Assuming that the total minus the borrower's bank lending principal difference of X formed in the next period of time credit operations , due to commercial bank credit in business transactions and international payments compared to the presence of significant differences exist in the international balance of payments the balance of payments deficit and balance of payments surplus , while bank credit business, the difference ( ie, total lending - borrowers principal = X), a non- positive, ie X ≥ 0 is always true , because we know that the total lending and borrower repayment of principal in theory, should be equal, so this type of business in commercial bank credit permanent establishment .

假定银行在未来时期内银行存款业务中贷出总数减去借贷人还本所形成的升水为X，因为经济活动银行银行存款业务收入支出：与国际收入支出：相形存在着差别，在国际收入支出：升水中存在着国际收入支出：贸易差额和国际收入支出：贸易顺差额，而银行银行存款业务中的升水（即贷出总数-借贷人还本=X），为非正的，也就是说X≥0恒设立，由于我们晓得，贷出总数和借贷人所还本金有理论上应当是对等的，所以该式在经济活动银行银行存款业务中恒设立.

Let's assume a bank 's credit business lending total amount of R, and the maturity of the principal borrower obtained as R1, then the bank's net interest income obtained as R1 (rd-ri), where rd, ri respectively as interest and deposit interest loans. We assume that there is a balance to be met:

无防如果某一银行的银行存款业务贷出总钱数为R，而到期所获得的借贷人的还本为R1，则该银行所得的礼钱净收益为R1（rd-ri），那里面rd、ri作别为贷款礼钱和积蓄礼钱。我们如果存在这么一个平衡，使其满意：

R = R1 + R1rd-R (rd-ri) (1)

I called the credit balance. ( 1) After finishing available :

X = R-R1 (2)

R-R1 = R1rd-R (rd-ri) (3)

The ( 2 ) , ( 3 ) the combined available

X = R1rd-R (rd-ri) (4)

Credit balance point can be defined by the author ( 4) simply represented. ? When X Feng R1rd-R (rd-ri), then the credit business to know the difference between the left side of the balance point , which is a loss point , I called the credit deficit ; ? When X Chu R1rd-R (rd- ) when ri, I called the credit surplus. You can get based on correlation analysis , X ie the difference between bank credit business can be seen as a random variable , because the long-term credit from the difference between the balance of payments equilibrium point is located , it can be assumed that the mean X is 0 , uncertainty the variance ? sediment 2 . Clearly , uncertainty variance of X ? Sediment 2 is larger, the size of the bank and uncertainties appear bad loans greater.

Random relationship between banks and credit cash flows between the balance of payments

The purpose of the bank is to have cash flow in order to meet credit payments deficit that may occur in the next period of time. Suppose a bank credit operations in order to deal with balance of payments deficit that may occur for some time the need for X , the cash flow to keep the bank in advance of F, then probability theory Chebyshev inequality , the deviation between X 0 is less than its mean F probability of P satisfy :

P {X-0 Chu F?} ≥ 1 - (5)

Or X probable deviation is greater than its mean 0 F satisfies :

P {X-0 ≥ F}? Chu ( 6 )

Formula ( 5 ) and ( 6 ) can be further written as:

P {X-0 Chu F?} = P {-F Chu X Chu F??} ≥ 1 - (7)

P {X-0 ≥ F} = P {X ≤-F} + P {X ≥ F}? Chu ( 8 )

From equation ( 7 ) and ( 8 ) can be seen the following two points : First, under the bank decided to keep the loan in advance based on the amount of cash flow F certain preconditions , the bank may occur in the next period of time credit operations ? balance deficit uncertainty dregs 2 X increases, the probability of X falls interval (-F, F) between the P {X-0 Chu F?} to the value 1 - the smaller ; while X fall outside (-F, F) interval probability P {X ≤-F} + P {X ≥ F} the larger values ; contrary, the opposite is true. Second, banks may arise credit balance deficit X uncertainty ? Under certain preconditions Tre 2 , the bank decided to advance the greater the cash flow to keep the F , then X falls interval (-F, F) the probability P {? X-0 of the value 1 Chu F} - greater ; the probability falls interval X (-F, F) other than the P {X ≤-F} + P {X ≥ F} of the smaller value ; contrary, just the opposite. Taking these two points of view, the bank 's credit operations may occur if the balance of payments deficit will fall in the interval X (-F, F) depends not only on the size of F , but also on the uncertainty of the variance of X ? Tre 2 size. That may arise in the coming period bank credit payments deficit X uncertainty ? Dregs two bigger banks decide in advance the cash flow to keep the F smaller, X falls interval (-F, F) within the possibilities 1 - the smaller the greater the likelihood of falling interval (-F, F) outside ; contrary, just the opposite .

Cost analysis of bank risk

Probability banks to maintain cash flow , adjust the size and cost

Since the purpose of the cash flow to keep the bank in response to credit payments deficit that may occur in the future for some time , so the bank prior subjectively hope to keep the size of the credit depends primarily on the cash flows expected future business transactions that may occur the size of the deficit X ; If the cash flow is not sufficient to cope with the prior remain possible credit balance deficit X, it will cause a cash flow shortage , severe cases may endanger the survival of the bank , such as the U.S. subprime mortgage crisis ; conversely, the problem of excess cash flow maintained occurs. Therefore , in order to further study the optimal bank credit scale problem that requires an accurate estimate of the cash flow in advance and keep the probability of occurrence of a shortage of cash flow , adjust the size and cost .

To play safe, you should not be out of cash flow shortage as large as possible to adjust cost estimates for some, but there will be no possibility of a shortage of cash flow estimates as smaller, so that banks can make adequate preparations to deal with credit payments deficit problems may occur. So the formula ( 8) P {X ≤-F} + possibility may arise in the coming period P {X ≥ F} ≤ reflect the bank's cash flow shortage P {X ≥ F} is the maximum possible value ; and the ( 7) P {-F Chu X Chu F??} ≥ 1 - probability reflects the possibility of a shortage of cash flow does not appear far smaller estimate of P {0 Chu X Chu F??} minimum A value of 1 - . Since banks maintain cash flow shortage may occur depending on the expected size of the next period of time credit balance of payments deficit and achieve scale comparison of cash flows remain equal to the difference between the two , namely (XF). Therefore , under the cash flow to keep the bank in a few cases, banks may arise in the next period of time credit payments deficit X can actually be seen as a cash flow shortfall that may arise in the future banks , and banks remain shortage of cash flow , the bank will have to take measures to adjust , and this regulation will lead to adjustment costs , because there are differences between the banks , regulate the way between them and regulation costs are not the same .

For banks, there are differences in local currency loans and foreign currency loans between the time when the loan in foreign currency , the currency can not be directly used for external payments , and the bank's ability to raise funds in foreign currency is relatively weak, anytime, anywhere access to financial markets can not be determined borrow at reasonable interest rates to the desired foreign currency funds . Therefore , the bank 's cash flow shortage of foreign currency in the form of X are circumstances , possibly through demand management policies to reduce the shortage of foreign currency loans to reduce the cash flow that may arise, and adjust policies to be taken to reduce the number of foreign currency loans in order to achieve X credit balance of payments equilibrium . If the amount of foreign currency loans to reduce X, it means reducing the amount of local currency loans eX, while output and income in local currencies to reduce eXri, also means reducing output and income denominated in foreign currencies , seen in terms of cash flow for banks shortages can lead to the greatest adjustment costs denominated as follows:

C1 = eXri (9)

From ( 9) we can see that no matter what a bank for the purpose of maintaining the cost of regulation may result in a shortage of cash flow and cash flow to keep the bank in advance is inversely proportional to the bank decided to keep the cash flow F is smaller, then the future a shortage of cash flow over time the probability P {X ≥ F} is greater the greater the maximum possible value ; contrary, the F , the smaller the adjustment costs, minimize credit from balance of payments deficit may cause adjustment cost perspective , should try to increase the cash flow to keep the bank .

Requires commitment to maintain cash flow opportunity cost

As mentioned earlier, from the reserves to minimize adjustment costs may cause a shortage of perspective, banks should as much as possible to maintain cash flow and cash flow to maintain the more opportunity costs banks to suffer greater losses . Therefore, the study of the optimal size of the bank issues to be considered in addition to the cost of regulation may result in reserves , but also must consider the opportunity cost of holding cash flows . If the foreign exchange rate is e, banks to invest in foreign currency cash flows are used as currency to invest in loans, these loans can make bank profitability :

C2 = eX (rd-ri) (10)

There are ( 10 ) can be seen , the banks the opportunity cost of holding cash flow and cash flow to keep the bank in advance of F a positive correlation . Therefore, to minimize the cash flow from the opportunity cost of keeping perspective , banks should be minimized to maintain cash flow F.

Optimal bank credit scale model

Bank credit scale optimal adjustment problems related to both cost and involves opportunity costs, minimize the opportunity cost from the perspective of the bank should minimize the amount of cash , and with the gradual decrease in cash flow to maintain the opportunity cost is correspondingly reduced, but reduced cash flow increasingly unable to effectively meet the needs of bank credit in business transactions that may arise in the future , resulting in increasing loss adjustment costs ; conversely , to minimize adjustment costs from the perspective of the bank in advance as possible the increase in cash flow holdings , cash flow and increase reserves can effectively respond to possible future credit balance of payments deficit , but the greater the greater the opportunity cost of the cash flow losses suffered ; If the cash flow significantly exceeded the bank's response to require credit balance of payments deficit , then the bank will suffer a greater loss of opportunity costs unnecessarily . Therefore, the rational bank policymakers should consider regulating integrated and opportunity costs of both cost and choose one of these two aspects can make cost and minimal cash flow holdings F.

T = C1 + C2 = eXrd + eX (rd-ri) (11)

Consolidated ( 3 ) , ( 4 ) and ( 11 ) finishing three type :

T = + eX (rd-ri) + Rri (12)

According to the maximum principle calculus on ( 12) Find the partial derivative with respect to R , and make it equal to 0, you can find the best bank credit scale expression:

R = (13)

From ( 13) we can see that no matter what a bank , a credit to their optimal adjustment costs are affected by the size of the opportunity cost of maintaining cash flow and reserve shortages could lead to two factors. On the one hand , the optimal size of credit bank deposit rate R and the current changes in the opposite direction into the relationship , it is because banks in order to avoid the loss of the opportunity cost too much to bear , you want to keep the cash flow in advance should be less , but the formula ( 13) r-1 showed changes in cash flow for the opportunity cost is greater than 1 , greater sensitivity . On the other hand , the bank holds the cash flow needs of R and they are expected to appear in future uncertainty may scale credit balance deficit of X ? Tre 2 , and adjust the unit cost when using r deficit into line with the changes relationship , it is because , expected future credit may arise balance of payments deficit and uncertainty the greater the size , the use of the higher costs to adjust policy deficit , bank regulation in order to avoid too much to bear the cost of losses, prior to retention the cash flow should be more . From ( 13 ) where X 1/ 3 power shows that the optimal size of credit bank credit balance of payments deficit of elastic movements of less than 1, which means the bank is not the optimal size of credit balance of payments deficit with the size of the credit business changes into a proportional change , but the latter is less than the magnitude of change . This reflects the increasing along with the best credit scale , cash flow reserve with economies of scale.

In addition, the optimal size of credit ( 13 ) display only from the perspective of possible future deal with credit balance of payments deficit , the optimal size of bank credit in accordance with regulation costs and opportunity cost minimization principle sum determined . In fact, apart from the cost point of view to deal with the shortage of reserves that may arise , but also from the perspective of risk, banking stability perspective , maintain domestic order and other aspects of financial research . Accordingly, in particular to determine the optimal size of credit , these aspects should be taken into account.

Bank credit to estimate the optimal size

Due to the current level of development of the UK commercial banks and foreign commercial banks have large compared with not a small gap , both in the capital adequacy ratio or in the credit risk management is not a small gap exists , the level of development of commercial banks with the UK typical characteristics of the development of the British state. Depending on the parameters ( 13) important parameters e, r, X and the estimated measure .

Non-performing loans on ICBC 's credit operations or balance of payments deficit is shown in Table 1, Table 2 and Table 3. To illustrate the volatility of non-performing loans is large, I mean as a measure to select a criteria:

Xt =

= 561.1063204 one hundred million yuan

According to Table 2, you can get ICBC nearly a decade of non-performing loans (see Table 4 ) .

Further solving equation ( 13 ) the uncertainty of X :

? Sediment 2 = [(X2009-Xt) 2 + (X2008-Xt) 2 (X2007-Xt) 2 + ...... + (X2001-Xt) 2 + (X2000-Xt) 2] = 106 774 865 132

According to Table 5, the author of the formula ( 13 ) in the weighted average estimate ri :

So ri == 3.280 2%

According to Table 6, the right weight relationship between the lending rate calculated weighted average lending rate :

rd == 4.373 2%

The ri, rd into equation ( 13 ) is calculated , and the calculated :

R =

=

= 2.201 1 × 105

When the size of these loans are denominated in local currency which amounts to :

R = 2.201 1 × 105

Where , e is the exchange rate between the local currency and foreign currency , but the bank 's credit operations when operated Renminbi business e = 1, the optimal loan size is R = 2 201.1 million.

In summary, the cost point of commercial bank credit operations optimal size is only possible from the credit balance of payments deficit to historical data, the optimal size of the commercial banks in accordance with the regulation of credit costs and the opportunity cost of the minimum sum principle determined .

Countermeasures and suggestions

The main problem for the UK banking presence that commercial bank credit scale applications can better carry out quantitative research , especially recommend the following:

Quantitative analysis of the ability of commercial banks to strengthen credit risk management and improve relevant laws and regulations. Credit risk measurement methods in 1997 by JP Morgan , and a method for measuring and managing credit risk developed by Union Bank of Switzerland . This method is based on the credit rating , the credit rating transition probability of the use of information and related loans reflected the degree of information between the stock market , and changes reflect changes in the market value of the credit risk of the loan , and by calculating the value to reflect the risk size of the loan or loan portfolio credit risk .

Strengthen credit risk management and quantitative research methods drawing applications can enhance variance method , applications, and application scope and effectiveness of different methods of sensitivity analysis, regression model law , economics, mathematics and other methods to make a quantitative standard .

Joint-stock reform of state-owned banks goal should be to establish a modern commercial banking system , not just the reform of property rights , not just improve the corporate governance structure , but do not just raise their capital adequacy ratio. The latter three are one-sided and incomplete . Only on the basis of the optimized structure of property rights , establish a sound corporate governance structure of science to achieve a separation of enterprise and scientific management , the many positive benefits of joint-stock reform was likely to generate .

Establish a sound platform for the commercial banks to collect data . The establishment of a sound commercial banking data management system for the development of the banking sector and quantitative research to predict great significance to establish the data platform enables commercial banks in the past on the basis of data research continually improve their management mode , from the inside to build a relatively complete and comprehensive analysis of quantitative research institutions . In order to advance learning and advancing in learning , truly " Wenguerzhixin " continuous improvement .

Encourage commercial bank credit business practice innovation. To encourage innovation model of commercial banks , management and other aspects , breaking its own constraints. But innovation is not blind to innovation , we have to analyze its feasibility , in some places to try , and then application.

Sharing good business model and draw on advanced concepts . Need to establish a platform for mutual exchange between the commercial banks to be able to instantly share the information available . As John Nash 's theory, is a group of commercial banks , only consider their own interests and does not promote the development of the entire banking industry , to create a win-win situation.

Strengthen the introduction of a knowledge-based and professional talents . Strengthen the introduction of a knowledge-based and professional personnel can effectively improve the quality of their own level of commercial banks , commercial banks and help the business model or business research and quantitative analysis , the development of their own history can make more objective evaluation. This is the significance of the implementation of our national " education strategy " where the purpose of education to promote the development of the whole society .