finc629 first lecture student version

8/12/2019 FINC629 First Lecture Student Version

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FINC629Credit Risk Management

Dr. Huong Dieu [email protected]

Skype: FINC311_FINC652_UC

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mailto:[email protected]:[email protected]


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Financial risk categories

Risk is the volatility of unexpected outcomes (businessrisk, financial risk, legal risk, etc.)

Risk faced by bondholders:

Credit risk: default risk, credit downgrade risk, credit spread risk Interest rate risk Yield curve risk Call and reinvestment risk Prepayment risk Liquidity risk Inflation risk Volatility risk Sovereign risk

Event risk 2


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Default Risk

Default risk is the risk that the issuer will fail to satisfy theterms of the bond obligation with respect to the timelypayment of principal and interest.

The percentage of a population of bonds that is expectedto default is called the default rate .

A default does not mean the investor loses the entireamount invested, a percentage of the investment may berecovered. This is referred to as the recovery rate .


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Credit Spread Risk

In the U.S. the Treasury security with the same maturity as the risky bondbeing evaluated is considered to be risk-free. The yield on a bond is made up of two components:

The yield on a similar default (risk-free) bond A premium above the yield on a default-free bond to compensate for the

additional risk of the bond (risk premium)

The risk that the pricean issuers bonds willdecline due to anincrease in the creditspread is called thecredit spread risk.

The credit spreadtrends to increaseduring recessions anddecrease duringeconomic expansions.


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Downgrade Risk

The quality of any bond is based on the issuer's financialability to make interest payments and repay the loan infull at maturity.

Bond Ratings: The bond's credit rating is the firstindication of the bond's quality.

Third-party ratings such as Standard and Poor's (S&P),Moody's, and Fitch assign ratings to bonds, which reflecttheir evaluation of the creditworthiness of an issuer.


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Credit ratings scales

S&P ratings

AAA AA+, AA, AA-

A+, A, A- BBB+, BBB, BBB- BB+, BB, BB- B+, B, B- CCC+, CCC, CCC- CC C

D (default)

Moodys ratings

Aaa Aa1, Aa2, Aa3

A1, A2, A3 Baa1, Baa2, Baa3 Ba1, Ba2, Ba3 B1, B2, B3 Caa1, Caa2, Caa3 Ca C

Investmentgrade ratings

Speculative(junk) grade

ratings

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Interest rate risk

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Prices and yields(required rates ofreturn) have an inverserelationship

The bond price curveis convex.Progressiveincreases in theinterest rate resultin progressivesmaller reductionsin the bond prices


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Yield Curve Risk Parallel Shift

The yield curve isactually a series ofyields, one for eachmaturity.

Duration can be used ona portfolio of fixedincome securities to

understand theapproximate change in aportfolios value for a 100basis point change in theyield for all maturities.

Duration is a measure ofthe effective maturity of abond

Duration =


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Yield Curve Risk Nonparallel Shift

To determine the impact of interest rate risk on a portfolio of bonds with differingmaturities, a rate duration is computed to measure the impact of a rate change in atparticular maturity

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Example of Measuring Price Sensitivity toYield Change

Percentage Price Change for four hypothetical Bonds

Initial yield for all bonds is 6%.

Percent Price Change

New Yield 6% 5 year 6% 20 year 9% 5 year 9% 20 year

4.00 8.98 27.36 8.57 25.04

5.00 4.38 12.55 4.17 11.53

5.50 2.16 6.02 2.06 5.54

5.90 0.43 1.17 0.41 1.07

5.99 0.04 0.12 0.04 0.11

6.01 -0.04 -0.12 -0.04 -0.11

6.10 -0.43 -1.15 -0.41 -1.06

6.50 -2.11 -5.55 -2.01 -5.13

7.00 -4.16 -10.68 -3.97 -9.89

8.00 -8.11 -19.79 -7.75 -18.4

Greatest change for lower coupon,longer maturity, lower yield


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Risks faced by bond holders (cont.)

Call and reinvestment risk The cash flow pattern of a callable bond is not known with

certainty because it is not known when the bond will becalled.

Falling interest rates may prevent bond coupon paymentsfrom earning the same rate of return as the original bond.

The price appreciation potential of the bond will be reducedrelative to a comparable option-free bond.

Prepayment rate: Investors in mortgage- and asset-backed bonds face the risk

that the borrower can prepay principal prior to scheduledprincipal payment dates

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Call and prepayment risk (cont.)

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If interest rates fall, priceof straight bond can riseconsiderably.The price of the callable

bond is flat over a rangeof low interest ratesbecause the risk ofrepurchase or call is high.When interest rates arehigh, the risk of call isnegligible and the valuesof the straight and thecallable bond converge.


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Risk faced by bond holders (cont.)

Liquidity risk Liquidity risk is the risk that the investor will have to sell

the bond below its indicated value, where the indication isrevealed by a recent transaction.

The primary measure of liquidity is the size of the spreadbetween the bid price (what the dealer is willing to pay)and the ask price (what the dealer is willing to sell).

A liquid market is generally defined by a small bid-askspread which does increase materially for largetransactions

Inflation risk Inflation or purchasing power risk arises from the decline in

the value of a bonds cash flows due to inflation. 13


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Volatility risk The risk that the price of a bond with an embedded option

will decrease when expected yield volatility changes. Basic option valuation: The price of an option increases

with more volatility of the underlying asset, all thingsequal.

Therefore, changing yield volatility affects the price of abond with an embedded option

The greater the expected yield volatility, the greater the value(price) of an option.

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Sovereign local currency debts default

Country Default date Rating one yearbefore default

Argentina 11/6/01 BBB-Dominican Republic 4/9/99 BBEcuador 12/15/08 B-Jamaica 1/14/10 BSuriname 1/1/00 Grenada 1/1/05 BB-Grenada 12/1/06 B-Cameroon 1/09/2004 B

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Sovereign foreign currency debt default

Country Default date Rating one year beforedefault Argentina 11/6/01 BBBelize 12/7/06 CCC-Dominican Republic 2/1/05 CCCEcuador 12/15/08 B-

Grenada 12/30/04 BB-Indonesia, first default 3/29/99 B-Indonesia, second default 4/17/00 CCC+Indonesia, third default 4/23/02 B-Jamaica 1/14/10 BPakistan 1/29/99 B+Paraguay 2/13/03 BRussia 1/27/99 BB-Seychelles 8/7/08 BUruguay 5/16/03 BB-Venezuela 1/18/05 B-

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Event risk: Occasionally an issuer is unable to make either interest

or principal payments because of unexpected events,such as a natural catastrophe or disaster, a corporatetakeover or restructuring, or a regulatory change

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Drivers of credit risks

Default probability p : A counterparty fails to make contractually promisedinterest/ principal payments or to comply with otherconditions of the debt agreement

The present value of its assets is smaller than the presentvalues of its liabilities It files for bankruptcy

Credit exposure (CE) / exposure at default (EAD): The

economic or market value of the claim on the counterparty Loss given default (LGD): the fractional loss due to default

LGD=1-recovery rate

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Default distribution for a single loan

Let us assume that There are only two possible states: default / no default Probability of default = p EAD=1$

LGD=100% We start with a portfolio containing only one loan:

p Default

no default

credit eventprobability

1 p

loan

Distribution of credit losses

0 1

1-p

p

CL

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Default distribution for independent loans

If default events are statistically independent p(A and B)=p(A) * p(B)

Example: Three loans with PD = p (independent) Prob(loan 1 defaults; others do not): p(1-p) 2

Prob(exactly one loan defaults) = 3*p(1-p)2

1= p 3 +3p 2 (1-p)+3p (1-p) 2 +(1-p) 3 In general: binomial distribution:

E(x) =N*p

Var(x) = N*p(1-p) Prob(exactly n defaults from N loans ) =

Where

(1 )n N n N

p pn

!

!( )!

N N

n n N n

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Default distributions for dependent loans

If default events are not independent, the probabilityof join default, p(A and B), depends on the marginalprobabilities and correlation

Example 1 . The correlation=0.5, and p(A)= p(B)=0.01

, ( ) ( ) A B A B A B A B E b b Cov b b E b E b p A p B

(1 ) (1 ) ( ) ( ) A B A A B B E b b p p p p p A p B

A B Default No default Marginal

Default 0.00505 0.00495 0.01

No default 0.00495 0.98505 0.99

Marginal 0.01 0.99

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Measuring credit losses (cont.)

Assume that (i) all creditors have the same distribution of p andLGD; and (ii) EAD are the same (EAD =1$) The expected credit loss is linear in the default probability p

where n is the number of actual losses Standard deviation of credit loss and probability of default p

have non-linear relationship

The dispersion of credit loss (SD[CL]) is greater than theexpected loss (E[CL]) for higher default rate p

( )i E CL E n E EAD E LGD Np E LGD

2 2{ } { }SD CL E n V LGD V n E LGD

2

{ } (1 ){ }SD CL NpV LGD Np p E LGD

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Example 2 A portfolio of N equal loans with total value of $100 mio.

Defaults are statistically independent (correlation=0). Loanshave equal probability of default p=1%. LGD=100%

N=1Expected loss (EL)=0.01*100mio+0.99*0=1mioSD ={0.01*0.99*1*(100mio)^2} 1/2 =9.94 mioHighly skewed distribution

N=10

N=100

26 2{ } (1 ){ }SD CL NpV LGD Np p E LGD


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Example 3

A portfolio with 3 bonds A, B, C Assume:

Exposures are constant Recovery rate if default occurs is zero Default events are independent across the three issuers

Expected loss=$13.25

Issuer Exposure Probability

A $25 0.05

B $30 0.1

C $45 0.2

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Expected loss vs. unexpected loss

losses

p r o b a b i l i t

y d e n s i t

y

Expected loss

95% quantile (Value at Risk)

(time horizon: 1 year)

Unexpected loss

The portfolio distribution is usually described through:

Expected Loss (EL) % quantiles: loss which exceeds % of all possible losses (credit VaR or total loss )

Unexpected Loss = credit VaR EL=$31.75

The expected credit loss depends on individual default probabilities but not on default correlation

The higher the default correlation the higher the unexpected credit loss

$13.25 $45

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Credit risk vs market risk

Credit risk

Sources: Default risk, recoveryrisk, market risk (EAD)

Distribution: Strongly skewedto the left Time horizon (corrective

actions) : Long term (years)

Legal issues: Very important Risk aggregation : Whole firm

vs. counterparty

Market risk

Sources: Market risk

Distribution : Mainlysymmetrical, fat tails Time horizon : short term

(days)

Legal issues: Not applicable Risk aggregation : Business/

Trading unit

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Example 4 (Jorion, p. 463, 19.7)

A portfolio consists of two bonds. The credit VAR isdefined as the maximum loss due to defaults at aconfidence level of 98% over a one-year horizon.The probability of joint default of the two bonds is

1.27%, and the default correlation is 30%. The bondvalue, default probability, and recovery rate forbond A are $1 mio, 3% and 60%, and for bond B are$600,000, 5% and 40%What is the expected credit loss of the portfolio?

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A B Default No default Marginal

Default 0.0127 0.0173 0.03

No default 0.0373 0.9327 0.97

Marginal 0.05 0.95 1

Default i Loss CLi Probability p i

Cumulativeprobability

Expected lossELi = CLi *p i

Variance p i *(CLi EL )2

None $0 0.9327 0.9327 0B $0.36 mio 0.0373 0.97 ?

A $0.4mio 0.0173 0.9873 ?

A and B 0.76mio 0.0127 1 ?

Sum $30,000

What is the best estimate of the unexpected credit loss for this portfolio?400000-30000=$370000

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A portfolio of bonds consists of five bonds whose defaultcorrelation is zero. The one- year probabilities of default ofthe bonds are 1%, 2%, 5%, 10%, and 15%. What is the one-year probability of no default within the portfolio?

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There are 10 bonds in a credit default swapbasket. The probability of default for each ofthe bond is 5%. The probability of any onebond defaulting is completely independent ofwhat happens to the other bonds in thebasket. What is the probability that exactly

one bond defaults?

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A bank has booked a loan with totalcommitment of $50,000 of which 80% iscurrently outstanding. The default probability

of the loan is assumed to be 2% for the nextyear, and loss given at default is estimated at50%. The standard deviation of loss given atdefault is 40%. Drawdown on default (i.e. thefraction of the undrawn loan) is assumed tobe 60%. Calculate the expected andunexpected losses (standard deviation)

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Example 8 (cont.)

EAD=80%*50,000+60%*(20%*50,000)=$46,000EL= $460V[CL]=pV[LGD]+p(1-p){E[LGD]}2

V[CL]=0.0810SD[CL]=0.09

Unexpected loss=$4,140

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Consider an A-rated bond and a BBB-rated bond.Assume that the one-year probabilities of default forthe A- and BBB-rated bonds are 2% and 4%

respectively, and that the joint probability of defaultof the two bonds is 0.15%. What is the defaultcorrelation between the two bonds?

Probability of joint default

(1 ) (1 ) ( ) ( ) A B A A B B E b b p p p p p A p B

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