Risk Retention Regulation of Bank Asset Securitization

Transcription

1 Risk Retention Regulation of Bank Asset Securitization Guixia Guo Institute of International Economy, UIBE / 30

2 Background: I Research Motivation Large volume of bank asset securitization has been criticized as a major contagion factor contributing to the financial crisis (Diamond and Rajan, 2009; Hellwig, 2009; Stein, 2010) Auto Credit Cards Equipment Home Equity Manufactured Housing Student Loans Other Total Figure 1: Issuance of ABS in US ( ; $ in billions) 2 / 30

3 Background: II Research Motivation Asset Pool of Banks (mortgages, loans, etc.) Originator True sale Proceeds from sale of assets SPV(Issuer) Credit Agency Issue Securities Note Structuring Proceeds from sale of notes Tranching Class A Notes (AAA) Class B Notes (A) Investors Class C Notes (BBB) Retained as a sort of credit enhancement Class D Notes (Equity or Unrated) Figure 2: Securitization Process Figure 1. The Securitization Process 3 / 30

4 Research Motivation Risk Retention Requirement" was proposed by US and EU to regulate bank asset securitization: skin in the game. Item Name of the Act The Regulated Retention Ratio US EU (1) : Financial Regulatory Reform: A New Foundation (2) : Dodd-Frank Act : Amendment to CRD (Directives 2006/48/EC and 2006/49/EC) -Creditors originating and transferring loans to third parties; -Securitizers of ABS. At least 5% of the involved credit exposure, hedging or risk transferring prohibited Figure 3: Risk Retention Requirement of US and EU Both US and EU require more information disclosure on ABS; not on retention ratio. 4 / 30

5 Research Motivation Risk Retention Requirement" was proposed by US and EU to regulate bank asset securitization: skin in the game. Item Name of the Act The Regulated Retention Ratio US EU (1) : Financial Regulatory Reform: A New Foundation (2) : Dodd-Frank Act : Amendment to CRD (Directives 2006/48/EC and 2006/49/EC) -Creditors originating and transferring loans to third parties; -Securitizers of ABS. At least 5% of the involved credit exposure, hedging or risk transferring prohibited Figure 3: Risk Retention Requirement of US and EU Both US and EU require more information disclosure on ABS; not on retention ratio. 4 / 30

6 Background: III Auto Credit Cards Equipment Research Motivation Home Equity Manufactured Housing Student Loans Other Total ABS CDO Weighted Average MBS Figure 4: Degree of Tranche Retention of US ABS (%; IMF Estimates) 5 / 30

7 Research Question Research Motivation Whether the flat rate of risk retention requirement is soundly-founded? Why 5%? How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Protecting investors? Enhancing social welfare? Should risk retention requirement be complemented by information disclosure requirement on it? 6 / 30

8 Research Question Research Motivation Whether the flat rate of risk retention requirement is soundly-founded? Why 5%? How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Protecting investors? Enhancing social welfare? Should risk retention requirement be complemented by information disclosure requirement on it? 6 / 30

9 Research Question Research Motivation Whether the flat rate of risk retention requirement is soundly-founded? Why 5%? How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Protecting investors? Enhancing social welfare? Should risk retention requirement be complemented by information disclosure requirement on it? 6 / 30

10 Relevant Literature Research Motivation Severe asymmetric information in ABS (primary) market: Morgan (2002); Duffie (2008). Reducing informational asymmetry by signalling: Leland and Pyle (1977); DeMarzo (2005). Unrelated to risk retention requirement. Reducing informational asymmetry by screening: Fender and Mitchell (2009); Kiff and Kisser (2010). Actually a moral hazard story. My purpose: to evaluate economic and welfare effect of risk retention requirement on bank asset securitization. 7 / 30

11 Relevant Literature Research Motivation Severe asymmetric information in ABS (primary) market: Morgan (2002); Duffie (2008). Reducing informational asymmetry by signalling: Leland and Pyle (1977); DeMarzo (2005). Unrelated to risk retention requirement. Reducing informational asymmetry by screening: Fender and Mitchell (2009); Kiff and Kisser (2010). Actually a moral hazard story. My purpose: to evaluate economic and welfare effect of risk retention requirement on bank asset securitization. 7 / 30

12 Relevant Literature Research Motivation Severe asymmetric information in ABS (primary) market: Morgan (2002); Duffie (2008). Reducing informational asymmetry by signalling: Leland and Pyle (1977); DeMarzo (2005). Unrelated to risk retention requirement. Reducing informational asymmetry by screening: Fender and Mitchell (2009); Kiff and Kisser (2010). Actually a moral hazard story. My purpose: to evaluate economic and welfare effect of risk retention requirement on bank asset securitization. 7 / 30

13 Research Motivation t = 0 Asset ( X, D K X ) t = 1 Securitize q proportion of X at price p Figure1 5: Timing t = 2 Uncertainty dissolved and payments made A bank and a continuum of dispersed investors, with mean-variance utility function with ARA γ and λ. At t = 0, B/S: Liability: D deposits (interest rate r D) and K capital (interest rate 1). No CAR. Asset: riskless asset (D + K X) (rate of return r f ) and a continuum of risky assets indexed by j [0, 1], each of amount X j and random time 2 rate of return r j N(ˆr j, σ 2 ). No maturity mismatch. ˆr j : asset quality. Representative risky asset with quality ˆr. 8 / 30

14 Research Motivation t = 0 Asset ( X, D K X ) t = 1 Securitize q proportion of X at price p Figure1 5: Timing t = 2 Uncertainty dissolved and payments made A bank and a continuum of dispersed investors, with mean-variance utility function with ARA γ and λ. At t = 0, B/S: Liability: D deposits (interest rate r D) and K capital (interest rate 1). No CAR. Asset: riskless asset (D + K X) (rate of return r f ) and a continuum of risky assets indexed by j [0, 1], each of amount X j and random time 2 rate of return r j N(ˆr j, σ 2 ). No maturity mismatch. ˆr j : asset quality. Representative risky asset with quality ˆr. 8 / 30

15 At t = 1 and t = 2 Research Motivation At t = 1, the bank securitizes q proportion of its assets to meet the liquidity needs. No re-investment. Informational asymmetry here: ˆr known only to the originating bank. For investors: ˆr U[r, r], and r > r f > 1. Information set: Ω. At t = 2, r realizes, all uncertainties are dissolved. 9 / 30

16 At t = 1 and t = 2 Research Motivation At t = 1, the bank securitizes q proportion of its assets to meet the liquidity needs. No re-investment. Informational asymmetry here: ˆr known only to the originating bank. For investors: ˆr U[r, r], and r > r f > 1. Information set: Ω. At t = 2, r realizes, all uncertainties are dissolved. 9 / 30

17 : Complete Information as the Benchmark Consider investor i s optimal demand y i for securitized asset, max Eˆr {E [y i ( r p) Ω,ˆr]} y i 1 2 λ {Varˆr [E (y i ( r p) Ω,ˆr)] + Eˆr [Var (y i ( r p) Ω,ˆr)]} =y i [E(ˆr Ω) p] 1 2 λy2 i [Var(ˆr Ω) + σ 2] (1) Bank chooses optimal securitization intensity q to maximize its expected utility derived from end-of-period wealth, max q Kr f + D(r f r D ) + qx[p(q) r f ] + (1 q)x(ˆr r f ) 1 2 γσ2 X 2 (1 q) 2 (2) 10 / 30

18 : Complete Information as the Benchmark Consider investor i s optimal demand y i for securitized asset, max Eˆr {E [y i ( r p) Ω,ˆr]} y i 1 2 λ {Varˆr [E (y i ( r p) Ω,ˆr)] + Eˆr [Var (y i ( r p) Ω,ˆr)]} =y i [E(ˆr Ω) p] 1 2 λy2 i [Var(ˆr Ω) + σ 2] (1) Bank chooses optimal securitization intensity q to maximize its expected utility derived from end-of-period wealth, max q Kr f + D(r f r D ) + qx[p(q) r f ] + (1 q)x(ˆr r f ) 1 2 γσ2 X 2 (1 q) 2 (2) 10 / 30

19 Competitive Market Equilibrium Definition 1 Given { D, X;ˆr, r D, r f ; λ, γ; σ 2}, a competitive market equilibrium is market price and securitization intensity {p, q}, and security demand {y i } i [0,1] so that: 1 Given the information set Ω derived from securitization intensity q, security demand y i of each investor i [0, 1] maximizes its expected utility (1); 2 Given market price p, securitization intensity q maximizes the bank s expected utility (2); 3 Security market clears: 1 0 y idi = qx. 11 / 30

20 Competitive Market Equilibrium of Benchmark Proposition 1 When asset quality is observable to both the originating bank and investors, the bank would like to securitize a constant proportion of its assets of any quality ˆr [r, r]: p B = ˆr λσ 2 X γ γ + 2λ, q B = γ γ + 2λ (3) 12 / 30

21 : Unregulated Equilibrium with Asymmetric Information Information set: Ω U = {q > 0}. Assumption A: γ < r r 2σ 2 X. Define η 2 Var(ˆr) = ( r r) / 30

22 The Equilibrium of Proposition 2 Under Assumptions A, the unregulated competitive market equilibrium is: { r + γσ 2 X λq U X (ηu 2 + σ 2 ), if r < ˆr < ˆr U p U = 0, if ˆr U < ˆr < r If γ < 2λ( γ2 σ 2 X 2 ), q U = { r+2γσ 2 X ˆr 2λX (ηu 2 +σ2 )+γσ 2 X, if r < ˆr < ˆr U 0, if ˆr U < ˆr < r If γ > 2λ( γ2 σ 2 X 2 ), 1, if r < ˆr < r + γσ 2 X 2λX(ηU 2 + σ 2 ) r+2γσ q U = 2 X ˆr 2λX (ηu 2 +σ2 )+γσ 2 X, if r + γσ2 X 2λX(ηU 2 + σ 2 ) < ˆr < ˆr U 0, if ˆr U < ˆr < r where η 2 U 1 3 γ2 σ 4 X 2, ˆr U r + 2γσ 2 X. 14 / 30

23 Distortion I of Informational Asymmetry q 1 q B q U r r r ˆr Figure Figure 6: Comparing 3 Securitization Intensity Û Securitization Level Distortion: LD AS U = r ˆr U. 15 / 30

24 Distortion II of Informational Asymmetry E( rˆ q ) E ( ˆ ) ˆ B r q r E ( ˆ ) U r q r r Û r ˆr Figure 7: Comparing Market Valuation Securitization Structural Distortion: SD ˆr U r q U X [ˆr Figure E(ˆr Ω 2 U Comparing )]dˆr, E(ˆr Ω Market U ) Valuation = r+ˆru / 30

25 Competitive Market Equilibrium of Scenarios R Risk retention requirement: q = q, and not disclosed to investors. Information set: Ω R = {q R = q > 0}, Proposition 3 Under Assumption A, the competitive market equilibrium of scenario R is: { r + 1 p R = 2 γσ2 X(2 q) 2λ qx (σ 2 + ηr), 2 if r < ˆr < ˆr R, 0 < q < q R 0, if otherwise { q, if r < ˆr < ˆr R and 0 < q < q R q R = 0, if otherwise 2γ where q R = γ+2λ is the upper bound of q for ˆr R > r to hold, and ηr 2 1 = 2λ 2 q 2 X 2 {3 + λ qx2 σ 2 [γ(2 q) 2λ q] 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q]} ˆr R = r + 1 { } λ qx 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q] 3 17 / 30

26 Competitive Market Equilibrium of Scenarios R Risk retention requirement: q = q, and not disclosed to investors. Information set: Ω R = {q R = q > 0}, Proposition 3 Under Assumption A, the competitive market equilibrium of scenario R is: { r + 1 p R = 2 γσ2 X(2 q) 2λ qx (σ 2 + ηr), 2 if r < ˆr < ˆr R, 0 < q < q R 0, if otherwise { q, if r < ˆr < ˆr R and 0 < q < q R q R = 0, if otherwise 2γ where q R = γ+2λ is the upper bound of q for ˆr R > r to hold, and ηr 2 1 = 2λ 2 q 2 X 2 {3 + λ qx2 σ 2 [γ(2 q) 2λ q] 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q]} ˆr R = r + 1 { } λ qx 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q] 3 17 / 30

27 Sub-optimality of Flat-Rate Retention Ratio Optimal q that maximizes expected social welfare is implicitly determined by 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q] [6 + λ q 2 σ 2 X 2 (γ + 4λ) ] (4) = 18 3λ q 2 γσ 2 X λ qγσ 2 X 2 + 2γ q 2 (λσ 2 X 2 ) 2 [γ(2 q)(1 2 q) 4λ q(1 q)] Proposition 4 Given volatility of risky asset return σ 2 and loan value X, there is no optimal flat rate of retention ratio requirement for all markets with securitizers and investors of different risk attitudes. 18 / 30

28 Sub-optimality of Flat-Rate Retention Ratio Optimal q that maximizes expected social welfare is implicitly determined by 9 + 6λ qx 2 σ 2 [γ(2 q) 2λ q] [6 + λ q 2 σ 2 X 2 (γ + 4λ) ] (4) = 18 3λ q 2 γσ 2 X λ qγσ 2 X 2 + 2γ q 2 (λσ 2 X 2 ) 2 [γ(2 q)(1 2 q) 4λ q(1 q)] Proposition 4 Given volatility of risky asset return σ 2 and loan value X, there is no optimal flat rate of retention ratio requirement for all markets with securitizers and investors of different risk attitudes. 18 / 30

29 Competitive Market Equilibrium of Scenarios D q D acts as a noiseless signal of asset quality. Information set: Ω D = {q D }. Proposition 5 The equilibrium asset price and securitization intensity in the market with asymmetric information and information disclosure regulation are: and q D is the inverse function of ˆr(q D ), where p D = ˆr λσ 2 q D X (5) ˆr(q D ) = γσ 2 X (q D ln q D ) + 2λσ 2 Xq D + r γσ 2 X(1 ln γ γ + 2λ ) (6) 19 / 30

30 Competitive Market Equilibrium of Scenarios D q D acts as a noiseless signal of asset quality. Information set: Ω D = {q D }. Proposition 5 The equilibrium asset price and securitization intensity in the market with asymmetric information and information disclosure regulation are: and q D is the inverse function of ˆr(q D ), where p D = ˆr λσ 2 q D X (5) ˆr(q D ) = γσ 2 X (q D ln q D ) + 2λσ 2 Xq D + r γσ 2 X(1 ln γ γ + 2λ ) (6) 19 / 30

31 Comprehensive Comparisons q 1 q B E( rˆ q ) E ( rˆ q) E ( rˆ q) rˆ B D q R q U E ( ˆ ) U r q q D E ( ˆ ) R r q r r ˆR r r ˆr Û r r ˆR r Û r ˆr Figure 8: Comprehensively Comparing Securitization Figure 3 Comparing Intensity Securitization Intensity Figure 9: Comprehensively Figure 2 Comparing Market Valuation Comparing Market Valuation 20 / 30

32 Corrected Distortions by R and D Regulation Proposition 6 Risk retention regulation is effective in correcting structural distortion resulted from asset opaqueness; information disclosure regulation is effective in correcting both structural and level distortions. R regulation corrects structural distortion: ˆr R r qx[r E(ˆr Ω R )]dr = 0, where E(ˆr Ω R ) = r+ˆrr 2 ; D regulation corrects structural distortion: r r q DX(r r)dr = 0; D regulation corrects level distortion: AS D = / 30

33 Corrected Distortions by R and D Regulation Proposition 6 Risk retention regulation is effective in correcting structural distortion resulted from asset opaqueness; information disclosure regulation is effective in correcting both structural and level distortions. R regulation corrects structural distortion: ˆr R r qx[r E(ˆr Ω R )]dr = 0, where E(ˆr Ω R ) = r+ˆrr 2 ; D regulation corrects structural distortion: r r q DX(r r)dr = 0; D regulation corrects level distortion: AS D = / 30

34 Corrected Distortions by R and D Regulation Proposition 6 Risk retention regulation is effective in correcting structural distortion resulted from asset opaqueness; information disclosure regulation is effective in correcting both structural and level distortions. R regulation corrects structural distortion: ˆr R r qx[r E(ˆr Ω R )]dr = 0, where E(ˆr Ω R ) = r+ˆrr 2 ; D regulation corrects structural distortion: r r q DX(r r)dr = 0; D regulation corrects level distortion: AS D = / 30

35 Corrected Distortions by R and D Regulation Proposition 6 Risk retention regulation is effective in correcting structural distortion resulted from asset opaqueness; information disclosure regulation is effective in correcting both structural and level distortions. R regulation corrects structural distortion: ˆr R r qx[r E(ˆr Ω R )]dr = 0, where E(ˆr Ω R ) = r+ˆrr 2 ; D regulation corrects structural distortion: r r q DX(r r)dr = 0; D regulation corrects level distortion: AS D = / 30

36 New Distortions of R and D Regulation Proposition 7 The level distortion resulted from informational asymmetry is aggravated by risk retention regulation: ˆr R < ˆr U. Intuition: Ω R = {q R = q > 0} has less effective information content than Ω U = {q U > 0}. New distortion of R Regulation: Securitization Level Distortion is aggravated. New distortion of D Regulation: Distortion of securitization intensity to send signals. 22 / 30

37 New Distortions of R and D Regulation Proposition 7 The level distortion resulted from informational asymmetry is aggravated by risk retention regulation: ˆr R < ˆr U. Intuition: Ω R = {q R = q > 0} has less effective information content than Ω U = {q U > 0}. New distortion of R Regulation: Securitization Level Distortion is aggravated. New distortion of D Regulation: Distortion of securitization intensity to send signals. 22 / 30

38 New Distortions of R and D Regulation Proposition 7 The level distortion resulted from informational asymmetry is aggravated by risk retention regulation: ˆr R < ˆr U. Intuition: Ω R = {q R = q > 0} has less effective information content than Ω U = {q U > 0}. New distortion of R Regulation: Securitization Level Distortion is aggravated. New distortion of D Regulation: Distortion of securitization intensity to send signals. 22 / 30

39 Evaluating Welfare Effects of R and D Regulation Scenarios Unregulated Scenario R Regulation over Unregulated Scenario D Regulation over R Regulation (Correcting) Level Distortion Higher if decreases Higher if decreases, or increases (Correcting) Structural Distortion Higher if increases, or decreases Higher if increases, or decreases Higher if increases, or decreases Regulatory Cost Aggregate Welfare Effect Lower if increases, or decreases Lower if increases Higher if increases, or decreases Higher if increases Figure 10: Welfare Effects of R and D Regulation Proposition 8 Risk retention regulation tends to increase expected social welfare when the bank is more risk averse (i.e. γ is relatively large); information disclosure regulation tends to dominate risk retention regulation when investors are more risk averse (i.e. λ is relatively large). 23 / 30

40 A Numerical 4 Example Research Motivation 2 Let σ 2 = 1, X = 1. Bolded line: q = 0.95 in Figure 9, and q = 0.5 in Figure Figure 11: q = 0.95 but Market Breaks Down 4 Figure 12: q = 0.5 and No Market Breakdown / 30

41 Research Motivation 0.2 A Numerical Example (Continued) =1 =3 =5 = =0.5 =1 =3 = Figure 13: q and Risk Attitude of Investors 0.7 =1 Figure 14: q and Risk Attitude of the =3 0.6 =5 Bank 0.5 = / 30

42 Research Motivation A Numerical Example -40 (Continued) =0.5 =1 =3 = Figure 15: When R Regulation Improves Social Welfare R Regulation improves social welfare upon the unregulated case when γ is relatively large. 26 / 30

43 A Numerical Example (Continued) 20 =0.5 =1 10 =3 = Figure 16: When D Regulation =0.5 Improves Upon R Regulation 40 =1 D Regulation can complement R Regulation when λ is relatively large. 35 =3 = / 30

44 : Back to the Questions Whether the flat rate of risk retention requirement is soundly-founded? It is impossible for a flat rate retention ratio requirement to be optimal for all markets. How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Only information disclosure requirement can. Protecting investors? Both. Enhancing social welfare? Neither. Should risk retention requirement be complemented by information disclosure requirement? Not necessarily. It complements the former when investors are relatively risk averse. 28 / 30

45 : Back to the Questions Whether the flat rate of risk retention requirement is soundly-founded? It is impossible for a flat rate retention ratio requirement to be optimal for all markets. How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Only information disclosure requirement can. Protecting investors? Both. Enhancing social welfare? Neither. Should risk retention requirement be complemented by information disclosure requirement? Not necessarily. It complements the former when investors are relatively risk averse. 28 / 30

46 : Back to the Questions Whether the flat rate of risk retention requirement is soundly-founded? It is impossible for a flat rate retention ratio requirement to be optimal for all markets. How to theoretically rationalize the risk retention requirement? Reducing asymmetric information? Only information disclosure requirement can. Protecting investors? Both. Enhancing social welfare? Neither. Should risk retention requirement be complemented by information disclosure requirement? Not necessarily. It complements the former when investors are relatively risk averse. 28 / 30

47 Future Directions Research Motivation Modelling securitization process, especially tranching. Form of retention. Risk retention regulation and double-sided moral hazard. 29 / 30

48 Future Directions Research Motivation Modelling securitization process, especially tranching. Form of retention. Risk retention regulation and double-sided moral hazard. 29 / 30

49 Thank You! 30 / 30