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Credit Risk§ Types of Loans
§ Return on Loans
§ Models of Credit Risk measurement
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全體金融機構資產類別
--
5,000,000
10,000,000
15,000,000
20,000,000
25,000,000
30,000,000
35,000,000
81 年 83 年 85 年 87 年 89 年 91 年
資料來源:金融統計月報
單位:百萬元
庫存現金
不動產投資
證券投資
國外資產
放款
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全體金融機構負債類別
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
81年 83年 85年 87年 89年 91年 資料來源:金融統計月報
單位:百萬元央行發行之國庫券、定存單金融債券
人壽保險準備
信託資金
政府存款
企業及個人存款通貨發行額
國外資產
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金融機構存放款利差比較
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
86 87 88 89 90 91 92資料來源:金融統計月報
%本國一般銀行
外國銀行在台分行中小企業銀行
信用合作社
農漁會 信用部
信託投資公司
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放款機構額度比較
--
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
14,000,000
16,000,000
81 82 83 84 85 86 87 88 89 90 91 92資料來源:金融統計月報
單位:百萬元
信託投資公司
信合社
農漁會
中小企銀
本國一般銀行
外國銀行
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放款期限別
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
84年 86年 88年 90年 92 ( 8 )年至 月資料來源:金融統計月報
一年以下
超過一年至三年
超過三年至五年
超過五年至七年
超過七年
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金融機構逾放比例
0.001.002.003.004.005.006.007.008.009.00
10.0011.0012.0013.0014.0015.0016.0017.0018.00
84年 86年 88年 90年 92 ( 6 )年 至 月資料來源:財政部金融局
單位:百分比總體逾放比率
本國銀行(含信託投
)資公司外國銀行在華分行
基層金融機構
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Types of Loans in Taiwan
貸款部門別
0.00%
5.00%10.00%
15.00%
20.00%
25.00%30.00%
35.00%
40.00%45.00%
50.00%
84年 86年 88年 90年 92 ( 8 )年 至 月資料來源:金融統計月報
公營事業民營事業個人等政府機關
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Types of Loans in Taiwan
貸款用途別
0.00%5.00%
10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00%55.00%60.00%
84年 86年 88年 90年 92 ( 8 )年至 月
資料來源:金融統計月報
購置不動 產
購置動產
企業投資
週轉金
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Types of U. S Bank Loans(March 2001)
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
C&I Real estate Consumer Other
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Commercial & Industrial Loans
◆Term
◆Amounts
─ Syndicated Loan
◆Secured & Unsecured
◆Spot Loan & Loan Commitment
Is Commercial Loan still important ??
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Real Estate Loans
◆Mortgage Loans
◆Revolving Home Equity Loans
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Real Estate Loan i n Tai wan
--
500,000
1,000,000
1,500,000
2,000,000
2,500,000
3,000,000
3,500,000
4,000,000
4,500,000
5,000,000
84 85 86 87 88 89 90 91 92(8)
資料來源:金融統計月報
單位:百萬元
非營利團體
政府機構
公民營企業
私人
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Residential Mortgage-Lending Process
Function Rewards Risks
Origination Fees Limited
Funding/underwriting
SpreadLiquidity , interest
rate , credit
SellingFees &
commissionsLiquidity , interest
rate , credit
Servicing Fees Limited
Investor Interest & principalLiquidity , interest
rate , credit
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Individual Loans
◆Nonrevolving
e.g : Auto Loans ; Mobile Home Loans
◆Revolving
e.g : Credit Card
Other Loans
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消費性貸款類別
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
50.00%
55.00%
60.00%
86年 87年 88年 89年 90年 91年 92 ( 7 ) 年至 月
購置住宅貸款
房屋修繕貸款
汽車貸款
機關團體職工福利貸款
其他消費性貸款
信用卡循環信用餘額
建築貸款
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Credit Card in Taiwan
信用卡業務統計
05000
10000150002000025000300003500040000450005000055000600006500070000
77年 81年 83年 85年 87年 89年 91年資料來源:財政部金融局
單位:千張
發卡數(千張)
流 通 卡 數
(千張)
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信用卡業務統計
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
800,000
900,000
1,000,000
76年 80年 82年 84年 86年 88年 90年 92 8年 月
單位:百萬元
簽帳金額
預借現金
循環信用餘額
信用卡循環利率 平均利率 最高 最低本國老銀行 18. 001 19. 893(新竹國際商銀) 13. 14( )台銀本國新銀行 19. 47318 20(中國信託、台新) 18( )誠泰外商銀行 19. 9735 20( )花旗、渣打 19. 929(HSBC)
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Return on LoansInfluence Factor :
◆ Interest Rate
◆ Fees
◆ Credit Risk Premium
◆ Other Factors
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ROA per dollar lent1+k=1+ {〔 f+(BR+m) 〕 / 〔 1- 〔 b(1-
R) 〕〕}k : Gross Return on the Loan
f : Loan Origination fee
BR : Base Lending Rate
m : Credit Risk Premium
b : Compensating Balance Requirement
R : Reserve Requirement
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Expected Return on a Loan
* E (r) = p (l+k)
p: probability of repayment of the loan
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Credit Risk
Two Dimensions to Control Credit Risk
◆1+k: price or promised return
◆quantity or credit availability
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Credit DecisionsRetail
◆accept or reject
◆sorted by loan quantity
Wholesale
◆Both interest rates &
credit quantity
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Default Risk Models – Qualitative Models
Borrower-specific Factors
◆Reputation
◆Leverage
◆Volatility of Earnings
◆Collateral
Market-specific Factors
◆Business Cycle
◆Level of interest rates
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Default Risk Models – Credit Scoring Models ◆Linear Probability Model
Z i = ∑n j=1βj X ij + error
◆Logit Model
F(Zi) =1/(1+e-z)
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Default Risk Models – Credit Scoring Models◆Linear Discriminant Models
Z=1.2X1+1.4X2+3.3X3+0.6X4+1.0X5
X1 : Working capital /total assets ratio
X2 : Retained earnings/total assets ratio
X3 : EBIT/total assets ratio
X4 : Market value of equity/book value of long-term debt
ratio
X5 : Sales/total assets ratio
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Discriminant Model
Problems
◆discriminate between extreme behavior
◆Are the weights and Xi constant?
◆Ignore hard-to-quantify factors
◆No centralized database
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New Models of Credit Risk Measurement and Pricing Term Structure Derivation of Credit Risk
Mortality Rate Derivation of Credit Risk
RAROC Models
Option Models of Default Risk
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Term Structure Derivation of Credit Risk The spreads between risk-free discount bounds issued
by the Treasury and discount bounds issued by corporate borrowers of differing quality reflect perceived credit risk exposures of corporate borrowers for single payments at different times in the future.
Probability of default on a one –period debt instrument
Probability of default on a multiperiod debt instrument
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Probability of default on a one –period debt instrument
p = the probability of repayment
= the risk premium
Example 11-4
ikp 1)1(
ik
k
i
1
1
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Probability of default on a one –period debt instrument i = 10% k = 15.8%
In this case, a probability of default of 5% on the corporate bond requires the FI to set a risk premium of 5.8%.
p , 1-p , ( k - i )
95.0158.1
100.1
1
1
k
i
= k - i = 5.8%
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= the proportion of the loan’s principal and interest that is collectible on default. > 0
and are perfect substitutes for each other.
An increase in collateral a decline in
ii
ik
11
ikk 1111
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i = 10% p = 0.95 r = 0.9
%55276.0
005527638.0
100.1995.0
100.1
%10195.09.095.09.0
%101
k = 10% + 0.55276% = 10.55276%
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n
iipC
1
1
Probability of default on a multiperiod debt instrument
: the probability of the debt surviving in the ith year i
1165.093.095.0193.0
95.0
2
1
C
Example
Cumulative Default probability:
The probability that a borrower will default over a specific multiyear period
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Probability of default on a multiperiod debt instrument
Marginal Default Probability No arbitrage Forward Rate
112
2 111 ckk
Example
12.1
1.1
11.11
2
1 f 112
2 111 fii
202.1
158.1
18.11
2
1 c
112 1)1( fcp 9318.02
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Advantages and Problems Advantages
Clearly forward looking and based on market expectations.
Liquid markets for Treasury and corporate discount bonds.
Problems Treasury markets _ deep Corporate markets_ small Discount yield curve
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Mortality Rate Derivation of Credit Risk Mortality Rate
Historical default rate experience of a bond or loan
Marginal Mortality Rate The probability of a bond or loan
defaulting in any given year of issue.Total value of grade B bonds defaulting in year i of issues
Total value of grade B bonds outstanding in year i of issuesiMMR =
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Mortality Rate Derivation of Credit Risk MMR curve can show the historic default
rate
Any shape to the mortality curve is possible
The higher Mortality rates the lower the rating of the bond
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Mortality Rate Derivation of Credit Risk Problems
historic or backward-looking measures. Implied future default probabilities tend t
o be highly sensitive to the period over which FI manager calculates the MMRs.
The number of issues and the relative size of issues in each investment grade.
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RAROC (Risk-Adjusted Return of Capital) Models RAROC =
RAROC > ROE the loan should be made
One year income on a loanLoan (asset) risk or capital at risk
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RAROC Models The first problem in estimating RAROC
The measurement of loan risk
R
RD
L
LL
1
RRLDL L 1
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RAROC Models
: The change in the yield spread between corporate bonds of credit rating class i (Ri) and matched durationmatched duration treasury bonds (RG) over the last year.
Max [ ] : only consider the worst-case scenario.
0 Gi RRMaxR
Gi RR
Gi RR
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RAROC Models Example 11-6
AAA borrower 400 publicly traded
bonds (AAA) The range of Risk
Premium is from -2%~3.5%
= 10% = 2.7 Spread = 0.2% *
$1m = $2’000 Fees = 0.1% * $1m
= $1’000
AAAR
LD
$2000 + $1000-(2.7) * ($1m)(0.11/1.1)
=11.1%RAROC =
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RAROC Models
Proportion of loan lost on defaultRAROC =
Unexpected default rate One-year income on loan
Expected income per dollar lent = 0.3 cents
Unexpected default rate = 4%
Proportion of loan lost on default = 80%
RAROC = 9.375%
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RAROC Models
Add more interest income or fees Curtail the size of the loan Shorten the duration of the loan
RRLDL L 1
One year income on a loanLoan (asset) risk or capital at risk
RAROC =
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Option Models of Default Risk The Borrower’s Payoff from Loans
buying a call option on the assets of the firm
The Debt Holder’s Payoff from Loans
Writing a put option on the value of the borrower’s assets with B, the face value of debt, as the exercise price.
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Call option
0
-S
Assets (A)
Payoff to stockholders
A1
B (debt)
A2
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Put optionPayoff to debt holders
A1 B (debt)
A20 Assets (A)
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Option Models of Default Risk Applying the Option Valuation Model to
the calculation of Default Risk Premium
211 hNhNdBeF i
/ln22
11 dh
/ln22
12 dh
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Option Models of Default Risk ,T: the maturity date ; t: today
the borrower’s leverage ratio
the probability that a deviation exceeding the calculated value of h will occur
the asset risk of the borrower
tT
2
)(hN
d ABe i /
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Option Models of Default Risk
Required yield on risky debt
@ Example 11-7
121ln1 hNdhNik
k
The lender should adjust the required risk premium as leverage and asset risk change
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Example 11-7 B = $100,000 = 1 year = 12% i = 5% d = 90%
938.0
12.0
9.0ln12.0 22
1
1
h
818.0
12.0
9.0ln12.0 22
1
2
h
174120.01 hN
793323.02 hN
17412.01111.1793323.005127.1
000,100$tL
18.866,93$986788.005127.1
000,100$
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The required risk spread or premium is
k
121ln1 hNdhNik
%33.1
]986788.0ln[)1(
5%+1.33%=6.33%
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The lender’s decision matrix :
Reject H0
Accept H0
H1 is trueH0 is true
Decision
Yes
No
Good loan Bad loan
Loan repaid
Type 2 error
Type 1 error
Loan denied
Result
1
1Type 1 error
Type 2 error
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H0:the customer would default Not Grant
H1:the customer could repay Grant
Type : reject the true HⅠ 0
Bankrupt Type : accept the wrong HⅡ 0
Damage reputation
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A. CreditMetrics
B. Credit Risk+
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CreditMetrics---Introduction
Introduced by J.P. Morgan & its co-sponsors, 1997
Based on the conception of VaR The difficulties to attain the P and σ of loa
ns & Methods to solve this problem
Rating Migration---changing credit spread
1.The borrower’s credit rating2.The rating Migration matrix3.Recovery rate of default loans4.Yield spreads in the bond market
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CreditMetrics---Rating Migration
Eg. 5yr $100m 6% loan for BBB borrower
Rating Migration Probabilities
Valuation
P=6+6/(1+r1+s1)+6/(1+r2
+s2)2+
6/(1+r3+s3)3+106/(1+r4+s
4)4
Rating Transition Prob
AAA 0.02%
AA 0.33%
A 5.95%
BBB 86.93%
BB 5.30%
B 1.17%
CCC 0.12%
Default 0.18%
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CreditMetrics---Prob. Distibution
Year- End Rating
Loan Value
AAA $109.37
AA $109.19
A $108.56
BBB $107.55
BB $102.02
B $98.10
CCC $83.64
Default $51.13
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CreditMetrics---VaR & Capital Requirements
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Credit Risk+---Introduction
Developed by Credit Suisse Financial Products (CSFP)
Derive from the conceptions of fire insurance
Unlike CreditMetrics, Credit Risk+ focus on
1.The frequency of Defaults
2.Severity of Losses
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Credit Risk+---Assumptions
The prob. of any individual loan defaulting in the portfolio of loans is random
The correlation between the defaults on any pair of loans is 0
Poisson Distribution is applied More appropriate for analyzing the default rate on a large portfolio of small loans rather than a
portfolio of just a few loans
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Credit Risk---pdf
1.Prob. of n defaults=e-m*mn
n! e=2.71828
m: Historic #of defaults for loans of this type
n: # of defaults
2.Severity of Losses---average $ loss per loan defaults
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Credit Risk---calculations
E.g.. A FI makes 100 loans, each of $10,0000 M=3 Severity of loss:20 cent per$1
Prob. of 4 loans defaulting = e-3*34
4!
Dollar loss of 4 loans defaulting=4*20C*$100,000=$80,000
Possible Drawbacks of this model
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Loan Portfolio and Concentration Risk
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Simple Models of Loan Concentration Risk FI widely
employed two simple models to measure the credit risk of a loan portfolio :
1.Loan migration matrix
2.Concentration limits
1 2 3 D
1 0.85 0.10 0.04 0.01
2 0.12 0.83 0.03 0.02
3 0.03 0.13 0.80 0.04
Risk Grade at Yr End Risk G
rade a
t yr
begin
nin
gConcentration limit=Maximum loss(% of capital)
1
* Loss rate
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KMV Portfolio Manager Model---Conceptions
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MPT Applied to Bank LendingModern Portfolio Theory
ALM LINE
SellingFed
Funds
PurchasingFed Funds
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FI Portfolio Diversification
B
C
A
N
Rp=∑ Xi Ri
i=1
Σσp2=∑Xi
2σi2+
∑∑XiXjσij
Σσp2=∑Xi
2σi2+
∑∑XiXjρijσiσj
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KMV Portfolio Manager Model
σi=ULi=σDi* LGDi=√EDFi(1-EDFi) *LGDi
Ri=AISi-E(Li)=AISi -(EDFi*LGDi)
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Comparing with Benchmark
National Bank A Bank B
Real Estate
10% 15% 10%
C&I 60% 75% 25%
Individuals
15% 5% 55%
Others 15% 5% 10%
σA=10.61% σB=26.69%
4
σj= ∑(Xij-Xi)2
i=1
N
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Loan Loss Ratio-Based Models
Involves estimating the systematic loan loss risk of a particular section or industry relatives to the loan loss of an FI’s total loan portfolio
=α+βi( Total loan losses/Total loans)
Sectoral losses in the iSectoral losses in the ithth sector sector
Loans to the iLoans to the ithth sector sector
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Credit Derivates---Introduction(1/3) Usually OTC, Off-balance sheet contracts Banks can use credit derivatives to achieve more efficient
risk-return combinations without hurting customer relationships
Four Components
Payment of credit derivatives 1.Cash Settlement 2.Physical Delivery
1.The notional amount 2.The term or maturity3.The reference party whose credit is being traded4.Reference Assets
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Credit Derivates(2/3)
Types of credit derivatives Pure-credit (default) Swap
Total-return Swap
Party1 Party 2
premium
Loss Compensation
Party1Party 2
premium
Promised int. + Mkt Value Loss
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Credit Derivates(3/3) Hedge ratio=LIED for the loan/LIED for the
reference assets LIED( loss in the event of default)=1-recovery
rate e.g.. A Bank holds a $10m,senior, syndicated,
floating rate loan (estimate recovery rate=70%) Reference asset: a Bond with 50% recovery rate
Hedge ratio=(1-0.7)/(1-0.5)=60%
$10m*60%=6m
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Thanks for Paying Attention