Credit Risk and Value-At-Risk

Credit Risk Introduction

Viral V. Acharya and Stephen M Schaefer NYU-Stern and London Business School (LBS), and LBS

Credit Risk Elective Spring 2009 Credit Risk: the Main Issues

• Understanding what determines the value and risk characteristics of instruments which are sensitive to default risk (“defaultable”)  corporate debt  (some) sovereign debt  most OTC derivatives (even derivatives on government debt)  credit derivatives (even if default free) • Why is this a “hot” topic?  risk management and regulatory rules: need to include credit risks  inefficiencies in pricing credit … profitable opportunities?  “Boom” and “bust” of credit derivatives  the 2007-09 (??) credit crunch – ouch!   Future of credit derivatives and their regulation

Acharya and Schaefer: Credit Risk - Introduction 2 Size of the Credit Derivatives Market

50,000 45,460 )

n 40,000 o i 34,400 l l i b

$ 30,000 ( l a n o i 20,000 17,100 t o N 10,000 8,420 1,189 1,952 40 180 350 5 86 893 0 1 1 1 1 2 2 2 2 2 2 2 9 9 9 0 0 0 0 9 0 0 0 9 9 9 0 9 0 0 0 0 0 0 0 7 8 9 0 4 5 6 7 1 2 - 9 6 year

Source: British Bankers Association; ISDA (2005 and after) – 2007: to mid-year

Acharya and Schaefer: Credit Risk - Introduction 3 Outstanding Credit Default Swaps (CDS) in Notional ($billions), Source: ISDA

Acharya and Schaefer: Credit Risk - Introduction 4 CDO Issuance ($millions), Source: SIFMA

100000 90000 80000 70000 60000 50000 M tgs 40000 Loans Other 30000 Tot 20000 10000 0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 01- 01- 02- 02- 03- 03- 04- 04- 05- 05- 06- 06- 07- 07- q1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3 q1 q3

Acharya and Schaefer: Credit Risk - Introduction 5 SIZE of Mortgage-backed CDO Issuance ($mm), Source: SIFMA

120000

100000

80000

60000

40000

20000

Acharya and Schaefer: Credit Risk - Introduction 6 Thriving banks may be needed for credit derivatives to thrive again… How soon will that be?

Acharya and Schaefer: Credit Risk - Introduction 7 Course objectives • Significant progress in credit risk modelling over last few years • All recent models use “option pricing” technology but two main strands have emerged:  structural models: look like option pricing models in which defaultable bond is contingent claim on assets of firm  reduced-form or “default intensity” models: these models look more like term structure models • Objectives: to understand  nature of default risk  alternative approaches to valuing credit risky instruments  credit derivatives: credit default swaps (CDS) and collateralised debt obligations (CDO)  liquidity effects NOT captured in current models and how some of these contributed to the ongoing crisis…

Acharya and Schaefer: Credit Risk - Introduction 8 Getting Started: the Price of a “Defaultable” Zero Coupon Bond

• The payoff on a defaultable zero-coupon bond is

Face Value - "Loss in Default"

• We can therefore think of the value of a defaultable zero-coupon bond as:

=PV(Face Value) − PV ("Loss in Default") 1 = Price(Riskless Zero) - ( RN-Prob(default) Loss in Default ) + 1 R f 1444444442444444443 Credit risk price discount

Acharya and Schaefer: Credit Risk - Introduction 9 Key Elements in Valuing the Credit Risk Discount

1 ( RN-Prob(default) Loss in Default ) + 1 R f 1444444442444444443 Credit risk price discount • Event of default  economic mechanism  definition – particularly important in credit derivative contracts • Probability of default? • Loss rate (or recovery) in default • Riskless term structure • Risky term structure or the dynamics of credit risk

Acharya and Schaefer: Credit Risk - Introduction 10 This lecture • Traditional approaches to assessment of credit risk  credit ratings  One-period  Multi-period  Z-score • Determinants of credit spreads – some very simple intuition  default rates  recovery rates  cyclicality of default rates and recovery rates • Conceptual introduction to structural and reduced-form models

Acharya and Schaefer: Credit Risk - Introduction 11 Traditional Approaches to Assessment of Credit Risk

The Rating System

Acharya and Schaefer: Credit Risk - Introduction 12 Credit Rating Systems • Traditional approach to assessment of credit risk employs credit ratings • These use accounting data, historical default frequencies, judgmental factors etc. Description Moody6s S&P Highest safety Aaa AAA High quality Aa1, Aa2, Aa3 AA+,AA,AA - Upper medium A1, A2, A3 A+, A, A - Lower medium Baa1, Baa2, Baa3 BBB+,BBB, BBB - Junk Bonds Low grade Ba1, Ba2, Ba3 BB+,BB,BB - Highly spec B1, B2, B3 B+, B, B -

Acharya and Schaefer: Credit Risk - Introduction 13 One Year, Weighted-Average Default Rates by Rating

7.00%

6.00% 1920-1997 1970-1997

5.00%

4.00%

3.00%

2.00%

1.00%

0.00% Aaa Aa A Baa Ba B Credit Rating Source: Moody’s Acharya and Schaefer: Credit Risk - Introduction 14 • What counts as default?

Acharya and Schaefer: Credit Risk - Introduction 15 Moody's Definition Of Default: Three Types of Credit Event 1. A missed or delayed disbursement of interest and/or principal, including delayed payments made within a grace period; 2. Bankruptcy, administration, legal receivership, or other legal blocks (perhaps by regulators) to the timely payment of interest and/or principal; 3. A distressed exchange occurs where: (i) the issuer offers bondholders a new security or package of securities that amount to a diminished financial obligation (such as preferred or common stock, or debt with a lower coupon or par amount, lower seniority, or longer maturity); or (ii) the exchange had the apparent purpose of helping the borrower avoid default.

• The definition of a default is intended to capture events that change the relationship between the bondholder and bond issuer from the relationship which was originally contracted, and which subjects the bondholder to an economic loss. • Technical defaults (covenant violations, etc.) are not included in Moody's definition of default.

Acharya and Schaefer: Credit Risk - Introduction 16 What do credit ratings mean?

• Credit ratings are intended partly, but not purely, as measures of default probability • Credit ratings are stable measures of credit quality through the business cycle  Lehman Brothers’ rating was A2 until 15 September 2008 when it filed for bankruptcy, and then B3! • Rating also reflects “quality of assets” and likely loss in event of default (loss-given-default or LGD) • Rating momentum: Bad news appears not to be incorporated in one step: a downgrade is more likely to be followed by another downgrade than an upgrade.

Acharya and Schaefer: Credit Risk - Introduction 17 Rating Momentum: Three-Year Default Rates Conditional on Last Rating Change within 12 Months

60 most recent rating change: Upgraded 50 unchanged Downgraded 40

0 Investment- Baa Ba B Caa Grade

Source: Moody’s, “Rating Transitions and Defaults Conditional on Watchlist, Outlook and Rating History”, 2004

Acharya and Schaefer: Credit Risk - Introduction 18 One-Year and Multiple Year Default Rates: Transition Matrices

Acharya and Schaefer: Credit Risk - Introduction 19 5, 10, 15, and 20-Year Default Rates, 1920-97

60.00%

50.00% 5-Year 10-Year 15-Year 20-Year

40.00%

30.00%

20.00%

10.00%

0.00% Aaa Aa A Baa Ba B Credit Rating Source: Moody’s

Acharya and Schaefer: Credit Risk - Introduction 20 Relation between one-year and multi-year default rates: transition matrices

• If one-year probability of default of a bond with current

rating A is pA then probability of survival is (1- pA) • But, default probability over two years is not 2 1− (1− pA )

because bond rating at end of year may be different and probability of default in second year higher or lower • The effect of rating migration can be modelled using transition matrices, the probability that a bond with a rating of A, say, at the start of the year is A, AA, AAA, BBB etc. at the end

Acharya and Schaefer: Credit Risk - Introduction 21 Multi-year transition matrices • E.g. assume “High” state and “Low” state of credit quality with a one period transition matrix H L M = H .9 .1   L .2 .8 • We want to find the two-period matrix: e.g., suppose current rating is A -- rating can remain A or migrate to B: .9 H 2 .9 H .9 + (.1)(.2) + = .83 .1 H .2

.1 L L (.1)(.8) + (.9)(.1) = .17 .8

Acharya and Schaefer: Credit Risk - Introduction 22 Multi-year transition matrices (cont’d)

• Two-period transition matrix is just square of one period transition matrix

  .9 .1.9 .1 .92 + (.2)(.1) (.9)(.1) + (.1)(.8) M 2 =    =   .2 .8.2 .8 (.2)(.9) + (.8)(.2) (.2)(.1)+.82  .83 .17 =   .34 .66

• n-period transition matrix is just Mn

Acharya and Schaefer: Credit Risk - Introduction 23 Credit Transition Matrix: Example

Rating at year-end (%) Initial AAA AA A BBB BB B CCC Default Rating AAA 90.81 8.33 0.68 0.06 0.12

AA 0.70 90.65 7.79 0.64 0.06 0.14 0.02

A 0.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06

BBB 0.02 0.33 5.95 86.93 5.30 1.17 0.12 0.18

BB 0.03 0.14 0.67 7.73 80.53 8.84 1.00 1.06

B 0.11 0.24 0.43 6.48 83.46 4.07 5.20

CCC 0.00 0.22 1.30 2.38 11.14 64.86 19.79

Default 100

Acharya and Schaefer: Credit Risk - Introduction Source: Moody’s 24 Transition Matrices and Default Rates

• Multiplying the one-year transition matrix by itself once, twice, three times etc., gives the default probabilities over 2, 3, 4 years etc.

Cumulative Default Rates AAA AA A BBB BB B CCC 1 year 0.00 0.00 0.09 0.43 2.18 5.98 20.46 10 years 2.34 2.72 3.87 7.26 27.71 38.59 53.79

7.26

Source: Standard & Poor’s CreditReview

Acharya and Schaefer: Credit Risk - Introduction 25 Z-scores

Acharya and Schaefer: Credit Risk - Introduction 26 Accounting-based Statistical Models

• Z-score by Altman (1968, 2000) and its variants • The Z-score is given by:

Z = 0.012 X1 + 0.014 X2 + 0.033 X3 + 0.006 X4 + 0.999 X5

• Contributors to the Z-score:

 X1 = Net Working Capital / Total Assets in % (e.g., 15 for 15%)

 X2 = Retained Earnings / Total Assets in %

 X3 = EBIT / Total Assets in %

 X4 = Market Value of Common and Preferred Stock / Book Value of Debt in %

 X5 = Sales / Total Assets expressed as a ratio (e.g., 1.5) Acharya and Schaefer: Credit Risk - Introduction 27 Z-score

• The higher the Z-score, the lower the probability of bankruptcy

• How is the Z-score calculated?  multiple discriminant analysis  linear function of accounting variables to discriminate between the two groups: defaulting vs. non-defaulting  minimize variance within groups while maximizing variance across groups

• The model predicts bankruptcy two years ahead with good accuracy and five years ahead with some accuracy

Acharya and Schaefer: Credit Risk - Introduction 28 Bankrupt and non-bankrupt firms

• Altman found the following values for bankrupt and non- bankrupt set of firms: BANKRUPT NON-BANKRUPT  Net WC = -6.1% 41.4%  Retained earnings = -62.6% 35.5%  EBIT = -31.8% 15.4%  Market Value = 40.1% 247.7%  Sales = 1.5% 1.9% • Based on these, Z-score for bankrupt firms = -0.25 and that for non-bankrupt firms = +4.88 • Z-score thresholds: Bankrupt Zone-of-ignorance Non-bankrupt <1.81 1.81-2.99 >2.99

Acharya and Schaefer: Credit Risk - Introduction 29 WorldCom Z-score

Ratio 1999 2000 2001

Working capital / Total Assets (0.08) (0.08) (0.00)

Retained Earnings / Total Assets (0.01) 0.03 0.04

EBIT / Total Assets 0.08 0.08 0.02

Market value of equity / Book value of total liabilities 3.58 1.13 0.54

Net Sales / Total Assets 0.39 0.40 0.34

Z-score 2.697 1.274 0.798

Acharya and Schaefer: Credit Risk - Introduction 30 Z-score predicted Enron default better than stock markets due to greater reliance on balance-sheet data EDF Equivalent Rating CC CCC

BBB

AAA

Acharya and Schaefer: Credit Risk - Introduction 31 Understanding the spread – first steps

Acharya and Schaefer: Credit Risk - Introduction 32 What Determines the Credit Spread? – A Very Simple Model

• Suppose a one-period defaultable bond pays  100: if no default (prob. = 1-p)  100 (1-L) if default (prob. = p) where L is the percentage loss-given-default (LGD) • Equating 100 discounted at “promised” yield to present value of expected payoff (using riskless rate to discount) :

100 100(1−p ) + 100(1 − L ) p −= spread y R Lp 1+y 1 + R i.e., spread is equal to Lp, the “expected loss rate” • if L = 1, i.e., if LGD is 100%, then – ignoring risk premia – spread is equal to default probability

Acharya and Schaefer: Credit Risk - Introduction 33 Average Credit Spreads and Default Probabilities

Average Default Probability Average Credit Spread Credit Rating 10 yrs 1 year 10 yrs

Aaa 0.77% 0.0077% 0.63

Aa 0.99% 0.099% 0.91

A 1.55% 0.156% 1.23

Baa 4.39% 0.448% 1.94

Ba 20.63% 2.248% 3.20

B 43.915 5.618% 4.70

Source: Huang, J. & Huang, M., “How Much of the Corporate-Treasury Yield Spread is Due to Credit Risk”, Working Paper, Smeal College of Business, Penn State Univ.

Acharya and Schaefer: Credit Risk - Introduction 34 The Credit Spread Puzzle • Loss-given-default (L) is typically around 50%, so – ignoring risk premia – a typical credit spread should be around half the annual default probability • This is far lower than we observe in practice: L x p (b.p.) Av Credit Spread (b.p.) A 8 123

B 281 470

• The jury is still out on precisely why, but progress is being made (cyclicality so risk premium, liquidity, …)

Acharya and Schaefer: Credit Risk - Introduction 35 Default Rates

Acharya and Schaefer: Credit Risk - Introduction 36 One-Year Corporate Issuer Default rate: Investment Grade and Sub-Investment Grade (1920-2004)

18 1.80

16 Sub-Investment Grade (left hand scale) 1.60 Investment Grade (right hand sclae) 14 1.40

) 12 1.20 ) % % ( (

e e t t 10 1.00 a a r r t t l l

u 8 0.80 u a a f f e e d 6 0.60 d

4 0.40

2 0.20

0 0.00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0

Source: Moody’s Acharya and Schaefer: Credit Risk - Introduction 37 Baa-Aaa Spread and One-Year Investment Grade Default Rates, 1920-2004

4.50 1.80 Baa - Aaa Spread (left hand scale) 4.00 Investment Grade (right hand sclae) 1.60

3.50 1.40 ) % (

3.00 1.20 ) d % a ( e r e

2.50 1.00 t p a S r

t l A

2.00 0.80 u A a A f

- e

d a 1.50 0.60 a B 1.00 0.40

0.50 0.20

- 0.00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 0 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0

Source: Moody’s Acharya and Schaefer: Credit Risk - Introduction 38 Quarterly Default Rate and Four-Quarter Moving Average, 1991–3Q 08 Source: Altman High Yield Bond Default and Return Report

Q uarterly M oving 6.0% 16.0% 14.0% 5.0% e g a

e 12.0% r t e a 4.0% v R

A t 10.0% l g u n a i f v

e 3.0% 8.0% o D

y l r r

6.0% e e t

t 2.0% r r a a u

u 4.0% Q

Q -

1.0% 2.0% 4 0.0% 0.0% 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 Q 8 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 9 9 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 0 0 8

Acharya and Schaefer: Credit Risk - Introduction 39 Cyclicality is potentially important

Acharya and Schaefer: Credit Risk - Introduction 40 Default Rates are Cyclical

Shaded areas are NBER-dated recessions. For annual data, any calendar year with at least 5 months being in a recession as defined by NBER is treated as a recession year. Data source: Moody's.

Source: “Macroeconomic Conditions and the Puzzles of Credit Spreads and Capital Structure”, Hui Chen, Working Paper, Graduate School of Business, University of Chicago, Jan. 2007. Acharya and Schaefer: Credit Risk - Introduction 41 Default Rate and the Business Cycle

::%

-: % Speculative Grade Default Rate % GDP Growth rate -: %

: 4 : 8 : 2 : 6 : 0 : 4 : 8 : 8 : 9 : 9 : 0 : 0 : 9 : 9 : 9 : 9 : 0 : 0 : 1 : 1 : 1 : 1 : 2 : 2

Acharya and Schaefer: Credit Risk - Introduction 42 NBER Definition of Recession

A recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. A recession begins just after the economy reaches a peak of activity and ends as the economy reaches its trough. Between trough and peak, the economy is in an expansion. Expansion is the normal state of the economy; most recessions are brief and they have been rare in recent decades.

Source: http://www.nber.org/cycles/recessions.html

Acharya and Schaefer: Credit Risk - Introduction 43 Recovery Rates are also Cyclical

Data source: Value-weighted average recovery rates for “All Bonds” and “Sr. Unsecured” are from Moody's. “Altman Data Recovery Rates” are from Altman and Pasternack (2006). Shaded areas are NBER-dated recessions.

π 1 no default -p B B 1

1 ( RN-Prob(default) Loss in Default) Bad 1+ R f p 1444444442444444443 B Credit risk price discount 1-LB default 1 = ( πm L + π m L ) + GGGBBB 1 R f

ms : stochastic discount factor • Cyclicality increases credit spread since, in “bad” state:

 higher market value of losses (stochastic discount factor, ms, high)  higher loss-given-default (L) Acharya and Schaefer: Credit Risk - Introduction 45 This Course…

Acharya and Schaefer: Credit Risk - Introduction 46 Modelling Default: Two Approaches Structural Approach Default Intensity Approach • Idea: default occurs as a result • Model probability f of default of deficiency of financial directly resources • In simple models: no relation to • Example: V(assets) < V(debt) firm value • More generally: firm value hits • Relative value approach some boundary • Rather like tossing a coin (but • “fundamental value” approach coin comes down on “default” 0.035 side very rarely)

0.030

0.025 y t i s n e 0.020 d y t i l i b 0.015 a b o r p 0.010 Level of debt = 0.005 Default threshold 0.000 60 80 100 120 140 160 Asset value at Debt Maturity

Acharya and Schaefer: Credit Risk - Introduction 47 Default predictors based on structural models fare much better than ratings…

Acharya and Schaefer: Credit Risk - Introduction 48 Dollar Denominated (Altman) Default Rate [t+1] Versus Yield Spread[t] Source: Altman High Yield Bond Default and Return Report Regression equation: Default Rate- 3.25= + 1.39 * Spread

Predictor Coef SE Coeftest P valu T e Constant -3.2493 0.9238- 3.52 0.002 Spread 1.3913 0.1778 7.83 0.000

R-Sq = 69.4% - Sq(adj) R = 68.3%

Acharya and Schaefer: Credit Risk - Introduction 49 Relation between structural and intensity approaches

Capital structure Long run financial policy Value of Firm assets Risk of firm assets Corporate debt

(structural) f o n n i n o e i s c o t e i t a v r i o u t p f l t a a d ) e v y v i n n r o t ? e i v e b s i d t f n a t o e l i t e d s n e i R r m ( c r e t

Value of credit derivatives

Acharya and Schaefer: Credit Risk - Introduction 50 Missing link…

Liquidity ???

• We will discuss liquidity issues in some detail

• The goal of understanding models WITHOUT LIQUIDITY EFFECTS is to get a good grasp of when the model will fail and LIQUIDITY EFFECTS MATTER…

Acharya and Schaefer: Credit Risk - Introduction 51 YTM Spread Between High-Yield Bonds and 10- Yr Treasury Notes, 1 Jun 07–31 Oct 08 Source: Altman High Yield Bond Default and Return Report

10/24/08 (1,567bp) 1,800 1,600 What is moving? Risky yield or 1,400 Risk-free rate? Flight to quality? 1,200 10/31/08 (1,468bp) 1,000 800 600 6/30/08 (715bp) 400 6/12/07 (260bp) 200

07 7 7 07 7 7 7 7 7 7 7 8 8 08 8 8 08 8 8 08 8 8 08 8 8 0 00 00 0 00 00 00 00 00 00 00 00 00 0 00 00 0 00 00 0 00 00 0 00 00 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /2 /1 2 3 /3 4 4 5 6 6 7 1 2 2 /4 5 5 /6 7 7 /8 9 9 /9 0 1 6 /2 /1 8 /2 /1 0/ /2 /1 2/ /3 /2 /1 3 /2 /1 5 /2 /1 7 /2 /1 9 /3 /2 6 7 8 9 1 10 11 1 12 1 2 3 4 5 6 7 8 9 10 Acharya and Schaefer: Credit Risk - Introduction 52