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B40.3312 Policymaking in Financial Institutions Professor A. Sinan Cebenoyan NYU-Stern-Finance Copyright 1999-A. S. Cebenoyan 1 Credit Risk • “ …we are moving into a financial world where credit has no guardian.” Henry Kaufman, Stern Opportunity, 11/9/98 Copyright 1999-A. S. Cebenoyan 2 •Measurement of credit Risk: •Pricing of loans •credit rationing •Japanese FI’s overconcentration in real estate and in Asia •bad loans of 20 trillion yen in 1998 •Japanese Life insurers exposed to these banks by about 14 trillion Yen in loans Copyright 1999-A. S. Cebenoyan 3 • C & I Loans •Different size and maturities •Secured or unsecured •Fixed or floating •Spot Loans or Loan Commitments •Commercial paper (large corporations, directly or via investment banker, sidestepping banks, lower rates) •Real Estate Loans •various features Copyright 1999-A. S. Cebenoyan 4 •Individual (Consumer) Loans •Revolving loans •High default rates (3-7 %, update the book) •Return on a Loan •Interest rate •fees •credit risk premium •collateral •nonprice terms (compensating balances, reserve requirements) Copyright 1999-A. S. Cebenoyan 5 •Prime Rate most commonly used for longer-term loans, fed-funds for shorter term •LIBOR The gross return on loan, k, per dollar lent is f ( L m) 1 k 1 1 [b(1 R)] Numerator is fees plus interest…promised cash flows Denominator is net outflow from the bank Copyright 1999-A. S. Cebenoyan 6 •Expected return on the Loan •Default risk E(r ) p(1 k ) Retail versus Wholesale Credit decisions •Retail •Accept-Reject decisions •credit rationing…….quantity restrictions rather than price or interest rate differences Copyright 1999-A. S. Cebenoyan 7 •Wholesale •Interest rate and credit quantity used to control credit risk •Prime plus a markup for riskier borrowers, BUT •Higher rates don’t necessarily imply higher return Measurement of Credit Risk •Need to measure probability of default •Information •Covenants Copyright 1999-A. S. Cebenoyan 8 Default Risk Models Three Broad Groups, Qualitative, Credit-Scoring, Newer Models •Qualitative Models (Expert systems) •Lack of public information leads to assembly of : •Borrower Specific information •Reputation, Long-term relationship, implicit contract •Leverage, or capital structure (D/E), threshold beyond which probability of default increases •Volatility of earnings (stable v.s. high-tech) •Collateral •Market Specific Factors (Business cycle, Interest rates) Copyright 1999-A. S. Cebenoyan 9 •Credit Scoring Models either calculate default probabilities or sort borrowers into different risk classes, Thus: •Numerically establish the factors that explain default risk •Evaluate the relative importance of these factors •Improve pricing of default risk •Better screening of bad loan applicants •better position to calculate reserves needed to meet expected future loan losses •Linear Probability Model n Z i j 1 j X ij error Copyright 1999-A. S. Cebenoyan 10 Example: Suppose there were two factors influencing the past default behavior of borrowers: the leverage or D/E and the sales/assets ratio (S/A). Based on past default (repayment) experience, the linear probability model is estimated as: Z i .5( D / E ) i .1( S / A) i Assume a prospective borrower has a D/E=.3, and a S/A=2.0, its expected probability of default (Zi ) can then be estimated as: Z i .5(.3) .1(2.0) .35 Also, E ( Z i ) (1 pi ) P is repayment probability Copyright 1999-A. S. Cebenoyan 11 Problem is probabilities can lie outside of 0 to 1. Logit Model fixes this by: 1 F (Z i ) 1 e Zi The left hand side is the logistically transformed value of Zi The Probit Model is an extension of Logit which considers a cumulative normal distribution rather than a logistic function. •Linear Discriminant Models •Altman’s (of NYU) Z-score, uses various financial ratios in classifying borrowers into high and low default risk classes: Z 1.2 X 1 1.4 X 2 3.3 X 3 0.6 X 4 1.0 X 5 Where, X1=WC/TA, X2=RE/TA, X3=EBIT/TA, X4=MVEq./BVLtd, and X5=Sales/TA, Low Z means high risk Copyright 1999-A. S. Cebenoyan 12 Altman’s Z has a switching point at 1.81. Problems: •Only two extreme cases discussed •Are the coefficients stable over time? •Are the ratios relevant over time? •Qualitative factors ignored •Lack of data Newer Models •Term Structure Derivation We extract implied default probabilities on loans or bonds using the spreads between risk-free discount Treasury bonds and discount bonds issued by corporations of different risks Copyright 1999-A. S. Cebenoyan 13 Probability of default on one-period Debt Instrument Assume risk-neutrality, and that the FI would be indifferent between the corporate and the Treasury of same maturity discount bonds: p(1+k) = (1+i) p = (1+i) / (1+k) with i = 10% and k = 15.8% p = (1.1) / (1.158) = .95 probability of repayment thus, 5% is the implied probability of default given the market rates, a 5.8% risk premium ( F ) goes along with it. F = k - i = 5.8% If all is not lost at default, if g is the proportion of the loan that can be collected, then g(1+k)(1-p) + p(1+k) = 1 + i the first term is the payoff to the FI if default occurs. Copyright 1999-A. S. Cebenoyan 14 The fact that there will be partial recovery reduces F (1 i ) 1 i g k i F (1 i ) (g p pg ) or p 1 k 1 g With i= 10%, and p=.95, and g=.9, risk premium F = 0.6 Mortality rate derivation of credit risk Focus on historic default risk experience. Substitute mortality rates for default rates. MMR1= Ratio of total value of bonds of a certain grade defaulting in year 1 of issue TO total value of same bonds outstanding in year1 of issue MMR2= Ratio of year 2 defaults TO total value of survivors in year2 Problems : backward-looking, period-sensitive, volume and size sensitive. Copyright 1999-A. S. Cebenoyan 15 RAROC Models Risk-adjusted return on capital, RAROC, is the ratio of loan income to loan risk. A loan is approved if RAROC exceeds a FI established benchmark rate (cost of capital) Estimating loan risk is possible using a Duration-type approach L R DL L 1 R R L DL L ( R) 1 Replacing interest-rate shocks with credit quality shocks R Max[( Ri RG ) 0] Do example in book, pages 207-209. Copyright 1999-A. S. Cebenoyan 16 Credit Risk Continued • Option Models of Default Risk • Borrower always holds a valuable default or repayment option. If things go well repayment takes place, borrower pays interest and principal keeps the remaining upside, If things go bad, limited liability allows the borrower to default and walk away losing his/her equity. • KMV corporation (www.kmv.com) has developed a model called Expected Default risk Frequency EDF used now by largest US banks. Copyright 1999-A. S. Cebenoyan 17 Payoff to stockholders Assets 0 A1 B A2 -S This is the borrower’s payoff function, s is the size of the initial equity investment, B is the value of Bonds, and A is the market value of the assets of the firm. Copyright 1999-A. S. Cebenoyan 18 Payoff to debt holders A1 B A2 Assets The payoffs to the bond holders are limited to the amount lent B at best. Copyright 1999-A. S. Cebenoyan 19 Merton’s model: F ( ) Be i [(1 / d ) N (h1 ) N ( h2 )] where T t i d borrower' s leverage ratio ( Be / A) h1 [1 / 2 ln(d )] / 2 h2 [1 / 2 ln(d )] / 2 N ( h) probability of deviation exceeding h 2 asset risk of borrower We can get the equilibriu m default risk premium k ( ) i ( 1 / ) ln[ N ( h2 ) (1 / d ) N (h1 )] k ( ) Required yield on risky debt Copyright 1999-A. S. Cebenoyan 20 On the last equation variance and leverage ratio would affect the risk premium. But NOTICE that the key variables are A, market value of assets, and asset risk 2 Neither of which are directly observable. An Option Model Example is given on page 212. The KMV model uses the OPM to extract the implied market value of assets (A), and the asset volatility of a given firm. This is done by viewing equity as a call-option on the firm’s assets and the volatility of a firm’s equity value will reflect the leverage adjusted volatility of its underlying assets. We have in general form: E f ( A, , B , i , ) and E g ( ) Where, the bars (-) denote variables that are directly observable. Since we have 2 equations with 2 unknowns (A,), we can solve.. Copyright 1999-A. S. Cebenoyan 21 The following is a graph that depicts the superior accuracy of KMV-EDF over agency ratings in capturing expected default probabilities. Source KMV Corp. Copyright 1999-A. S. Cebenoyan 22 Loan Portfolio Risk • We move beyond default risk measurements to more aggregate contexts, i.e. portfolios. • I will focus on two models that are not treated in detail in the current edition of the Saunders book. – A simple model : Migration Analysis – A more sophisticated model: KMV Corporation’s “Portfolio Manager Model” Copyright 1999-A. S. Cebenoyan 23 Migration Analysis • A Loan Migration Matrix measures the probability of a loan being upgraded, downgraded, or defaulting over some period. Historic data is used, as such it can be used as a benchmark against which the credit migration patterns of any new pool of loans can be compared. • In a Loan migration matrix the cells are made up of transition probabilities. • The number of grades are generally around 10 for most FI’s. Copyright 1999-A. S. Cebenoyan 24 A Hypothetical Rating Transition Matrix: Risk Grade at end of year 1 2 3 D=Default Risk Grade 1 0.85 0.1 0.04 0.01 at beginning 2 0.12 0.83 0.03 0.02 of year 3 0.03 0.13 0.8 0.04 If the FI is evaluating the credit risk of of grade 2 rated borrowers, and observes that over the last few years a much higher %, say 5%, have been downgraded to3, and 3.5% have defaulted, the FI may then seek to restrict its supply of lower quality loans (grades 2 and 3), concentrating more on grade 1. At the very least it should seek higher credit risk premiums on lower quality loans. Migration ana- lysis is used on commercial, credit card, and consumer loan portfolios. Copyright 1999-A. S. Cebenoyan 25 KMV Portfolio Manager Model • KMV Portfolio Manager is a model that applies Modern Portfolio Theory to the loan portfolio. To estimate an efficient frontier for loans as in the above figure, and the proportions (Xi), we need to measure : Copyright 1999-A. S. Cebenoyan 26 •Expected return on a loan to borrower i, (Ri) •The risk of a loan to borrower i, (i) •The correlation of default risks between loans to borrowers i and j KMV measures each of the above as follows: Return on the Loan: Ri AISi E( Li ) AISi [ EDFi LGDi ] Where, AIS = annual ‘all-in-spread’ on a loan = (Annual Fees earned) + (Loan rate - Cost of Funds) E(L) = expected loss on the loan EDF = expected default frequency LGD = loss given default Copyright 1999-A. S. Cebenoyan 27 Risk of the Loan: i ULi Di LGDi EDFi (1 EDFi ) LGDi The Unexpected Loss (UL) is a measure of loan risk, i. It reflects the volatility of the loan’s default rate, Di, times LGD. To measure Di we assume loans either default or repay (no default), then defaults are binomially distributed, then the of the default rate for the ith borrower Di, is equal to the square root of the probability of default times one minus the probability of default, as above with EDF, (1-EDF). Correlation : ij Correlation between the systematic return components of the equity returns of borrower i and j. Generally low. A number of large banks are using this model or variants to actively manage their loan portfolios. Some are reluctant especially if involving long-term customers. Diversification versus Reputation. Copyright 1999-A. S. Cebenoyan 28 Sovereign Risk • Large Exposure Japan US Britain France Germany Other Foreign banks’ share of total Asian debt at the end of June 1997 (excluding Singapore and Hong Kong. Source BIS) Copyright 1999-A. S. Cebenoyan 29 •Prior to July 97 Thai crisis, Foreign banks had $389 billion in loans and other debt outstanding. See slide on page 29. •This crisis is still unfolding •Bailouts and loan restructuring packages (South Korea $57 billion IMF organized loan package) •Credit Risk •Sovereign Risk should dominate •Repudiation (common before WWII) bonds •Rescheduling (common since WWII) bank loans •Relatively small number of banks (1/98 South Korea loans just over 100 banks involved) Copyright 1999-A. S. Cebenoyan 30 •Same group of banks involved •Cross-default provisions •Governments view social costs of default on international bonds less worrisome than on loans. Possible incentive problems? Read Handout. Country Risk Evaluation •Outside Evaluation Models •Euromoney Index •Institutional Investor Index •Internal Evaluation Models •Similar to our Credit-risk scoring models based on explaining probability of a country rescheduling, like Z-scores Copyright 1999-A. S. Cebenoyan 31 Common variables in CRA: •Debt Service ratio=(interest+amortization on debt)/Exports positive relation with probability of rescheduling •Import Ratio=(Total imports/Total FX reserves) positive relation •Investment Ratio= Real Investment/GNP +/- relation, arguments on both sides •Variance of Export Revenue= ER 2 + relation •Domestic Money Supply Growth= M / M + relation Copyright 1999-A. S. Cebenoyan 32 Problems •Measurement •Population groups (a finer distinction than rescheduler or not) •Political risk factors •Portfolio aspects (systematic risk more important) •Incentive Aspects (Benefits and Costs) Read section •Stability (of variables) Use of Secondary market for LDC Debt to measure risk •The structure of the market •Brady Bonds ($ loans exchanged for $ bonds-US Treasury bonds are used to collateralize the bonds). •Sovereign Bonds. No US-Tbonds used as collateral Copyright 1999-A. S. Cebenoyan 33 •Performing Loans •Non-performing loans LDC Market Prices and CRA Regression analysis of price changes to key variables. LHS= periodic changes in prices of LDC debt in the secondary markets, RHS= set of key variables. Once the parameters are estimated, FI can combine these with forecasts of key variables to estimate price changes. Has problems but hopefully reduces errors. Copyright 1999-A. S. Cebenoyan 34 Dealing with Sovereign Risk Exposure •Debt-Equity Swaps (Industries like motor, tourism, chemicals have been desirable fo outside investors.) FI may sell $100 million loan to a company for $93, Company negotiates with foreign gov. And swaps $100 million for $95 million worth equity in local currency. Company has $2million buffer, country gets rid of US$ debt, company has to invest in local markets in local currency. •MYRA (Multiyear Restructuring Agreements) •concessionality: The amount the bank gives up in present value terms as a result of a MYRA. example:From appandix of chapter. •Loan sales •Debt for Debt Swaps (Brady Bonds) Copyright 1999-A. S. Cebenoyan 35 Capital Adequacy • Functions of capital – To absorb unanticipated losses with enough margin to inspire confidence and enable the FI to continue as a going concern – To protect uninsured depositors, bondholders, and creditors in the event of insolvency and liquidation – To protect the FI insurance funds and the taxpayers – To acquire the plant and other real investments necessary to provide financial services Copyright 1999-A. S. Cebenoyan 36 The Cost of Equity Capital D1 D2 D P ... (1 k ) 0 (1 k ) (1 k ) 2 If dividends are assumed to grow at a known and constant rate g, then D0 (1 g ) P 0 kg The above can be extended to P/E and D/E ratios Capital and Insolvency Risk •Capital •Net Worth a market value accounting concept Copyright 1999-A. S. Cebenoyan 37 The market value of capital and credit risk Simple examples on declines on Loan values and its effects on Net worth can be easily constructed. The larger the FIs net worth, the more protection The market value of capital and Interest Rate risk Example in Table 20-4 FASB Statement No.115, requires securities classified as ‘available for sale’ to be marked to market. Regulators in 12/94 exempted banks. The Book value of capital •Par value of shares •Surplus value of shares Copyright 1999-A. S. Cebenoyan 38 •Retained Earnings •Loan Loss Reserve BV=Par value+Surplus value+Retained Earnings+Loss reserves •Book Value of Capital and Credit Risk (reluctance to recognize losses) •Table 20-6, recognizes partial loss •Book value of capital and Interest rate risk : No change •Discrepancy between MV/BV •Arguments Against MV Accounting •difficult to implement (dubious) •Introduces excessive variability to Net Worth (not all is held to maturity) •Credit Crunch Copyright 1999-A. S. Cebenoyan 39 Actual Capital Rules Two different capital requirements since 1987 •The Capital-Assets ratio (Leverage ratio) •L = (Primary or Core Capital) / Assets Core capital=BV of Common + qualifying cumulative preferred stock + minority interests in equity of consolidated subsidiaries Table 20-7 •Problems: •Market Value (could be massively insolvent) •Asset Risk (not all assets have same credit+int.rate risks) •Off-balance-sheet activities (no capital required) Copyright 1999-A. S. Cebenoyan 40 Risk Based Capital Ratios (to improve on the previous) The following may be changed in the next couple of years. BIS has proposed to remove the 8% requirement and implement capital adequacy guidelines based on ratings (S&P, Moody’s, etc.) Basel Agreement implemented two new risk-based capital ratios Total risk-based cap ratio= Total cap / Risk-adj.assets > 8% where Total capital= Tier I plus Tier II and Tier I (core) cap ratio = Core cap / Risk-adj. Assets > 4% Table 20-8 summarizes Prompt Corrective Action Provisions of FDICIA of 1991. Table 20-9 gives definitions of Tier I and Tier II capital Copyright 1999-A. S. Cebenoyan 41 Calculations will be done in class examples Criticisms of the Risk-based Capital ratio •Risk weights •Balance sheet incentive problems •Portfolio aspects •Bank specialness •All commercial loans have equal weight •Other Risks •Competition Capital requirements for securities firms Net Worth / Assets > 2% Copyright 1999-A. S. Cebenoyan 42 Capital Requirements for Life Insurance Firms NAIC model C1= Asset Risk (Table 19-15) C2= Insurance Risk C3= Interest rate Risk C4= Business risk CBR 4 C 22 C 2 )3C 1C( (Total Surplus and capital) / RBC > 1 Capital requirements for Property-Casualty Insurance Firms Tables 19-16 and 19-17 will be discussed in class examples Copyright 1999-A. S. Cebenoyan 43 Securitization • In 1998 47% of all residential mortgages securitized. • Worldwide value of outstanding securitized issues rapidly approaching $500 billion. • Similar to loan sales, but with creation of securities • Three major types: – Pass-through security – Collateralized Mortgage Obligation (CMO) – Asset-backed security Copyright 1999-A. S. Cebenoyan 44 •The Pass-Through Security Securitization of residential mortgage loans: •GNMA: Ginnie Mae, Government national Mortgage Assoc., split in 1968 from Fannie Mae, directly owned by government. •Sponsors mortgage-backed securities programs of Fis •Acts as guarantor to investors regarding the timely pass- through of principal and interest, i.e. provides timing insurance •GNMA supports only FHA, VA, FMHA insured pools. •FNMA: Fannie Mae 1938, now private , implicit government •FNMA creates MBSs by purchasing mortgage packages from FI’s. finances them thru sale of MBSs to Life insurers and pension funds. Engages in swaps of MBSs with original mortgages. • Unlike GNMA, FNMA securitizes conventional mortgages. •FHLMC: Freddie Mac similar to FNMA but primarily deals with savings banks. Copyright 1999-A. S. Cebenoyan 45 The incentives and mechanics of Pass-through Security Creation •The creation of a GNMA pass-through security •Bank originates 1,000 new $100,000 mortgages, $100 million total size . Each has 30 year maturity, 12 % coupon. FHA insured. Financed by deposits and equity. •Bank faces capital adequacy requirements. Risk adjusted value of residential mortgages is 50% of face value, and the risk-based capital requirement is 8%, bank capital needed to back the mortgage portfolio: Capital requirement= $100 mill. X .5 X .08 =$4 million •Bank also faces reserve requirements of 10%. Needs $96 million in deposits after reserves, and the $4 million in equity capital. Copyright 1999-A. S. Cebenoyan 46 Balance sheet may look like: Assets Liabilities Cash Reserves $10.66 Demand Deposits $106.66 Long-term mortgages 100.00 Capital 4.00 Bank also has to pay insurance premium to FDIC (assuming 27 basis points) $106.66 million X .0027 = $287,982 These amount to 3 levels of regulatory taxes (incentive enough?): 1. Capital requirements 2. Reserve Requirements 3. FDIC insurance premiums. Copyright 1999-A. S. Cebenoyan 47 Two more problems: •Duration mismatch (core DD generally have a duration of less than 3 years, whereas mortgages depending on prepayment assumptions normally have durations of at least 4.5 years) •Illiquidity exposure. May lead mortgage asset fire sales if large unexpected DD withdrawals happen. •Bank can deal with the above by a variety of tools, lengthening durations, swaps, etc.. BUT regulatory burden stays, By contrast: •creating GNMA pass-through securities can largely resolve the duration, and illiquidity risk problems and reduce the burden of regulatory taxes. •Bank packages the loans and places them with a third party, removing them from the B/S. Next gets the GNMA guarantee for a fee, and arranges to service the mortgages for a fee. Copyright 1999-A. S. Cebenoyan 48 The GNMA pass-through securities are issued and sold in the capital markets. These are desirable to investors as they are FHA/VA insured against default by homeowners, and GNMA insured against default by the originating bank or the trustee. The relevant rates: Mortgage coupon rate 12% minus servicing fee 0.44 minus GNMA insurance fee 0.06 equals GNMA pass-through bond coupon 11.50% Barring prepayment, the investor receives a constant stream of monthly payments. Copyright 1999-A. S. Cebenoyan 49 Post-securitization Balance Sheet of the FI: Assets Liabilities Cash reserves $10.66 Demand Deposits $106.66 Cash proceeds from mtge securitization 100.00 Capital 4.00 Dramatic change. Illiquid mortgages replaced by cash. Duration mismatch has been reduced. Regulatory taxes reduced, e.g. capital requirements reduced as cash has 0 risk-adjusted asset value. Reserve requirements and insurance (FDIC) fees will also be reduced if FI retires some DD. More importantly, The FI can generate new mortgages with the new cash and securitize those. Act like a broker. Fee income becomes more important. BUT, prepayment risk may reduce demand for MBSs. Copyright 1999-A. S. Cebenoyan 50 Prepayment Risk Most conventional mortgages are fully amortized: An annuity problem. Given: Size of pool = $100,000,000 Maturity = 30 years (n=30) # of monthly payments = 12 (m=12) r (annual mtge coupon rate) = 12 % R = constant monthly payment To get the monthly payments, we need to solve the following equation for R: Copyright 1999-A. S. Cebenoyan 51 r 1 r 360 100,000,000 R[(1 ) ... (1 ) ] m m 1 1 r mn (1 ) 100,000,000 m R PVAF R r m With our numbers, r= 12%, m=12, n=30, we get R= $1,028,613.00 This amount fully amortizes the loan, thus each R has a different principal and a different interest component. Table 28-3, page 675. Copyright 1999-A. S. Cebenoyan 52 With a 1/2 percent fee (insurance and servicing), the R that is passed through is R = $990,291.00 this assumes no prepayment. Prepayment has 2 major sources: •Refinancing •Housing Turnover Prepayment is a function of the gap spread between mortgage pool rates, and the current mortgage coupon rates. Without prepayments: R1=R2=R3=……….=R360 With prepayments CF1<CF2<CF3…<CF60>CF61>……>CF360 Copyright 1999-A. S. Cebenoyan 53 Prepayment has : • Good News Effects: Lower rates increase present values Lower rates lead to faster principal recovery •Bad News effects: Fewer interest payments, and reinvestment risk •Prepayment Models •WSJ reports Bear Sterns prepayment model based data. Among other thing Weighted Average Life WAL is reported: WAL = [S(time x Expected Principal received)] / Total principal outsd. E.g. Loan with 2 years maturity, $40 year 1, $60 year 2 principal pmts. WAL = 160/100 = 1.6 years. Copyright 1999-A. S. Cebenoyan 54 PSA (public securities association) Model •develops and average rate of prepayment based on past experience. •PSA behavior assumes: 0.2% per annum in the first month, going up by 0.2 % per month for the first 30 months, leveling off at 6% annualized rate for the remaining life of the pool. •A Number of reasons why a specific pass-through may differ from PSA, such as: Age of pool, coupon of pool relative to current coupons, fully amortized R or not, Assumability, Size of pool, Conventional or not, Geographic location, age and jobs of mortgagees. •One approach would be to assume a fixed deviation from PSA, like 150% PSA, 50% PSA.. Other Empirical Models •the better the prepayment model the more the FI makes. Variations on PSA theme. Considering conditional probabilities, burn-out factors. Copyright 1999-A. S. Cebenoyan 55 Option Models: Use Option Pricing theory to figure out the fair yield spread of pass-throughs over securities (Option-adjusted spread, OAS models). PGNMA PTBOND PPREPAYMENTOPTION •The value of a GNMA bond to an investor is equal to the value of a standard noncallable Treasury bond of the same duration minus the value of the mortgage holder’s prepayment call option. •In yield terms: YGNMA YTBOND YOPTION •The investors’ required yield on a GNMA should equal the yield on a similar duration T-bond plus an additional yield for writing the valuable call option. Copyright 1999-A. S. Cebenoyan 56 •How to calculate the value of the OAS on GNMAs •Assume: > Refinancing only reason for prepayment > T-Bond yield curve flat > mortgage coupon rate 10%, principal balance $1 million > mortgages have 3-year maturity, and annual payments > mortgages fully amortized, no servicing fee. > Prepayment only after 3% drop from mortgage coupon rate (10%) > maximum yearly interest rate move is 1% up or down > In any year, CF is either R ($402,114 here), R+repayment of any outstanding principal, or zero if all paid off. We start out with current yields at 9%, GNMA bond sells at a premium. >Cash Flow at end of year 1 is R with certainty, as no prepayment >Cash Flow at end of year 2 is tricky: rates now may have gone down to 7% which is going to trigger prepayment. The probability of that is 25%. So, with 25% chance investor receives R plus Principal balance remaining at end of year 2. Copyright 1999-A. S. Cebenoyan 57 Principal balance remaining at end of year 2 (after 2 payments have been made) is going to be $1,000,000 minus principal paid with first payment and minus principal paid with second payment: principal1 402,114 (.1)1,000,000 302,114 principal2 402,114 (.1)697,886 332325 4 . balance 1,000,000 302,114 332,325.4 365,560.6 Cash Flow received by invest or in year 2 wit h repayment: $402,114 $365,560.6 $767,674.6 T hus expect ed cash flow at end of year 2 will be : CF2 .25($767,674.6) .75($402,114) $493,504.15 Cash Flow at end of year 3 : CF3 .25(0) .75($402,114) $301 585.5 , Copyright 1999-A. S. Cebenoyan 58 Derivation of the option-adjusted spread: E (CF1 ) E (CF2 ) E (CF3 ) P (1 d1 Os ) (1 d 2 Os ) 2 (1 d 3 Os ) 3 assuming d1 d 2 d 3 8% solve for O s 402,114 493,504 301,585.5 1,017,869 (1 .08 Os ) (1 .08 Os ) 2 (1 .08 Os ) 3 Os 0.96% YGNMA YBOND Os 8% 0.96% 8.96% Copyright 1999-A. S. Cebenoyan 59 Collateralized Mortgage Obligations (CMOs): •Uncertainties about the maturities of mortgage pass-throughs make them unattractive to market participants. •CMOs reduce the uncertainty concerning maturity of mortgage- backed security, thereby provides a risk-return pattern not available with typical mortgage pass-through securities. •CMO is a mortgage backed bond issued in multiple classes or tranches. •GNMA bonds placed in a trust (REMIC) as collateral •CMO with 3-17 classes created. Class A, B, C, thru Z. •Value is created, n P i 1 i ,CMO PGNMA Where n=3,…17. Let’s discuss a 3-class CMO : Copyright 1999-A. S. Cebenoyan 60 Investment bank buys $150 million GNMAs and places them in trust as collateral. Issues CMO with A, B, C classes: •Class A: Annual fixed 7% coupon, $50 million size •Class B: ……………..8%…………………………. •Class C:………………9%………………………… •The underlying GNMA may have had 9% coupon, and maybe 25 years to maturity. •The logistics of the CMO: •Each month R is received by the trustee, which distributes Coupons to all classes, and then principal to Class A first, once A is paid off then Class B and so on… Example: R= $2.5 million A gets coupon of [(.07/12)x50 million]=$291,667. B gets coupon of [(.08/12)x50 million]=$333,333. C gets coupon of [(.09/12)x50 million]=$375,000. Interest adds up to $1,000,000. Copyright 1999-A. S. Cebenoyan 61 •Principal payments: •Only Class A gets the $1.5 million left after interest payments. Thus class A now has $48.5 million outstanding. •After Class A is retired B is paid off, and so on. •Most times there is an additional Class Z, which is like a zero but not quite. It starts paying interest and principal only after all preceding classes have been paid off. •There is also a residual R class. This gives the owner the right to any collateral remaining in the trust after all other bond classes have been retired PLUS any reinvestment income earned by the trust. This is a high risk bond. It is also a unique bond: as there is more left in the pool, more will be reinvested, and less will be retired, Thus a higher value at end. But this means negative duration! As interest rates rise value of class R goes up. Very attractive for hedging portfolios. Copyright 1999-A. S. Cebenoyan 62 Mortgage Backed Bond (MBB) Mortgage-backed bonds stay on the Balance sheet. •MBBs have no direct link to the CFs of underlying mortgages, the relationship is one of collateralization . •If the FI fails, MBB bondholders have a first claim to a segment of the FI’s mortgage assets. •FIs back most MBB issues with excess collateral, Thus receiving AAA ratings for the MBB, even when the FI may be rated BBB or lower. The cost is thus lower. •Example: •FI finances $20 million in mortgages with $10 million in uninsured deposits (wholesale, over $100,000), and $10 million in insured deposits (retail, less than$100,000). •Duration of assets greater than leverage adjusted duration of liabilities, and uninsured depositors are worried about interest rate and default risk, requiring high risk premiums. Copyright 1999-A. S. Cebenoyan 63 •Insured depositors are not worried, and are charging next to risk free rate. •Genius strikes!: FI puts up $12 million of its mortgages as collateral backing a $10 million long-term MBB issue. Because of the overcollateralization, MBB will cost less than uninsured deposits. FI uses the MBB to retire the uninsured deposits. •Duration Gap improved, costs reduced. •At the expense of FDIC! The insured depositors are only backed by $8 million in unpledged assets. If FDIC were not there, these depositors would have required high rates for compensation. •FDIC discourages high risk institutions from excessive MBB sales. •Other than regulatory interference, MBB are undesirable as they tie up mortgages on the B/S, increasing the illiquidity of the assets. •FI still liable for reserve requirements and capital adequacy taxes. Copyright 1999-A. S. Cebenoyan 64 IO Strips •A bond whose cash flows reflect the monthly interest payments received from a pool of mortgages. IO IO2 IO360 IO ... 1 P y y 2 y 360 (1 ) (1 ) (1 ) 12 12 12 •Discount effect: As y falls price rises •Prepayment effect: As y falls, more prepayments, value falls. •As interest rates fall below coupon, prepayment starts to dominate and value of the bond falls. Again negative duration. •Thrifts have been buying Ios to hedge their portfolios. •See graphs. Page 697. Copyright 1999-A. S. Cebenoyan 65 PO Strips •A bond with cash flows that reflect the monthly principal payments received from a pool of mortgages. PO1 PO2 PO360 PPO ... y y 2 y 360 (1 ) (1 ) (1 ) 12 12 12 •Discount effect: As y falls, value rises •Prepayment effect: As y falls, more early payoffs, value goes up. •Most other assets can and have been securitized. Copyright 1999-A. S. Cebenoyan 66