GRADUATE SCHOOL OF BUSINESS Global Risk Management: A Quantitative Guide. Securitization. Ren-Raw Chen Fordham University

Transcription

1 GRADUATE SCHOOL OF BUSINESS Global Risk Management: A Quantitative Guide Securitization Ren-Raw Chen Fordham University

2 Introduction What To make a large asset transactable How divisibility 細小化 standardization 規格化 liquidity 流動性 Why shift risk reduce risk (diversification) 2

3 Introduction Who Mortgage backed securities Credit derivatives When After WW2 GNMA, FNMA, FHLMC Where United States 3

4 Introduction Classification Mortgages Financial loans Old fashion (not really satisfies 3 hows) leasing asset swaps Modern investment banks 4

5 Mortgage backed securities Origin Passthroughs Ginnie Mae guaranteed the first mortgage passthrough security of an approved lender in In 1971, Freddie Mac issued its first mortgage pass-through, called a participation certificate, composed primarily of private mortgages. In 1981, Fannie Mae issued its first mortgage pass-through, called a mortgage-backed security. 5

6 Mortgage backed securities Origin CMOs first created in 1983 by the investment banks Salomon Brothers and First Boston for the U.S. mortgage liquidity provider Freddie Mac. 6

7 Mortgage backed securities Issuer agency vs. non-agency Property Residential (RMBS) vs. Commercial (CMBS) Credit quality Prime vs. Alt-A vs. Sub-prime Slicing (partition) PT vs. CMO (vs. IO/PO) vs. other types (MBB) 7

8 Mortgage backed securities Banks no longer suffer mis-matched risks Banks make servicing fees Banks can grow in size FRM (fixed rate mortgage) becomes possible affordable mortgage American dream 8

9 Mortgage backed securities Mortgage securitization complete capital markets Investors decide mortgage rates MBS stocks RE Treasury CAPM 9

10 Mortgage backed securities Agencies provide credit guarantees charge a fee guaranteed by the U.S. government no more, FNMA and FHLMC are private but bailed out in 2008 not sure what they are! investors worry no default risk 10

11 RMBS underwriting process mortgages banks GNMA dealers individuals primary market underwriting secondary market 11

12 Mortgage pool 1 - $ $ $13.42 mil $13.42 mil $ $13.42 mil 12

13 Partition (slicing) $13.42 mil $13.42 mil $13.42 mil 13

14 Mortgage backed securities RMBS suffers no default risk (agencies) non-agency RMBS do suffer default risk but suffer prepayment risk lower rates, faster prepayment -> investors lose interest income higher rates, slower prepayment Causes of prepayement economical: refinance non-economical: divorce/marriage, new child, relocation (jobs), etc. 14

15 Mortgage backed securities Prepayment models between 0~1 tangent function (90-degree rotation) S curve (response function) logit/probit function economic modeling (Andrew-Davidson) 15

16 Mortgage backed securities To qualify for prime mortgage: LTV (loan-to-value ratio) < 0.8 PI (payment-income ratio) < 1/3 FICO > 620 ( ) etc. Fair, Isaac, and Company in

17 Mortgage backed securities Alt-A and subprime residential mortgages default risk non-agency small percentage (4% before crisis, 10~15% during crisis) Mortgage size $13.58 trillion unknown: unknown: reserve.gov/econr reserve.gov/econr esdata/releases/ esdata/releases/ mortoutstand/curr mortoutstand/curr ent.htm ent.htm $543 billion before crisis and $1~2 trillion after crisis S&L crisis $402~407 billion in 1995 (like $754 billion in 2008) 17

18 Mortgage backed securities CMBS is different non-agency default risk no prepayment risk (prepayment penalty, known as maintenance yield) examples: casinos, hotels, rentals, shopping centers, parking lots, auto floorspace, etc. 18

19 Mortgage backed securities Finally there is ABS credit card loans, home equity (HE) loans, auto loans, student loans (Sallie Mae - Student Loan Marketing Association), agriculture loans (Farmer Mac - Federal Agricultural Mortgage Corporation) 19

20 Collateral mortgage obligation An important type of MBS Waterfall Give birth to CDO 20

21 Collateral Debt Obligation (CDO) 21

22 Collateral Debt Obligation (CDO) Types cash CDO (real bonds) synthetic CDO (CDS) by action cash-flow CDO (boxed) market-value CDO (non-boxed) by sponsor arbitrage CDO (active) balance-sheet CDO (passive) 22

23 Collateral Debt Obligation (CDO) 23

24 Collateral Debt Obligation (CDO) CDX a CDX CDO is a CDO with 125 credit default swaps (8% each) with US$10 million notional 0-3%, 3-7%, 7-10%, 10-15%, and 15-30%. very liquid (more liquid than single name CDS) 24

25 Collateral Debt Obligation (CDO) Waterfall Tranche loss Equity tranche Senior tranche Mezzanine tranche K0 K1 K2 K3 Total loss 25

26 Synthetic CDO Risky bond + CDS = risk-free bond hence, risky bond = risk-free bond - CDS i.e. risky bond = long risk-free bond and short CDS (provide protection) e.g. $100 mil risky bonds = $100 mil Treasury and $100 mil CDS (which has no value) Treasury is collateral if no collateral, then no treasury 26

27 default Synthetic CDO CDS CDS CDS POOL A BB ZZ $1,250 million $1,250 million 27

28 $4 million WDFA $1,250 million $6 million LOSS 28

29 Synthetic CDO Sizing key to securitization size of tranches = size of pool cash flows from tranches = cash flows to CDS pool match market spreads, for example AAA 20bps, AA 50 bps, A 80 bps, BBB 120 bps, etc. each tranche is given a size, a rating, and a spread 29

30 Collateral Debt Obligation (CDO) Copula (how to correlate defaults) Gaussian copula (solve the dependency problem) Key equations x = ρwˆ + 1 ρwˆ i M i ( ) ( ρ ρ ) pˆ = Pr x < K W = f = Pr f+ 1 W < K if i i M i i = = = N ρf Ki Pr( Wi< 1 ρ ) Ki ρf N( 1 ρ ) 1 N ( pˆ i) ρf ( 1 ρ ) 30

31 31 Loss distribution Fourier inversion Recursive algorithm Collateral Debt Obligation (CDO) prob(rho=0) Loss prob(rho=0.5) Loss prob(rho=0.9) Loss

32 Collateral Debt Obligation (CDO) Problems with such a loss distribution thin tranches (100 tranche CDO) CDO^2, CDO^3,... mezzanine tranches difficult to price 32

33 Collateral Debt Obligation (CDO) Tranche loss/spread plots here 33

34 Collateral Debt Obligation (CDO) A Cat analogy Cats have nine lives (JPM) 34

35 Crisis and securitization Securitization caused crisis Off-balancesheet transactions: swaps (IRS/CDS) Over-leverage Securitization is a solution to relieve capital 35

36 Crisis and securitization Goldman Sachs 2014 BS 9.67% equity Cash And Cash Equivalents 237,254,000 0% Net Receivables 123,417, % Other Assets 22,599,000 4% Long Term Investments 472,970,000 4% Total Assets 856,240, % Total Liabilities 773,443, % Total Stockholder Equity 82,797, % Cash And Cash Equivalents 237,254,000 0% Net Receivables 123,417, % Other Assets 22,599,000 4% Long Term Investments 472,970,000 4% Total Assets 856,240, % Total Liabilities 773,443, % Total Stockholder Equity 82,797, % To reach 15% ROE Total Assets 856,240, % Total Liabilities 802,256, % 93.70% Total Stockholder Equity 53,983, % 7.30% Total Assets 856,240, % Total Liabilities 883,112, % 97.30% Total Stockholder Equity 53,983, % 2.70% 36

37 Securitization in China China s bond market - world s largest Yet not liquid U.S. fixed income markets Treasuries ($16 trillion), residential mortgages ($15 trillion), corporate debts (?? $40 trillion), bank loans (??) IRS $500 trillion CDS $30+ trillion Other swaps (asset swaps, index swaps, TRS, etc.) 37

38 Securitization How Cash flow projection Cash flow matching Market valuation of assets If not then model valuation Optimization Hopefully 1-1>0 38

39 Extreme Liquidity Cases Lehman $4 on Friday, bankruptcy on Sunday Summer trouble started Prior to Labor day talked to KDB Tuesday (9/9) stock fell 45% Thursday (9/11) JPM demanded $3 bn Starr-Merrill Deal (7 out of $1) Buffett buying GS $115 39

40 Extreme Liquidity Cases Bear March 14, 2008: Bailout talk began, stock at $30 March 16: $2 March 17: $10 AIG Wachovia Morgan Stanley 40

41 Value of liquidity If you have to provide liquidity, how much do you charge? Value of liquidity liquidity quantification Liquidity gap management (A vs. A*) 41

42 Basic Ideas Gamma analogy Perfect liquidity = delta hedging Example: ATM option near maturity Lose money Always sells when price is low (b/c delta is low) Always buys when price is high (b/c delta is high) Money lost = liquidity premium Higher gamma securities ~ higher liquidity risk 42

43 Basic Ideas Demand/Supply squeeze Liquidity is option Theoretical framework Illiquid price is liquid price +/- an option An example Equilibrium pricing An example CAPM for the utility 43

44 Liquidity and Term Structure Italy 44

45 Liquidity and Term Structure Spain 45

46 Liquidity and Term Structure Greece 46

47 Application 2: Pricing Illiquid Assets Liquidity Default (Going Concern) Enough liquid assets to pay for imminent cash obligation, K1 A* > K1 Economic Default (Geske/Leland) Negative equity I.e., Any time a firm can issue equity A > Sum of all debts E > K1 (Geske) 47

48 Application 2: Pricing Illiquid Assets Under illiquidity Assets are LVA, 0 or partial liquidity (m) LVA = cash + a*mvfa as MVE drops, m drops, a drops (MVFA fixed) Q1 represents liquidity-tampered economic PD 48

49 Application 2: Pricing Illiquid Assets Chen model for liquidity discount risk aversion market information (vols, prices, etc.) Geske model for corporate finance based upon Black-Scholes-Merton multiple debts 49

50 Application 2: Pricing Illiquid Assets 50

51 Application 2: Pricing Illiquid Assets 51

52 Application 2: Pricing Illiquid Assets In March, Market Cap = $20.75 Billion Market Value of Assets = $115 Billion Default probability high Assume an equity infusion that increases cash by a like amount - assets increases assets but no increase in debt Lehman needs to raise equity nearly equal to 30% of its assets to reduce default probability below 10% 52

53 Application 2: Pricing Illiquid Assets Lehman actions Lehman raised $4 billion in April and $6 billion in June Volatility fell from over 150% to 90% to under 55% during this period of time Default probabilities fell as well during this period, however, clearly it was not enough Both volatility and default probabilities spiked again in July and August just prior to Lehman s bankruptcy filing 53

54 Application 2: Pricing Illiquid Assets In order to decrease the risk of default much larger amounts of capital would have been needed Raising capital is only one tool [albeit an important one] 54

55 Application 2: Pricing Illiquid Assets Data Comprehensive corporate debt dataset from FactSet Once a month from 12/07 to 08/08 Filter the data by issue date and redemption date to get all outstanding debt as of specified day At any given time Lehman had several thousand different bond issues outstanding Stock information price and volatility 55

56 Application 2: Pricing Illiquid Assets Lehman asset values (liq vs. ill.) A0 A0* /2/2004 3/2/2004 5/2/2004 7/2/2004 9/2/ /2/2004 1/2/2005 3/2/2005 5/2/2005 7/2/2005 9/2/ /2/2005 1/2/2006 3/2/2006 5/2/2006 7/2/2006 9/2/ /2/2006 1/2/2007 3/2/2007 5/2/2007 7/2/2007 9/2/ /2/2007 1/2/2008 3/2/2008 5/2/2008 7/2/

57 Application 2: Pricing Illiquid Assets The failure of Lehman Brothers represents a major inflection point in the financial crisis and an instance where our model would have been particularly useful Excessive leverage Uncertainty about asset values Passive in recapitalizing Lax regulatory requirements 57

58 Application 2: Pricing Illiquid Assets Regulator Reduces default probability If insufficient capital is raised, firm has an incentive to increase the volatility of assets to increase value of equity Increase volatility increases default risk BOTTOM LINE: Regulators have to target both volatility and capital ratio in order to reduce default risk 58

59 Application 2: Pricing Illiquid Assets Conclusion A fully-endogenous structural credit risk model can be used for determining the capital adequacy of financial institutions Can accommodate complex capital structures Especially useful during rapidly changing market conditions, i.e. in a financial crisis 59

60 Application 2: Pricing Illiquid Assets Conclusion Debt is serviced by issuing new equity For a maximum acceptable default probability we can solve for the minimum amount of equity that the financial institution would have to raise 60

61 Application 2: Pricing Illiquid Assets Lehman unaffected 61

62 Application 2: Pricing Illiquid Assets Lehman like 62 62

63 Application 2: Pricing Illiquid Assets Lehman spillover 63

64 Application 2: Pricing Illiquid Assets FHLMC and FNMA 64

65 Application 3: Liquidity Index Banks Liquidity Discount Ratio Index (All Banks) monthly data from Jan mkt_weight eql_weight median discount ratio Liquidity Discount Ratio Index (US Commercial Banks) monthly data from Jan mkt_weight eql_weight median discount ratio 1.2 Liquidity Discount Ratio Index (Non-US Commercial Banks) monthly data from Jan mkt_weight eql_weight median discount ratio

66 Application 3: Liquidity Index Banks 1.2 Liquidity Discount Ratio Index (Eastern-US Commercial Banks) monthly data from Jan mkt_wei eql_weig median discount ratio Liquidity Discount Ratio Index (Southern-US Commercial Banks) monthly data from Jan mkt_weight eql_weight median discount ratio Liquidity Discount Ratio Index (Western-US Commercial Banks) monthly data from Jan mkt_weight eql_weight median discount ratio

67 Application 3: Liquidity Index Banks 1.2 Liquidity Discount Ratio Index (Commercial Banks Central US) monthly data from Jan mkt_weight eql_weight median discount ratio Liquidity Discount Ratio Index (Regional Non-US Banks) monthly data from Jan mkt_weight eql_weight median discount ratio Liquidity Discount Ratio Index (Super Regional Banks US) monthly data from Jan mkt_weight eql_weight median discount ratio

68 Application 3: Liquidity Index Banks Liquidity Discount Ratio Index (Mortgage Banks) monthly data from Jan mkt_ eql_w medi discount ratio Liquidity Discount Ratio Index (Fiduciary Banks) monthly data from Jan mkt_weight eql_weight median discount ratio Liquidity Discount Ratio Index (Diversified Banks) monthly data from Jan mkt_weight eql_weight median discount ratio

69 Application 3: Liquidity Index Use the models to build a risk metric for liquidity risk Help decide if a portfolio is liquid (trading book) or not (banking book) Existing Indices Chordia, Roll and Subrahmanyam (2001), Hasbrouck and Seppi (2001), Amihud (2002), Jones (2002), Huberman and Halka (2001) 69

70 Application 3: Liquidity Index Use leverage Use volume Use credit spreads Use bid-offer A ratio between 0 and 1 70

71 Application 4: Systemic risk Many ways to generate high correlation Jumps common factor etc. Liquidity-driven correlation good measure for systemic risk good driver for stress tests good for a liquidity barometer 71

72 Application 4: Systemic risk Liquidity like a common factor but non-linear better capture large swings endogenous (less ad-hoc) better capture feedback effects stable (part of structure) better than regressions nice link to the theory put option premium easier to model 72

73 Application 4: Systemic risk A simple model for liquidity squeeze K is related to convexity (liquidity risk). When K is high, risk is high. x = X P; y = Y Q; X Y K Sigma P_X, P_K Q_Y, Q_K Price

74 Application 4: Systemic risk Liquidity-constrained correlation vs. unconstrained correlation 2 2 X Y XY PX QY PQ K KσKK cov[ dxdy, ] = σ σ ρ (1 )(1 ) XX PX PKσKK var[ dx] = σ (1 ) Y Y KσK var[ dy] = σy (1 Q ) + Q K cov[ dxdy, ] corr[ dxdy, ] = = a+ bρ var[ dx]var[ dy] 74

75 Application 4: Systemic risk K from 0 ~ 200 (small to large)

76 Application 4: Systemic risk Vol from 0.1 ~ 4 (small to large)

77 Application 4: Systemic risk K-sigma from 0.1 ~ 4 (small to large)

78 Application 5: Stress Testing Define scenarios historical historically worst in a defined period hypothetical stress parameters ideal stress economic variables, such as liquidity 78

79 Application 5: Stress Testing Price-volume K is related to quantity. When K is high, quantity is low. P/ Q is more severe under liquidity squeeze Price Illiquid PQ Liquid PQ 0 Quantity

80 Application 5: Stress Testing Example: Morgan Stanley Volume Price 80 7/1/2013 5/4/1999 3/1/2000 1/2/ /1/2001 9/3/2002 7/1/2003 5/3/2004 3/1/2005 1/3/ /1/2006 9/4/2007 7/1/2008 5/1/2009 3/1/2010 1/3/ /1/2011 9/4/2012

81 Application 5: Stress Testing Drop in Modelimplied Asset Value Drop in Equity Value Modelimplied Spread Quantity discount Name AIG 1.02% 21.66% 1.50% 48.04% ALL 1.02% 17.52% 1.50% 48.04% AXP 1.02% 22.99% 1.50% 48.04% BAC 3.62% 65.01% 6.04% 64.81% BBT 1.02% 27.87% 1.50% 52.64% BK 1.02% 26.03% 1.50% 52.64% BRK.A 1.02% 16.71% 1.50% 48.04% C 3.22% 59.25% 4.86% 63.53% COF 1.02% 25.93% 1.50% 52.64% FITB 1.02% 23.77% 1.50% 48.04% GNW 3.88% 38.59% 3.81% 56.59% GS 1.03% 26.08% 1.51% 52.64% PFG 1.02% 18.40% 1.50% 48.04% PNC 1.02% 28.32% 1.50% 52.64% PRU 1.08% 28.95% 1.58% 52.64% SLM 21.82% 97.46% 12.86% 65.35% STI 1.04% 28.48% 1.53% 52.64% STT 1.03% 29.68% 1.51% 52.64% TRV 1.02% 16.56% 1.50% 48.04% USB 1.02% 22.78% 1.50% 48.04% 81

82 Application 5: Stress Testing Decrease in volume when market liquidity dries up estimate the loss of value to reach $820 billion part of this loss is due to price drop and the remaining part of it (quantity drop) is the amount of wealth gets transferred out of the equity market and flown to the Treasuries market, known as fly to quality. This value is estimated to be $650 billion, which is half of the pre-crashed market value. 82

83 Application 6: Cap.Str.Arb. CDX vs. SPY Duration neutral and play on convexity 83

84 Appendix Services/Banking---Capital-Markets/Basel-III- liquidity-requirements-and-implications--- Regulatory-rules-operational-and-strategicimplications ers/2010/sr1006a1.pdf d=