Download Analyses of the Herding Behavior for the SMEs Financing Plight

Analyses of the Herding Behavior for the SMEs Financing Plight
DENG Qizhong , ZOU Xinyue
School of Management,Hunan University of Science and Technology, Xiangtan, 411201
[email protected]
Abstract: There has been a vast of thorough researches and advice about the financing plight of SMEs
from the side of asymmetric information among the domestic and foreign researchers. This paper is
trying to use the theories of behavior finance to analyze the difficulty in essence and illustrate that the
intrinsic reason of financing plight for such enterprises is herd behavior of decision made by managers
through establishing the utility function of bank loan managers. The results indicate that the managers
will be inclined to invest in large enterprises instead of SMEs considering their own reputation and
reward.
Keywords: small and medium-sized enterprises, credit market, herd behavior
1 Introduction
As a significant factor influencing domestic economic development, small and medium-sized
enterprises(SMEs) have played vastly and increasingly importance in not only increasing tax and
promoting scientific and technological innovation but also absorbing labor force and maintaining social
stability. According to the relevant statistics, till October 2005, the amount of Chinese SMEs has
reached as much as 42,420,000, accounting for 99.6% of total enterprises in China. Especially, the value
of ultimate production and service created by the SMEs took up 58.7% of GDP, devoting to 48.6% of
national tax collection. However, the financial loan created by such enterprises only accounted for
7%~8% of total credit funds in society. Moreover, the statistics from China banking regulatory
commission shows that the commercial bank lending still flows to and concentrates on the big clients
currently. Till the end of June 2006, the number of big customers that bore the loan above 100 million
just occupied 0.5% of total number of customers of 17 large commercial banks, compared to the amount
of loan which took up to as far as 50%. On the contrary, the loan created by the SMEs just occupied
16% of the dominant social financial loan, generating almost 60% of GDP.
Obviously, credit financing is inevitable and most serious constraints that influence the sustainable and
stable development of SMEs. Since most of such enterprises have the incompletely well stabilized
financial system and bear higher credit risk and risk of bankruptcy, commercial banks are reluctant to
lend the money to them to some extent. Further more, the amount of loan created by such enterprises is
quite small and the period is quite short, otherwise the loan procedure can’t be shortened, thus the cost
of trade per unit of commercial banks would be much higher. In other words, this will reduce the
enthusiasm of releasing the loan by commercial banks.
Considering the financing plight of the SMEs, there is a great deal of thoroughly, abundant and in-depth
discussion from the domestic researchers currently. Zhaodi Wang (2003) pointed out that the main
reasons of the financing difficulties were the asymmetrical arrangement in financing system and
regulations between state-owned banks and SMEs. Besides, financial reform, system transformation and
deflation increased the discrimination towards the lending to such enterprises. Moreover, he pertinently
brought forward the advise regarding the policy of solving the difficulty of financing underlying the
SMEs and intensifying the performance and influence of monetary policy. Guangdao Han (2005)
believed that to dredge the financial channel between the commercial banks and SMEs required all of
government, banks and enterprises’ efforts together and adopting economic system combination. In
other words, the government should play its unique and dominant role in the macroeconomics that
establishes a series of policy and regulations as well as the good circumstances about the social services
which is considered to be advantageous to the development of SMEs and the state-owed commercial
banks providing loans to such enterprises.
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Obviously, the domestic researchers have contributed a lot in relieving or solving the financing plight of
the SMEs. However, most of the existing solutions are from the side of the government without
considering the rational behavior of the loan decision makers. Thus, in order to anatomize the essential
reason of financing plight, it is advanced to take the loan decision making behavior of the manager in
the commercial banks into account. Therefore, this paper is based on the rational behavior of the loan
managers using the theories of behavior finance trying to figure out the financing plight of SMEs in
substance. Moreover, referring to the model of managerial herd behavior based on ‘safety in numbers’
by Thomas I. Palley (1995), this paper uses the utility function model of bank managers to illustrate the
herd behavior about decision making of the loan managers of banks is the intrinsic reason of financing
plight of SMEs, providing a new explanation.
2 Utility Function Model for Bank Managers
Suppose that there are only two kinds of both credit funds suppliers and funds demanders in Chinese
credit market. Credit funds suppliers can be classified into two categories: large commercial banks credit
loan manager (manager I ) and small commercial banks credit loan manager (manager II ). Credit
funds demanders can be divided into large enterprises (state 1) and small and medium-sized enterprises
(state 2). We assume that all of the credit loan managers stick to the hypothesis of rational behavior that
they pursue the maximum of their personal utilities and they are risk averse. Meanwhile, the payment of
single bank loan manager not only depends on benefits of personal credit loan investment but also is
determined by the relative performance in the credit funds supply market. In other words, the bank loan
managers, which perform under the average level of the market return would be punished. However, if
the performance is subject to the unpredictable and inevitable macroeconomic situation, there is neither
punishment nor award.
By this way, the target about the utility function of bank loan managers can be summarized to maximize
the personal utility return under the condition of limited credit loan funds and their rational behavior by
considering different credit demand of different types of enterprises. Explicitly speaking, manager I is
specialized at selecting the allocation of credit loans, which can increase the expected utilities through
rational allocations of credit funds among the demand of both large and small and medium-sized
enterprises under the target of maximizing the personal utilities. As a result, the utility function of
investing activities of manager I can be expressed as:
M ax
EU
X 1, X
2
I
= p1 Z 1c + p 2 Z
subject to
X 1 + X 2 = 1, X
x 1 = (1 + r ) X
x 2 = (1 + r ) X
1
> 0, X
2
c
2
,0 < c < 1
> 0
(1)
1
2
Z 1 = a x1 + b ( x1 − y1 ), a > 0 , b > 0
Z
= a x 2 + b ( x 2 − y 2 ).
EU I = expected utility of manager I ; p1 = manager I ’s subjectively held belief regarding the
probability to fulfill the loan demand of state 1; p2 = manager I ’s subjectively held belief regarding
the probability to fulfill the loan demand of state 2; X i = allocation of resources by manager I to
investment i ; xi = revenue earned by manager I in state i ; r = exogenous rate of return on
2
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investments; a=performance royalty rate of loan manager; b=relative performance royalty rate of loan
manager; c=risk preferences of loan manager( c>1,risk-taking, c=1, risk-neutral, 0<c<1, risk-averse);
Z i = payment to manager I in state i ( Z i >0, i = 1, 2 ).
Similar to decision making of investment by the manager I , manager II has an entirely
symmetric problem which is shown as:
M ax
EU
II
= q 1W 1 c + q 2 W
c
2
,0 < c < 1
Y1 , Y 2
subject to
Y 1 + Y 2 = 1, Y 1 > 0 , Y 2 > 0
(2)
y 1 = (1 + r ) Y 1
y 2 = (1 + r ) Y 2
W 1 = a y1 + b ( y1 − x1 ), a > 0 , b > 0
W
= a y 2 + b ( y 2 − x 2 ).
EU II = expected utility of manager II ; q1 = manager II ’s subjectively belief about the
probability of state 1; q2 = manager II ’s subjectively belief about the probability of state 2; Yi =
allocation of resources by manager II to investment i ; yi = revenue earned by manager II in state
i ; Wi = payment to manager II in state i ( Wi >0 , i =1,2 ). Besides, the rest of the parameters and
2
variables can be referred to the mode of manager I .
2.1 Analysis of herd behavior of commercial banks to large enterprises
In the credit market, the decision making about allocation of loan by the bank managers can relate and
subject to each other in some extent. In other words, this represents the manager’s decision rules that the
decision of each manager depends on the decision of the other, leading the balance of the financing
among different types of enterprises consulted with loan decision makers of different types of banks. By
appropriate substitution of constrains into the objective functions, the utility function that the loan
managers try to maximize their expected return can be expressed as:
Max EU I = { p1 [ aX 1 + b ( X 1 − Y1 )]c + p 2 [ a (1 − X 1 ) + b (Y1 − X 1 )]c }(1 + r ) c
(3)
Max EU II = {q1[aY1 + b(Y1 − X 1 )]c + q2 [a (1 − Y1 ) + b( X 1 − Y1 )]c }(1 + r )c .
(3’)
From the above equations, the key feature about these choice problems is that each manager’s
decision is affected by the decision of the other manager through the reward function which incorporates
a relative performance effect.
Differentiating Eqs. (3) and (3’) with respect to the appropriate choice variable, setting equal to
zero, and simplifying yields the first order conditions which are:
dEU I / dX 1 = p1 [ aX 1 + b ( X 1 − Y1 )] c −1 − p 2 [ a (1 − X 1 ) + b (Y1 − X 1 )] c −1 = 0
c −1
dEU II / dY1 = q1[ aY1 + b(Y1 − X 1 )]
c −1
− q2 [ a(1 − Y1 ) + b( X 1 − Y1 )]
= 0.
(4)
(4’)
Differentiating equation (4) and (4’) with respect to Y1 and X 1 , which are given by:
dX1 / dY1 |EUI =b /(a+b) > 0
(5)
dY1 / dX 1 |EU II = b / ( a + b) > 0.
(5’)
Taking the relationship between managers’ subjectively held belief regarding the probability to
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fulfill the loan demand of state 1 and the allocation of resources, we can easily get:
dX 1
|Y1 = − Z 1 c − 1 / ( c − 1)(1 + r )( a + b )( p 1 Z 1 c − 2 + p 2 Z 2 c − 2 ) > 0 (6)
d p1
dY1
| X = −W1c−1 / (c − 1)(1 + r )(a + b)(q1W1c − 2 + q2W2 c − 2 ) > 0.
(6’)
dq1 1
From the above equations two managers’ investment decisions are affected by each other. Moreover,
there is positive correlation between the managers’ subjectively held belief regarding the probability to
fulfill the loan demand of state 1 and the allocation of resources. Generally speaking, due to the more
sufficient knowledge about the management status of the state 1, manager I definitely will increase
the held belief to fulfill the loan demand of state 1 when they apply for it. Besides, from equation (6),
the relationship between X 1 and p1 is positive that increases in p1 will shift up manager I ’s
subjectively held belief about the probability of state 1. Then we take the manager II ’s decision
making into account.
From Equation (4) and (5’) , the equilibrium condition for manager II to maximize their utility is a
function with respect to X 1 and Y1 . In addition, X 1 is positively related to the increases in Y1 .
Thus, to fulfill the balance condition to maximize the utility of manager, increases in X 1 will induce
the rise in Y1 that manager II will increase his allocation of fund resources to state 1. Besides, from
equation (5), the rise in Y1 will shift up the allocation X 1 .
Thoroughly speaking, the economic logic is when manager I invests in state 1, they will consider the
allocation of resources by manager II . Meanwhile, when the manager II makes the investment
decisions they will refer to the allocation by manager I either. Therefore, increasing the allocation of
resources in state 1 by manager I will stimulate and influence the manager II investment decisions
that accounts for the herd behavior of the commercial banks managers to allocate the fund resources to
state 1.
2.2 Analysis about the herd behavior for commercial banks to invest in SMEs
If differentiating equation (3) and (3’) with respect to X 2 and Y2 , we can get the equilibrium
condition to maximize their expected utilities for managers to fulfill the loan demand of SMEs . These
are given by:
dEU I / dX 2 = p2 [aX 2 + b( X 2 − Y2 )]c −1 − p1[a(1 − X 2 ) + b(Y2 − X 2 )]c−1 = 0
c −1
c −1
dEU II / dY2 = q2 [aY2 + b(Y2 − X 2 )] − q1[a (1 − Y2 ) + b( X 2 − Y2 )]
d X 2 / d Y2 |E U I = b / ( a + b ) > 0
=0
dY2 / dX 2 |EU II = b / (a + b) > 0.
(7)
(7’)
(8)
(8’)
Besides, we take the relationship between managers’ subjectively held belief about the probability of
state 2 and the allocations of loan into account, and we can find:
dX 2 / dp 2 |Y 2 = − Z 2c −1 / ( c − 1)(1 + r )( a + b )[ p 2 Z 2c − 2 + p1 Z 1c − 2 ] > 0
c −1
2
dY2 / dq2 | X 2 = −W
c− 2
2
/ (c − 1)(1 + r )(a + b)[q2W
c−2
1
+ q1W
] > 0.
(9)
(9’)
Apparently, the subjectively held belief about the probability of state 2 is affected by the information
gathered from individual investigation in private from manager I . Normally speaking, manager I
has incomplete and insufficient knowledge about the management and risk taking ability of SMEs so
that it will reduce the subjectively held belief for manager I in state 2. In addition, from above
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p2 and X 2 that the variation of p2 will directly
influence the allocation of manager I in state 2. To be brief, the reduction of p2 will lead to the fall
of X 2 .
Further more, from the illustration of equation (8), there is the positive correlation between X 2 and
Y2 as well that reduction of Y2 is depend on the reducing of X 2 , so the induced activity of credit
equation (9), there is positive correlation between
market in reality can be shown as: the decreases of manager I ’s subjecting held belief about the
probability of state 2( p2 ) , directly influencing the allocation of manager I in state 2 and leading the
herd behavior of the commercial banks to move with the herd and reluctantly to allocate the fund
resources to SMEs.
3 Generalization of the Utility Function of Managers
From the above discussion we only take the herd behavior of two types of loan providers into
consideration, whereas we can generalize the model to a world with N managers, various loan
providers making investment decision regarding both large and small and medium-sized enterprises.
Therefore, we can express the utility function of several loan managers making investment decisions as
followed:
M ax EU
i
= p1 K
subject to
X i 1 + X i 2 = 1, X
x i j = (1 + r ) X
i1
c
i1
+ p2K
> 0, X
i2
c
i2
,0 < c < 1
> 0
(10)
ij
y i j = (1 + r ) Y i j
K
ij
= a x ij + b ( x ij − y ij ) , a > 0 , b > 0 .
EU i = expected utility of manager i ; p1 = manager i ’s subjectively held belief regarding the
probability of state 1; p2 = manager i ’s subjectively held belief regarding the probability of state 2;
X ij = allocation of fund resources by manager i to investment j ; xij = revenue earned by manager
（
）
i in state j ; K ij = reward earned by manager i in state j K ij > 0 ; yij = average revenue earned
by the other managers in state j ; Yij = average allocation of fund resources by the other managers in
state j . The rest of the parameters can be referred to the definition of utility function of decision
making of managers regarding large enterprises ( i = 1, 2, L , n; j = 1, 2 ) .
The condition to maximize the expected utility when manager i and the other managers are trying to
fulfill the loan demand of large enterprises in investment j ( j =1) is described as:
dEU i / dX i1 = p1[aX i1 + b( X i1 − Yi1 )]c −1 − p2 [ a(1 − X i1 ) + b(Yi1 − X i1 )]c−1 = 0
dX
i1
/ d Y i1 | E U i = b / ( a + b ) > 0 .
(11)
(12)
Based on the above illustration, there is positive correlation between X i1 and Yi1 thus the allocation
made by manager i in state 1 is influenced by the other managers’ investment decisions. In other
words, when the other managers increase the average loan allocation in large enterprises, manager i
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will move with the herd and raise the allocation either, accompanying with the positive reaction. Vice
versa, manager i will reduce the allocation in SMEs depending on the other managers’ decreasing
average allocation in state 2. Therefore, there is obvious herd behavior when applying the resources
allocation in both enterprises by managers in credit market.
4 Conclusion
This paper is trying to use the expected utility function of loan managers to analyze the herd behavior of
fund allocation in both large enterprises and SMEs under the information asymmetric situation. From
results of some researches, in the information asymmetric financial credit markets, the loan managers
can’t hold the precise estimation about the ability to pay back the loan by creditors that large state-owed
commercial banks treat the incident that the large enterprises fail to pay back the loan to maturity as the
small probability and ascribe the individual circumstance that some exceptional SMEs are not capable of
paying back the interest and principal on time till maturity to the multitude incident, exaggerating the
unwell credit situation of total SMEs. Thus when the managers evaluate and estimate the loan provision
of such enterprises, they will increase their defending consciousness of risk and exercise less weight on
the objectively held belief of allocation to such enterprises as well. Meanwhile, they will highlight their
objectively held belief of allocation to large enterprises and somewhat ignore the risk exposure of the
loan concentrated on enterprises, leading to the recognition as the rational behavior when allocating
funds to large enterprises.
Further more, under the situation of information asymmetric, small or medium commercial banks, which
are lack of sufficient information, are more difficult to make the rational decisions. Besides, under the
existing subjectively held belief of allocation between the large and the small and medium-sized
enterprises in the financial credit market, such banks will believe the move with the herd ignoring their
own private information as well as following with the allocation of large state-owed commercial banks,
which is their best and rational behavior in some extent.
Objectively speaking, the managers prefer to obey the rule to maximize their own benefits rather than
the clients’ benefits and their reputation and reward will be deeply affected by the relative performance.
Thus, the failure of investment has nothing to do with their reputation when they move with the herd.
Otherwise, due to the reward regulation of relative performance, the failure of investment will badly
destroy their reputation when they reluctant to follow the herd. Therefore, due to the consideration of
their own reputation and reward, the managers will incline to invest in large enterprises instead of
SMEs.
References
[1]. HAN Guangdao. Problem Analysis of Borrowing Difficulty by Small-and-Medium Sized
Enterprises and Lending Difficulty by State-Owned Commercial Banks and Countermeasures.
Finance Forum,2005,(5):52 55.(in Chinese)
[2]. Thomas I.Palley. Safety in Numbers: A Model of Managerial Herd Behavior. Journal of Economic
Behavior and Organization ,1995,(28):443 450.
[3]. WANG Zhaodi. On Financing Problem of Small and Medium-sized enterprises. Journal of
Finance,2003,(1):90 97. (in Chinese)
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Author in brief
DENG Qizhong, Ph.D. candidate, mainly engaged in Applied Econometrics, Financial Econometrics.
TEL: 15973201246, E-mail: [email protected].
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