Intro SubPrime Crisis

8/7/2019 Intro SubPrime Crisis

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Spring 2010

Lecture Notesfor

Mathematical Methods in Financial Economics

c

Tom Cosimano (Finance) & Alex Himonas (Mathematics)

University of Notre Dame

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Preface

These notes have been designed for Mathematical Methods in Financial Economics (MMFE),which is listed as Math 40570 & 50570 and Fin 40820 & 70820. MMFE is an interdisciplinary coursein that it has been developed by faculty from and is designed for students of different disciplines.We have found in our research that major advances in financial economics can be achieved through

the cooperation across disciplines. The hope is that students will go on to make contributions tofinancial economics. We want the students to interact with other students who are not in the samefield of study. For example, math majors can help business students with their analytic trainingand business majors can help math students with their business knowledge.

This is the third time that the MMFE has been taught. In the previous two times each of ustaught the material in which we specialize. Now we are going to rotate from year to year in whichone of us teaches the course and the other person acts as a facilitator. The facilitator serves as aresource for the class in case a situation arises in which his expertise are needed. Also, this willenhance the interdisciplinary knowledge of both of us.

These notes are written so that all the necessary mathematical background is provided for financeand economics majors, while all the necessary financial information is developed for mathematicsand economics majors. They are subdivided into units which cover a broad range of topics in financeand economics as well as the mathematical methods needed for their quantitative analysis.

The first unit provides an overview of the subprime lending crisis. This unit provides anoverview of the challenges faced by quantitative analysts of financial problems given thatmost people view the financial crisis as an outgrowth of mathematical finance.

A survey of financial instruments which will be analyzed in this course.

How do financial analysts assess risk and investors reaction to it?

The binomial model of derivative pricing and how it leads to the Black-Scholes model.

Estimating the probability of a default by a corporation using the Black-Scholes model.

How do individuals choose portfolios of stocks and bonds?

The determination of the equilibrium price of stocks in a binomial world, including the rela-tionship between equilibrium and no arbitrage price of stocks.

Stochastic calculus.

Derivation of Black-Scholes-Merton option pricing formulas using stochastic calculus and par-

tial differential equations. The equilibrium pricing of stocks and bonds using stochastic calculus.

We benefited from the comments of students who have taken this course in the past. In par-ticular, we would like to thank Marianne Beyer, Conor Bruen, Kyle Dempsey, Curtis Holliman,John Holmes, David Karapetian, Peter Kelly, Katherine Manley, Jonathan Poelhuis, Rachel Sunand Dan Xu for providing detailed comments on earlier drafts of these notes. Finally, we wouldlike to thank Provost Thomas Burish for providing the initial support for the development of thiscourse as part of the Provosts Initiative on Team Teaching.

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1 Introduction: The Subprime Lending Crisis and Quants

In these lectures we will use the Subprime lending crisis to illustrate various ways quantitative ana-lysts, quants, used risk management techniques and financial instruments to increase the availabilityof home mortgages. We also discuss some of the mistakes and fraudulent behavior by quantitativeanalysts which occurred during the Subrime lending crisis. Through this discussion we want to pro-

vide examples as to why managers need to learn about quantitative methods. In addition, we wantto caution quantitative analysts about the possible misuses that can occur with these techniques.

In this overview of the Subprime crisis we will introduce various terms and concepts which youwill become familiar with over the semester. To focus your attention we highlight unresolved issueswhich will be discussed throughout the semester. Also, those terms in bold are defined in theglossary at the end of the chapter.

1.1 Commercial Banking and Mortgage Loans

The core business of a commercial bankis to accept deposits from millions of in-dividuals who have small amounts to save.These funds are then invested in manycompanies and mortgage loans whichare lent to corporations and individuals. Itis the banks fiduciary responsibility tomake sure the borrowers have a reasonablechance of paying back the loan. Thus, themain service provided by a bank is to mon-

itor these borrowers, so that the depositorsdo not lose any of their funds.

Figure 1. Balance Sheet Commercial Banks

Businesses and homeowners usually are going to undertake a project which usually takes a longtime to pay off, such as the building of a factory. As a result, they want long term loans with afixed interest rate. This means that loans are not liquid in that it is not easy to sell the factory orhouse without taking a substantial loss. This makes the banks revenue relatively certain for a longperiod of time. On the other hand the depositors like the flexibility of being able to withdrawaltheir funds whenever they want. This makes the funding from deposits unstable and subject tofluctuation in market interest rates.1 As a result, the bank has liquid liabilities and illiquid assets.

To meet unanticipated deposit withdrawals a prudent bank holds 5% in cash and 14% in marketablesecurities such as U. S. government securities (see the balance sheet for top 508 banks that have

1Since the 1930s the federal government insures small deposits through the Federal Deposit Insurance Corporation(FDIC). In September 2008, the insurance was increased from $100 , 000 to $250, 000 for individual deposit accounts,the insurance now covers all commercial checking accounts. The insurance applied to money market funds forone year, because of concerns raised by the Subprime lending crisis. In particular, depositors of money market fundswithdrew over $400 Billion after the failure of Reserve Market Fund to maintain 100% net asset value for its moneymarket fund. This failure followed large losses by Reserve Market Fund from holding of Lehman Brothers commercialpaper.

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more than $1 Billion).2 As a result, the bank can serve both the needs of the depositors and theborrowers. The bank holds equity to guard against the fluctuation in deposits, as well as possibledefault of some loans. In the balance sheet above we see that the typical commercial bank issues56% of its assets as loans and holds 10% of its assets as equity. Equity is the difference betweenthe banks assets and liabilities. Equity is how much assets would be left over after all the banksliabilities are paid off. This equity is the property of individuals who hold shares of stock in the

bank.

Unresolved Issue 1: How does one calculate the current value of assets? How does one measurethe sensitivity of an asset to changes in interest rates?

In this discussion we will focus on home mortgages, since they are the source of the Supprimelending crisis. The typical home mortgage is for 30 years and has a fixed rate for the term of theloan, 5.09% in January 2010. To qualify as a prime mortgage borrower the home owner puts up

20% of the home value and must have a good credit rating. These mortgages are relatively safe,since the price of a house would have to fall by 20% before it is in the interest of the borrower todeclare bankruptcy. As a result, a prime mortgage goes into default only when the homeownerfaces some difficulty such as unemployment and/or poor heath. In this case the bank has theright to repossess the property in a legal procedure which is called a foreclosure. Even today theforeclosure of prime home mortgages is less than 2% of mortgages per year.

Historical Note: Before 1930 home loans were for a much shorter term, so that the homeownerhad to refinance the mortgage every few years. If banks did not have enough deposits, they wouldnot issue a new loan. In this case the homeowner had to sell the house to pay off the loan. To solve

this problem in 1932 the U.S. government set up Federal Home Loan Banks to insure primehome mortgages, when a bank did not have sufficient funds. In this case FHLB would provide thebank with sufficient funds, when there was a sudden decline in deposits, so that the bank did nothave to force early repayment of the loan by the borrower. As a result, FHLB was designed to helpbanks with the illiquidity of home mortgages. Freddie Mac was a private corporation set up in 1970by U. S. Government to further increase the availability of home mortgages.

Example 1. A Typical Mortgage has a term to maturity of 30 years. Assume a homeownertakes out a $100, 000 mortgage on a house worth $125, 000. At current rates of 5.09% the monthlypayment would be $433.87 for 30 years. In the first month the interest payment is $339.33 and the

payment of principal is $94.54. In the 360th

month the interest payment is $1.83 and the paymentof principal is $430.77.

Exercise 1. Verify these numbers using Math 10260 (Calculus for Business) formulas.

2Data is from FDIC call reports for commercial banks.

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1.2 The Advent of Mortgage Backed Securities

A Savings and Loan Association S&L is a financial corporation that accepts deposits and onlyinvests in home mortgages. As a result of the large increase in interest rates in the late 1970s andearly 1980s many S&Ls went into bankruptcy, since the cost of deposits went up but the revenueon the fixed rate mortgage loans stayed constant.3

Example 2. In December 1971 the 30 year home mortgage rate was 7.48%, while the six monthcertificate of deposit (CD) rate was 4.89%. By December, 1979 the six month CD rate was at13.42%. As a result, S&Ls that issued mortgages in December 1971 made 2 .59% for expenses andprofits per each dollar of mortgages. Yet, by December 1979, the banks were losing 5.49% on the30 year home mortgages which were issued in 1971. They also had to cover their expenses. As aresult, the S&Ls lost substantial amount of equity in 1979. In addition, the CD rate did not dropbelow the 1971 mortgage rate until 1986.4

Figure 2. Balance sheet of SIV Figure 3. Balance sheet of Insurance Company

Based on this experience the commercial banks wanted to reduce the reliance on home mortgages.As a result, quants developed mortgage backed securities. In this case the bank sets up aseparate company called an Structured Investment Vehicle (SIV) to fund the mortgage backedsecurity. Suppose the bank wants to remove $100 million of 1000 mortgages, worth $100, 000 each,from its balance sheet. For a plain vanilla mortgage backed security the bank would enter into acontract with the SIV which promises the interest and principal payment each month for 30 yearsfrom the 1000 mortgages.5 For the typical mortgage in example 1 the payment would be $433, 870per month for 360 months. This promise is recorded as an asset on the balance sheet of the SIV inFigure 2. The SIV would then issue $100 million of mortgage backed security to pay the bank forthe mortgages. The SIV would then sell the MBS to someone with long term liabilities such as aninsurance company. As a result, the MBS becomes an asset of the insurance company in Figure 3.The insurance company pays for the MBS with the proceeds from insurance policies which promisespayments to individuals heir when the policy holder dies. As a result, the insurance company has

3The estimated cost to the U.S. government was $124.6 billion. See Wikipedia (2008).4You can find historical data as in this example at http://research.stlouisfed.org/fred2/ .5MBS can also be structured so that one MBS pays only the interest and another MBS pays only the principal.

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long term assets and liabilities, while the bank ends up with short term assets and liabilities. Toencourage this activity Fannie Mae and Freddie Mac would provide insurance for these mortgagesin case of default by the original borrower.

Why use an SIV? The commercial banks used SIVs to circumvent regulations. Commercial

banks are required to hold at least 6% of their risk adjusted assets as equity which the regulatorscall Tier 1 capital.6 They also must hold at least 10% of their risk adjusted assets in the formof total capital. Total capital is equity plus long term bonds. These long term bonds are calledsubordinated debt.

By setting up an SIV which is legally separated from the bank, the assets of the SIV are notincluded in the assets of the commercial bank. As a result, the bank does not have to hold anyequity to back up the mortgages. This procedure is called moving assets off balance sheet. It turnsout that this was mainly an illusion created for the regulators. When the SIVs created by Citibankas well as other major banks failed because of the decline in MBS prices, these banks recorded thelosses on the MBS as a decline in their equity.

The mortgage backed security provides a useful function. The MBS reduces the risk of boththe banks and the insurance company by reducing the exposure of both companies to fluctuationin interest rates. With less risk the banks charge the homeowner a smaller interest rate, since thebanks do not have to collect as many funds to pay for the fluctuations in market interest rates. Inaddition, the banks can focus on credit evaluation and monitoring of the borrowers, while insurancecompanies specialize in providing insurance. Thus, everyone is made better off from the instrumentdeveloped by the quants.

Unresolved Issue 2: Explain how changes in interest rates can cause bankruptcy when the assetsand liabilities of a financial corporation have different terms to maturity. Why does it make sensefor pension funds and life insurance companies to hold mortgage back security?

1.3 The Development of New Financial Instruments

With MBS the banks role is to originate the loan, monitor the borrowers payments, collect themonthly payments, and distribute these payments to the holder of the MBS. This role for the finan-cial intermediatory is called the Originate-to-distribute model of mortgage financing. Eventu-

ally, companies that specialized in the origination of home mortgages, such as Countrywide, becamethe major providers of home mortgages.

The problem with this business model is that the originator of the loan was paid based on theorigination of the loan.7 Once the loan was sold off as a mortgage backed security, the originatorhad little interest in whether the mortgage was paid off. As a result, the originators started to lessenthe credit standards to qualify for a loan. To fund these riskier mortgages, MBS were developed

6The regulators allow the banks to hold less equity for safer assets, like Treasury Securities, while they have tohold more equity to back up loans.

7Typically, the originator of the mortgage is paid 1% of the mortgage.

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for Alt-A and Subprime loans. Alt-A mortgages were more risky than prime mortgages, andSubprime mortgages are riskier than Alt-A mortgages. The riskier the mortgages, the higher is theprobability of default. As the probability of default increases the expected losses increase so thatthe ultimate lenders insist on higher interest rates.

Eventually, the mortgage originators could not find enough lenders to sell the Subprime MBS.

They turned again to the quants who created a derivative security called a Collateralized debtobligation (CDO).8 In this case the MBS payments are divided into three main tranches, eachwith an associated return and priority in case of default: Senior (lowest risk AAA), Mezzanine(intermediate risk BBB), and Equity (highest risk, not rated). This is illustrated in Figure 4.Usually, the Subprime CDO would have 75% of its value in the Senior tranche which are sold toaverage investors who want a low risk investment. The basic idea is that if less than 25% of themortgages went into default, then the senior investors would not lose on any of their investment,see Figure 5.9 The riskier investments were sold to Hedge Funds which use leverage to increasethe return, and attract investors willing to assume additional risk for higher return. A companyincreases leverage by borrowing more to finance assets rather than using its own equity.

Figure 4. Balance sheet of a CDO Figure 5. Payment priority for CDO

Example 3. How can leverage boost return on investment? Suppose a $100 investment pays $110in one year under normal circumstances. Also suppose there is a 5% chance the investment canfall to $95 in one year. You do not have $100 to buy this investment so you borrow $96 from afriend for one year. In one year 95% of the time you pay back the $96 and end up with $14, so youmake a return of 144

4= 2.5 or a return of 250%. However, 5% of the time use lose 100% of your

investment. Notice your former friend losses $100 in the bad case.

To make the CDOs attractive the quants turned to another derivative product called a CreditDefault Swap (CDS). The issuer of a CDS guarantees that the holder of the CDO is paid even if themortgages goes into default. In this case the credit risk is transferred to someone willing to take onthe additional risk. These CDS were sold by insurance firms, such as AIG, and investment banks,such as UBS.

8This CDO was a modified version of a derivative created by Drexel Burnham in 1987.9See Barajas (2008).

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Unresolved Issue 3: How does the quant establish the price of the CDO and CDS? How wouldthis product be structured so that the investor would take on little risk?

The role of Repurchase Agreements: Lehman Brothers and Bear Stearns relied on repurchase

agreements to lower the cost of their short term funding for mortgage backed securities. A Re-purchase or REPO agreement is a short term loan with a security used as collateral on the loan.Initially, Repos were negotiated in terms of U.S. government securities which are relatively safeand liquid. The borrower sends a government security for 100% of the value of the loan to thelender or an independent agent under the conditions that the security is sent back to the borrowerwhen the loan matures as well as an agreed upon interest payment. The loan is considered safesince the lender possesses the security so that they can keep the security when a borrower declaresbankruptcy. The length of the Repo is generally from 1 to 90 days. Thus, Repos are considered safeshort term investments. Eventually, Repos were developed in which the security was a mortgagebacked security. If the MBS were considered riskier, then the borrower would require a hair cut. A

hair cut would let the borrower receive less than 100% of the security. The riskier the security thebigger the hair cut.

Lehman Brothers Bankruptcy and CDOs: Lehman Brothers declared bankruptcy on Septem-ber 14, 2008 as a result of large losses on subprime mortgages. Figure 6 illustrates the financialposition of Lehman Brothers before bankruptcy. They had invested in MBS and equity trancheCDOs. Lehman Brothers had a leverage ratio of about 30 to 1 in that they held only about 3% inthe form of equity.10 They funded these assets with commercial paper which was highly rated be-cause of the the past history of Lehman Brothers. As the default rate on subprime mortgages wentup the market price of the MBS and CDOs decreased so that Lehman Brothers assets declined bymore than 3% in value and the equity of Lehman Brothers went negative. Thus, they had to declare

bankruptcy.11

When the subprime crisis first developed in the summer of 2007 MBS decreased invalue. The hair cut on Repos for MBS started at 1% in July 2007 and increased to 8% by November2007 and 45% by November 2008.12 As the haircut increased Bear Stearns and Lehman Brothersfaced a liquidity crisis since they could not fund their holding of MBS with Repos. First, BearStearns was sold to J.P. Morgan on March 19, 2008 which was financed by $29 Billion in loans fromthe Federal Reserve Board. On September 14, 2008 Lehman Brothers declared bankruptcy sincethe Federal Reserve and U.S. Treasury did not find someone like J.P. Morgan to buy the assets ofLehman Brothers.13

10The leverage ratio is total assets dividend by equity.11When a company declares bankruptcy the individuals who hold the companys liabilities are paid off according

to the language in the contracts. The individuals who hold share of stock in the company are paid whatever is left

over once all the liabilities are met.12See Gorton and Metrick (2009).13See Wessel (2009).

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MBS and

CDOs$990

Cash Reserves

$10

Commercial

Paper $970Equity $30

Lehman Brothers Merrill Lynch

Commercial Paperof Lehman

$970

U.S. Treasury Securities$1030

Money Market Funds$1999

Equity $1

Figure 6. Balance sheet of a CDO Figure 7. Payment priority for CDO

This bankruptcy of Lehman Brothers had severe repercussions for the commercial paper market.The commercial paper of Lehman Brothers was bought by investment banks like Merrill Lynch whoattracted short term deposits from average investors (see Figure 7) . These deposits are called

money market funds. Merrill Lynch promised investors that they would only invest in short termUS Treasury securities and short term commercial paper issued by highly rated companies. As aresult, Merrill Lynch did not hold much equity or cash reserves, since they invested in short termsafe assets. On September 16, 2008 Reserve Primary Fund declared that its mutual fund was nowworth 97% of its original value, since it had a large exposure to Lehman Brothers commercial paper.Over the next few weeks institutional investors withdrew $193 Billion from money market funds.As a result, the collapse of Lehman Brothers lead to a collapse of the funding for commercial paperfor all companies. This collapse of money market funds is similar to the collapse of banks in the1930s in that investors became concerned about the value of the companys assets so they withdrewthe liquid deposits. On September 19, 2008 the US Treasury stepped in an announced that moneymarket funds would be insured like bank deposits for the next year.

If one compared the balance sheet of a commercial bank in Figure 1 with the combined balancesheet of Lehman Brothers and Merrill Lynch one can see why there was a collapse of this shadowbanking system. The combined companies funded long term illiquid assets with short term liabilities.Once the underlying assets lost more value then the equity the depositors become concerned aboutthe possibility of getting their deposits back. The depositors are concerned because they would notget their funds back if they are the last person to withdrawal their funds since there is not enoughassets to pay all the depositors. As a result, the depositors rush to get their funds out of the bank.This explains why the US treasury stepped in to insure these deposits to avoid a further collapse.14

AIG Bankruptcy and CDS: At the end of 2007 AIG held $562 Billion in CDS for MBS whichwas more than half AIGs assets. A London based subsidiary of AIG which was called AIGFP, andmanaged by Joseph Cassano, had sold these CDS. When the Subprime lending crisis started AIGhad to pay off on these CDS. As a result, a small subsidiary of the largest insurance company in theworld was able to force AIG to the brink of Bankruptcy in September 2008.15 One question to askis why the managers of AIG let this rogue group continue to operate without appropriate hedging

14See Diamond and Rajan (2009).15Forbes September 28, 2008. See WSJ article 10/31/08 Behind AIGs Fall, Risk Models Failed to Pass Real-World

Test, for article on role of quant, Gary Gorton, in the downfall of AIG.

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of risk. Was it because the Managers of AIG did not realize the risk taken on by AIGFP? Was itbecause the Managers of AIGFP were given incentives to take on excessive risk? Was the Bailoutof AIG by the U.S. Treasury appropriate? In particular, should they have allowed 100% paymenton the CDS to large financial firms such as Goldman Sachs?

1.4 The Subprime MeltdownTo understand the Subprime lending crisis we need to recall the economy after the 2001 recession.There was a general expansion of global liquidity and savings which led to an investment boomacross the world. Global savings per year increased from $35 trillion in 2000 to $68 trill in 2006.Most of this increase in savings was done in emerging markets such as Brazil, China, India, andOPEC countries. As a result, total financial investment increased from $94 trillion in 2000 to $167trillion in 2006. Most of these financial investments were made in the United States and Europe.This lead to relatively low interest rates across the world. In addition, U.S. monetary policy waseasy. For example the federal funds rate fell from 6.5% in early 2001 to a minimum of 1% in2003 where it stayed for over a year.16

16See Barajas (2008).

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In this environment of chasingreturns, the new mortgage in-struments proved to be attrac-tive. The MBS market grewfrom $2, 800 Billion in 2000 to$6, 600 Billion in 2007. The

Alt-A mortgages went from $44Billion in 2000 to $765 Billionin 2007. The Subprime mort-gages increased from $81 Billionin 2000 to $730 Billion in 2007.a

With the huge expansion inmortgage lending there was acorresponding increase in theprice of housing through 2005(see Figure Housing Prices).b As

a result, more people thought theprice of housing would always goup. To accommodate this per-spective home owners originatorsdeveloped what are called 2/28Subprime loans. For a borrowerwho had not saved 20% of thevalue of the house, they would bequalified for a Subrime mortgagewith a very small down payment.

a

Source Gordon (2008).bSource Federal Reserve Monetary

Report to Congress July 2008.

The interest rate on the 2/28 Subprime would be fixed for the first two years at a low rate, thenafter two years it would increase to a higher rate, equal to LIBOR plus a risk premium to accountfor the high probability of default. Some of these borrowers could not afford the higher payment,but it was presumed that housing prices would increase enough so that the borrower could take outa prime loan after two years. The originator would make more money when the prime mortgagewas issued after two years, since they would originate a new loan. As a result, these Subprimeloans were more risky if the price of housing fell. The trend in down payment on mortgages wasremarkable. For mortgages issues in 1976 the down payment was 18% on average. By 2005 2006the median down payment decreased to 2%, and more than half of the borrowers had no downpayment.

As the price of housing increased less and less individuals could afford a home. In particular,housing became more expensive relative to renting (see Figure 1 from Ceccehti (2008)). As aresult starting about 2005 the increase in the price of housing started to decline. Subsequently,delinquency rates on Subprime mortgages increased from a usual 5% to 15% by 2005 and stayedthere (see Figure 1.8, IMF (2008)).

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Figure 1 Ratio of home prices to rents

Source: Ratio of F ederal Reserve Board ow of funds v alue of residential real estate, table B.100 line 4 to Bur eau of Economic Analysis national

income and product accounts housing service consumption, table 2.3.5 line 14.

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1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Average 1960 to 1995 = 10.0

For Subprime loans originated at the peak of prices in 2005 (2006) delinquency rates increased to30% (35%) by 2008. A similar pattern developed in Alt-A and prime loans, however the delinquencyrates decreased as the riskiness of the loan declined.

With the increase in default rates the hedge funds started to lose money. Although initially itwas a relatively small amount. When a home owner defaults there is maybe 90% of the house valueleft, so the loss on the portfolio would equal 30% default rate 10% loss on each default = 3%.Thus, only the equity tranche of the CDO suffered losses. Thus, hedge funds losses increased butit was not catastrophic.

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If the story stopped here, then the impacton the economy would have been minor.Also, few individuals would care if some

rich people, who invested in hedge funds,went into bankruptcy. However, as mort-gages are foreclosed the originating banksells off the houses, so that an increase inforeclosures leads to a further decline inhome prices. With a decline of home pricesmore foreclosures occur. As the foreclo-sures and expected losses on loans escalate,the senor tranches of the CDOs start tolose money as well. The realization, thatsenior CDOs were not as safe, led hold-ers of MBS to question the safety of theseassets as well. Thus, the market price ofMBS started to fall relative to the originalvalue (see Figure 1.9, IMF (2008)). Whilethe losses on MBS backed by GovernmentSponsored Enterprises (GSE), such as Fan-nie Mae and Freddie Mac, were not too big,the MBS not backed by GSEs lost as muchas 90% of the market value (see Figure 1.9,IMF (2008)).

The subcrime crisis finally became appar-ent at the end of June 2007, when a ma-

jor disruption to liquidity occurred. Sev-eral hedge funds, operated by Bearns Sternand Lehman Brothers, had to meet mar-gin calls.

The margin calls were due to the loss ofvalue for Lehman Brothers investments inCDOs, precisely at a time in which therewas little liquidity in the market for MBS.A lender issues a margin call when thevalue of a the collateral on a loan goes be-low the amount of the loan. The Hedgefunds had to either sell assets or announcetheir inability to meet margin calls. Thisled to a huge increase in uncertainty aboutthe value of CDOs so that transactionsstopped in this market.

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Sources: Merrill Lynch; and LoanPerformance.

Figure 1.8. U.S. Mortgage Delinquencies by

Vintage Year(60+ day delinquencies, in percent of original balance)

2005

2005

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Without effective transactions taking place inCDO, little information for pricing the differentCDO tranches was available. As a result, hedgefunds stopped trading and credit originators hadnowhere to sell their Alt-A and Subprime mort-gages. Thus, originators stopped originating

new loans, many originators went bankrupt, andCountrywide was taken over by Bank of Americain December 2007.

Generalized lack of confidence in asset qualitymeant that the asset bank commercial paperABCP market shut down. Subsequently, anyinvestment bank and commercial bank, that hada large amount of MBS, were unable to borrowfunds needed to finance their holding of MBS.This led to the failure of Bearns Sterm in March

2008 in which the Federal Reserve managed itstake over by JP Morgan Chase. In addition, thecommercial banks had to raise almost $600 Bil-lion (see Figure 1.14, IMF (2008)).

Figure 1.9. Prices of U.S. Mortgage-Related

Securities(In U.S. dollars)

Jumbo MBS

Agency MBS

ABX BBB

ABX AAA

Alt-A

Sources: JPMorgan Chase & Co.; and Lehman Brothers.

Note: ABX = an index of credit default swaps on mortgage-related

asset-backed security; MBS = mortgage-backed security.

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2006 07 08

Subsequently, Fannie Mae and FreddieMac was taken over by Federal Home Loan

on September 7, 2008. On September 14,2008 the federal government decided tolet Lehman Brothers go into bankruptcy,which led to complete shut down of lendingbetween banks and corporations within theweek. As a result, the U.S. Governmenthad to lend AIG $85 Billion the next dayfollowed by a loan of $37.8 Billion. October3, 2008 Congress established the TroubledAsset Relief Act to lend the banks $700Billion. By November 10, 2008 the AIGbailout increased to $150 Billion with $40Billion in preferred stock being funded byTARP.a

aSee WSJ 11/10/2008.

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800Americas Europe Asia

Bank writedowns by region

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SIVs/conduitsTradingMonolines

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Hedge funds/otherInsurersGSEs

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Sources: Bloomberg L.P.; and IMF sta estimates.

Note: SIVs = structured investment vehicles; GSEs = government-sponsored

enterprises.

Figure 1.14. Financial Sector Losses(In billions of U.S. dollars; 2007:Q2 through August 2008)

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Unresolved Issue 3: How does the correlation between foreclosures and housing prices lead toa viscous cycle in which the Senior tranche of the CDO losses value? How does the change inforeclosure rates impact the market price of CDOs. How does this change in the price of CDOslead to the failure of Bearns Stern, Lehman, and AIG.?

1.5 Federal Reserve Policy in Response to the Crisis

The financial crisis started with the shadow banking system which consist of financial institutionslike Countrywide, Lehman Brothers and Bear Stearns which were not subject to the regulationsimposed on commercial banks.17 These regulations included capital requirements and deposit insur-ance. In addition, the shadow banking system did not have the safety nets such as deposit insuranceand an ability to borrow from the Federal Reserve Banks. As a result, the Federal Reserve and theU.S. Treasury had to be creative in developing programs which may or may not be authorized by theCongress and President. These programs prevented the complete collapse of the financial system asin the early 1930s.18 Eventually, these programs lead to the purchase of a large percentage of the

assets held by the shadow banking system by the Federal Reserve. In particular, Figure 8 showsthat the assets of the Federal Reserve increased by about $1, 142 Billion through the crisis. Thus,the Fed nationalized the shadow banking system.

Figure 8. Federal Reserve Balance Sheet

Policy actions to address the impact of the crisis on commercial banks tended to focus on easingliquidity conditions. Starting in August 2007, the Federal Reserve embarked on a series of interestrate cuts totaling 2.25% over seven months, and toward the end of the year began a process ofexpanding access to existing lending facilities and creating others, both for banks and for non-bankfinancial institutions. As Sarkar (2009) argues, two separate stages can be distinguished. During

17This section comes from Barajas, Chami, Cosimano and Hakura (2010).18For example the Term Securities Lending Facility TSLF to make loans (up to $200 billion) to primary dealers

with collateral such as US Treasuries, federal agency debt, federal agency MBS and investment]grade debt securities.Previously the Fed was only a lender of last resort to commercial banks.

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the first stage, the Fed acted to provide liquidity to solvent institutions, in response to a severecontraction in interbank markets that threatened to bring financial intermediation to a halt viaan illiquidity spiral. This was followed by a second stage, in which credit risk was the primaryconcern, and liquidity was provided directly to key borrowers and investors.

As the crisis developed, and particularly in the wake of the Lehman Brothers bankruptcy in

September 2008, the focus of policy began to move beyond liquidity provision and toward injectionof capital. In particular, the well-known Troubled Asset Relief Program (TARP) dedicated asubstantial portion of its funds ($250 billion out of the total $700 billion) to the Capital PurchaseProgram (CPP), designed to purchase preferred stock of financial institutions. After an initialinjection of $125 billion into nine large and systemically important institutions on October 14 th, 2008the program has broadened to include over 550 smaller institutions, with an overall injection of justover $200 billion as of October 2009.

Both types of policies appear to have yielded benefits. There is evidence that specific liquidityprovision efforts helped to offset the extreme tightness in market liquidity which became evident inthe summer of 2007. For instance, the Term Auction Facility (TAF), introduced in early December

2007, has been associated with at least temporary reductions in the LIBOR-OIS spread, in the excessdeviations from covered interest parity that had spiked during the crisis, and in the divergence ofLIBOR over the Federal Funds rates. As for the capital injections undertaken through the CPP,there is evidence that the funds were well-targeted, in terms of being allocated to larger, systemicallyimportant banks that had suffered greater capital losses but had relatively strong loan portfolios,that is, healthy but vulnerable banks. Furthermore, the injections themselves were associated withpositive valuation effects for the recipient banks - excess stock returns - which were also greater forthose banks that had suffered greater capital losses.

However, to date it is not clear whether there has been a positive impact of these two types ofpolicies - either focused on liquidity or capital - specifically on bank lending. In fact, a particular

concern has arisen that these policies have done little to reactivate credit, and that instead, excessreserves held by banks have risen to unprecedented levels. From a level of about $1.5 billionthroughout 2007 and most of 2008, excess reserves climbed rapidly following the Lehman Brothersbankruptcy, reaching $900 billion by January 2009, and remaining above $800 billion through June2009.

Barajas, Chami, Cosimano, and Hakura (BCCH 2010) examined the behavior of large bankholding companies from 2006 Q1 to 2009 Q2 in response to the financial crisis of 2007-2009. Themain conclusion was that banks with less capital had smaller growth of deposits and loans but werenot liquidity constrained-at least when measured by the liquid asset ratio.

Next, BCCH implemented a test of a model of bank regulatory capital, according to which banks

hold additional capital when they anticipate that the regulatory constraint is going to bind in thefuture. Additional bank capital is demanded by banks when they have less initial total capital andlower interest expense, as well as non-interest expenses. In addition, this demand for bank capital isconvex in each of these variables. The overall predictive power of this model was quite satisfactoryfor all three measures of capital and the main predictions of the model were confirmed. Thus, thereis strong evidence that banks optimally choose their capital position.

Finally, BCCH implemented a test of monopoly power In this case they reject the two extremesof competitive and monopolistic behavior in the banking industry, so that there is, monopolisticcompetition pricing practiced by the large bank holding companies. In particular, the banks sys-

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tematically raised the net interest margin as the Federal Reserve lowered the cost of funding by 5percent from 2007 through December 2008. Thus, the evidence suggests that the large bank hold-ing companies responded to their capital constraints by raising the net interest margin, the spreadbetween the loan and deposit rates, so as to optimally build up bank capital over time. Lending bybanks will not expand appreciably until this buildup of bank capital is completed.

The results of BCCH can help in designing a policy by which the Federal Reserve privatizesthe excess assets which they have acquired over the crisis. As pointed out by Cochrane (2009)the flight to safe liquid assets throughout the crisis has increased the present value of all futureexpected surpluses of the US government since they are now being discounted at a lower effectiverate of return. This has allowed the Federal Reserve to acquire 1, 142 billion of additional assetswhich were held by the shadow banking system. While this amount is 152 billion below the peakin December 2008, the 793 billion decline in TALF, CP and Foreign Swaps has been replaced by507 billion in private and agency mortgage backed securities (see Figure 8). As the crisis abates,the liquidity premium will disappear so that the US government will have to privatize these assetsto avoid a fiscal crisis within the U.S. government.

In privatizing these assets the Federal Reserve will want to avoid a replay of the financial crisisso that the assets must be sold to private intermediaries subject to prudent regulations. Thismeans that 114.2 billion in total capital-10 percent of the required balance sheet expansion-mustbe added to the banking system for these institutions to be well qualified under current regulationsof commercial banks. The results here imply that the banks must be given a clear signal that theywill be able to acquire these assets at a competitive risk adjusted rate of return. Given such clearsignals the banks would find it optimal to raise sufficient capital to fund these assets without takingon excessive risk. In addition, the higher loan rate required to fund these loans will help to alleviateexcessive risk taken by borrowers.

1.6 Final ThoughtsThe IMF estimates the losses from the Subprime lending to be $1, 405 Billion. The break down ofthe losses are summarized in Table 1.1 (See IMF (2008)).

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Table 1.1. Estimates of Financial Sector Potential Writedowns

(In billions of U.S. dollars)

Base Case Estimates of WritedownssnaoL.S.UnosnwodetirWsnaoL.S.Uno

Outstandings

April

estimatedlosses

October

estimatedlosses Banks Insurance

Pensions/Savings

GSEs andgovernment

Other

(hedgefunds, etc.)

5101505004530554003emirpbuS015505052025303006A-tlA

505554505003525804008,3emirPCommercial real estate 2,400 30 90 6065 510 05 1020Consumer loans 1,400 20 45 3035 05 05 1015Corporate loans 3,700 50 110 8085 05 05 2530Leveraged loans 170 10 10 510 05 05 05

Total for loans 12,370 225 425 255290 540 035 4555 6010

Base Case Estimates of Mark-to-Market Losses

seitiruceSnosessoLseitiruceSdetaleRno

Outstandings

Aprilestimated

mark-to-marketlosses

Octoberestimated

mark-to-marketlosses Banks Insurance

Pensions/Savings

GSEs andgovernment

Other(hedge

funds, etc.)

5201510155535404011001012012001,1SBA0351025154035755061541092042004sODCSBA

Prime MBS 3,800 0 80 2025 1015 1020 2025 0502510201535152020908061012049SBMC

Consumer ABS 650 0 0 High-grade corporate debt 3,000 0 130 6575 2030 2035 520High-yield corporate debt 600 30 80 4550 1015 1520 515

015505002510303053sOLC

Total for securities 10,840 720 980 470530 155210 125215 5580 55125

Total for loans and securities 23,210 945 1,405 725820 160250 125250 100135 11522

Sources: Goldman Sachs; JPMorgan Chase & Co.; Lehman Brothers; Markit.com; Merrill Lynch; and IMF sta estimates.

Note: The prime residential loans category includes a portion of GSE-backed mortgage securities. ABS = asset-backed security; CDO = col-lateralized debt obligation; CLO = collateralized loan obligation; GSE = government-sponsored enterprise; CMBS = commercial mortgage-backedsecurity; MBS = mortgage-backed security.

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Figure 1.13 (See IMF (2008)) shows thatthe losses by commercial banks are esti-mated to be about the same as the 1990sbanking crisis in Japan. Whether this cri-sis will harm the U.S. and Global economyas much as the Japanese economy is still

an open question and dependent on gov-ernment policy undertaken over the nextyear.

The Subprime crisis gives us an opportu-nity to study the cost and benefits of quan-titative analysis in finance.a Throughoutthe semester we will study the quantita-tive finance issues which arose in the Sub-prime crisis. This analysis will help you torealize what can and cannot be done with

quantitative methods.aFor example, the bankruptcy proceedings are

made public, so that we will have detailed infor-mation about what various groups within the cor-porations did to fulfill their legal responsibility.

0

200

400

600

800

1000

1200

1400

1600

U.S.

subprime crisis

(2007present)

Asia

banking crisis

(199899)

Japan

banking crisis

(199099)

U.S. savings

and loan crisis

(198695)

2

3

3

4

Sources: World Bank; and IMF sta estimates.

Note: U.S. subprime costs represent sta estimates of losses on banks and othe

nancial institutions from Table 1.1. All costs are in real 2007 dollars. Asia includes

Indonesia, Malaysia, Korea, the Philippines, and Thailand.

Figure 1.13. Comparison of Financial Crises

Banking losses (in billions of U.S. dollars, left scale)

Percent of GDP (right scale)

Other nancials(in billions of U.S. dollars, left scale)

Discussion Questions

1. Why does the il-liquidity of assets and liquidity of liabilities for a financial institution lead toperiodic financial crisis in which lenders rush to withdrawal their funds from financial firms?

2. Explain why MBS were developed to alleviate this mismatch of assets and liabilities.

3. Why did the holding of MBS and CDO by Lehman Brothers and Bear Stearns lead to thefinancial crisis?

4. Explain the role of Repos in the demise of Lehman Brothers and Bear Stearns.

5. How did the failure of subprime lenders spiral into the collapse of the financial system?

6. Discuss the steps undertaken by the Federal Government to minimize the fallout from thefinancial crisis.

7. Suppose Ron Paul rather than Ben Bernanke was Chair of the Federal Reserve Board so thatthe federal reserve would not have intervene in the financial markets. What do you thinkwould happen? Do you think society would be better off?

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Glossary of Terms19

An Alt-A mortgage Short hand for Alternative A-paper, is a type of U.S. mortgage that,for various reasons, is considered riskier than prime, and less risky than subprime, theriskiest category. Alt-A interest rates, which are determined by credit risk, therefore tend tobe between those of prime and subprime home loans.

Asset-backed commercial Commercial paper (ABCP) Commercial paper is a loan to a cor-poration for a period of less than one year. Commercial paper collateralized by a pool ofloans, leases, receivables, or structured credit products is called ABCP.

Balance sheet (T-account) A statement of the financial position for an individual or legalorganization. It is a summary of a persons or organizations balances. Assets (Own), liabilities(Owe) and ownership equity are listed as of a specific date, such as the end of its financialyear.

Bankruptcy A legally declared inability or impairment of ability of an individual or organi-zation to pay their creditors.

Collateralized debt obligation (CDO) A structured credit security backed by a pool ofsecurities, loans, or credit default swaps, where interests in the security are divided intotranches with differing repayment and interest earning streams. The pool can be eithermanaged within preset parameters or static. If the CDO is backed by other structured creditsecurities, it is called a structured- finance CDO, and if it is backed solely by other CDOs, itis called a CDO-squared.

Commercial banks A corporation that accepts deposits and makes loans, as well as other

fee based services. Corporate Bond A bond issued by a corporation. The term is usually applied to longer-term

debt instruments, generally with a maturity date falling at least a year after their issue date.

Commercial paper An unsecured promissory note with a fixed maturity of one to 270 days.

Credit default swap (CDS) A default-triggered credit derivative. Most CDS default settle-ments are physical, whereby the protection seller buys a defaulted reference asset from theprotection buyer at its face value. Cash settlement involves a net payment to the protec-tion buyer equal to the difference between the reference asset face value and the price of thedefaulted asset.

Credit derivative A financial contract under which an agent buys or sells risk protectionagainst the credit risk associated with a specific reference entity (or entities). For a periodicfee, the protection seller agrees to make a contingent payment to the buyer on the occurrenceof a credit event (default in the case of a credit default swap).

Credit score A number that is based on a statistical analysis of a persons credit report, andis used to represent the creditworthiness of that person, the likelihood that the person willpay his or her debts.

19Definitions come from IMF (2008), and Wikipedia.

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Credit spread The spread in interest rates between benchmark securities and other debtsecurities that are comparable in all respects except for credit quality (e.g., the differencebetween yields on U.S. Treasuries and those on single A rated corporate bonds of a certainterm to maturity).

Derivative A financial contract whose value derives from underlying securities prices, interest

rates, foreign exchange rates, commodity prices, or market and other indices.

Deposit account an account at a banking institution that allows money (currency or deposits)to be deposited and withdrawn by the account holder, with the transactions and resultingbalance being recorded on the banks books.

Equity Shares of stock in a corporation on a stock market by individuals and funds inanticipation of income from dividends and capital gain as the value of the stock rises.

Fannie Mae The Federal National Mortgage Association is a stockholder-owned corporationchartered by Congress in 1968 as a government sponsored enterprise (GSE), but founded in1938 during the Great Depression.

Federal Funds Rate Interest rate on an overnight loan from one commercial bank to anotherin the United States. It is the interest rate used by the Federal Reserve to control the moneysupply and inflation.

FICO score A credit score calculated using one particular credit scoring system.

Fiduciary duty A legal relationship of confidence or trust between two or more parties, mostcommonly a fiduciary or trustee and a principal or beneficiary.

Foreclosure Foreclosure is the legal and professional proceeding in which a mortgage, or

other lienholder, usually a lender, obtains a court ordered termination of a mortgagors equi-table right of redemption. Usually a lender obtains a security interest from a borrower whomortgages or pledges an asset like a house to secure the loan.

Freddie Mac The Federal Home Loan Mortgage Corporation (FHLMC) is a governmentsponsored enterprise (GSE) of the United States federal government which was created in1970.

Government-sponsored enterprise (GSE) A financial institution that provides credit to spe-cific groups or areas of the economy, such as farmers or housing. Most GSEs maintain legaland/or financial ties to the U.S. government.

Hedge fund Investment pool, typically organized as a private partnership and often residentoffshore for tax and regulatory purposes. These funds face few restrictions on their portfoliosand transactions. Consequently, they are free to use a variety of investment techniques in-cluding short positions, transactions in derivatives, and leverage to attempt to raise returnsand risk.

Investment banks A corporation who issues and sells securities in the capital markets (bothequity and bond), as well as providing advice on transactions such as mergers and acquisitions.

Home Mortgage The pledging of a house to a lender as a security for a loan.

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Leverage The proportion of debt to equity (also assets to equity and assets to capital).Leverage can be built up by borrowing (on-balance-sheet leverage, commonly measured bydebt-to-equity ratios) or by using off-balance-sheet transactions.

Liquidity An assets ability to be easily converted to cash through an act of buying or sellingwithout causing a significant movement in the price and with minimum loss of value.

London Interbank Offer Rate (LIBOR) Interest rate on an overnight loan from one com-mercial bank to another in the United Kingdom.

Loan A borrower initially receives an amount of money from the lender (bank), whichthey pay back, usually but not always in regular installments, to the lender. This service isgenerally provided at a cost, referred to as interest on the debt. A loan is of the annuity typeif the amount paid periodically (for paying off and interest together) is fixed.

Margin Call A margin is collateral that the holder of a position in securities, options, orfutures contracts has to deposit to cover the credit risk of his counterparty (most often hisbroker). The margin call occurs when the value of the collateral falls below some criticalvalue.

Money Market Funds A mutual fund that invest in short-term debt instruments such astreasury bills and commercial paper.

Mortgage-backed security (MBS) A security that derives its cash flows from principal andinterest payments on pooled mortgage loans. MBSs can be backed by residential mortgageloans or loans on commercial properties.

Mutual fund A professionally managed type of collective investment scheme that poolsmoney from many investors and invests it in stocks, bonds, short-term money market instru-

ments, and/or other securities.

Originate-to-distribute model A business model of financial intermediation, under whichfinancial institutions originate loans such as mortgages, repackage them into securitized prod-ucts, and then sell them to investors.

Prime mortgage the home owner puts up 20% of the home value and has a good creditrating.

Quantitative analyst (quant) A person that uses numerical or quantitative techniques todevelop financial instruments and manage risk.

A Repurchase or REPO agreement is a short term loan with a security used as collateral onthe loan.

Savings and Loan association (S & L) A financial institution that specializes in acceptingsavings deposits and making mortgage loans.

Structured investment vehicle (SIV) A legal entity whose assets consist of asset-backedsecurities and various (SIV) types of loans and receivables. An SIVs funding liabilities areusually short- and medium-term debt;

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Subprime mortgage A mortgage to borrowers with impaired or limited credit histories, whotypically have low credit scores.

Commercial banks A corporation that accepts deposits and makes loans, as well as otherfee based services.

The federal takeover of Fannie Mae and Freddie Mac refers to the placing into conservatorshipof government sponsored enterprises Fannie Mae and Freddie Mac by the US Treasury inSeptember 2008. It was one financial event among many in the ongoing Subprime mortgagecrisis.

References

IMF Global Financial Stability Report, October 2008.

Wikipedia, The Free Encyclopedia.

Monetary Policy and the Financial Crisis of 2007 2008 by Stephen G. Cecchetti, Center forEconomic Policy Research, POLICY INSIGHT No. 21. April 2008

The Subprime Crisis in the United States by Adolfo Barajas, IMF Institute, 2008.

The Subprime Panic by Gary Gorton, NBER working paper 14398, October 2008.

Securitized Banking and the Run on the Repo Market by Gary Gorton and Andrew Metrick,Yale ICF working paper 09-14, November 2009.

In Fed We Trust: Ben Bernankes War on the Great Panic by David Wessel, Crown Business

Publishing 2009.

The Credit Crisis: Conjectures about Causes and Remedies by D. W. Diamond and R. G.Rajan, University of Chicago working paper 2009.

U.S. Commercial Bank Behavior in the Wake of the 2007-2009 Financial Crisis by AdolfoBarajas, Ralph Chami, Thomas Cosimano, Dalia Hakura, IMF working paper 2010.

Liquidity Risk, Credit Risk, and the Federal Reserves Responses to the Crisis by Asani Sarkar,Federal Reserve Bank of New York, Staff Report no. 389 2009.

Understanding Fiscal and Monetary Policy in 2008-2009 by John Cochrane. University of

Chicago working paper 2009.

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