Accounting Fundamentals for Financial Institutions Midterm

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Asset and Liability Manangement

FIN6102

Ferriter Spring 2018

Overview

This chapter discusses types and characteristics of loans made by U.S. FIs, models for measuring credit risk, and applicable technological advances.

Important for purposes of:

Pricing loans and bonds

Setting limits on credit risk exposure

Ch 10-2

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Objectives for Individual Loans

There are two primary questions that need to be answered about individual loans.

First, what is the potential return on the loan

Second, what is the probability of default

What options do we have to measure the probability of default?

Why is credit risk important?

Credit Risk is perhaps the most important consideration for a loan.

Loans have a fixed and defined payment, this means that there is very limited upside and more downside compared to equity investments

Because of the greater emphasis on downside risk, bond and loan markets are very focused and very responsive to changes.

Credit Quality Problems

Problems with junk bonds, LDC loans, and residential and farm mortgage loans

Late 1990s, credit card and auto loans

Crises in other countries such as Argentina, Brazil, Russia, and South Korea

2006-2007, mortgage delinquencies on subprime loans surged

Emphasizes importance credit risk analysis

Ch 10-5

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Credit Quality Problems

Over the early to mid 1990s, improvements in NPLs for large banks and overall credit quality

Late 1990s and early 2000, Telecommunication and tech companies

DotCom bubble – get big fast

WorldCom

Alan Greenspan – raises interest rates

Mid 2000s, economic growth accompanied by reduction in NPL rates

Mortgage crisis

Increased emphasis on credit risk evaluation

Ch 10-6

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What is a junk bond?

Many investors incorporate bondsinto their portfolios to benefit from the interest payments they typically provide. But a bond's investment value is only as good as its issuer's ability to make those payments. When a bond's credit rating falls below what's considered investment-grade level, it's referred to as a junk bond.

Though junk bonds carry more risk than investment-grade bonds with higher ratings, they tend to offer much higher yields, and as such, they're an attractive option for some buyers.

Bonds that have a high enough credit rating are considered investment-grade, which means that they're suitable for most investors. On the other hand, bonds with a low enough rating are considered non-investment-grade, or junk.

There are three major ratings agencies used to evaluate bonds' creditworthiness: Standard & Poor's (S&P), Moody’s and Fitch

These agencies analyze a number of factors, such as assets, liabilities, and cash flow management, when assigning ratings to issuers. S&P and Fitch use a similar ratings system where issuers can receive as high a rating as AA, and as low a rating as D. Moody's uses a slightly different system where issues can go as high as Aaa and as low as C. A bond that carries a credit rating of BB or lower by S&P and Fitch, or Ba or lower by Moody's, is considered non-investment-grade, or junk.

Junk Bond Crisis

From the 1970’s to the 1980’s the junk bond market grew exponentially at a a pace of around 34% per year. During this period of time junk bonds achieved a superior risk adjusted return. Essentially, junk bonds in this period were a superior investment compared to other investments with the same amount of risk.

However, this period of growth came to a sudden stop in 1989. There is some disagreement as to what caused it, but most point to the collapse of the US$6.75bn buyout of UAL as the main trigger. A buyout group consists of pilots union and an investment bank sought to take United Airlines private for $6.79 billion couldn't secure the necessary loans.

Others point to the Ohio Mattress fiasco, a deal that would become known as “burning bed” and remains widely considered to be among the worst deals in modern finance. The Cleveland-based company that Gibbons, Green bought for $1.1 billion in April amid criticism that it was wildly overpaying. In August, Gibbons, Green had to shelve its efforts to line up permanent financing for the acquisition when investors in the high-risk, high-yield ''junk bond'' market refused to buy the bonds

The culmination of the crash is considered to be the collapse of Drexel Burnham Lambert, which was forced into bankruptcy in early 1990, largely due to its heavy involvement in junk bonds. At one point it had been the fifth-largest investment bank in the US.

Credit Card and Auto Collapse

At the close of the 1990s, against the backdrop of the economic boom, many low- and moderate-income families were struggling financially and taking on credit card debt at rates unprecedented in American history. There is growing evidence that a combination of structural and economic trends coupled with abusive credit card industry practices left working families with few options other than to borrow heavily.

Between 1989 and 2001, credit card debt in America almost tripled, from $238 billion to $692 billion. The savings rate steadily declined, and the number of people filing for bankruptcy jumped 125 percent.

During the 1990s, the average American family experienced a 53 percent increase in credit card debt, from $2,697 to $4,126 (all figures measured in 2001 dollars). Low-income families saw the largest increase—a 184 percent rise in their debt—but even very high-income families had 28 percent more credit card debt in 2001 than they did in 1989.

With an increase in bankruptcy filings, it led to the drafting of a bankruptcy reform bill, which was considered by the Congress, and passed as Bankruptcy Abuse Prevention and Consumer Protection Act of 2005. It made filing chapter 7 (liquidating) bankruptcy, more difficult and introduced a means-test.

Effects of Deregulation

Since the late 1970s, America’s credit card industry has enjoyed a period of steady deregulation. Two Supreme Court rulings, the first in 1978 and the second in 1996, effectively hobbled state usury laws that protected consumers from excessively high interest rates and fees.

Aggressive Marketing

Relentless Credit Extension.

Between 1993 and 2000, the industry more than tripled the amount of credit it offered to customers, from $777 billion to almost $3 trillion.

Lowering of Minimum Payment Requirements

The amount of their balance customers can pay without incurring a penalty—dropped from 5 percent to only 2 or 3 percent, making it easier for consumers to carry more debt. Assuming an interest rate of 15 percent, it would now take more than 30 years to pay off a credit card balance of $5,000 by making the minimum payment. Or sometimes, never.

Skyrocketing Late Fees and Penalties.

Late fees have become the fastest growing source of revenue for the industry, jumping from $1.7 billion in 1996 to $7.3 billion in 2001. Late fees now average $29, and most cards have reduced the late payment grace period from 14 days to 0 days. In addition to charging late fees, the major card companies use the first late payment as an excuse to cancel low, introductory rates—often making a zero percent card jump to between 22 and 29 percent.

Asian Financial Crisis

The Asian Financial Crisis occurred in 1997 and affected Indonesia, South Korea, Thailand, Hong Kong, Laos, Malaysia and the Philippines. Indonesia, South Korea, Thailand being the most affected.

The causes are disputed but most agree that current account deficits, foreign currency denominated debt and a fixed exchange rate contributed to the crisis. In the mid-1990s, the maintenance of fixed exchange rates encouraged external borrowing and led to excessive exposure to foreign exchange risk in both the financial and corporate sectors.

Most recognize the devaluation of the Chinese Renminbi, the devaluation of the Japanese Yen as a result of the Plaza accord and a strengthen US dollar and a rise in US interest rates as triggers for the collapse.

Asian Financial Crisis

This made the United States a more attractive investment destination relative to Southeast Asia, which had been attracting hot money flows through high short-term interest rates, and raised the value of the U.S. dollar. For the Southeast Asian nations which had currencies pegged to the U.S. dollar, the higher U.S. dollar caused their own exports to become more expensive and less competitive in the global markets.

The resulting panic among lenders led to a large withdrawal of credit from the crisis countries, causing a credit crunch and further bankruptcies. In addition, as foreign investors attempted to withdraw their money, the exchange market was flooded with the currencies of the crisis countries, putting depreciative pressure on their exchange rates. To prevent currency values collapsing, these countries' governments raised domestic interest rates to exceedingly high levels (to help diminish flight of capital by making lending more attractive to investors), and to intervene in the exchange market - buying up any excess domestic currency at the fixed exchange rate with foreign reserves. Neither of these policy responses could be sustained for long.

Thailand

On 14 May and 15 May 1997, the Thai baht was hit by massive speculative attacks. However, Thailand lacked the foreign reserves to support the USD–Baht currency peg, and the Thai government was eventually forced to float the Baht, on 2 July 1997, allowing the value of the Baht to be set by the currency market.

As a result of high interest rates, Thailand's booming economy came to a halt amid massive layoffs in finance, real estate, and construction that resulted in huge numbers of workers returning to their villages in the countryside and 600,000 foreign workers being sent back to their home countries. The baht devalued swiftly and lost more than half of its value. The baht reached its lowest point of 56 baht to the U.S. dollar in January 1998. The Thai stock market dropped 75%.

Indonesia

In July 1997, when Thailand floated the baht, Indonesia's monetary authorities widened the rupiah currency trading band from 8% to 12%. The rupiah suddenly came under severe attack in August. On 14 August 1997, the managed floating exchange regime was replaced by a free-floating exchange rate arrangement. The rupiah dropped further.

Although the rupiah crisis began in July and August 1997, it intensified in November when the effects of that summer devaluation showed up on corporate balance sheets. Companies that had borrowed in dollars had to face the higher costs imposed upon them by the rupiah's decline, and many reacted by buying dollars through selling rupiah, undermining the value of the latter further. Before the crisis, the exchange rate between the rupiah and the dollar was roughly 2,600 rupiah to 1 U.S. dollar. The rate plunged to over 11,000 rupiah to 1 U.S. dollar on 9 January 1998, with spot rates over 14,000 during 23–26 January and trading again over 14,000 for about six weeks during June–July 1998. On 31 December 1998, the rate was almost exactly 8,000 to 1 U.S. dollar. Indonesia lost 13.5% of its GDP that year.

South Korea

The banking sector was burdened with non-performing loans as its large corporations were funding aggressive expansions. During that time, there was a haste to build great conglomerates to compete on the world stage. Many businesses ultimately failed to ensure returns and profitability. The chaebol, South Korean conglomerates, simply absorbed more and more capital investment. Eventually, excess debt led to major failures and takeovers.

In the wake of the Asian market downturn, Moody's lowered the credit rating of South Korea on 28 November 1997, and downgraded again on 11 December. That contributed to a further decline in South Korean shares since stock markets were already bearish in November. The Seoul stock exchange fell by 4% on 7 November 1997. On 8 November, it plunged by 7%, its biggest one-day drop to that date. And on 24 November, stocks fell a further 7.2% on fears that the IMF would demand tough reforms. In 1998, Hyundai Motors took over Kia Motors. Samsung Motors' $5 billion venture was dissolved due to the crisis, and eventually Daewoo Motors was sold to the American company General Motors (GM).

The IMF provided US$57 billion as a bailout package. In return, Korea was required to take restructuring measures. The ceiling on foreign investment in Korean companies was raised from 26 percent to 100 percent. In addition, the Korean government started financial sector reform program. Under the program, 787 insolvent financial institutions were closed or merged by June 2003.

The South Korean won, meanwhile, weakened to more than 1,700 per U.S. dollar from around 800, but later managed to recover. South Korea’s national debt-to-GDP ratio more than doubled (approximately 13% to 30%) as a result of the crisis.

What is the current account?

The components of the current account: goods, services, income and current transfers.

1. Goods - These are movable and physical in nature, and for a transaction to be recorded under "goods," a change of ownership from/to a resident (of the local country) to/from a non-resident (in a foreign country) has to take place. Movable goods include general merchandise, goods used for processing other goods, and non-monetary gold. An export is marked as a credit (money coming in), and an import is noted as a debit (money going out).

2. Services - These transactions result from an intangible action such as transportation, business services, tourism, royalties or licensing. If money is being paid for a service, it is recorded like an import (a debit), and if money is received, it is recorded like an export (credit).

3. Income - Income is money going in (credit) or out (debit) of a country from salaries, portfolio investments (in the form of dividends, for example), direct investments or any other type of investment. Together, goods, services, and income provide an economy with fuel to function. This means that items under these categories are actual resources that are transferred to and from a country for economic production.

4. Current Transfers - Current transfers are unilateral transfers with nothing received in return. These include workers' remittances, donations, aids and grants, official assistance and pensions. Due to their nature, current transfers are not considered real resources that affect economic production.

Mortgage Crisis of 2008

The immediate cause or trigger of the crisis was the bursting of the United States housing bubble which peaked in approximately 2005–2006. An increase in loan incentives such as easy initial terms and a long-term trend of rising housing prices had encouraged borrowers to assume risky mortgages in the anticipation that they would be able to quickly refinance at easier terms.

However, once interest rates began to rise and housing prices started to drop moderately in 2006–2007 in many parts of the U.S., borrowers were unable to refinance. Defaults and foreclosure activity increased dramatically as easy initial terms expired, home prices fell, and adjustable-rate mortgage (ARM) interest rates reset higher.

Several other factors set the stage for the rise and fall of housing prices, and related securities widely held by financial firms. In the years leading up to the crisis, the U.S. received large amounts of foreign money from fast-growing economies in Asia and oil-producing/exporting countries. This inflow of funds combined with low U.S. interest rates from 2002 to 2004 contributed to easy credit conditions, which fueled both housing and credit bubbles. Loans of various types (e.g., mortgage, credit card, and auto) were easy to obtain and consumers assumed an unprecedented debt load.

Ch 10-18

ARMs’ Share of Total Loans Closed, 1987-2014

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Ch 10-19

Annual Net Charge-Off Rates on Loans

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Ch 10-20

Nonperforming Asset Ratio for U.S. Commercial Banks

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Types of Loans

C&I loans: secured and unsecured

Syndication

Spot loans, loan commitments

Decline in C&I loans originated by commercial banks and growth in commercial paper market

Effect of financial crisis on commercial paper market

RE loans: Primarily mortgages

Fixed-rate, ARMs

Mortgages can be subject to default risk when loan-to-value rises and house prices fall below amount of loan outstanding

Ch 10-21

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Individual (Consumer) Loans

Consumer loans: personal, auto, credit card

Nonrevolving loans

Automobile, mobile home, personal loans

Revolving loans

Credit card debt (i.e., Visa, MasterCard)

Proprietary cards, such as Sears and AT&T

Risks affected by competitive conditions and usury ceilings

Bankruptcy Reform Act of 2005

High default rates during finance crisis highlight the importance of risk evaluation prior to making a credit decision

Ch 10-22

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Other Loans

Other loans include:

Farm loans

Other banks

Nonbank FIs, such as broker margin loans

Foreign banks and sovereign governments

State and local governments

Municipal bankruptcies

Detroit,MI Central Falls, RI, Harrisburg, PA

Ch 10-23

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Calculating Return on a Loan

Factors: Interest rate, fees, credit risk premium, collateral, and other nonprice terms, such as compensating balances and reserve requirements

Return = inflow/outflow

1+k = 1+(of + (BR + ø))/(1-[b(1-RR)])

Ch 10-24

©McGraw-Hill Education.

k is the promised gross return

of = direct fees (origination fees)

BR + ø = loan interest rate

b= Compensating balance

RR = Reserve Rate

Note that the text displays 1+ E(r) = p(1+k) + (1-p)0 but this simplifies to the form displayed above.

Return on Loan Equation

Return = inflow/outflow

1+k = 1+(of + (BR + ø))/(1-[b(1-RR)])

Of = origination fee, this is the fee paid by the customer to initiate and process the loan application

BR = Base rate

Ø = risk premium of the customer

b = compensating balance requirement

RR = reserve requirement

k = the gross return on the loan

Example 10-1

Suppose a Bank does the following

Sets a loan rate of 10% (BR = 6% and Ø =4%)

Charges a .125% origination fee

Imposes an 8% compensating balance requirement to be held in non-interest accounts

Sets aside reserves of 10% per Federal Reserve

1 + k = 1 + (.00125+ (.06+.04))/(1-(.08)(.9)

1 + k = 1 + (.10125)/(.928)

1 + k = 1.1091

k = .1091 or 10.91%

Expected Return on a Loan

Expected return: 1 + E(r) = p(1+k) + (1- p) 0

where p equals probability of complete repayment

1- p is the probability of non-payment or default

This can be considered and binomial option as there are only two possible outcomes

It’s important to note that Ø and p are not completely independent

Loan originators consider the probability of default when setting the risk premium. This is to compensate for default risk

To an extent it can be self-reinforcing, high interest rates equal higher payments, all else equal

Higher fixed payments increases the likelihood of default which leads to higher interest rates

Note that realized and expected return may not be equal

Example

Calculate the promised return (k) on a loan if the base rate is 13%, the risk premium is 2%, the compensating balance requirement is 5%, origination fees are .5% and the reserve requirement is 10%

1+k = 1+(of + (BR + ø))/(1-[b(1-RR)])

1+k = 1 +((.005+(.13+.02))/(1-[.05(.9))

1+k = 1+.155/ .955

1 + k = 1.1623

What is the expected return on the loand is the probability of default is 5%

Retail versus Wholesale Credit Decisions

At retail

Usually a simple accept/reject decision rather than adjustments to the rate

Credit rationing

If accepted, customers sorted by loan quantity

For mortgages, discrimination occurs via loan-to-value rather than adjusting rates

At wholesale

Use both quantity and pricing adjustments

Ch 10-29

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Managing Credit Quality

How do banks and financial institutions manage individual loan quality?

Most banks have guidelines for various loan types

Some guidelines come from outside the organization, others are internally developed

Many banks use benchmarks rating to ensure market competitiveness and market share

All banks have some form of Risk Model to estimate exposure to default risk

Risk Models

Availability, quality, and cost of information are critical factors in credit risk assessment

Facilitated by technology and information

Qualitative models consider borrower specific factors as well as market, or systematic, factors

Borrowed-specific factors include reputation, leverage, volatility of earnings, and collateral

Market specific factors include business cycle and interest rate levels

Ch 10-31

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Linear Probability Model

Credit scoring models are quantitative models that use borrower characteristics to gauge an applicant’s probability of default

Major weakness is that estimated probabilities of default can often lie outside of the [0,1] interval

Since superior statistical techniques are readily available, there is rarely justification for employing linear probability models

Ch 10-32

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Altman’s Discriminant Function

Z=1.2X1+ 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

Critical value of Z = 1.81

X1 = Working capital/total assets ratio

X2 = Retained earnings/total assets ratio

X3 = EBIT/total assets ratio

X4 = Market value equity/ book value of total liabilities

X5 = Sales/total assets ratio

Ch 10-33

©McGraw-Hill Education.

History of Altman Z-Score

The Z-score formula for predicting bankruptcy was published in 1968 by Edward I. Altman, who was, at the time, an Assistant Professor of Finance at New York University.

The formula may be used to predict the probability that a firm will go into bankruptcy within two years. Z-scores are used to predict corporate defaults and an easy-to-calculate control measure for the financial distress status of companies in academic studies. The Z-score uses multiple corporate income and balance sheet values to measure the financial health of a company. There are many variants of the Altman model depending on the nature of the company and industry.

None of the Altman models or other balance sheet-based models are recommended for use with financial companies. This is because of the opacity of financial companies' balance sheets and their frequent use of off-balance sheet items. Market based estimate are used instead.

Example 10-23

MNO, Inc., a publicly traded manufacturing firm, has provided the following financial information in its application for a loan.

Assets Liabilities and Equity

Cash $ 20 Accounts payable $ 30

Accounts receivables 90 Notes payable 90

Inventory 90 Accruals 30

Long-term debt 150

Plant and equipment 500 Equity (ret. earnings = $0) 400

Total assets $700 Total liabilities and equity $700

Also assume sales = $500,000 cost of goods sold = $360,000 taxes = $56,000 interest payments = $40,000 net income = $44,000 the dividend payout ratio is 50 percent, and the market value of equity is equal to the book value.

Part a

What is the Altman discriminant function value for MNO, Inc.? Recall that:

Net working capital = Current assets - Current liabilities.

Current assets = Cash + Accounts receivable + Inventories.

Current liabilities = Accounts payable + Accruals + Notes payable.

EBIT = Revenues ‑ Cost of goods sold ‑ Depreciation.

Net income = EBIT ‑ interest ‑ taxes.

Retained earnings = Net income (1 ‑ Dividend payout ratio

Part A solution

Altman’s discriminant function is given by: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5

X1 = (20+90+90‑30‑30-90)/ 700 = .0714 X1 = Working capital/total assets (TA)

X2 = 44(1-.5) / 700 = .0314 X2 = Retained earnings/TA

X3 = (500-360) / 700 = .20 X3 = EBIT/TA

X4 = 400 / 150 = 2.67 X4 = Market value of equity/long term debt

X5 = 500 / 700 = .7143 X5 = Sales/TA

Z = 1.2(0.07) + 1.4(0.03) + 3.3(0.20) + 0.6(2.67) + 1.0(0.71) = 3.104

= .0857 + .044 + .66 + 1.6 + .7143 = 3.104

Part b

Based only on the Altman’s Z-score, should you approve MNO, Inc.'s application to your bank for a $500,000 capital expansion loan?

Since the Z-score of 3.104 is greater than 2.99, ABC Inc.’s application for a capital expansion loan should be approved.

Part c

If sales for MNO were $300,000, the market value of equity were only half of book value, and all other values are unchanged, would your credit decision change?

ABC’s EBIT would be $300,000 - $360,000 = -$60,000.

X1 = (20 + 90 + 90 ‑ 30 ‑ 30 ‑ 90) / 700 = .0714

X2 = 22 / 700 = 0.0314

X3 = ‑60 / 700 = ‑0.0857

X4 = 200 / 150 = 1.3333

X5 = 300 / 700 = 0.4286

Z = 1.2(0.0714) + 1.4(0.0314) + 3.3(-0.0857) + 0.6(1.3333) + 1.0(0.4286) = 1.0754

Since ABC's Z‑score falls to 1.0754 < 1.81, credit should be denied.

Part d

Would the discriminant function change for firms in different industries? Would the function be different for retail lending in different geographic sections of the country? What are the implications for the use of these types of models by FIs?

Discriminant function models are very sensitive to the weights for the different variables. Since different industries have different operating characteristics, a reasonable answer would be yes with the condition that there is no reason that the functions could not be similar for different industries. In the retail market, the demographics of the market play a big role in the value of the weights. For example, credit card companies often evaluate different models for different areas of the country. Because of the sensitivity of the models, extreme care should be taken in the process of selecting the correct sample to validate the model for use.

Logit Model

Logit models

Overcomes weakness of the linear probability model by restricting the estimated range of default probabilities from the linear regression model to lie between 0 and 1

Quality of credit scoring models have improved, providing positive impact on controlling write-offs and default

Ch 10-41

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Linear Discriminant Model

Problems associated with discriminant analysis model:

Only considers two extreme cases (default/no default)

No reason to expect that the weights in a credit scoring model will be constant long-term; sensitivity to variable weights

Ignores hard to quantify factors, including business cycle effects and reputation

Database of defaulted loans is not available to benchmark the model

Ch 10-42

©McGraw-Hill Education.

Newer methods of modeling Default Risk

Newer models of credit risk use a combination of financial theory and financial data to infer the possibility of default. Because of the use of financial data these are primarily used to model the credit risk of large corporate firms.

Term Structure of credit risk

Mortality Rate models

RAROC – Risk Adjusted Return on Capital Models

Option Models – Black-Scholes

Term Structure Derivation of Credit Risk

If the risk premium is known, we can infer the probability of default

Risk premium can be computed using Treasury strips and zero-coupon corporate bonds

p (1+ k) = 1+ i

Ch 10-44

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Implied Probability of Default

By looking at the spread between Treasury Strips and zero-coupon corporate bonds, we can ascertain the implied probability of default. By comparing a risk-free asset to a risky asset we’ll be able to impute the difference in perceived credit risk

One of the major assumptions is that there is no potential for arbitrage.

p (1+ k) = 1+ i

p(1+k) = Expected return on the loan: p is the probability of repayment and 1-p is the probability of default

1 + i = the risk free rate

if i = 2.05% and k = 7.80% then

p = (1+i)/(1+k)

and 1.0205/1.078 = .94967 and 1-p = .0575 or 5.75%

10-32

The bond equivalent yields for Government of Canada and A-rated corporate bonds with maturities of 93 and 175 days are given below:

Bond Maturities 93 days 175 days

Government 8.07% 8.11%

A-rated corporate 8.42% 8.66%

Spread 0.35% 0.55%

What are the implied forward rates for both an 82-day Government of Canada and an 82-day A-rated bond beginning in 93 days? Use daily compounding on a 365-day year basis.

Part A

The forward rate, f, for the period 93 days to 175 days, or 82 days, for the Government of Canada is:

(1 + 0.0811)175/365 = (1 + 0.0807)93/365 (1 + f )82/365  f = 8.16 percent

The forward rate, f, for the corporate bond for the 82-day period is:

(1 + 0.0866)175/365 = (1 + 0.0842)93/365 (1 + f )82/365  f = 8.933%

Part B

What is the implied probability of default on A-rated bonds over the next 93 days? Over 175 days?

The probability of repayment of the 93-day A-rated bond is:

p(1 + 0.0842)93/365 = (1 + 0.0807)93/365  p = 99.92 percent

Therefore, the probability of default is (1 - p) = (1 - .9992) = 0.0008 or 0.08 percent.

The probability of repayment of the 175-day A-rated bond is:

p(1 + 0.0866)175/365 = (1 +0.0811)175/365  p = 99.76 percent

Therefore, the probability of default is (1 - p) = (1 - .9976) = 0.0024 or 0.24 percent

Part C

What is the implied default probability on an 82-day A-rated bond to be issued in 93 days?

The probability of repayment of the A-rated bond for the period 93 days to 175 days, p, is:

p (1.08933)82/365 = (1 + 0.0816)82/365  p = .9984, or 99.84 percent

Therefore, the probability of default is (1 - p) or 0.0016 or 0.16 percent.

Mortality Rate Models

Similar to the process employed by insurance companies to price policies; the probability of default is estimated from past data on defaults

Marginal Mortality Rates:

MMR1 = (Value Grade B default in year 1) (Value Grade B outstanding yr.1)

MMR2 = (Value Grade B default in year 2) (Value Grade B outstanding yr.2)

Has many of the problems associated with credit scoring models, such as sensitivity to the period chosen to calculate the MMRs

Ch 10-50

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Monthly Mortality

The first table below is a schedule of historical defaults (yearly and cumulative) experienced by an FI manager on a portfolio of commercial and mortgage loans.

Years after Issuance

Loan Type 1 Year 2 Years 3 Years 4 Years 5 Years

Commercial:

Annual default 0.00% ______ 0.50% ______ 0.30%

Cumulative default ______ 0.10% ______ 0.80% ______

Mortgage:

Annual default 0.10% 0.25% 0.60% ______ 0.80%

Cumulative default ______ ______ ______ 1.64% ______

10-34

Complete the blank spaces in the table.

Commercial: Annual default 0.00%, 0.10%, 0.50%, 0.20%, and 0.30%

Cumulative default: 0.00%, 0.10%, 0.60%, 0.80%, and 1.10%

Mortgage: Yearly default 0.10%, 0.25%, 0.60%, 0.70%, and 0.80%

Cumulative default 0.10%, 0.35%, 0.95%, 1.64%, and 2.43%

Note: The annual survival rate is pt = 1 – annual default rate, and the cumulative default rate for n = 4 of mortgages is 1 – (p1* p2* p3* p4) = 1 – (0.999*0.9975*0.9940*0.9930).

Part b

What are the probabilities that each type of loan will not be in default after 5 years?

The cumulative survival rate is = (1-mmr1)*(1-mmr2)*(1-mmr3)*(1-mmr4)*(1-mmr5) where mmr = marginal mortality rate

Commercial loan = (1-0.)*(1-0.001)*(1-0.005)*(1-0.002)*(1-0.003) = 0.989 or 98.9%.

Mortgage loan = (1-0.001)*(1-0.0025)*(1-0.006)*(1-0.007)*(1-0.008) = 0.9757 or 97.57%.

Part C

What is the measured difference between the cumulative default (mortality) rates for commercial and mortgage loans after four years?

Looking at the table, the cumulative rates of default in year 4 are 0.80% and 1.64%, respectively, for the commercial and mortgage loans. Another way of estimation is:

Cumulative mortality rate (CMR) = 1- (1 - mmr1)(1 - mmr2)(1 - mmr3)(1 - mmr4)

For commercial loan = 1- (1 - 0.0010)(1 - 0.0010)(1 - 0.0020)(1 - 0.0050)

= 1- .9920 = 0.0080 or 0.80 percent.

For mortgage loan = 1- (1 - 0.0010)(1 - 0.0025)(1 - 0.0060)(1 - 0.0070)

= 1- .98359 = 0.01641 or 1.641 percent.

The difference in cumulative default rates is 1.641 - .80 = .8410 percent.

RAROC Models

Risk-adjusted return on capital

One of the most widely used models

RAROC = (One year NI on a loan)/(loan risk)

Loan risk estimated from loan default rates, or using duration

The idea is that a loan should only be made if the income from the loan will lead to an equity increase for the financial institution

The most commonly used denominator for loan risk is duration

Ch 10-55

Using Duration to Estimate Loan Risk

For denominator of RAROC, duration approach used to estimate loss in value of the loan:

LN /LN = -DLN x (R/(1+R))

Ch 10-56

RAROC Example

RAROC = (One year NI on a loan)/(loan risk)

One year NI on a loan = (Spread + fees) x Dollar Value of the Loan

FI wants to evaluate the credit risk of a $1million loan with a duration of 2.7 years. The expected change in interest rate is 1.1%. And the current interest rate is 5%

Given this information the loan/capital risk is: -DLN x (R/(1+R))

-2.7(1,000,000((.011/.05)) = -$28,286

Given that the spread is .2% and the fees associated with the loan are .1% What is the One year NI on the loan

(.002+.001) x (1,000,000) = 3,000

With this information 3,000/28,286 = 10.61%

Note: When we describe change we drop the negative sign

If the RAROC is above the internal benchmark, then the loan should be approved.

10-38

A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years and a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. Assume the bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 percent, based on two years of historical data. The current market interest rate for loans in this sector is 12 percent.

Part A

Using the RAROC model, determine whether the bank should make the loan.

RAROC = Fees and interest earned on loan/ Loan or capital risk

Loan risk, or LN = -DLN*LN*(R/(1 + R) = = -7.5 * $5m * (.042/1.12) = -$1,406,250

Expected interest = 0.12 x $5,000,000 = $600,000

Servicing fees = 0.0050 x $5,000,000 = $25,000

Less cost of funds = 0.10 x $5,000,000 = -$500,000

Net interest and fee income = $125,000

RAROC = $125,000/1,406,250 = 8.89 percent. Since RAROC is lower than the cost of funds to the bank, the bank should not make the loan.

Part B

What should be the duration in order for this loan to be approved?

For RAROC to be 10 percent, loan risk should be:

$125,000/LN = 0.10  LN = 125,000 / 0.10 = $1,250,000

 -DLN * LN * (R/(1 + R)) = 1,250,000

DLN = 1,250,000/(5,000,000 * (0.042/1.12)) = 6.67 years.

Thus, this loan can be made if the duration is reduced to 6.67 years from 7.5 years.

Option Models

Employ option pricing methods to evaluate the option to default

Used by many of the largest banks to monitor credit risk

KMV Corporation markets this model widely

Ch 10-61

Option Framework

The option framework holds that when borrowing a borrower has two options, to repay the loan or to default. Similar to financial options, these real options have value. In a sense, the borrower has only the loss of its invested equity, but maintains upside if the company goes well. Thus the decision to borrow, can be modeled much like a call option.

The most famous model for options valuation is Black-Scholes, which we will be applying here.

Applying Option Valuation Model

Merton showed value of a risky loan:

L() = Be-i[(1/d)N(h1) +N(h2)]

Written as a yield spread:

k() - i = (-1/)ln[N(h2) +(1/d)N(h1)]

where

k() = Required yield on risky debt

ln = Natural logarithm

i = Risk-free rate on debt of equivalent maturity

Remaining time to maturity

Ch 10-63

Black-Scholes Option Pricing Model

Model used to value European options:

Ch 10-64

Where:

C = call option price

S = price on the asset underlying the option

E = exercise price of the option

r = riskless rate of interest over one year

Sigma = standard dev of the underlying asset’s return

T = time to expiration of the option as a fraction of one year

e = base of the natural logarithm, or the exponential function

Ln (S/E) = natural log of S/E

N(d) = value of the cumulative normal distribution evaluated at d1 and d2

Model Assumptions

Capital markets are frictionless

Constant variability in underlying asset’s return

Log normal probability distribution of underlying asset’s price

Constant risk-free rate that is known over time

No dividends on underlying asset

No early exercise on option

Ch 10-65

Formula continued

H1=-[(1/2)ơ2 -ln(d)/ơ√ 

H2=-[(1/2)ơ2 +ln(d)/ơ√ 

10-40

A firm is issuing a two-year debt in the amount of $200,000. The current market value of the assets is $300,000. The risk-free rate is 4 percent, and the standard deviation of the rate of change in the underlying assets of the borrower is 20 percent. Using an options framework, determine the following:

a. The current market value of the loan.

b. The risk premium to be charged on the loan.

Answer

The following need to be estimated first: d, h1 and h2 .

d = Be-iτ /A = $200,000e-0.04(2)/300,000 = 0.6154 or 61.54 percent.

h1 = -[0.5 x (0.20)2 x 2 - ln(0.6154)]/(0.20)(2)1/2 = -1.8578

h2 = -[0.5*(0.20)2 *2 + ln(0.6154)]/(0.20)(2)1/2 = 1.5750

Current market value of loan = l(τ) = Be-iτ [N(h1)1/d + N(h2)]

= $184,623.27[N(-1.8578) x 1.62493 + N(1.5750)]

= $184,623.27[1.62493 x 0.031654 + 0.94265] = $183,531

The risk premium, ϕ = k(τ) – i = (-1/τ) ln[N(h2) + (1/d)N(h1)]

= (-½)ln[0.94265 + 1.62493 x 0.031654] = 0.002966 = 0.2966%

Credit Analysis and Loan Underwriting

Real Estate Lending

Two considerations dominate FI’s decision to approve mortgage application:

Applicant’s ability and willingness to make timely interest and principal repayments

Value of borrower’s collateral

Ch 10-69

Real Estate Lending

Determining a customer’s ability to maintain mortgage payments:

GDS = (Annual mortgage payments + Property taxes) / Annual gross income

TDS = Annual total debt payments / Annual gross income

Ch 10-70

Lending

Consumer and small-business

Similar techniques as mortgage loans

Mid-market commercial and industrial

Annual sales revenues from $5 million to $100 million, recognizable corporate structure, but no access to liquid capital markets

5 C’s of credit are: character, capacity, collateral, conditions, and capital

Ch 10-71

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