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Research on Financial Early Warning SHANG Hongtao, SONG Shan School of Economic and Management, Beijng University of Technology, China [email protected] ,100124 Abstract: The change process of the enterprise financial rate is a random process. It’s difficult to find a precise forecast result through the normal analytical method which according to some historical data. However Markov mainly used to analyze the future trend of development and change of random incident. So this paper selects rate of return on common stockholders’ equity(ROE), total assets increase and operating cash flow per share to forecast the enterprise finance with totally twenty quarterly data from 2003 to 2007 of Zhongwugaoxin Co. Ltd. Markov is also used to research their change rules empirically. The result of empirical study may forecast promptly the business finance risk. Key Words:Financial Crisis, Financial Early-Warning, Markov , 1 Introduction , Markov was produced by Audrey Markov, a Russian mathematician then developed by Monte Carlo. It mainly used to analyze the future trend of development and change of random incident. In other words, the present state and pulse of a variable are used to forecast the future state and pulse of the variable, so that the relevant countermeasure can be adopted.[1] The change process of the enterprise financial rate is a random process. It’s difficult to find a precise forecast result through the normal analytical method which according to some historical data. The changes of state are called transitions. Markov researches the transitions of the system which looks as a whole to explain the random of the change of financial index. So Markov is used to analyze the change rules of financial indexes in this paper to forecast the risk of company finance.[2] 2 Introduction of Markov () ∈ Process of random is a sequence of random variables X t ,t T. The possible values of t form a countable set T call the parameter space. The possible values of X(t) form a countable set S call the state space. The process of random can be divided into four kinds according to whether S and T are discrete aggregate or not. Markov is only refer part of it in the process of random. We often call it Markov process. Definition: Let {Xn n=0 1 2 …} is a sequence of random variables. Xn=i means a event that the system is in the state i at the moment n. pij n =p Xn+1│Xn=i means that at the condition Xn=i, the condition probability of Xn+1=j . We also call it one step transition probability of the system. {Xn} is claimed a Markov Chain if p (Xn +1 = j │ Xn = i, Xk = ik, k = 1,2,…, n-1) = p(Xn +1 = j │ Xn = i) = pij (n) for any of the non-negative integer i1 , i2,…, i, j and all n ≥ 0. The definition means the states in every moment depend on the states in former process but they are independent of the past states. This is non-aftereffect or non-memory of Markov chain. If one step transition probability pij (n) = p (Xn +1 = j │ Xn = i) has nothing to do with the initial moment n, pij can be recorded shortly. Clearly, one step transition probability has the property as follows: pij≥0 i nj=1 2 … n ∑pij=1 i=1 2 … n One step transition probability in every state can form a matrix: , ,,, ( , , , , ), ()( ( ,, ,) 719 ) p11 p 21 P= M pi1 M p12 L p1 j L p22 L p2 j L M M pi 2 L pij L M M () < (< ) () , P11 P12 … P1n…P21 P22 P2nP= … … Pn1 Pn2 Pnn is a transition matrix. Let parameter of X n means Time. tm means present state while tm+1 tm are future states and t1 t2 t3…… tm-1 tm are past states. {X tm =im} is claimed Present shortly. {X tm+1 =im+1} is Future and {X t1 =i1 …….. X tm-1 =im-1} is Past. We can describe it like this: P{Future Past Present} P{ Future Present } Easily we can find: P{ Future Past Present } P{ Future Present }P{ Past Present } P{ Past Present Future } P{ Past Present } Markov equation is applied to have the conclusion: P(n) =P(n-1) •P= Pn in the other words, n steps transition matrix is equal to the power of n of one step transition matrix. ( ) () ∣ , , ∣ ∣ , (> ) = = = << ( ) ∣ ∣ ∣ ∣ , , 3 Selection of variable index for financial early warning Selection of variable index for financial early warning must consider every factor fully. Zhao Xiangtao(2007) chose seventy companies of financial crisis which were treated specially and seventy companies of non-financial crisis as the model. He used some statistical analysis methods like independent-samples test, factor analysis and relevance analysis integrally to select twelve variables. Then Logistic regression analysis was handled to regress twelve variables. Logistic discriminance model was produced to test Logistic model. [3] Test results showed that: In these twelve variables, ROE, total assets increase and operating cash flow per share have the important influence on the financial situation of enterprise. The formula is: ……………………………(1) (X1 is ROE. X2 is total assets increase. X3 is operating cash flow per share). P<0.5 means the enterprise is on the state of non-financial crisis, otherwise, it is on the state of financial crisis. From testing of 30 listed companies which were first treated specially in 2006, its prediction accuracy rate reached 85.33%. So this paper chooses ROE, total assets increase and operating cash flow per share as the early warning indexes. Markov is also used to research their change rules. Finally, according to formula (1) we can forecast the risk of enterprise finance. 4 The process of empirical research 4.1 Samples selection China Tungsten and High-tech Materials Co. Ltd formerly named Hainan Jinhai Co. Ltd. Its former company was Hainan Jinhai Materials Co. which wholly owned by Hainan Jinhai Industrial Co. The main business of the company is manufacturing and the processing of non-ferrous metal and the hard alloy product. This paper selects twenty quarterly data from 2003 to 2007 to analyze the sample. 4.2 Indicators summary 720 Below are data summary of three indicators of China Tungsten and High-tech Materials Co. Ltd. (1)ROE Rate of Return on Common Stockholders’ Equity = net profit /Stockholders’ Equity As shown in table1. ( ) Tab.1 Summary of ROE in varies period 2003-6-30 2003-9-30 2003-12-31 Time 2003-3-31 2004-3-31 Sequence 1 2 3 4 5 ROE 1.19% 3.00% 3.84% 6.39% 0.99% Time 2004-6-30 2004-9-30 2004-12-31 2005-3-31 2005-6-30 Sequence 6 7 8 9 10 ROE 1.44% 1.40% 3.43% 0.31% 0.87% Time 2005-9-30 2005-12-31 2006-3-31 2006-6-30 2006-9-30 Sequence 11 12 13 14 15 ROE 1.52% 0.56% -0.79% -1.65% -1.91% Time 2006-12-31 2007-3-31 2007-6-30 2007-9-30 2007-12-31 Sequence 16 17 18 19 20 ROE -14.82% -0.90% -4.42% -7.27% -54.96% (2) Operating cash flow per share= operating cash flow / Stockholders’ Equity As shown intable2. Tab.2 Time Summary of operating cash flow per share in varies period 2003-3-31 2003-6-30 2003-9-30 2003-12-31 2004-3-31 Sequence 1 2 3 4 5 operating cash flow per share Time -0.61 0.07 0.12 0.41 -0.68 2004-6-30 2004-9-30 2004-12-31 2005-3-31 2005-6-30 Sequence 6 7 8 9 10 operating cash flow per share Time -0.71 -0.49 -0.41 -0.04 0.12 2005-9-30 2005-12-31 2006-3-31 2006-6-30 2006-9-30 Sequence 11 12 13 14 15 operating cash flow per share Time 0.09 0.19 0.00 0.34 1.07 2006-12-31 2007-3-31 2007-6-30 2007-9-30 2007-12-31 Sequence 16 17 18 19 20 operating cash flow per share 0.68 -0.23 -0.16 0.18 -0.11 (3) Total assets increase= (total assets this year-total assets last year)/ total assets last year As shown in table3. 721 Tab.3 Summary of total assets increase in varies period 2003-6-30 2003-9-30 2003-12-31 2004-3-31 2004-6-30 Time 2004-9-30 Sequence 1 2 3 4 5 6 Total assets increase 5.89% -1.54% -3.69% 11.78% 11.04% 2.92% Time 2004-12-31 2005-3-31 2005-6-30 2005-9-30 2005-12-31 2006-3-31 Sequence 7 8 9 10 11 12 Total assets increase -4.31% -2.60% 0.06% -1.05% 1.64% 1.67% Time 2006-6-30 2006-9-30 2006-12-31 2007-3-31 2007-6-30 2007-9-30 Sequence 13 14 15 16 17 18 Total assets increase -2.77% -12.88% -3.79% 9.69% -10.66% 2.87% 4.3 Analyze data with Markov chain Let’s use Markov chain analyze the above information. 4.3.1Construct state and determine the appropriate state probability According to the data we select, the change range of ROE, the first indicator, is mainly between -1%-2%. We must consider the limited data and data distribution when we classify it. The state range is shown in table4. Indicator state Tab.4 S1 Indicator range below-1% (-1%,2%) (2%,5%) above5% 6 8 5 1 Frequence Calculation of earning per share base on varies status S2 S3 S4 ROE is divided into four ranges, the range is 3%. Frequence is the number that data of samples fall into the four ranges. The frequence in the first range is 6. The frequence in the second range is 8. The frequence in the third range is 5. The frequence in the last range is 1. The change range of operating cash flow per share, the second indicator, is mainly between 0.05-0.35. The state range is shown in table5. Indicator state Tab.5 Calculation of operating cash flow per share base on varies status S1 S2 S3 S4 below-0.6 (-0.6,0.1) (0.1,0.7) above0 7 3 9 7 1 Indicator range Frequence . Operating cash flow per share is divided into four ranges, the range is 0.7. Frequence is the number that data of samples fall into the four ranges. The frequence in the first range is 3. The frequence in the second range is 9. The frequence in the third range is 7. The frequence in the last range is 1. The change range of total assets increase, the third indicator, is mainly between -5%-5% The state range is shown in table6. 722 Tab.6 Calculation of total assets increase base on varies status Indicator state S1 Indicator range below-5% (-5%,0) (0,5%) above5% 3 7 5 4 Frequence S2 S3 S4 4.3.2 The state transfer probability matrix is constructed by the state transfer According to the information shown in the above two, transform condition of ROE is shown in Table7. Tab.7 The next state The current state Transform of ROE in different state S1 S2 S3 S1 S2 S3 S4 5 1 2 0 1 5 1 1 0 1 3 0 S4 0 1 1 0 One step transition probability matrix: 0 5 / 6 1/ 6 0 1 / 8 5 / 8 1 / 8 1/ 8 P= 0 1/ 5 3 / 5 1/ 5 0 1 0 0 The matrix means the probability that index of sample transfer from one state to another state. Transform condition of operating cash flow per share is shown in table8. Tab.8 The next state The current state Transform of operating cash flow per share in different state S1 S2 S3 S1 S2 S3 S4 1 0 1 0 2 3 4 0 One step transition probability matrix: 0 1/ 3 2 / 3 0 0 3/8 5/8 0 P= 1 / 7 4 / 7 1/ 7 1/ 7 0 0 1 0 Transform condition of total assets increase is shown in table9. 723 0 5 1 1 S4 0 0 1 0 Tab.9 The next state The current state Transform of total assets increase in different state S1 S2 S3 S1 S2 S3 S4 0 1 1 1 1 2 3 1 1 2 1 1 S4 0 2 0 1 One step transition probability matrix: 0 1 / 7 P= 1/ 5 1 / 4 1/ 2 2/7 3/5 1/ 4 1/ 2 0 2/ 7 2 / 7 1/ 5 0 1 / 4 1 / 4 4.3.3 The state vector of various states are inferred by the transition probability matrix According to one step transition probability matrix and -54.96%, the current status of ROE , we can find: Л 0 1 0 0 0 ( )=( , , , ) 0 5 / 6 1/ 6 0 1/ 8 5 / 8 1/ 8 1/ 8 Л 0 ×P (1 0 0 0) 0 1/ 5 3 / 5 1/ 5 0 1 0 0 ( )= ( ) = Л 1 ( )=(5/6,1/6,0,0) So, Л 1 The annual report in March 31, 2008 is forecasted under the stability condition. The probability of ROE falls into the range S1 is 5/6. The probability of ROE falls into the range S2 is 1/6. The probability of ROE falls into the range S3 is 0. The probability of ROE falls into the range S4 is 0. So Л 1 of ROE is -5%. According to one step transition probability matrix and -0.11, the current status of operating cash flow per share , we can find: Л 0 0 1 0 0 () ( )=( , , , ) 0 1/ 3 2 / 3 0 0 3/8 5/8 0 Л 0 ×P (0 1 0 0) 1/ 7 4 / 7 1/ 7 1/ 7 0 0 1 0 ( )= ( ) = Л 1 , ( )=(0,3/8,5/8,0) So Л 1 The annual report in December 31, 2007 is forecasted under the stability condition. The probability of operating cash flow per share falls into the range S1 is 0. The probability of operating cash flow per 724 share falls into the range S2 is 3/8. The probability of operating cash flow per share falls into the range S3 is 5/8. The probability of operating cash flow per share falls into the range S4 is 0. So Л 1 of operating cash flow per share is 1.825. According to one step transition probability matrix and -17.63%, the current status of total assets increase, we can find: Л 0 1 0 0 0 () ( )=( , , , ) 0 1 / 7 Л 0 ×P (1 0 0 0 ) 1/ 5 1 / 4 1/ 2 2/7 3/ 5 1/ 4 ( )= ( ) = Л 1 , ( )=(0,1/2,1/2,0) 1/ 2 0 2 / 7 2 / 7 1/ 5 0 1 / 4 1 / 4 So Л 1 The annual report in December 31, 2007 is forecasted under the stability condition. The probability of total assets increase falls into the range S1 is 0. The probability of total assets increase falls into the range S2 is 1/2. The probability of total assets increase falls into the range S3 is 1/2. The probability of total assets increase falls into the range S4 is 0. So Л 1 of total assets increase is -2.0433. Finally, let’s put the three data into formula (1): () ln p = −10.454 X 1 − 3.869 X 2 − 3.271X 3 + 0.828 1− p Because P=0.9>0.5 , So the company is on the state of financial crisis. 5 Conclusion This paper selects rate of return on common stockholders’ equity(ROE), total assets increase and operating cash flow per share to forecast the enterprise finance with totally twenty quarterly data of Zhongwugaoxin Co. Ltd. According to the change randomcity of financial index , Markov is used to analyze the change rule of financial index empirically in this paper to forecast the risk of company finance. The result of empirical study may forecast promptly the business finance risk. Besides this, it urges the enterprise to adopt the rectification measures immediately and avoids the enterprise moving toward the bankrupt settlement. But time and quantities of samples are limited in the quarterly reports, so the results may be not accurately highly. 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