Transcript Loan Portfolio Credit Risk

CREDIT RISK –
LOAN PORTFOLIO AND
CONCENTRATION RISK
Class 15; Chap 12
Lecture outline

Purpose: Gain a working knowledge of how FIs measure and
manage the risk of a loan portfolio
1.
Simple models
a)
b)
2.
Modern Portfolio Theory Models
a)
b)
3.
Migration analysis
Concentration limits
Portfolio Diversification
KMV model
Loan Concentration Models
a)
Loan volume-Based Model
Simple Models
Migration Analysis
Basic Idea:


FI managers want to know how the credit risk (Rating) of loans in their
portfolio should change over time (that is, what can managers expect).
If the actual change is different from what managers expect they can ration
credit or adjust premiums
For Example:

Suppose that on average over the last five years 11 out of 100 loans have been downgraded from
a rating of BBB to a rating of BB each year.

If the FI has a portfolio of 500 BBB rated loans How many loans should the manager expect to
be rating of BB by the end of the year? 55 loans should drop to a rating BB

Suppose that over the last year, on average, 15 out of 100 BBB loans were downgraded to a
rating of BB, would the manager be concerned? Yes! More loans than expected were downgraded


This would suggest that BBB rated loans have become riskier – So what can the manager do?
The manager could then cut-back on lending to this rating category or increase the credit risk
premium
Measuring Rating Migration
Loan Rating Migration Matrix

The migration matrix tells us the percentage of bonds that start in one rating category and
move to another
The column header tells us
the rating category where
bonds end the year
The row header tells us the
rating category where loans
begin the year



AAA-A
BBB-B
CCC-C
D*
AAA-A
0.85
0.10
0.04
0.01
BBB-B
0.12
0.83
0.03
0.02
CCC-C
0.03
0.13
0.80
0.04
We read the table by rows across columns DO NOT READ DOWN THE COLUMNS
The number inside the matrix are called transition probabilities. They tell us what portion of
an FIs portfolio is expected to transition to a new rating each year
Example:

Of the loans that started the year in AAA-A category 85% remained in AAA-A
10% transitioned to BBB-B
4% transitioned to CCC-C
1% Defaulted
Migration Analysis Example
Suppose an FI manager has 211 BB rated loans, 310 AA rated loans and 130 C rated loans what
would the manager expect his portfolio to look like at the end of the year
Begin with the AA rated Loans
•
•
•
•
AAA-A = (310)(.91) = 282.1
BBB-B = (310)(.08) = 24.8
CCC-C = (310)(.01) = 3.1
D
= (310)(0) = 0
AAA-A
BBB-B
CCC-C
D*
AAA-A
0.91
0.08
0.01
0.00
BBB-B
0.08
0.83
0.05
0.04
CCC-C
0.03
0.10
0.80
0.07
BB rated Loans
•
•
•
•
AAA-A = (211)(0.08) = 16.88
BBB-B = (211)(0.83) = 175.13
CCC-C = (211)(0.05) = 10.55
D
= (211)(0.04) = 8.44
Loan Portfolio at the end of the year
C rated Loans
•
•
•
•
AAA-A = (130)(0.03) = 3.9
BBB-B = (130)(0.10) = 13
CCC-C = (130)(0.80) = 104
D
= (130)(0.07) = 9.1
•
•
•
•
AAA-A = 302.88
BBB-B = 212.93
CCC-C = 117.65
D
= 17.54
Sum each category
Suppose an FI has 100 BBB rated loans, 500 A rated loans, and 13 C rated loans. Calculate the
expected loss of the portfolio if all loans have face value of $100,000. The average recovery rate for
loans is 60%. The transition matrix is shown below
AAA-A
BBB-B
CCC-C
D*
AAA-A
0.85
0.10
0.03
0.02
BBB-B
0.11
0.80
0.05
0.04
CCC-C
0.03
0.10
0.81
0.06
Step #1 – calculate the number of bonds in each category expected to fail
AAA-A 500*.02 = 10
BBB-B 100*.04=4
CCC-C 13*.06 = .78
Step #2 – calculate the loss on the portfolio
AAA-A 10*100,000*0.6 = 600,000
BBB-B 4*100,000*0.6
= 240,000
CCC-C 0.78*100,000*0.6 = 46,800
Total
$886,800.00
Concentration Limits
Basic Idea:
The FI can set limits on the amount lent to an individual borrower or a sector
to limit exposure to a particular borrower or sector

If defaults of a borrower/sector are highly correlated the FI will usually set one
combine limit

Geographic limits are also commonly used

Regulators have limited the amount lent to one borrower to 10% of equity capital
Concentration limits Example
Suppose management has placed a limit on lending to the auto manufacturing sector such
that the maximum potential loss is no greater than 10% of equity capital. The firm has total
assets of 500 mill and liabilities of 450 mill. Historical recovery from the Auto
manufacturing sector is 40%. How much can the FI lend to the auto manufacturing sector?
Step #1 calculate the maximum equity capital the firm can lose
(0.10)(500mill  450mill)  5mill
Step #2 Calculate the loan principal that can be lent to auto manufactures
If the full amount lent to auto
manufactures (X) defaults the FI will
lose 1-.4= 60% of the principal lent
(1  .40) X  5m ill
$5,000,000
.60
X  $8,333,333.33
X
Loan concentration limit
The maximum amount the FI
can lend to auto manufactures
Example: Managers at Manhattan bank have limited lending to the computer software sector.
No more than 5% of total loan value can be lent to this sector. The bank is currently at its
limit. How much software loan value will the bank have to sell if the value of their loan
portfolio decreases by 20% but the value of their software loans stays constant. Assume that
the loan portfolio currently has a value of $50M.
Step #1 calculate the maximum equity capital the firm can lose
(capital)(0.05)
Step #2 Calculate the loan principal that can be lent to auto manufactures
( X )(.15)  capital(.05)
0.05
0.15
X  capital(0.3333333)
X  capital
X ≤33.333%
Modern Portfolio Theory Models
Portfolio Diversification
Basic Idea:

FIs can reduce the level of loan portfolio risk by ensuring that the portfolio is
well diversified – changes in default probabilities are not perfectly correlated.

The portfolio diversification model also allows the manager to measure the
level of risk in his/her portfolio

The portfolio diversification model also allows FI managers to measure how
well their portfolio is performing relative to other allocations (portfolios) with
the same risk level
Portfolio Diversification- Risk and Return
Expected Return of a portfolio:

Given historical returns of the individual assets, how do you calculate the
expected portfolio return?

It is just the weighted average of individual returns
N
N
i 1
i 1
ERP    i ERi    i R i
Risk of a Portfolio:

Risk is measured by the volatility (standard deviation) of portfolio returns

This can be calculated using the variance of individual asset returns
N
N
N
      2i  j i j  i , j
2
p
i 1
2
i
2
i
i 1 j i
Portfolio Diversification – Example
2 Loan Portfolio:
Given the following statistics for two loans, find the risk and return of the portfolio
i
 i, j
 i2
Loan
Market Value
Ri
1
40 mill
0.1
0.0857
0.007340
2
60 mill
0.12
0.0980
0.009604
-0.84
Step #1 Calculate the portfolio expected return
40m ill
60m ill




R p  1 R1  2 R2  
  0.1  
  0.12
40
m
ill

60
m
ill
40
m
ill

60
m
ill




Rp  0.4 0.1  0.6 0.12  .112  11.2%
Step #2 Calculate the risk (volatility) of the portfolio
 p2  1212  22 22  21 21  2 1,2
 p2  (0.42 )(.00734)  (0.62 )(.009604)  2(0.4)(0.6)(0.0857)(0.098)(0.84)  .0012462
 p  0.0012462 .0353 3.53%
Portfolio Diversification – Example
Portfolio Performance (Side Note):


The question here is can portfolio manager do better with a different
allocation?
The answer is maybe – in the 2 asset case NO (if there are only 2 assets in
the universe )
Example: Suppose an FI holds a bond portfolio that is fully invested in two sectors: $20 million
to consumer durables and $50 million to the healthcare sector. The expected return and volatility
for the consumer durables sector portfolio is .125 p.a. and .081 p.a. respectively. The expected
return and volatility for the health care sector portfolio is .083 p.a. and .041 p.a. respectively.
Find the risk and return of the portfolio. Correlation between the two portfolios is .32
Moody’s KMV Model
Basic Idea:




Diversification models are only appropriate for assets with normally
distributed returns but bond & loan returns are not usually considered normal
Loans are also infrequently traded – this makes estimating the expected return
and standard deviation from market data very difficult
The Moody’s KMV portfolio manager model addresses these shortcomings
Main contribution – they use proprietary probabilities of default (EDF) to
directly estimate the return on the loan and use that return in the portfolio
diversification model

We add one more step
Moody’s KMV – Loan Risk & Return
Loan Returns:
ERi   AIS  EDFi  LGDi
The return on the loan i.e. “k”
All-in-spread AIS = (return on loan – funding cost) + annual fees
Expected default frequency EDF = probability of default
Loan Risk:
Volatility of the company’s EDF
 i   i  LGD  EDFi 1  EDFi   LGD
Correlation:
In the KMV model the correlation is the correlation between the systematic
component of a bank asset returns (e.g. the systematic component of loan 1 and loan 2
returns)
Moody’s KMV Model – Example
Given the following portfolio of loans calculate the risk and return of the portfolio
Loan
Value
Return on loan
– funding cost
Annual Fees
LGD
EDF
1
30 mill
5%
2%
25%
3%
2
20 mill
4.5%
1.5%
20%
2%
Corr
-.25
Step #1 Calculate Expected Loan Returns for each loan
ERi   AISi  EDFi  LGDi
ER1   (0.05  0.02)  .03 .25
ER1   (.07)  0.0075 .0625 6.25%
ER2   (0.045 0.015)  .02 .2
ER2   (.06)  0.004  .0056 5.6%
Moody’s KMV Model – Example
Given the following portfolio of loans calculate the risk and return of the portfolio
Loan
Value
Return on loan
– funding cost
Annual Fees
LGD
EDF
1
30 mill
5%
2%
25%
3%
2
20 mill
4.5%
1.5%
20%
2%
Corr
-.25
Step #2 Calculate Loan Risk (volatility) - for each loan
 i  EDFi 1  EDFi   LGD
1  (0.03)(1  0.03)  0.25
 2  (0.02)(1 0.02)  0.2
1  .0291 0.25  .04265 4.265%
 2  .0196 0.2  0.028  2.8%
Moody’s KMV Model – Example
Given the following portfolio of loans calculate the risk and return of the portfolio
Loan
Value
Return on loan
Return Volatility
1
30 mill
6.25%
0.04265
2
20 mill
5.6%
.028
Step #3 Calculate the portfolio return
 
E R p  1 ER1   2 ER2 
 
E Rp 
 
30
20
 .0625 
 .056
50
50
E R p  0.6  .0625 0.4  .056  5.99%
Corr
-.25
Moody’s KMV Model – Example
Given the following portfolio of loans calculate the risk and return of the portfolio
Loan
Value
Return on loan
Return Volatility
1
30 mill
6.25%
0.04265
2
20 mill
5.6%
.028
Corr
-.25
Step #4 Calculate the risk (volatility) of the portfolio
 p2  1212  22 22  21 21  2 1,2
 p2  (0.62 )(.042652 )  (0.42 )(.0282 )  2(0.4)(0.6)(0.04265)(0.028)(0.25)
 p2  0.0006369
Portfolio Risk = 2.52%
Portfolio return = 5.99%
 p2  0.0006369 0.252  2.52%
Example: Suppose an FI has holds 2 loans in its
portfolio with the given characteristics. Find the
portfolio return if the correlation between the two
firms assets is 0.45
Loan #1
EDF = 0.05
LGD = 0.30
AIS = 0.12
Principal = 25 mill
Loan #2
EDF = 0.07
LGD = 0.60
AIS = 0.20
Principal = 75 mill
Loan Volume Concentration Models
Loan Volume-Based Model
Basic Idea:


Loan prices are difficult to obtain but volume (aggregate principal) is available
The volume based model measures how different a bank’s lending activity is
from the average bank in a pier group
Loan Volume-Based Model - Example
Given the concentration of lending to each of the four sectors for bank A and bank
B along with the national average below, which of the two bank differs more in its
lending activity from the average national bank
National Average
Bank A
Bank B
Real Estate
45%
65%
10%
C&I
30%
20%
25%
Individual
15%
10%
55%
Other
10%
5%
10%
Step #1 Calculate the squared difference between the national average and each bank
Bank A
Bank B
(.45  .65) 2  .04
(.45  .10) 2  .1225
(.30  .20) 2  .01
(.30  .25) 2  .0025
(.15  .10) 2  .0025
(.15  .55) 2  .16
(.10  .05) 2  .0025
(.10  .10) 2  0
Loan Volume-Based Model - Example
Given the concentration of lending to each of the four sectors for bank A and bank
B along with the national average below, which of the two bank differs more in its
lending activity from the average national bank
National Average
Bank A
Bank B
Real Estate
45%
65%
10%
C&I
30%
20%
25%
Individual
15%
10%
55%
Other
10%
5%
10%
Step #2 average the squared differences and take the square root
Bank A
0.04  0.01  .0025  .0025
 0.01375
4
0.01375 11.73%
Bank B
0.1225  0.0025  0.16  0
 0.071
4
0.071  26.69%
Loan Volume-Based Model - Example
Given the concentration of lending to each of the four sectors for bank A and bank
B along with the national average below, which of the two bank differs more in its
lending activity from the average national bank
National Average
Bank A
Bank B
Real Estate
45%
65%
10%
C&I
30%
20%
25%
Individual
15%
10%
55%
Other
10%
5%
10%
Is it bad to be different?


Banks may specialize in certain types of lending
Banks may be located in a region where certain types of lending is more
prevalent
Lecture Summary

We saw 5 different ways to measure the credit risk
of a portfolio of assets
1.
Simple models
a)
b)
2.
Modern Portfolio Theory Models
a)
b)
3.
Migration analysis
Concentration limits
Portfolio Diversification
KMV model
Loan Concentration Models
a)
Loan volume-Based Model