset But, subject to certain model hazard problem Work or shirk; shirking hurts fund return by but gives private bene t of b A ne contract between H and M: fee K and share φ No wealth e ect in CARA preference, so ignore the fee K Say fund deliver R F ; manager gets φr F and households get (1 φ) R F We will see that the agency problem imposes a minimum threshold for φ Skin-in-the-game requirement

11 Managers Problem and C Constraint Manager is making decisions on 1) intermediary s position x F and 2) shirking or not max φ [x F (µ p) s ] x F,s2f0,1g Working if and only if C holds x 2 F φ2 σ 2 2ρ M + sb φ b ) φ b µ Portfolio decision. Recall x M = ρ M σ exposure. Then 2 x F = x M φ Households risk holding p, manager s desired risk x H = (1 φ) x F = 1 φ φ x M = 1 φ φ ρ M µ p σ 2 A lower bound on φ translates to an upper bound on xh

12 C Constraint and Equity Constraint Recall C constraint φ b Let m b 1. Then the sharing rule φ, which is the share to manager, satis es φ m Equity implementation. This says that if manager contributes 1 dollar of inside equity, at most households are willing to contribute m outside equity This model does not have leverage (or debt) constraint ntroducing regulatory capital type of constraint will add some additional cost But, equity constraint is more primitive than debt constraint Leverage constraint (say, Kiyotaki-Moore) binds only if equity constraint binds otherwise just issue more equity at a fair price

13 Equilibrium Asset Prices Depending on parameters, equity constraint might not bind The equilibrium asset price is given by 8 < θσ µ 2 ρ p = M +ρ if m > ρ H H /ρ M so equity constraint slack : if m ρ H /ρ M so equity constraint binds µ θσ 2 (1+m)ρ M When agency friction is small, m = b 1 is large, there is a large intermediation capacity, equity constraint is slack The equilibrium asset price is sensitive to agency parameter m only if equity constraint binds sensitive to ρm, θ, and σ 2 in both regions, but more so when equity constraint binds Side note: ρ =wealth 1 relative risk-aversion. Capital loss drives down ρ M, more likely to bind He-Krishnamurthy (2012 Restud; 2013 AER)

14 Pricing Kernel and Stochastic Discount Factor (SDF) n asset pricing, SDF is the word you often hear No arbitrage, exists an SDF that prices EVERYTHNG The SDF proposed by theory often is too simple (say two-factor) With structural model, SDF (pricing kernel) says that agent who can adjust his/her portfolio is happy Marginal investors are those unconstrained; whose FOC helps us to identify pricing kernel... High level take-away: Manager s pricing kernel always holds whether or not constraint binds Households pricing kernel will not work when constraint binds To show "intermediary is not a veil," someone need to show households pricing kernel fails to work

15 Equilibrium Risk-Return Relation and SDF Test The standard factor-based pricing is in terms of λ-β language µ i r {z } = β {z} i expected return quantity of risk for asset i λ {z} price of risk n CAPM, the factor is R M. So β i = Cov (R i,r M ) Var and λ is the (R M ) expected return of the asset with unit beta n standard setting, The factor can be thought of the marginal investor s wealth return R W The quantity of risk βi is again Cov (R i,r W ) Var (R W ) The price of risk λ equals relative risk aversion times wealth return volatility Note, the "λ-β" relation is an equilibrium relation, and does not say anything causal More importantly, no attempt to claim it!

16 ntroducing Second Asset To show SDF test in our model, consider the second asset, say free of agency problem Set θ1 = θ 2 = 1 CARA-Normal framework, iid, and equity constraint slack (m 2 = ) p 2 = µ 2 σ 2 2 ρ M + ρ H And consider the situation m 1 ρ H /ρ M so constraint binds for asset 1 Households terminal wealth Managers terminal wealth m D 1 + m f ρ 1 + H fd ρ M + 2 ρ H m f D 1 + ρ M ρ M + ρ H fd 2

17 Cross-Sectional Asset Pricing Test Factor based asset pricing holds for manager s SDF, for both assets: p 1 µ 1 = p 2 µ 2 = σ 2 1 (1 + m) ρ M = σ 2 2 ρ M + ρ H = 1 ρ {z} M ARA of M σ 2 1 (1 + m) 2 + ρ 2 M σ2 2 (ρ M + ρ H ) 2 σ ρ2 {z } (1+m) 2 M σ2 2 (ρ M +ρ H ) 2 variance of M s wealth {z } {z } price of risk λ β 1 = Cov(R 1,R W,M ) Var(R W,M ) 1 ρ {z} M ARA of M σ 2 1!! σ m ρ M σ 2 2 ρ M +ρ H (1 + m) 2 + ρ 2 M σ2 2 (ρ M + ρ H ) 2 σ ρ2 {z } (1+m) 2 M σ2 2 (ρ M +ρ H ) 2 variance of M s wealth {z } {z } price of risk λ β 2 = Cov(R 2,R W,M ) Var(R W,M ) One can show asset 2 holds for household but not asset 1

18 Empirical Literature Two camps Study some shocks, and show certain assets are a ected more (than others) CP violation (Du, Tepper, Verdelhan, 2017) CDS pricing after Tsunami shock (Siriwardane, 2016) SDF-type test Gabaix, Krishnamurthy, and Vigneron (2007) He, Kelly, and Manela (2017)

19 CP Violation Du, Tepper, Verdelhan (2017) show CP violation aftercrisis Higher demand of dollar, S t F t 1 + it Euro > 1 + it USD

20 Gabaix, Krishnamurthy, and Vigneron (2007) Study MBS market before crisis At that time, the major risk for institutional investors who specialize MBS is prepayment risk These investors pricing kernel is tightly linked to CBARt R t CBARt : average coupon outstanding in the mortgage market; R t : prevalent 10-year treasury rate Time-varying price of risk λt Cross-sectionally, MBS that have higher β to this risk earns higher return A positive risk premium for prepayment risk When CBARt R t is high, households prepay ) loss of MBS investors Controlling interest rate uctuation, households consumption " when CBAR t R t " Standard model will imply a negative risk premium

21 Gabaix, Krishnamurthy, and Vigneron (2007)

22 He, Kelly, and Manela (2017) Construct an intermediary pricing kernel based on equity capital ratio of Primary Dealers Primary Dealers: counterparties of the Federal Reserve Bank of New York ( NY Fed henceforth) in its implementation of monetary policy We choose them because they are large and active in many asset markets Market Equity i,t i η t = Market Equity i,t + Book Debt i,t i n contrast to GKV (2007), we carry out traditional asset pricing test for a wide range of asset classes Equities, US government and corporate bonds, foreign sovereign bonds, options, credit default swaps (CDS), commodities, and foreign exchange (FX) Theory suggests that the price of risk λ should be similar across these asset markets, a surprising result that holds roughly in the data

23 ntro Model Data Results Conclusion Primary Dealers as of February 11, 2014 Primary Dealer Holding Company Since Goldman, Sachs & Co. Goldman Sachs Group, nc Barclays Capital nc. Barclays PLC 1998 HSBC Securities (USA) nc. HSBC Holdings PLC 1999 BNP Paribas Securities Corp. BNP Paribas 2000 Deutsche Bank Securities nc. Deutsche Bank AG 2002 Mizuho Securities USA nc. Mizuho Financial Group, nc Citigroup Global Markets nc. Citigroup nc UBS Securities LLC UBS AG 2003 Credit Suisse Securities (USA) LLC Credit Suisse Group AG 2006 Cantor Fitzgerald & Co. Cantor Fitzgerald & Co 2006 RBS Securities nc. Royal Bank of Scotland Group 2009 Nomura Securities nternational,nc Nomura Holdings, nc Daiwa Capital Markets America nc. Daiwa Securities Group nc J.P. Morgan Securities LLC JPMorgan Chase & Co Merrill Lynch, Pierce, Fenner & Smith Bank of America Corporation 2010 RBC Capital Markets, LLC Royal Bank Holding nc SG Americas Securities, LLC Societe Generale 2011 Morgan Stanley & Co. LLC Morgan Stanley 2011 Bank of Nova Scotia, NY Agency Bank of Nova Scotia 2011 BMO Capital Markets Corp. Bank of Montreal 2011 Jefferies LLC Jefferies LLC 2013 TD Securities (USA) LLC Toronto-dominion Bank 2014

24 Evolution of ntermediary Capital Risk

25 ntro Model Data Results Conclusion Correlations with Other Macro Variables Market Capital Ratio corr(state variable,level) Market Capital Ratio corr(factor,growth) Book Capital Ratio Market Excess Return 0.78 E/P Unemployment GDP Financial Conditions Market Volatility Equity capital ratio is procyclical

26 ntro Model Data Results Conclusion Test Portfolios Equity: Fama-French 25 size/value portfolios US Bonds: Government: Fama 10 maturity sorted portfolios from CRSP Corporate: 10 spread sorted portfolios of Nozawa (2014) who combines TRACE, Lehman, etc Sovereign Bonds: 6 portfolios of Borri and Verdelhan (2012) Options: 18 portfolios of S&P 500 index options sorted on moneyness and maturity from Constantinides et al. (2013) CDS: 20 portfolios sorted on spread using individual name 5-year CDS from Markit beginning in 2001 Commodities: Commodities Research Bureau, Yang (2013) FX: 6 portfolios sorted on yield differential (Lettau et al., 2014) 6 portfolios sorted on momentum (Menkhoff et al., 2012) All Ptfs.: Combines all classes into single large cross section

27 ntro Model Data Results Conclusion Empirical Design Portfolio i in asset class k Cross-section: first-order condition (pricing kernel equation E [ mr i k] = 1) [ ] E Rk i R f = λ η k βi,η k + λ W k β i,w k + νk i Risk loadings β i k from a first-stage time-series regression Fama-Macbeth to estimate λ η k for asset class k Separately estimate risk price within each asset class, then do this once for all portfolios Theory says λ η k = λη for the same factor (only depends on the pricing kernel m)

28 ntro Model Data Results Conclusion ntermediary Capital Risk Price ˆλ η by Asset Class FF25 US bonds Sov. bonds Options CDS Commodities FX All

29 ntro Model Data Results Conclusion Cross-sectional Results by Asset Class 1970Q1 2012Q4 FF25 US bonds Sov. bonds Options CDS Commod. FX All Capital (2.16) (2.58) (1.66) (2.02) (3.44) (1.90) (3.12) (2.52) Market (0.78) (0.82) (0.32) (0.67) (0.41) (-0.25) (2.17) (0.80) ntercept (0.36) (1.44) (0.33) (-0.31) (-2.77) (0.83) (-0.83) (-0.00) R MAPE, % MAPE-R, % RRA Sharpe ratio Assets Quarters

30 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns

31 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o FF

32 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o 0.04 FF25 US Bonds

33 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o 0.04 FF25 US Bonds Sov. Bonds

34 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o 0.04 FF25 US Bonds Sov. Bonds Options

35 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o 0.04 FF25 US Bonds Sov. Bonds Options CDS

36 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o 0.04 FF25 US Bonds Sov. Bonds Options CDS Commod

37 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o FF25 US Bonds Sov. Bonds Options CDS Commod. FX

38 ntro Model Data Results Conclusion Actual vs. Predicted Average Excess Returns o FF25 US Bonds Sov. Bonds Options CDS Commod. FX Exotic Bonds CMBS β η=0.13 ; Muni β η=0.12 ; High Yield β η=0.03 ; Convert β η=0.04. Average US bonds portfolio β η=0.03. (Data source: BoA-Merrill.)

39 ntro Model Data Results Conclusion Capital Ratio vs. Other Pricing Factors Benchmark: CAPM FF3F FF5F Momentum PS-liquidity LMW Capital (2.52) (1.98) (2.46) (2.84) (1.75) (1.76) Market (0.80) (0.90) (0.74) (0.81) (0.69) SMB (0.42) (0.68) HML (1.36) (1.46) CMA (-0.09) RMW 0.08 (0.04) MOM (-0.14) PS nt 5.71 (0.64) LMW 0.77 (0.58) LMW 0.63 (0.31) Adj. R MAPE, % RRA Assets Quarters Adj. R 2 w/o Capital MAPE w/o Capital

40 ntro Model Data Results Conclusion Placebo Test: Are Primary Dealers Special? What if we use capital risk factor constructed based on non-primary brokers? FF25 US bonds Sov. bonds Options CDS Commod. FX All Capital (2.45) (0.69) (1.24) (-2.33) (2.55) (-1.52) (-0.12) (1.04) Market (-1.66) (2.51) (1.74) (-1.20) (2.99) (-0.49) (2.45) (0.80) ntercept (3.36) (1.49) (0.22) (1.48) (-2.72) (-0.62) (-2.14) (0.95) R MAPE, % MAPE-R, % RRA Assets Quarters

41 ntro Model Data Results Conclusion Equity Shock vs Debt Shock? Decompose capital shock into equity growth shock and debt growth shock FF25 US bonds Sov. bonds Options CDS Commod. FX All ME (1.62) (1.34) (0.86) (1.54) (1.32) (1.56) (4.30) (2.35) BD (-1.51) (1.53) (-2.24) (-0.93) (-2.12) (1.14) (-0.08) (-0.07) Market (0.46) (2.01) (0.48) (0.19) (-0.17) (0.00) (2.12) (0.93) ntercept (0.56) (1.19) (-0.12) (-0.02) (-3.25) (0.38) (-0.76) (-0.40) R MAPE, % MAPE-R, % RRA Assets Quarters

42 ntro Model Data Results Conclusion ntermediary Equity Return as Factor Primary dealers equity return as single factor (direct test of He-Krishnamurthy with log preferences) FF25 US bonds Sov. bonds Options CDS Commod. FX All Capital (-0.14) (3.10) (1.77) (2.99) (2.91) (0.31) (3.44) (1.07) ntercept (1.79) (1.68) (0.48) (-2.67) (-3.73) (0.46) (-1.38) (-0.06) R MAPE, % MAPE-R, % RRA Assets Quarters FF25 US bonds Sov. bonds Options CDS Commod. FX All Capital (1.89) (2.55) (1.52) (1.71) (3.00) (1.77) (3.40) (2.39) Market (0.89) (1.15) (0.60) (0.54) (0.56) (0.03) (1.81) (0.97) ntercept (0.24) (2.23) (0.22) (-0.24) (-2.60) (0.57) (-0.68) (-0.26) R MAPE, % MAPE-R, % RRA Assets Quarters

43 ntro Model Data Results Conclusion Potential Difference from AEM t is intriguing that we have countercyclical leverage while Adrian-Etular-Muir (AEM, 2014) have procyclical leverage Equilibrium leverage pattern depends on the theory you write (either equity-constraint or debt-constraint) But what differ in our data? AEM HKM Data Source Flow of Funds CRSP/Compustat/Datastream Universe Public+Private Public Book vs. Market Book values Market equity, book debt Reporting if hold. co. BD operations only Holding company mportance of private/public distinction unlikely due to size concentration (can show that even in public universe, all driven by largest 25 firms)

44 ntro Model Data Results Conclusion Book vs Market One common thought: FoF is accounting data (book leverage), while we use market leverage Not the answer. For primary dealers, market and book capital ratios exhibit a correlation of 50% Mark-to-market accounting for broker-dealers make the difference small For stand-alone public broker-dealers (SC 6211,6221), we find a 75% correlation between market leverage and book leverage For our sample of primary dealers including big banks (mark-to-market?), book and market leverages are also positively correlated

45 ntro Model Data Results Conclusion Holding Company vs Subsidiary We include primary dealers entire balance sheet Holding company level, not just their trading arms Say JPMorgran. Losses on JPMorgan s other businesses likely adversely affect the trading arm s risk-return trade-off We postulate this drives the difference A piece of suggestive evidence AEM implied capital ratio (i.e., inverse of AEM leverage) has -59% correlation with primary dealers But, AEM implied capital ratio is 12% correlated with non-primary dealers (smaller with broker-dealer arms only) Which is the right measure?

46 s ntermediary a Veil? Note, so far the evidence does not rule out that households SDF works as well Standard consumption based framework goes a long-way in explaining equity market There are some attempts to explain dynamics of index options under standard consumption based framework, but no cross-section Doubt these models work for other derivatives markets say CDS He, Kelly, Manela (2017) present two pieces of evidence along this line First, other widely-used factors that work in equity market (FF ve-factor, Pastor-Stambaugh liquidity factor) fail Second, the equity capital ratio of non-primary-dealers works for equity but fails on others Non-primary dealers tend to be smaller, standalone broker-dealers for the equity market but with little activity in derivatives markets Their pricing kernel may re ect SDF of their clients (households) in equity market