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1、-Study Notes-第 21 页Study Notes: Risk Investment & Risk Management Chapter 1 IntroductionChapter 2 Risk Management: Some conceptsChapter 3 Bank Regulation and Basel IIChapter 4 VaRChapter 5 Market Risk VaR: Historical Simulation ApproachChapter 6 Market Risk VaR: Model-building ApproachChapter 7 Cred

2、it Risk: Estimating Default ProbabilitiesChapter 8 Credit Risk Loss and Credit VaRChapter 9 Credit DerivativesChapter 10 Operational RiskChapter 11 Model Risk and Liquidity RiskChapter 12 Economic Capital and RAROCChapter 13 Energy and Insurance DerivativesNotice: Every student should understand the

3、 knowledge in black, which is required in our teaching. The student who wants to know more about risk management can read the knowledge in blue.Study Notes for “Financial Risk Management”Introduction做这个Study Notes，主要是基于两个原因。其一是基于John C. Hull的Risk Management and Financial Institutions一书，对本课程中的Risk Ma

4、nagement主要内容进行整理，帮助学生掌握风险管理的重点和难点知识点；其二是通过对风险管理重要知识点的整理与归纳，希望能为那些对风险管理知识有进一步学习欲望的学生提供指导，为其参加FRM考试做一定的知识准备。同时，由于风险管理的专业技术性较强，对于非金融专业学生而言，想达到深入地理解与掌握风险管理内容这一目标，具有一定的难度；况且每位学生自身的知识水平与学习目标不同，因此，各位同学可根据上课内容与要求，结合自身的职业规划与知识要求，有选择地学习此Study Notes。 Shaojun Xu Nov. 5, 2012Chapter 2 Risk Management: Some conce

5、ptsKnowledge: 1. Risk vs Return: There is a trade off between risk and expected return, the higher the risk, the higher the expected return.2. Financial products and how they are used for hedging: Companies trade a variety of financial instruments to manage their risks. Some of these instruments are

6、 referred to as standard or “plain vanilla” products, most forward contracts, futures contracts, swaps, and options fall into this category. Others are designed to meet the particular needs of a corporate treasurer, which are referred to as “exotics” or structured products. How do these instruments

7、trade ? When does a company should hedge, how much hedging should it do, and what instruments should be used ?3. How traders manage their exposures: Linear products is a product whose value is linearly dependent on the value of the underlying asset price. Forward, futures, and swaps are linear produ

8、cts, while options are not. the “Greeks” measures a different aspect of the risk in a trading position: (assume is the value of the portfolio; S is the value of the underlying market variable; is the volatility of the underlying market variable.) Delta: Gamma: , so Gamma is positive for a long posit

9、ion in an option, and a linear product has zero Gamma. Vega: , so spot positions, forwards, and swaps do not depend on the volatility of the underlying market variable, but options and most exotics do, and Vega is positive for long call and put.Theta: the rate of change of the value of the portfolio

10、 with respect to the passage of time with all else remaining the same, or it can be explained by the time decay of the portfolio. Theta is usually negative for an option.Rho: the rate of change of a portfolio with respect to the level of interest rates.Taylor expansions: if ignoring terms of high or

11、der dt and assuming delta neutral and volatility and interest rates are constant, then 4. Interest rate risk: LIBID, the London Interbank Bid Rate. Practitioners usually assume that the LIBOR/swap yield curve provides the risk-free rate, and the T-rate are regarded as too low to be used as risk-free

12、 rates. Duration: the duration of an instrument is a measure of how long, on average, the holder of the instrument has to wait before receiving cash payments. (Assume the condition of continuous compoudings, D is the duration of the bond, B is the price, and y is the yield.)Convexity: . The convexit

13、y of a bond portfolio tends to be greatest when the portfolio provides payments evenly over a long period of time.So this is the weighted average of the square of the time to the receipt of cash flows:5. Volatility: What causes volatility ?Volatility is to a large extent caused by trading itself. Im

14、plied volatility: it is used extensively by traders, however, risk management is largely based on historical volatilities. the volatility model:EWMA ( exponentially weighted moving average model):GARCH(1,1) MODEL:, where . Volatility term structures: the relationship between the implied volatilities

15、 of the options and their maturities.6. Correlations and Copulas: Correlation measures linear dependence. There are many other ways in which two variables can be related. E.g. for normal values, two variables maybe unrelated. However, their extreme values may be related. During a crises the correlat

16、ions all go to one. Copulas: the marginal distribution of X ( unconditional distribution) is its distribution assuming we know nothing about Y. There are many types of copulas: Gaussian copula approach, Student t-copula approach, etc.Further Reading:Taleb,N.N., Dynamic hedging: managing vanilla and

17、exotic options, New York: Wiley, 1996.Chapter 3 Bank Regulation and Basel IIKnowledge:1. The capital a financial institution requires should cover the difference between expected losses over some time horizon and worst-case losses over the same time horizon.The idea is that expected losses are usual

18、ly covered by the way a financial institution prices its products, and capital is a cushion to protect the bank from an extremely unfavorable outcome.2. The history of bank regulating: PRE-1988: bank regulators in different countries tended to regulate bank capital by setting minimum levels for the

19、ratio of capital to total assets. But with the quick development of derivatives, the total assets was no longer a good indicator of the total risks being taken. The 1988 BIS ACCORD: it was the first attempt to set international risk-based standards for capital adequacy. It defined two minimum standa

20、rds for meeting acceptable capital adequacy requirements. The first standard was similar to that existing prior to 1988 and required banks to keep capital equal to at least 8% of the risk-weighted assets. The second standard introduced what became known as the Cooke ratio. However, it has been subje

21、ct to much criticism as being too simple and somewhat arbitrary. The G-30 Policy Recommendations: It contained 20 risk management recommendations for dealers and end users of derivatives and fore recommendations for legislators, regulators, and supervisors. The report is not a regulatory document, b

22、ut is has been very influential in the development of risk management practices.It also suggests how to deal with netting. The 1996 Amendment which was implemented in 1998 ( sometimes referred to as BIS 98): It requires financial institutions to hold capital to cover their exposure to market risks a

23、s well as credit risks. It distinguishes between a banks trading book and its banking book. The credit risk capital charge in the 1988 Accord continued to apply to all on-balance-sheet and off-balance-sheet items in the trading and banking book, except positions in the trading book that consisted of

24、 debt and equity traded securities and positions in commodities and foreign exchange. In addition there was a market risk capital charge for all items in the trading book whether they were on balance sheet or off balance sheet. It also outlined a standardized approach for measuring the capital charg

25、e for market risk. However, it does have significant weakness, for example, all loans by a bank to a corporation have a risk weight of 100% and require the sane amount of capital without considering the credit rating of the corporation. Besides, there was no model of default correlation. Basel II: a

26、 final set of rules agreed to by all members of the Basel Committee was published in June 2004, which was updated in November 2005.Basel II is based on three pillars: Pillar 1: Minimum capital requirements. The minimum capital requirement for credit risk in the banking book is calculated in a new wa

27、y that reflects the credit ratings of counterparties. The capital requirement for market risk remains unchanged from the BIS98, and there is a new capital charge for operational risk. Total Capital=0.08*(Credit risk RWA+Market risk RWA+Operational risk RWA). Pillar 2: Supervisory review. It is conce

28、rned with the supervisory review process, allows regulators in different countries some discretion in how rules are applied but seeks to achieve overall consistency in the application of the rules.Pillar 3: Market discipline. It requires banks to disclose more information about the way they allocate

29、 capital and the risks they take.For credit risk under Basel II: There are three choices to measure credit risk-the standardized approach, the foundation internal ratings based approach (IRB), the advanced IRB approach.For operational risk under Basel II: There are three choices to measure operation

30、al risk-the basic indicator approach, the standardized approach, the advanced measurement approach.For market risk, its the same with BIS98. Basel III in September 2010: The draft Basel III regulations include-(1) tighter definitions of Common Equity; banks must hold 4.5% by January 2015, then a fur

31、ther 2.5%, totalling 7%, (2) the introduction of a , (3) a framework for capital buffers, (4) measures to limit , (5) and short and medium-term quantitative ratios.Questions and Problems:(1) Explain the difference between the standardized approach, the IRB approach, and the advanced IRB approach for

32、 calculating credit risk capital under Basel II.(2) Explain the difference between the basic indicator approach, the standardized approach, and the advanced measurement approach for calculating operational risk capital under Basel II.Further Reading:BIS, Basel II: international convergence of capita

33、l measurement and capital standards: a revised framework, November, 2005, .Chapter 4 VaRKnowledge: 1. Choice of parameters for VaR: - Assuming normal distribution and the mean change in the portfolio value is zero, where X is the confidence level, sigma is the standard deviation (in dollars) of the

34、portfolio change over the time horizon. - The time horizon: N-day VaR = 1-day VaR * square root N. - autocorrelation the above formula a rough one. - The confidence level: if the daily portfolio changes are assumed to be normally distributed with zero mean convert a VaR to another VaR with different

35、 confidence level. 2. Marginal VaR: where xi is the ith component of a portfolio. For an investment portfolio, marginal VaR is closely related to the CAPMs beta. If an assets beta is high, its marginal VaR will tend to be high. 3. Incremental VaR:It is the incremental effect on VaR of a new trade or

36、 the incremental effect of closing out an existing trade. It asks the question: “what is the difference between VaR with and without the trade.” If a component is small relative to the size of a portfolio, it may be reasonable to assume that the marginal VaR remains constant as xi is reduced to zero

37、4. Component VaR:It is the part of the VaR of the portfolio that can be attributed to this component: - The ith component VaR for a large portfolio should be approximately equal to the incremental VaR. - The sum of all the component VaRs should equal to the portfolio VaR. 5. Back testing: - The perc

38、entage of times the actual loss exceeds VaR. Let p = 1-X, where x is confidence level. m = the number of times that the VaR limits is exceeded, n the total number of days. Two hypotheses: a. The probability of an exception on any given day is p. b. The probability of an exception on any given day is

39、 greater than p. The probability (binominal distribution) of the VaR limit being exceeded on m or more days is: We usually use confidence level as 5%. If the probability of the VaR limit being exceeded on m or more days is less than 5%, we reject the first hypothesis that the probability of an excep

40、tion is p. The above test is one-tailed test. Kupiec has proposed a two-tailed test (Frequency-of-tail-losses or Kupiec test). If the probability of an exception under the VaR model is p and m exceptions are observed in n trials, then should have a chi-square distribution with one degree of freedom.

41、 The Kupiec test is a large sample test - Sizes-of-tail-losses test: compare the distribution of empirical tail losses against the tail-loss distribution predicted by model Kolmogorov-Smirnov test (it is the maximum value of the absolute difference between the two distribution functions). - The exte

42、nt to which exceptions are bunched: in practice, exceptions are often bunched together, suggesting that losses on successive days are not independent. 6. Stress testing: It involves estimating how the portfolio would have performed under extreme market moves. Two Main approaches: a. Scenario analyse

43、s, in which we evaluate the impact of specified scenarios (e.g., such as a particular fall in the stock market) on our portfolio. The emphasis is on specifying the scenario and working out its ramifications. b. Mechanical stress tests, in which we evaluate a number (often a large number) of mathemat

44、ically or statistically defined possibilities (e.g., such as increases or decreases of market risk factors by a certain number of standard deviations) to determine the most damaging combination of events and the loss it would produce. 7. stress testing scenario analyses: - Stylized scenarios: Some s

45、tress tests focus on particular market variables. a. Shifting a yield curve by 100 basis points b. Changing implied volatilities for an asset by 20% of current values. c. Changing an equity index by 10%. d. Changing an exchange rate for a major currency by 6% or changing the exchange rate for a mino

46、r currency by 20%. - Actual historical events: stress tests more often involve making changes to several market variables use historical scenarios. E.g. set the percentage changes in all market variables equal to those on October 19, 1987. - If movements in only a few variables are specified in a st

47、ress test, one approach is to set changes in all other variables to zero. Another approach is to regress the nonstressed variables on the variables that are being stressed to obtain forecasts for them, conditional on the changes being made to the stressed variables (conditional stress testing) 8. Stress testing mechanical stress testing - Factor push analysis: we push the price of each individual security or (preferably) the relevant underlying risk factor in the most disadvantageous direction and work out the combined effect of all such changes on the value of