1、现代金融风险理论,上海财经大学 朱文革,目录,风险的定义风险的分类金融风险理论概述金融风险的非经济学模型金融经济学介绍金融风险的经济学模型风险管理理论概述风险管理实务概述,现代金融风险理论第一讲,风险的定义,Historical background,The term risk may be traced back to classical Greek rizikon (Greek , riza), meaning root, later used in Latin for cliff. The term is used in Homers Rhapsody M of Odyssey Sire
2、ns, Scylla, Charybdee and the bulls of Helios (Sun) Odysseus tried to save himself from Charybdee at the cliffs of Scylla, where his ship was destroyed by heavy seas generated by Zeus as a punishment for his crew killing before the bulls of Helios (the god of the sun), by grapping the roots of a wil
3、d fig tree.,Historical background,For sociologists, the term risk is a neologism which appeared with the transition from traditional to modern society. In the Middle Ages the term riscium was used in highly specific contexts, above all sea trade and its ensuing legal problems of loss and damage. In
4、the vernacular languages of the 16th century the words rischio and riezgo were used, both terms derived from the Arabic word , rizk, meaning to seek prosperity. This was introduced to continental Europe, through interaction with Middle Eastern and North African Arab traders. In the English language
5、the term risk appeared only in the 17th century, and seems to be imported from continental Europe.“ When the terminology of risk took ground, it replaced the older notion that thought in terms of good and bad fortune. Niklas Luhmann (1996) seeks to explain this transition: Perhaps, this was simply a
6、 loss of plausibility of the old rhetorics of Fortuna as an allegorical figure of religious content and of prudentia as a (noble) virtue in the emerging commercial society.,风险的教科书定义,常见的定义为：uncertainty concerning loss。发生财务损失的不确定性，为个人日常生活或企业生命中之常态。是对主观上不确定性的客观衡量。某一事件，在一特定期间后，实际结果与原所预期者，产生偏差的情况。,风险的Web
7、ster定义,Exposure to the chance of injury or lossA hazard or dangerous chanceInsurance: The hazard or chance of lossThe degree of probability of such lossThe amount that the insurance company may loseA person or thing with reference to the hazard involved to the insurerThe type of loss against which a
8、 policy is drawn,风险三要素,风险标的系指暴露在危险情况下之有形的或无形标的危险事故(Peril)源于自然界 - 天灾(Acts of God) 源于人为因素 - 人祸(Humans acts)源于物之本质 - 物性(Nature of material)危险事故发生的经济结果,危险因素,实质的危险因素(Physical hazard)心理的危险因素(Morale hazard)道德的危险因素(Moral hazard)法律危险因素（Legal hazard）,风险三要素与风险因素之间的关系,图 1-1 危险因素、危险事故与損失之关系图,风险的物理和心理原因,测不准原理非线性动
9、力系统博弈论,风险的现代汉语词典定义,可能发生的危险危险的定义:有遭到损害或失败的可能,风险的普通定义,One set of definitions presents risks simply as future issues which can be avoided or mitigated, rather than present problems that must be immediately addressed. E.g. Risk is the unwanted subset of a set of uncertain outcomes.“居安思危，思則有备，有备则无患。春秋魏绛左
10、传,风险的数学期望定义,More formally (and quantitatively), risk is proportional to both the results expected from an event and to the probability of this event. E.g. Risk is a combination of the likelihood of an occurrence of a hazardous event or exposure(s) and the severity of injury or ill health that can be
11、 caused by the event or exposure(s). Mathematically, risk often simply defined as,风险数学期望定义的问题,It is argued that defining risk as the product of impact and probability presumes (probably incorrectly) that the decision makers are risk neutral. Only for a risk neutral person is the certain monetary equ
12、ivalent exactly equal to the probability of the loss times the amount of the loss. For example, a risk neutral person would consider 20% chance of winning $1 million exactly equal to $200,000 (or a 20% chance of losing $1 million to be exactly equal to losing $200,000). However, most decision makers
13、 are not actually risk neutral and would not consider these equivalent choices.,风险的概率定义,It is proposed instead that risk is a kind of vector quantity that does not collapse the probability and magnitude of a risk by presuming anything about the risk tolerance of the decision maker. Risks are simply
14、described as an set or function of possible loss amounts each associated with specific probabilities. How this array is collapsed into a single value cannot be done until the risk tolerance of the decision maker is quantified.,风险的统计决策定义,In statistics, risk is often mapped to the probability of some
15、event which is seen as undesirable. Usually, the probability of that event and some assessment of its expected harm must be combined into a believable scenario (an outcome), which combines the set of risk, regret and reward probabilities into an expected value for that outcome.,风险的统计决策定义,Thus, in st
16、atistical decision theory, the risk function of an estimator (x) for a parameter , calculated from some observables x, is defined as the expectation value of the loss function L,统计决策三要素,样本空间与样本分布族行动空间损失函数选择决策函数的准则容许性准则最小化最大准则贝叶斯准则最优同变性准则,风险的经济学定义,Expected utility function EU(X) where X is a random v
17、ariable.Concave utility U and risk aversionStochastic DominanceFirst Order Stochastic Dominance (FOSD)X FOSD YEu(X)Eu(Y) for all increasing uSecond Order Stochastic Dominance (SOSD)X SOSD Y Eu(X)Eu(Y) for all increasing and concave uBut stochastic dominance can not compare all different risks.,风险的经济
18、学定义,Von Neumann-Morgenstern 公理Axiom 1: The preference is complete and transitiveAxiom 2: Substitution/IndependenceAxiom 3: Continuity/ArchimedeanTheorem: a preference relation satisfies Axiom 13 iff there exists a expected utility function,风险和不确定性,Uncertainty: The lack of complete certainty, that is
19、, the existence of more than one possibility. The true outcome/state/result/value is not known. Measurement of uncertainty: A set of probabilities assigned to a set of possibilities. Example: There is a 60% chance this market will double in five years Risk: A state of uncertainty where some of the p
20、ossibilities involve a loss, catastrophe, or other undesirable outcome. Measurement of risk: A set of possibilities each with quantified probabilities and quantified losses. Example: There is a 40% chance the proposed oil well will be dry with a loss of $12 million in exploratory drilling costs.,风险和
21、不确定性,In this sense, one may have uncertainty without risk but not risk without uncertainty. We can be uncertain about the winner of a contest, but unless we have some personal stake in it, we have no risk. If we bet money on the outcome of the contest, then we have a risk. In both cases there are mo
22、re than one outcome. The measure of uncertainty refers only to the probabilities assigned to outcomes, while the measure of risk requires both probabilities for outcomes and losses quantified for outcomes.,现代金融风险理论第二讲,风险的分类:Ch1,风险的分类,纯粹风险及投机风险静态风险与动态风险人身风险、财产风险与责任风险,26,纯粹风险和投机风险,依危险事故发生的经济结果，分为：纯粹风险
23、(Pure risk)投机风险(Speculative risk)：即金融风险,风险的分类,Pure RiskLife RiskNonlife RiskFinancial Risk (Speculative Risk)Systematic Risk (Market Risk)Credit RiskLiquidity RiskOperational RiskLegal Risk,Pure Risk,Uncertainty regarding frequency and severity (process risk)Uncertainty regarding models to estimate
24、losses (parameter risk),Ruin of Probability and Loss Value,Loss Value,Frequency,Risk,Risk Management,Pure Risk:Natural and Man-made,Market Risk,Systematic riskInterest rate riskInflation riskStock market riskForeign exchange risk,Inflation 1960-2002,Crude Oil Price,Interest rate risk,Stock Market Ri
25、sk,Foreign Exchange Risk,Returns on foreign and domestic investment are not perfectly correlated.FX rates may not be correlated.Example: $/DM may be increasing while $/ decreasing.Undiversified foreign expansion creates FX risk.,Country or Sovereign Risk,Result of exposure to foreign government whic
26、h may impose restrictions on repayments to foreigners.Lack usual recourse via court system.Examples: South Korea, Indonesia, Thailand.More recently, Argentina.,Credit Risk,Risk that promised cash flows are not paid in full.Firm specific credit riskSystematic credit risk,Technology and Operational Ri
27、sk,Risk of direct or indirect loss resulting form inadequate or failed internal processes, people, and systems or from external events.Some include reputational and strategic riskTechnological innovation has seen rapid growthAutomated clearing houses,Technology and Operational Risk,Risk that technol
28、ogy investment fails to produce anticipated cost savings.Risk that technology may break down.,Liquidity Risk,Risk of being forced to borrow, or sell assets in a very short period of time. Low prices result.May generate runs.Runs may turn liquidity problem into solvency problem.Risk of systematic ban
29、k panics.,Legal Risk,New Statues, court opinions, regulationLegal risk arises from the activities of an institutions management, employees and agents.,现代金融风险理论第三讲,风险的非经济学模型:Ch 2&3,非经济学观点的金融风险模型,数学家的观点以死亡风险和灾害风险为例以利率风险为例,数学家的观点:拟合风险分布,常用的概率分布离散分布连续分布分布函数特征函数,Measure of Risk,Frequency,Value,SmallLoss,
30、Large loss,Extreme Loss,99.9%Confidence,肥尾分布,正态分布的问题其它分布:尖峰分布t-分布混合分布平稳分布:分形分布 Pareto分布尾部的拟合中央部分的拟合,随机过程,连续过程维纳过程跳跃过程Poisson过程平稳过程宽平稳严平稳,平稳的随机过程,自相关系数白噪声过程自回归过程移动平均过程ARMAHeavy Tailed Time Series“Modelling Extremal Events” by P.Embrechts, C Kluppelberg and T. Mikosch, Springer-Verlag 世界图书出版社,时间序列,线性时
31、间序列AR ModelsMA ModelsARMA ModelsARIMA Models非线性时间序列GARCH和ARCH Fan and Yao 非线性时间序列科学出版社,死亡风险,生存函数,生存函数的估计,生命表的编制长寿风险,灾害风险,赔款频率 赔款额度 损失额度的分布信息不完全时怎么办?信度理论巨灾风险,利率风险: Measures of Interest Rate Risk,Macaulay duration recognizes that the sensitivity of the price of a fixed income asset is approximately re
32、lated to the (present value) weighted average time to maturityModified duration is the negative of the first derivative of price with respect to interest rates, divided by the priceModified duration = Macaulay duration/(1+r),Macaulay and Modified Duration,Duration is the Slope of the Tangency Line f
33、or the Price/Yield Curve,Price,Yield,r,Price-yield curve forfinancial instrument,Immunization: an Example,Immunization,Example (the X corporation) The X Corporation has an obligation to pay $1 million in 10 yrs. It wishes to invest money now that will be sufficient to meet this obligation. X is plan
34、ning to select from the three bonds in the previous slide,please find the immunized portfolio.,Assumptions Underlying Macaulay and Modified Duration,Cash flows do not change with interest ratesBut: this does not hold for:Collateralized Mortgage Obligations (CMOs)Callable bondsP-L loss reserves due t
35、o inflation-interest rate correlationFlat yield curveBut: generally, yield curves are upward-slopingInterest rates shift in parallel fashionBut: short term interest rates tend to be more volatile than longer term ratesThe real problem is the duration model is not a good economic model,非经济学金融风险模型的问题,
36、优点缺点,现代金融风险理论第四讲,金融经济学概述,风险的经济学观点,何为经济学风险的经济学研究方法有何特点,What is Economics?,The allocation of scarce resourcesOpportunity costEfficiencyMicro v. MacroMicro: Decisions of individuals and firmsMarkets for individual goods and servicesMacro: Study of economy as a wholeEconomic fluctuations, inflation, etc
37、. Economic theory and empirical analysis,Basic Structure,Demand what do consumers do?Supply what do firms do?Equilibrium what happens when you put consumers and firms together?,The Demand Side,Preferences, utility and budget constraintsIndividual demand curvesChoice over timeTime preference & discou
38、ntingChoice under uncertaintyRisk & returnDemand for hedging / insurance,The Supply Side,Allocation of resources in productionAll about costsMarginal, average, sunk, opportunityEconomic versus accounting profitsMaximizing present valueSupply curves,Market Equilibrium,How equilibrium worksWinners (an
39、d losers?) from market equilibriumEfficient marketsFinancial marketsGovernment intervention,What is Finance?,What is FinanceMicro: Financial EconomicsMacro: Monetary EconomicsWhat is Financial Economics时间和风险的市场均衡,Typical Problems in Finance,InvestmentFinancingRisk ManagementPricing,金融经济学:Fisher 模型介绍
40、,I.Fisher的简单模型模型的假设：消费者（投资者）在多和少之间偏好多消费者（投资者）只考虑现在和将来两期存在理想银行（资本市场），其借贷款利率相同投资机会没有风险,Fisher 图形,将来的消费,H,F,B,D,现在的消费,消费者现有OB，将来有OF。利用银行可以实现不同的选择,O,将来,现在,￥25,000,￥20,000,通过适当借贷，你可以取得HD上的任何一点,.,H,D,￥36,000,例：假设利率为10%，你现在有￥20，000，将来有￥25，000。如果现在借出￥10，000，将来会有￥25，000+￥10，000*1.1=￥36，000。,利率和资产的现值,利率是在银行（资
41、本市场上）借（或贷）资本必须支付（或得到）的价格。资产的现值是该资产未来收入在现在的价值。例：年利率为10%，问一年后的110元现在值多少？答：PV=,挥霍的消费者的选择,挥霍的消费者现在借BC，消费OC；将来消费OE,将来,H,F,B,D,现在,C,E,挥霍的消费者的选择,O,最初的财富,节约的消费者的选择,节约的消费者现在贷AB，消费OA；将来消费OG,将来,H,F,B,D,现在,A,G,节约的消费者的选择,O,将来,现在,￥20,000,H,D,我应该选择哪一点?,￥25,000,将来,现在,H,D,无差异曲线代表消费者效用相同的所有选择,￥25,000,￥20,000,将来,现在,H,
42、D,消费者效用增加,将来,现在,L,所有的投资机会：现在投资PD，将来得到SP,S,P,O,D,将来,现在,L,D,现在有财富OD，利用投资可以把财富现值增加到OK,K*,P,J,M*,K,T,最优策略：利用的投资机会总共为JD,O,将来,现在,L,D,J,M*,K,T,Fisher模型的几个基本结论,技术上的投资机会和所有投资者的主观时间偏好相互作用决定利率。利率决定了资产的价格。在确定的利率下，消费者根据自己的时间偏好确定自己的借贷比例。在确定的利率和投资机会下，企业根据自有资产的多少确定自己的资本结构。资本结构不影响企业的价值,如何解决现实世界中的金融问题,现实世界和Fisher模型的区
43、别风险投资期利率的期限结构交易成本信息不对称行为理性假设新的模型和金融理论的发展现代金融理论Nobel Laureates: Markowitz, Modigliani, Miller, Sharpe, Black & Scholes, Merton,现代金融理论,利率期限结构理论组合理论和CAPMMM理论动态消费和投资组合理论 (Markowitz Theory- Merton)动态资产定价理论 (CAPM - ICAPM)期权和衍生产品理论 (Black-Scholes)公司金融理论(MM - Non-Perfect Market)其它(行为金融学),The Starting Point
44、for Finance,The starting point for every financial model involves the impect of uncertainty on the behavior of investors and, ultimately, on market prices. Indeed, in the absence of uncertainty, the problems of financial economics reduce to exercises in basic microeconomics. The very existence of fi
45、nancial economics as a discipline is predicted on uncertainty.Campbell, Lo and Mackinlay,金融风险经济学建模的基本原则,现金流原则比较原则无套利原则动态原则风险规避原则,现代金融风险理论第五讲,金融风险经济学模型:资产组合理论 Ch49,风险和收益,收益率的度量风险的度量资产配置,收益率的度量-单期,持有期收益率(HPR),投资的不确定性和风险,投资有风险不同金融工具的不同风险风险的度量收益率的概率分布通过历史数据估计收益率的概率分布,投资收益率风险的描述,风险描述的特征量：期望值和方差,期望值(均值)方差
46、及标准差,期望值和方差：例题,初期投入：$100,期望值= 0.3(0.5)+0.5(0.2)+0.2(-0.4)=17%,方差= 0.3(0.5-0.17)2+0.5(0.2-0.17) +0.2(-0.4-0.17)2 = 0.0981,标准差= (0.0981)0.5 = 0.313,通过历史数据估计投资风险,收益率的均值估计样本的平均值收益率的方差估计样本方差,资产配置例题,假设只有两种资产风险资产: E(rp) = 15% p = 22%无风险资产: rf = 7%你应该选择怎样的投资组合?,资产配置- 资本市场线, p = 22%,E(rc) = E(rp) * y + rf *
47、(1-y) c = y * p,F,资产配置（续）,改变投资组合中风险资产的份额，其组合对应的均值和方差落在一条直线上- the Capital Allocation Line (CAL)(CAL) 的斜率称为Reward-to-Variability Ratio,最优组合的选择,和投资者的风险厌恶程度有关风险厌恶的定义：在收益率均值相同的所有投资组合中选择方差最小的。风险厌恶程度的度量风险厌恶程度越大，选择的投资组合相应的点越靠近F经济学中用Von Neuman-Morgenstern效用函数描述风险的厌恶程度,效用函数描述风险厌恶,SD,CAL,无风险利率,效用增加,无差异曲线,资产配置例
48、题,两种风险资产的组合,协方差和相关性,何为协方差?度量风险资产收益率变化的相关程度 相关系数 在 +1 和 -1 之间. “+1” 意味着完全正相关 “-1” 完全负相关,投资组合机会集,风险的分散,B,A, = -1, = -0.3, = 1, = 0,当 1时, 两个风险资产组合的标准差小于这两个资产标准差的和,组合的方差,组合中的资产数目,系统风险,非系统风险,随着投资组合中证券数目的增加.组合的风险越来越小不能通过资产组合分散的风险称为系统风险。,风险的分散（续）,最优投资组合的选择,Markowitz理论最优投资组合的选择分3步:找出有效边界利用无风险资产找出CAL根据投资者的风险厌恶程度得到最优组合,有效边界,有效边界,Capital Allocation Line “M”,最优组合“M”,
