HHI does not show the relationship between industry credit risk and concentration risk in the loan portfolio, and does not provide the amount of risk provisions that commercial banks need to prepare for the loan portfolio.
b. Gini coefficient
The Gini coefficient is one of the classic indicators to measure the concentration risk of a loan portfolio. The formula is as follows:
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In there:
n is the total number of components of the loan portfolio (depending on the classification purpose);
j is the order of the components in the loan portfolio (arranged
in order from low to high);
μ is the average value of the loan portfolio;
: is the value of loan i, in period t.
The value of the Gini coefficient ranges from 0 to 1. The closer it is to 0, the more evenly distributed the value of loans in the portfolio is, or the risk of concentration decreases. The closer it is to 1, the less evenly distributed the value of loans in the portfolio is, or the risk of concentration increases. Similar to the HHI, the Gini coefficient is used to calculate the risk of concentration of the loan portfolio [73].
According to the study of Lagrin and Roach (2008), the value
of coefficient
Gini
higher than 0.3, the loan portfolio has concentration risk [73]. The calculation
coefficient math
The Gini coefficient is also quite complex. However, the
This has disadvantages.
score does not reflect the value of the loan portfolio. For example, if
classifying loan portfolios by economic sector, a portfolio with many sectors of the same size will have a smaller Gini coefficient than a highly diversified portfolio with many sectors with large loans. Or, if adding some sectors
Adding other assets to the loan portfolio may increase the value of the Gini coefficient (i.e. reflect increased concentration risk), but in fact it reduces concentration risk.
c. VAR (Value at risk) model
VAR is one of the traditional risk assessment methods, using supporting tools from mathematics and statistics. VAR model is used to measure the maximum loss when the worst case scenario occurs in a specified period of time based on a given probability level (or
called degree
confidence) and this VAR is called absolute VAR. To
identify
The level of economic capital that commercial banks need to hold, VAR is usually calculated by
difference between unexpected loss and expected loss
Expected Loss, in which the expected loss
loss and damage
calculate
determined from the bank's future loss distribution. [22]
Conceptually, VAR is quite easy to understand, however when implemented in
The reality is complicated, especially in measuring lending risk.
The reason is that most of the loans of commercial banks are not purchased.
sold on the market
second school
provide the data
whether necessary to help
wish
The distribution of future credit losses is very limited. To overcome this difficulty, researchers have approached credit risk models based on certain assumptions as well as economic theories to model
simulate the distribution of credit losses, from which credit VAR is determined. To measure
In measuring the risk of loan portfolios at commercial banks, there are currently four main VAR model groups in the world, including: CreditMetrics by JP Morgan, PortfolioManager by KMV, CreditRisk+ by Credit Suisse, and CreditPortfolioView by McKinsey [53].
c1. CreditMetrics
This model measures the risk of a loan portfolio based on a probability matrix of changes in credit quality. This matrix is usually determined based on credit ratings according to the standards of rating agencies.
independent rating agency (Standard & Poor's or Moody's) [78]. Then, the credit loss when the customer defaults is estimated by simulation
based on the Beta distribution. Next, CreditMetrics estimates the correlation
between changes in asset values of customers to estimate the correlation of non-repayment between customers. This is an important parameter to help determine the probability of simultaneous non-repayment of customers. However, the market value of assets owned by companies is difficult to observe in practice. Therefore, this method uses the stock prices of
companies like
a proxy variable to estimate value correlation
asset
between companies. Finally, the correlation between debts is not
The payoff will be estimated from the simultaneous non-repayment probabilities of the
customers. First, CreditMetrics
Estimated values
threshold (Z)
corresponding to each credit class according to the probability matrix of quality change
amount of credit offered
access
on (corresponding symbol)
corresponding to ZAAA, ZAA, …
ZBBB…), this threshold value varies from customer to customer depending on
initial rating and the probability of change in credit quality of that customer. Based on these threshold values, the probability that two customers are simultaneously in any pair of ratings (e.g. AABB or AABBBB….) will be easily calculated. Next, we determine the correlation of quality changes
customer creditworthiness, and the fact that two debts are not owed at the same time
The repaid debt is a special case. Specifically, the formula showing the correlation between two simultaneously unpaid debts would be as follows:
In which: p(def1,def2): Probability that two debts are not repaid
At the same time, this is a special case of the probability of simultaneous credit quality changes;
P1, P2: the probability that customer 1 and customer 2 do not repay respectively. This probability is determined based on the initial credit change probability matrix.
After determining the correlation between credit changes of customers, the value distribution of the loan portfolio is determined. The credit VAR is determined based on the threshold value of the distribution corresponding to the given confidence level (usually 99.9%). In the case of a commercial bank's loan portfolio consisting of many debts, CreditMetrics uses Monte Carlo simulation to calculate the complete value distribution of the portfolio, thereby finding the credit VAR [42].
c2. KMV PortfolioManager
In this model, the non-repayment probability of each customer is calculated directly based on the Merton option pricing approach.
(1974), this probability is called the expected default frequency EDF
(Expected Default Frequency) . This probability is calculated as a function of the capital structure components of the borrowing company, the stability of the company's asset value, and the current value of the company's assets.
Based on Merton's options approach, the borrowing of
The company is considered as
company is owning
own a put option (Put)
Option) on the company's assets, with an Exercise Price equal to the value of the debt at maturity. If the value of the company's assets is lower than the value of the debt at maturity, the company will default on the debt, which is equivalent to exercising its put option. Using the usual assumptions in option pricing theory, the price
This put option can (1973).
determined by the BlackScholes formula
According to Merton, to find EDF, the following three steps need to be taken:
Step 1: Estimate themarket value of the company's assets (V) and the volatility of that value (.
KMV estimates the market value (V) and volatility of the asset value.
corporate assets (based on the Merton model analysis that the firm's own capital
The company is equivalent to a call option on the asset.
firm with an exercise price equal to the value of the debt at maturity. The value of this call option (symbol S) and the volatility of the firm's equity value (s) are functions of the following variables:
S = f(V,,LR, c, r) (1)
s = g(V,, LR, c, r) (2)
In there:
LR: Current value of the company's capital structure;
c: the average value of the periodic interest payments on the company's long-term debt;
r: risk-free interest rate compounded continuously.
Step 2 : Determine the gap between the expected value of the company'sassets
to value
non-refundable threshold
(This distance is denoted by DD –
Distance to Default);
In there:
E(V1): expected value of the company's assets, determined under the assumption of lognormal distribution;
DPT: non-refundable threshold point.
EDF is determined from
empirical, based on
DD synthesis of
KMV. Then, credit loss in case the customer does not pay
pay
that's OK
estimated by simulations based on the Beta distribution.
Determining the correlation between two debts
non-refundable
copper
similar to CreditMetrics. Finally, the credit loss distribution is the basis for determining the credit VAR that will be found using Monte Carlo simulation.
Step 3: Convert the DD value into EDF based on historical debt and bond issuance data of a large sample of companies.
c3. CreditRisk+
This model only describes the customer's ability to default but does not take into account the possibility of changing credit quality (in other words, it does not take into account the impact of changing credit rating on the customer's ability to default). CreditRisk + is based only on value.
on the book
customer book to
conduct the model
not based on
market price framework as the two models above. CreditRisk+ is based on the principle
insurance, meaning the customer either repays or does not repay the debt
of their due date. Probability distribution of the number of loans
The non-refundable is assumed to follow a Poisson distribution. n=0,1,2,3……
In there:
: Average number of customers who do not repay over a pre-defined period of time (e.g. 1 year);
n: Number of customers who do not repay within a predetermined period.
Losses in the event of customer non-repayment are determined based on a pre-determined debt collection rate for each customer type.
and no side
depends on the model. To
find the loss distribution of a
In the loan portfolio, customers are divided into groups according to their expected losses. Each group is defined by an average number of defaults. To account for the correlation of defaults across customers, CreditRisk+ further assumes that the average default rate in each group varies randomly according to a Gamma distribution. Finally, the loss distribution of the loan portfolio is found based on
the probability of non-repayment of the groups. Since the loss distribution is determined
Based on the assumption of the probability distribution of non-repayments, VAR calculation is conveniently carried out by a closed formula without using simulation [78].
c4. CreditPortfolioView
This model is built on the assessment of the possibility of non-repayment and changes in credit quality under the influence of the macroeconomic situation. Therefore, the credit risk of the loan portfolio will be calculated based on macroeconomic variables. Suppose, the loan portfolio is divided into groups according to a specific criterion (by business sector or by loan term...) with a defined research period of t. The CreditPortfolioView model will include the following steps:
Step 1 : Determine the values of the macroeconomic variables that are determined to affect customer group j in the research period t. Eachmacroeconomic variable is given with the assumption that it can be determined by a quadratic regression model, AR(2).
Xj,t = (Xj,1,t, Xj,2,t,,… Xj,m,t); m is the number of macroeconomic variables studied.
Step 2 : Calculate Yj,t value index corresponding to customer group j in researchperiod t.
+ Xj,1,t + Xj,2,t + …..+ Xj,m,t +
: coefficient of the mth macroeconomic variable.
Step 3 : Estimate the probability of non-repayment using the following logit function:
Where: Pj,t : Conditional probability of non-repayment in period t for a certain customer segment j.
In this model, the non-repayment probability Pj,t involves the correlation
non-repayable among customers. Then, to estimate the probability of changing the conditional credit quality (Mt), we will use a matrix
future
This matrix is constructed according to the data.
historical data
belong to
Standard & Poor (symbol ΦM). Adjust ΦM by the ratio
(in which the body
The unconditional non-refundable interest rate of the jth group) is estimated by Mt .
Rely on Mt to use Monte Carlo simulation to generate distributions
value
loan portfolio with ratio
loss ratio
randomly determined
However, from there VAR can be calculated [78].
Criteria for evaluating commercial bank loan portfolio
Profitability assessment criteria
a. Proportion of income from lending activities
Profit is the ultimate goal of commercial banks, which is the surplus generated from loans. When the growth rate of income from lending activities is lower than the growth rate of lending costs, it will lead to a decrease in profits. The profitability of a loan portfolio depends largely on the ratio of
income from
lending
Ability
profitability
loan portfolio will
highly appreciated if the income ratio from lending activities is good.
Proportion of income from lending activities
= Interest income from lending activities Total income of the bank
X 100%
Based on the above indicators, we can evaluate profitability.
of the loan portfolio, thereby seeing its importance in order to have measures to improve the efficiency of loan portfolio management. The higher the proportion of income from lending activities, the more it proves that the loan portfolio management activities achieve the profit target and vice versa [40].
b. Net income from lending activities
Net income ratio
= Net income from interest on loans Total outstanding loans
X 100%
Only
This is used to
reflect ability
portfolio profitability
loans at commercial banks. Its meaning is how much net income will be generated from lending activities for one dong of outstanding debt; the higher the ratio, the higher the profit from lending activities.