corporate risk and credit risk

7/29/2019 corporate risk and credit risk

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Massachusetts Institute of TechnologySloan School of Management

Course 15.415: Finance Theory I

Class Notes #25

Nonlinearities, Skewness and the Credit Option:

Corporate Bonds, Bank Loans and Bank Stocks

Douglas T. Breeden*August, 2012

Several slides are from D. T. Breeden, Bank Risk Management, Chapter 34 in The

Handbook of Modern Finance, Dennis Logue, Editor, 1989.


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U.S. Bond Market:Governments, Corporates, Mortgages,

Consumer Credit and Municipals ($Trillions)Source: Federal Reserve Board Q1 2011 (solid), Q4 2008 (pattern)

02

468

101214161820

Treasurys,Agencies

Corporate &ForeignBonds

Mortgages ConsumerCredit

Municipals

2


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I. Bank Loans and Corporate Bonds

in an Option Context

3


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Black-Scholes-Merton (1973, 1974)Debt and Equity as Options

In their pathbreaking, Nobel Prize winningworks, Black and Scholes in 1973 and Merton in1974 showed that equity is like a call option on

the value of the firms assets.

They also showed that the debt of a firm is likeowning the firm and having written a call to the

shareholders. Option formulae can help pricecorporate bonds.

4


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5

Bank Loans In An Option Context

Douglas T. Breeden

1. Bank Loans and Their Credit Options.

2. Hedging Bank Loans with options andFutures.

3. Pricing Bank Loans for Credit Risk.

5


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6

Bank Loans In an Option Context

Crude Oil: A firm owns a crude oil storage facilitythat currently contains 1 million barrels of oil. At theJune, 2011 price of $100.00 per barrel, this oil isworth $100 million.

A bank lends $66.67 million (Loan/Value = 2/3) tothe firm for one year at an interest rate of 5.00%(3.25% prime + 1.75%) using the oil as collateral,

which results in a promised payment of $70 millionin one year ($66.67 x 1.05). The current 1-yearfutures price is $99.85.

6


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Loan Risk Exposure To Commodity PricesValue of Firm Payment to Bank Shareholders Equity

Crude Oil Price ($MM) ($MM) ($MM)$40.00 $40.0 mln $40.0 $0.0

$50.00 $50.0 $50.0 $0.0

$60.00 $60.0 $60.0 $0.0

$70.00 $70.0 $70.0 $0.0

$80.00 $80.0 $70.0 $10.0

$90.00 $90.0 $70.0 $20.0

$100.00 $100.0 $70.0 $30.0

$110.00 $110.0 $70.0 $40.0

$120.00 $120.0 $70.0 $50.0$130.00 $130.0 $70.0 $60.0

$140.00 $140.0 $70.0 $70.0

$150.00 $150.0 $70.0 $80.0

$160.00 $160.0 $70.0 $90.0

Mathematically: V B + E 7


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8

$70

70 million


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9$70


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10

10 20 30 40 50 60 70 80 90 100 110 120 130

35

70

105

140

175


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Hedging Loans With Put OptionsCrude Oil Value Payment Put X=70 Put Net

Price of Firm to Bank Payoff Cost Cash

($/Barrel) ($Mln) ($Mln) ($Mln) ($Mln) ($Mln)$40.00 $40.0 $40.0 $30.0 $-2.32 $67.68

$50.00 $50.0 $50.0 $20.0 $-2.32 $67.68$60.00 $60.0 $60.0 $10.0 $-2.32 $67.68

$70.00 $70.0 $70.0 $ 0.0 $-2.32 $67.68

$80.00 $80.0 $70.0 $ 0.0 $-2.32 $67.68

$90.00 $90.0 $70.0 $ 0.0 $-2.32 $67.68

$100.00 $100.0 $70.0 $0.0 $-2.32 $67.68

$110.00 $110.0 $70.0 $0.0 $-2.32 $67.68$120.00 $120.0 $70.0 $0.0 $-2.32 $67.68

$130.00 $130.0 $70.0 $0.0 $-2.32 $67.68

$140.00 $140.0 $70.0 $0.0 $-2.32 $67.68

$150.00 $150.0 $70.0 $0.0 $-2.32 $67.68

$160.00 $160.0 $70.0 $0.0 $-2.32 $67.6811


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Hedging Loan: Short Futures, Long Call OptionCrude Oil Value Payment Short Call X-=70 Call Net

Price of Firm to Bank Futures Gain Payoff Cost Cash

($/Barrel) ($Mln) ($Mln) ($Mln) ($Mln) ($Mln) ($Mln)$40.00 $40.0 $40.0 $59.85 $ 0.0 $-32.17 $67.68

$50.00 $50.0 $50.0 $49.85 $ 0.0 $-32.17 $67.68

$60.00 $60.0 $60.0 $39.85 $ 0.0 $-32.17 $67.68

$70.00 $70.0 $70.0 $29.85 $ 0.0 $-32.17 $67.68

$80.00 $80.0 $70.0 $19.85 $10.0 $-32.17 $67.68$90.00 $90.0 $70.0 $ 9.85 $20.0 $-32.17 $67.68

$100.00 $100.0 $70.0 $- 0.15 $30.0 $-32.17 $67.68

$110.00 $110.0 $70.0 $-10.15 $40.0 $-32.17 $67.68$120.00 $120.0 $70.0 $-20.15 $50.0 $-32.17 $67.68

$130.00 $130.0 $70.0 $-30.15 $60.0 $-32.17 $67.68

$140.00 $140.0 $70.0 $-40.15 $70.0 $-32.17 $67.68

$150.00 $150.0 $70.0 $-50.15 $80.0 $-32.17 $67.68

$160.00 $160.0 $70.0 $-60.15 $90.0 $-32.17 $67.6814


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15

Example: Option Adjusted Spread on BankLoan (OAS)

Terms: 1-year loanPrincipal: $66.67 million

Repayment: $70.00 million in 1 year

Interest =Interest Rate = 5.00%

= Prime + 1.75%

(Prime = 3.25%)

Collateral: 1 million barrels of oil

Current value = $100.00/barrel

Loan-to-value ratio = = 66.7%

Million

Million

67.66$

33.3$

MillionMillion

00.100$67.66$

15


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Option-Adjusted Return Calculation1-Year Put option on crude oil with strike price of $70/barrel

insures this loans payoff risk.

Put cost = $2,320,000 ( = 35%) or $2.32 per barrel.

Banks total cash out = + =

Cash received back = Loan payoff + Put = $70,000,000

with credit risk Payoff

Hedged or risk-adjusted return = - 1 =

Hedged

Loan = Weak risk-adjusted return

Return

Loan

000,670,66$

stPutHedgeCo

000,320,2$

utTotalCashO

000,990,68$

000,990,68$

000,000,70$

1.47%

Prime - 1.78%

16

~ ~


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17

Effects of Option Volatilityon Cost of Put Hedge for Loan

Put Options Implied Volatility = 45% 25% =

Put Option Cost ($70 strike, 1 year) = $4,490,000 $720,000 = P

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Option-Adjusted Loan Return With = 25%

Banks total cash out = $66,670,000 + $720,000

= $67,390,000

Banks cash received back = $70,000,000

Hedged or risk-adjusted return = - 1=

= risk-adjusted

= High risk adjustedreturn

000,390,67$000,000,70$

3.87%

Prime + 0.62%

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Option-Adjusted Loan Return With = 45%

Banks Cash Out = $66,670,000 + $4,490,000 = $71,160,000

Banks Cash Back = $70,000,000

Hedged Return = - 1 =

=

= Very poor return (unprofitable)

000,160,71$000,000,70$

-1.63%

Prime - 4.88%

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20

Computing The Interest RateThat Gives A Desired OAS

Assume:

Cost of Funds (LIBOR) = 0.5% = COF

Desired hedged profit = 1.5% =

Desired hedged return = 2.0% = HR

20


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Analysis: Let the amount loaned be variable =

Put hedge cost = P

Total proceeds from risky loan and hedge = L

Pricing Formula: = 1 +

Solve for :

RH

PL

= - P

HR

L

1

21

C ti Th I t t R t


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In the example: = - $4,490,000( = 45%)

= $64,137,500

Loan interest rate = -1

( = 45%) = - 1 =

=

Note: If = 25%, P = $720,000, then =

=

23

020.1

000,000,70$

Prime +5.90%

L

R500,137,64$000,000,70$

9.15%

LR 3.07%

Prime - 0.18%

LRL 1


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Summary of Fair Interest Rates on 1-Year OilLoans Hedged with Put Options (Oil Price=$100)

PromisedPaymentin 1 Year

Loan/ValueRatio

Put Option Costs

Millions of dollars

Interest Rate for Bank toEarn Hedged Spread of 1.5%(Prime=3.35%, LIBOR=0.5%)

= 45% =35% = 25% = 45% =35% = 25%

$75 million approx70%

$6.05 $3.46 $1.33 11.14% 7.03% 3.88%

$70 million 65% $4.49 $2.32 $0.72 9.15% 5.57% 3.07%

$65 million 60% $3.21 $1.46 $0.34 7.41% 4.40% 2.55%

$60 million 55% $2.18 $0.86 $0.14 5.93% 3.51% 2.25%

23


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Junk Bonds: Market Adjusted Debt Ratio (Quasi-Debt Ratio)vs. Yield to Worst Call 5 Yr Treasury

(.10 interval MAD1 bucket Averages from 1800 bonds sampled)MAD1= Face Val Debt/(Face Debt + Mkt Equity) Merton (1974, J. Finance)

25Source: Douglas T. Breeden and John B. Sprow, Smith Breeden Associates, 1989


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29

Main Point:

The fair rate on a loan depends on the cost of the

options required to cover the banks credit risks. Ifoption costs are high (as with high volatility), thenloan rates must be high. Correspondingly, lowoption costs permit low loan rates.

The loan to value ratio affects the exercise prices ofthe options purchased. Intuitively, a lower loan tovalue ratio reduces the credit risk and the cost ofoption coverage.

29

B k C dit Ri k F P ti ll H d d Fi


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30

Bank Credit Risks For a Partially Hedged FirmOld Example with $11 mln promised debt payment (Fut=$14.82)

Oil Unhedged Futures Hedge Gains Bank Receipt on Loan

Prices Firm Value H=25% H=50% H=75% H=0% H=25% H=50% H=75%

$8.00 $8.0 m $1.71 $3.41 $5.12 $8.00 $9.71 $11.00 $11.00

$9.00 $9.0 m $1.46 $2.91 $4.37 $9.00 $10.46 $11.00 $11.00

$10.00 $10.0 m $1.21 $2.41 $3.62 $10.00 $11.00 $11.00 $11.00

$11.00 $11.0 m $0.96 $1.91 $2.87 $11.00 $11.00 $11.00 $11.00

$12.00 $12.0 m $0.71 $1.41 $2.12 $11.00 $11.00 $11.00 $11.00

$13.00 $13.0 m $0.46 $0.91 $1.37 $11.00 $11.00 $11.00 $11.00

$14.00 $14.0 m $0.21 $0.41 $0.62 $11.00 $11.00 $11.00 $11.00

$15.00 $15.0 m ($0.04) ($0.09) ($0.13) $11.00 $11.00 $11.00 $11.00

$16.00 $16.0 m ($0.29) ($0.59) ($0.88) $11.00 $11.00 $11.00 $11.00

$17.00 $17.0 m ($0.54) ($1.09) ($1.63) $11.00 $11.00 $11.00 $11.00

$18.00 $18.0 m ($0.79) ($1.59) ($2.39) $11.00 $11.00 $11.00 $11.00

$19.00 $19.0 m ($1.05) ($2.09) ($3.14) $11.00 $11.00 $11.00 $11.00

$20.00 $20.0 m ($1.30) ($2.59) ($3.89) $11.00 $11.00 $11.00 $11.00

Note: Loan promises payment of $11 million in one year;

H = Percent of oil risk hedged; V = Total firm value

30

H d i S b di t d D bt With S d f P t O ti


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Hedging Subordinated Debt With Spread of Put Option

Oil Payment to Subordinated Buy Put Write Put Hedged

Price Firm Value Senior Debt Debt Payoff X = $11 X = $10 Sub. Debt

$8.00 $8.0 m $8.0 m $0.0 m $ 3.0 m $-2.00 m $1.00 m

$9.00 $9.0 m $9.0 m $0.0 m $ 2.0 m $-1.00 m $1.00 m

$10.00 $10.0 m $10.0 m $0.0 m $ 1.0 m $-0.00 m $1.00 m

$11.00 $11.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$12.00 $12.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m$13.00 $13.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$14.00 $14.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$15.00 $15.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$16.00 $16.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$17.00 $17.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$18.00 $18.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$19.00 $19.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

$20.00 $20.0 m $10.0 m $1.0 m $ 0.0 m $-0.00 m $1.00 m

31

Old Example with $11 mln promised debt payments,$10 mln senior debt, $1 mln subordinated

C fli t f I t t


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32

Conflicts of InterestBetween Bondholders and Stockholders

Once debt is outstanding, stockholders have theincentives to take actions that benefit themselves at theexpense of the bondholders.

With debt outstanding, the objectives of maximizing thevalue of the firm and the value of the equity are notidentical.

Examples of bondholdersstockholder conflicts Claim dilution

Dividend payout

Asset substitution32


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33

Types of Bond Covenants

Restrictions on production and investment policy

Mergers Financial assets

Sale of assets

Line of business

Restrictions on financial policy

Dividend payouts Priority

Total debt

Provisions for auditing

Bond Covenants reduce but do not eliminate agency costs

Components of Agency Costs

Monitoring costs

Bonding costs

Residual loss

33


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II. Risk and Return inCorporate Bonds and Bank Loans

Quarterly Data: 1926-2011 Q3

34


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Empirical Duration/Price Elasticity Estimates


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Empirical Duration/Price Elasticity Estimatesfor Treasuries and Corporates

(Monthly Data 1989-2010)

Quarterly returns regressed on 3-month changes in thecorresponding 5, 10, 30-Year Treasury Rates:

Slope R-Squared

5-Year Treasury -4.4 0.97



Quarterly returns regressed on 3-month changes in the

10-Year Treasury Rate:

AAA Corporate -4.8 0.77 A Corporate -4.0 0.41

BBB Corporate -3.1 0.23

Junk Corporate(ex 07-10) -1.3 0.02

Mortgage Master -3.0 0.7136


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Bond Ratings

37

Moodys S&P Quality of IssueInvestment-grade bonds:

Aaa AAA Highest quality. Very small risk of default.Aa AA High quality. Small risk of default.A A High-Medium quality. Strong attributes, but potentially vulnerable.Baa BBB Medium quality. Currently adequate, but potentially unreliable.

High-yield (Junk) bonds:Ba BB Some speculative element. Long-run prospects questionable.B B Able to pay currently, but at risk of default in the future.

Caa CCC Poor quality. Clear danger of default.Ca CC High speculative quality. May be in default.C C Lowest rated. Poor prospects of repayment.D - In default.


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40

Moodys Average Cumulative Issuer-WeightedGlobal Default Rates by Alphanumeric Rating, 1998-2007

Rating Year 1 Year 10

Aaa 0.00 0.00

Aa 0.00 0.00

Aa2 0.00 0.00Aa3 0.00 0.17

A1 0.00 0.06

A2 0.05 0.52

A3 0.05 0.54

Baa1 0.20 1.66

Baa2 0.19 2.57

Baa3 0.39 4.49

4040

Rating Year 1 Year 10Ba1 0.42 3.68Ba2 0.77 10.16Ba3 1.05 17.79

B1 1.70 28.37B2 3.89 32.41B3 6.18 51.10Caa1 10.54 50.51Caa2 18.98 46.83Caa3 25.54 54.38

Ca-C 38.27 65.63Investment-Grade 0.10 1.13Speculative-Grade 4.69 27.38All Rated 1.78 9.28


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Global Corporate Default Rates By Rating Category (source: S&P)

(%) AAA AA A BBB BB B CCC/C

1981 0.00 0.00 0.00 0.00 0.00 2.27 0.00

1982 0.00 0.00 0.21 0.34 4.22 3.13 21.43

1983 0.00 0.00 0.00 0.32 1.16 4.55 6.67

1984 0.00 0.00 0.00 0.66 1.14 3.39 25.00

1985 0.00 0.00 0.00 0.00 1.48 6.44 15.38

1986 0.00 0.00 0.18 0.33 1.31 8.33 23.08

1987 0.00 0.00 0.00 0.00 0.37 3.08 12.28

1988 0.00 0.00 0.00 0.00 1.04 3.62 20.37

1989 0.00 0.00 0.00 0.60 0.71 3.37 31.58

1990 0.00 0.00 0.00 0.58 3.55 8.54 31.25

1991 0.00 0.00 0.00 0.55 1.67 13.84 33.87

1992 0.00 0.00 0.00 0.00 0.00 6.99 30.19

1993 0.00 0.00 0.00 0.00 0.69 2.62 13.33

1994 0.00 0.00 0.14 0.00 0.27 3.08 16.671995 0.00 0.00 0.00 0.17 0.98 4.58 28.00

1996 0.00 0.00 0.00 0.00 0.67 2.89 4.17

1997 0.00 0.00 0.00 0.25 0.19 3.47 12.00

1998 0.00 0.00 0.00 0.41 0.96 4.59 42.86

1999 0.00 0.17 0.18 0.19 0.94 7.28 32.35

2000 0.00 0.00 0.26 0.37 1.24 7.73 34.12

2001 0.00 0.00 0.35 0.33 3.22 11.23 44.55

2002 0.00 0.00 0.00 1.00 2.78 8.10 44.12

2003 0.00 0.00 0.00 0.22 0.56 3.97 33.13

2004 0.00 0.00 0.08 0.00 0.52 1.55 15.11

2005 0.00 0.00 0.00 0.07 0.20 1.71 8.87

2006 0.00 0.00 0.00 0.00 0.29 0.80 13.08

2007 0.00 0.00 0.00 0.00 0.19 0.24 14.81

2008 0.00 0.38 0.38 0.47 0.76 3.82 26.53

Source: Standard & Poors Global Fixed Income Research and Standard a& Poors Credit Pro.


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Default Rates on Corporate Bonds andChargeoffs on Bank Loans 1920-2009e

0

2

4

6

8

10

12

14

16

18

1920

1924

1928

1932

1936

1940

1944

1948

1952

1956

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000

2004

2008

SpecGradeBondD

efaultRate

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

LoanCharge

off%

Moody Spec Grade Default Rate Bank Chargeoff %

42


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51

Corporate Bonds Have Major Nonlinearities:


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Corporate Bonds Have Major Nonlinearities:Stock Market Betas Increase in Risky Times

Quarterly Data: 1926-2011

Junk Bond Spread 500 bp(123 Observations in risky times)

vs5-YrGovt

t-stat vsS&P500

t-stat

Corr.RSQ

vs5-YrGovt

t-stat vsS&P500

t-stat Corr.RSQ

InvestmtGrade(Aaa,Aa)

1.4835.5

0.096.1 0.86

1.109.4

0.052.8 0.43

Baa

RatedBonds

1.07

23.7

0.11

7.1 0.75

0.94

7.8

0.27

15.8 0.71

JunkBonds


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Nonlinearity: Banks Loan Betas and Stock Equity

Betas Change with Changing Credit Quality

CorporateBondRating

Junk Bond Spread 500 bp(123 Observs in risky times)

Loan PortfolioBeta vs. SP500

Bank EquityLevered 10/1

Loan PortfolioBeta vs. SP500

Bank EquityLevered 10/1

Aaa 0.09 0.90 0.05 0.50

Aa 0.09 0.90 0.10 1.00

A 0.10 1.00 0.15 1.50

Baa 0.11 1.10 0.27 2.70

Junk(


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The Financial Panic of 2008/2009 and

the Tepid Recovery in 2010-2011

56

Six Sigma Drop In Real Estate Prices


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5757

Six Sigma Drop In Real Estate Pricesand Loan Delinquencies Soar

Real estate prices have dropped by amounts thatwere truly unmeasured previously. Recent movesreflect many (6?) standard deviation events.

We tend to gauge what is a bad scenario bylooking at historical data to see how bad situationscan be. We need to think out of the box toworlds and equilibria that have not been seen, but

are possible.

Doug, the recent Turner report in the UK suggests that one problem was that the historyUsed in the empirical analysis, often just 5-6 years, was insufficient. JWPayne

D.T. Breeden, January 2011

F f H i P i 4Q % Ch


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Frequency of Housing Price 4Q % ChangesCase Shiller 1987-2009: 6 Sigma Event.

58

0

2

4

6

810

12

14

16

18

20

D.T. Breeden, January 2011

Housing Price Percentage Declines By Metro


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59

Area to 2009/2010 Lows from 2006-2007 PeaksSource: S&P Case Shiller

-60 -50 -40 -30 -20 -10 0

PhoenixLas Vegas

MiamiSan Diego

San Francisco

Los AngelesDetroitTampa

Washington, D.C.Composite 10 MktsComposite 20 Mkts

Minneapolis

ChicagoBoston

New YorkAtlantaSeattle

ClevelandPortland

DenverCharlotte

Dallas


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2008


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Leverage Matters And if you are levered and


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Leverage Ratios (Assets/Equity) for Bear Stearns,Goldman, Morgan Stanley and Lehman 1996-2007

15.0

20.0

25.0

30.0

35.0

40.0

Dec-96

Dec-97

Dec-98

Dec-99

Dec-00

Dec-01

Dec-02

Dec-03

Dec-04

Dec-05

Dec-06

Dec-07

BSC GS MS LEH

Leverage Matters. And if you are levered andCorrelations go to 1.0 in extreme markets

63

Financial Panic of 2008/2009:Bank Stocks Fell 80% as Much As In the Great Depression


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Bank Stocks Fell 80%, as Much As In the Great DepressionEnd of Month, June 2007- Jan 2010 vs. Aug 1929- Aug1933

Fin

0

10

20

30

40

50

60

70

80

90

100

110

6/30/2007

8/31/2007

10/31/2007

12/31/2007

2/29/2008

4/30/2008

6/30/2008

8/31/2008

10/31/2008

12/31/2008

2/28/2009

4/30/2009

6/30/2009

8/31/2009

10/31/2009

12/31/2009

Bank Stocks: Great Depression 8/1929-12/1932 KBW Bank Stock Index (12/31/06=100) to 2/20/2009

64

Stock Price Falls of Big 5 Investment Banks


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Stock Price Falls of Big 5 Investment Banksin the Financial Panic of 2008/2009

Price

12/31/2006

2008

LowPrice

2009

Low Price

Feb 2010 June 30

2012

Bear Stearns $162.78 $ 4.81 Sold toJPM for

$10

GoldmanSachs

$199.35 $ 78.20 $47.41 $156.70 $95.86

Lehman

Brothers

$ 78.12 $ 0.05 Bankrupt

Merrill Lynch $ 93.10 $ 13.10 Sold toBAC

(For $27?)

MorganStanley

$ 67.20 $ 9.58 $ 6.71 $ 27.15 $14.5965

Stock Price Falls of Commercial Banks


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Stock Price Falls of Commercial Banksin the Financial Panic of 2008/2009

12/31/2006

2008 Low 2009 Low Feb 2010 June 302012

Bank ofAmerica

$53.39 $18.52 $ 2.53 $15.94 $8.18

Citigroup $55.70 $11.52 $ 0.97 $ 3.35 ($27.41/10

)= $2.74

JP Morgan $48.30 $31.02 $14.96 $39.88 $35.73

National City $36.56 $ 1.36 Sold toPNC nr 0

Wachovia $56.95 $ 1.84 Sold toWFC nr 0

Wells Fargo $35.56 $20.51 $ 7.80 $27.29 $33.4466

Stock Price Falls of Insurers and Thrifts


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Stock Price Falls of Insurers and Thriftsin the Financial Panic of 2008/2009

Price12/31/2006

2008Low Price

2009Low Price

Feb 2010 November2011

Fannie Mae $59.39 $0.43 $0.30 $ 0.96

Freddie

Mac

$67.90 $0.26 $0.25 $ 1.18

WashingtonMutual

$45.49 $0.03 Bankrupt

AIG $71.66 $1.35 $0.33 $ 1.21 ($23.91/20?)= $1.19

Ambac $89.07 $1.16 $0.35 $ 0.69

MBIA $73.06 $3.90 $2.17 $ 4.93 $8.32

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Nonlinear Risks in Corporate Bonds In the Financial


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Panic of 2008/2009: Betas Increase in Bad Times Junk Bond Return 10 Year Treasury Return vs. S&P 500 Stock

Return:

1989-2006 Data: -0.05 + 0.20 SP500

t=-0.3 t=4.7 RSQ=0.09

2007-2009 Data: 0.16 + 0.74 SP500

t=0.2 t=5.1 RSQ=0.45------------------------------------------------------------------------------------------

Baa Bond Return 10 Year Treasury Return vs. S&P 500 StockReturn:

1989-2006 Data: 0.02 + 0.06 SP500

t=0.3 t=3.4 RSQ=0.05

2007-2009 Data: 0.12 + 0.36 SP500

t=0.2 t=3.7 RSQ=0.31

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Nonlinear Credit Option Risks in Bank Stocks:


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Nonlinear Credit Option Risks in Bank Stocks:2002-2006 Growth Period Betas vs. Betas in the

Financial Panic and Great Recession of 2007-2011

Betas Increase in Bad Times

Bank Stock Return (KBW Bank Stock Index, BKX) regressed onS&P 500 Stock Return, Monthly data:

2002-2006 Data (N=60): 0.42 + 0.88 SP500

t= 2.0 t=15.3 RSQ=0.80

2007-2011 Data (N=57): -1.26 + 1.33 SP500

t=0.2 t=15.3 RSQ=0.81

And Value Lines beta estimates for many troubled banks went to

2.0 to 3.0 in the financial crisis (Citigroup, Wachovia, Bank ofAmerica and the investment banks, insurers and others). 71


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Goldman Sachs

50

100

150

200

250

300

350

5/16/2008

4/18/2008

3/21/2008

2/22/2008

1/25/2008

12/28/2007

11/30/2007

11/2/2007

10/5/2007

9/7/2007

8/10/2007

7/13/2007

6/15/2007

5/18/2007

140

160

180

200

220

240

260

(18) GOLDMAN SACHS GROUP INC Bond Spread (right axis)

Equity Prices

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Citigroup Corporate Bond Spreads vs. Equity Prices

-50

0

50

100

150

200

250

300

350

400

15 20 25 30 35 40 45 50 55 60

Stock Price

BondSpreadtoUS

t-stat: 19.4

R2: 0.54

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Bear Stearns

0

100

200

300400

500

600

700

800

9001000

5/16/

2008

4/18/

2008

3/21/

2008

2/22/

2008

1/25/

2008

12/28/

2007

11/30/

2007

11/2/

2007

10/5/

2007

9/7/

2007

8/10/

2007

7/13/

2007

6/15/

2007

5/18/

2007

0

20

40

60

80

100

120

140

160180

(1) BEAR STEARNS CO INC Bond Spread (right axis) Equity Price

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Black-Scholes-Merton Theory?


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Black-Scholes-Merton Theory?Bear Stearns Stock vs. Bond Price

0

20

40

60

80

100

120

140

9/28/2007 '10/31/07 '11/30/08 '12/31/07 '1/31/08 '2/29/08 '3/31/08 '4/30/08

Stock

Price

75

80

85

90

95

100

105

Bond

Price

Stock Bond 5.55 17 Bond 6.4

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Summary of the Main Results


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Summary of the Main Results1. The credit put option in corporate bonds and bank loans is apparent

in their returns. Returns on corporate bonds, bank loans and bankstocks (which contain portfolios of bank loans) have negative convexity,written options, and negative skewness. The Financial Panic of2008/2009 gave a dramatic demonstration of these points.

2. Risks (betas) of corporate bonds, bank loans and bank stocks allincrease in times of economic stress such as recession or whendefault fears are so great that the yield spread on junk bonds is 500basis points over Treasury. Risks are not stable on theseinvestments.

3. Merton, Black and Scholes Nobel Prize winning option insights arevery helpful in understanding the nature of proper pricing of bankloans and corporate bonds. Exact pricing of actual loans andbonds is so complex that precise formulae do not exist for all loans

Documents

corporate risk and credit risk