Download Implication of the Financial Crisis and Credit Risk Controlling Model

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Implication of the Financial Crisis and Credit Risk Controlling
Model
XU Weide, WEN Guoquan
The School of Management of Southwest University for Nationalities, Chengdu, 610041
The School of Economy of Southwestern University of Finance and Economics, Chengdu, 610072
Abstract: Credit spread is the important reason of the current round of financial crisis. Thus, it is not
only significant on theory, but also important in practice to find out the credit control levels. For those,
many scholars have achieved some important results. No doubt, these results are helpful to form this
paper. In this paper, we, basing on influence on investment multiplier from credit, firstly analyze “push
effects” and “destruction effects”(when there is bad debts) on the national economy from credit; after
that, we obtain some characteristic credit control levels about maximum credit ratio and optimal credit
ratio. With some basic assumptions, we propose a mathematical model reflecting the inner connection
between social credit levels and operating situation of national economy.
Keywords: credit risk, investment multiplier under credit condition, income increase function,
maximum credit ratio, optimal credit ratio, credit risk controlling model
1 Increase of Investment Multiplier Resulted from Credit
1.1 The general multiplier principle under credit effects
Back to history, though credit appeared early, the development of it is much slower. During the Keynes’,
credit is not in great use as today, and its influence on the national economy is weak. So it’s natural that
Keynes did not consider the effect of credit in his multiplier principle. In this principle, he argues that
because all the sectors in the economy depend on and affect each other, a new additional investment
∆I will certainly lead to a series purchasing activities in all sectors, and finally multiple the income.
It’s the basis of his proposal----the government should intervene the function of economy. Keynes states
1
, where C is the marginal propensity to consume. If considering
1− C
1
the induced investment and induced consumption, it will become larger, that is K 2 =
,
1 − (C + I e )
where I e is the marginal efficiency of investment. In the 1970’s, all the main western industrial
the multiplier as follows, K1 =
countries adopted the deficit policy, which advocated preceded consumption and encouraged people to
consume in advance, credit then made a full development. Debt-investment, debt-operation and debt
consuming have become the main mode of the economy. Even the government uses the credit tools to
intervene national economy. Debts thus profoundly affect every aspect of the national economy and
become the major force of the high-growth national economy. As an example, America issued bonds up
to 52% of its GDP in year 1992. Meanwhile, more than one third of the consumer rely on credit. Similar
to America, Japan issued bonds up to its GDP’s 52.7% in the same year. Apparently, it’s impractical for
the multiplier that reflects the interdependence of the sectors in the national economy to avoid the
influence of credit. Actually, the multiplier will be enlarged when there is widespread credit in the
：
（ —）
About Author Xu , WeiDe . male 1965
, ChengDu , vice professor of The School of Management of
Southwest University for Nationalities, and Research field is the corporate strategy. Wen, GuoQuan . male 1972
NeiJiang, Doctor, vice secretary of The School of Economy of Southwestern University of Finance and
Economics , vice county head of XuYong County and Research field is the economic growth .
（
—），
628
ORIENT ACADEMIC FORUM
economy.
In order to study the effects that credit has on the national economy, the society purchasing power must
be divided into the purchasing power that use one’s own money and the purchasing power that uses the
credit offered by society. Suppose a new additional investment that use one’s own money ∆I , the
investor then can enlarge his purchasing power through credit. Assume α is the ratio of credit to one’s
own money and we will call α the credit ratio in this paper. The purchasing power will be enlarged to
∆I (1 + α ) . Therefore, income will be increased by ∆I (1 + α ) . Suppose that the marginal propensity
to consumption is stable when this income is used to purchasing and the credit ratio is still α , then the
purchasing power will be increased to ∆I (1 + α )C (1 + α ) . Therefore, the income will increase again
2
3
by ∆I (1 + α ) C . The same as the above analysis, the income will then increase by ∆I (1 + α ) C
2
again. If this activity is going on infinitely, eventually national income will increase by ∆Y , here the
equation of ∆Y is:
∆Y = ∆I (1 + α ) + ∆I (1 + α ) 2 C + ∆I (1 + α ) 3 C 2 + LL
(1 + α ) ∆I
=
1 − C (1 + α )
Thus, we may obtain the investment multiplier under credit condition as follows:
K3 =
1 +α
1 − C (1 + α )
Where α is the ratio of credit to one’s own money and it reflects the credit scale of an economy
society; C is the marginal propensity to consume (MPC).
It is easy to deduce out that the investment multiplier K 3 under credit conditions is larger than
Keynes’ multiplier K1 . Meanwhile, the ratio of debt to national income is generally as follows:
δ =
α
1+α
1.2 Enlarged multiplier principle
If considering induced investment and induced consumption, we think that the above multiplier will be
further enlarged. Like the above analysis, we may obtain that the multiplier is
K4 =
1 +α
.
1 − (C + I e )(1 + α )
2 Credit Risk Controlling
2.1 Income Increase Function
Basing on the above analysis, we know that there are many debts that have to be paid upon their date;
otherwise they will be considered as bad debts that should be excluded from current income, thus the
national income will decrease. Meanwhile, because of the multiplier effect, national income will
decrease multiplicatively[1]. Suppose that the probability of bad debt is θ and the total debt is
∆IK 4δθ , then national income will be decreased by ∆IK 4δθK 4 because of the leverage of the
multiplier. Hence, the ultimate increase in the national income is as follows:
∆Y = ∆IK 4 − ∆IK 42δθ .
[1]
MaYong. Financial Structue, Bank Development and Economic Growth. Finance & Economics. February,2010
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ORIENT ACADEMIC FORUM
We should indicate that in the above interest parameter is not included because interest payment is
debtor’s responsibility and it’s in fact the distribution of social wealth between the debtors and creditors,
which does not change the total social wealth. Because δ and K 4 are all a function of α , so ∆Y
is also a function of α . For convenience, we call the relation between ∆Y and α as Income
Increase Function and their graph as Income Increase Curve or ∆Y − α curve. As an example, we
give the two following ∆Y − α curves when ∆I = 1 , C = 0.6 and I e = 0.2 .
35
30
θ =5%
25
Income Increase
Y
△ 20
15
θ =10%
10
5
0
C r e d it R e t io
-5
Graph 1:
∆Y − α
α
curve and the relations between θ and its shape
From the graph we can see:
First, there is a close relation between shape of a ∆Y − α curve and θ . When θ increases,
∆Y − α curve will lean to left and income will decrease. On the other hand, when α increases,
income will decreases.
Second, for the same curve, its shape is not symmetric by its maximum point, but the former of the
curve is smooth and the rear is steep. This character is more clear when θ is smaller.
2.2 Maximum Probability of a Social Bad Debt
2
Let ∆Y = 0 . We have ∆IK 4 − ∆IK 4 δθ = 0 , that is,
So
θ max =
θ=
1
.
δK 4
1
δK 4
which is the maximum probability of a bad debt.
1
, the debt will have negative effects on national income.
δK 4
1
When θ ≤
, the debt will have positive effects on national income.
δK 4
When
θ≥
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When
θ=
1
, the debt will have no effect on national income.
δK 4
2.3 Maximum Credit Ratio
Actually, the probability of a nation’s bad debt is determined by some of basic situation conditions, such
as mature levels of credit system, credit moral standards in society, future profitability, interests of debts,
phases in business cycles, etc.. It is independent to the former model and has considerable stability[2].
Therefore, it is of great importance to make certain the maximum credit ratio for controlling credit risks
under the condition that average probability of bad debts is stable.
Let ∆Y = 0 . We may get that
α max =
1− C − Ie
C + Ie + θ
The above equation is the maximum credit ratio that the national economy could afford.
It is easy to see that the interval (0, α max ) is the debt’s contribution one, in which ∆Y
> 0.
2.4 Optimal Credit Ratio
According to the former analysis in 2.3, we see easily that ∆Y (0 ) = ∆Y (α max ) = 0 and
∆Y (α ) > 0 in [0, α max ] . Then we may get that in (0, α max ) , ∆Y (α ) have its maximum.
d
d
Let
∆Y (α ) = 0 that is,
(∆IK 4 − ∆IK 42δθ ) = 0 . Thus, we have
dα
dα
(1 − C − I e )(1 − θ )
α opt =
2θ + (C + I e )(1 − θ )
，
The above equation is the optimal credit ratio under the former same assumptions.
3 Conclusion
(1) To ensure sustained and stable development of the economy, social average debet level should be
equal to the optimal credit ratio.
(2) Optimal credit ratio is determined by such economic variables as marginal propensity to consume,
marginal rate of investment and the incidence of bad debts .
References
[1]. MaYong. Financial Structure, Bank Development and Economic Growth. Finance & Economics.
February, 2010
[2]. Tang,yinan. Group Dynamics and Prediction of the Financial Crisis. Economic Research Journal.
June, 2010
[2]
Tang,yinan. Group Dynamics and Prediction of the Financial Crisis. Economic Research Journal. June, 2010
631