1、 1 Banks analysis of financial data Andreas P. Nawroth, Joachim Peinke Institut fu r Physik, Carl-von-Ossietzky Universita t Oldenburg, D-26111 Oldenburg, Germany Available online 30 March 2007 Abstract A stochastic analysis of financial data is presented. In particular we investigate how the statis
2、tics of log returns change with different time delays t. The scale-dependent behaviour of financial data can be divided into two regions. The first time range, the small-timescale region (in the range of seconds) seems to be characterised by universal features. The second time range, the medium-time
3、scale range from several minutes upwards can be characterised by a cascade process, which is given by a stochastic Markov process in the scale . A corresponding FokkerPlanck equation can be extracted from given data and provides a non-equilibrium thermodynamical description of the complexity of fina
4、ncial data. Keywords: Banks； Financial markets； Stochastic processes； FokkerPlanck equation 1.Introduction Financial statements for banks present a different analytical problem than manufacturing and service companies. As a result, analysis of a banks 2 financial statements requires a distinct appro
5、ach that recognizes a banks somewhat unique risks. Banks take deposits from savers, paying interest on some of these accounts. They pass these funds on to borrowers, receiving interest on the loans. Their profits are derived from the spread between the rate they pay for funds and the rate they recei
6、ve from borrowers. This ability to pool deposits from many sources that can be lent to many different borrowers creates the flow of funds inherent in the banking system. By managing this flow of funds, banks generate profits, acting as the intermediary of interest paid and interest received and taki
7、ng on the risks of offering credit. 2. Small-scale analysis Banking is a highly leveraged business requiring regulators to dictate minimal capital levels to help ensure the solvency of each bank and the banking system. In the US, a banks primary regulator could be the Federal Reserve Board, the Offi
8、ce of the Comptroller of the Currency, the Office of Thrift Supervision or any one of 50 state regulatory bodies, depending on the charter of the bank. Within the Federal Reserve Board, there are 12 districts with 12 different regulatory staffing groups. These regulators focus on compliance with cer
9、tain requirements, restrictions and guidelines, aiming to uphold the soundness and integrity of the banking system. As one of the most highly regulated banking industries in the world, investors have some level of assurance in the soundness of the banking system. As a result, investors can focus mos
10、t of their efforts on how a bank will perform in different economic environments. Below is a sample income statement and balance sheet for a large bank. The first thing to notice is that the line items in the statements are not the same as your typical manufacturing or service firm. Instead, there a
11、re entries that represent interest earned or expensed as well as deposits and loans. 3 As financial intermediaries, banks assume two primary types of risk as they manage the flow of money through their business. Interest rate risk is the management of the spread between interest paid on deposits and
12、 received on loans over time. Credit risk is the likelihood that a borrower will default on its loan or lease, causing the bank to lose any potential interest earned as well as the principal that was loaned to the borrower. As investors, these are the primary elements that need to be understood when
13、 analyzing a banks financial statement. 3. Medium scale analysis The primary business of a bank is managing the spread between deposits. Basically when the interest that a bank earns from loans is greater than the interest it must pay on deposits, it generates a positive interest spread or net inter
14、est income. The size of this spread is a major determinant of the profit generated by a bank. This interest rate risk is primarily determined by the shape of the yield curve. As a result, net interest income will vary, due to differences in the timing of accrual changes and changing rate and yield c
15、urve relationships. Changes in the general level of market interest rates also may cause changes in the volume and mix of a banks balance sheet products. For example, when economic activity continues to expand while interest rates are rising, commercial loan demand may increase while residential mor
16、tgage loan growth and prepayments slow. Banks, in the normal course of business, assume financial risk by making loans at interest rates that differ from rates paid on deposits. Deposits often have shorter maturities than loans. The result is a balance sheet mismatch between assets (loans) and liabilities (deposits). An upward sloping yield curve is favorable to a bank as the bulk of its deposits are short term and their loans are longer term. This mismatch of maturities generates the net interest
