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1、Risk Management Selected Concepts,AgendaDefinitionsBasic Concepts of Modern Portfolio TheorySelected Risk Management MetricsInvestment Policy and Conclusions,Definitions,Quite often risk is perceived only with negative connotationsD defines risk as:1.The possibility of suffering harm or loss;danger.
2、2.A factor,thing,element,or course involving uncertain danger;3.a.The danger or probability of loss to an insurer.b.The amount that an insurance company stands to lose.4.a.The variability of returns from an investment.b.The chance of nonpayment of a debt.5.One considered with respect to the possibil
3、ity of loss:a poor risk.However,risk may also contain another element The Chinese use two symbols to define risk:1.The first symbol is for“danger”2.The second is for“opportunity”,What is Risk?,From our previous definition,Risk Management(RM)would entail administering a mix of danger and opportunity.
4、A more classic approach defines RM as a process(an attempt,really)to identify,measure,monitor and control uncertainty in an orderly and methodical manner(often using mathematical models).Both approaches to RM are correct.However,RM is more of avoiding dangers than seeking the opportunities.RM in a m
5、odern acception entails following a pre-established management process and performing mathematical models(Greek letters and other sophisticated financial metrics).RM is about understanding human behavior and finding a“comfortable”trade-off between expected reward and potential loss.,What is Risk Man
6、agement?,RM entails managing exposure and uncertainty.,Risk Topologyin the Investment Management context,Investment Risks,Liquidity,Operational,Regulatory,Human Factor,Market Risk,Credit,PortfolioConcentration,Issuer,Counterparty Risk,Equity/commodity(price),Interest Rates,Currency,Legal,Systemic,Ma
7、rket risk is the uncertainty of changes in the assets returns relative to changes in the market.Derives from market-wide factors which affect issuers and investors.Such factors will include(but will not limited to):Interest rates;Inflation rates;Currency exchange rates;Demographics(remember Michael
8、Cichons comments about demographic implications!);Unemployment rates;General legislation;Risk of natural disasters(Katrina,Rita,earthquakes,floods,fire,etc.).,Market Risk,-Credit risk is the uncertainty in a counterpartys(or obligors)ability to meet payment of its obligations.Associated concepts:Def
9、ault probability is the likelihood that the obligor will default on its obligation either over the life of the transaction or at an specific timeframe.Credit exposure is the amount of outstanding at the time of a potential default.Recovery rate is the fraction of the exposure that might be recovered
10、.Credit quality is the perceived ability(usually by a credit rating agency)of an issuer or counterparty to meet its obligation.Credit rating is assigned by credit analysts to the counterparty(or specific obligation)and can be used for making credit decisions.,Credit Risk,Standard&Poors Credit Rating
11、s,AAABest credit quality-Extremely reliable with regard to financial obligationsAAVery good credit quality-Very reliableA More susceptible to economic conditions-still good credit qualityBBB Lowest rating in investment gradeBB Caution is necessary-Best sub-investment credit qualityB Vulnerable to ch
12、anges in economic conditions-Currently showing the ability to meet its financial obligationsCCC Currently vulnerable to nonpayment-Dependent on favorable economic conditionsCC Highly vulnerable to a payment defaultC Close to or already bankrupt-Payment on the obligation currently continuedD Payment
13、default on some financial obligations has actually occurred,Simple,market wide,common,homogeneous(to a broad range of assets),easily available and(+-)objective.But have limitations(remember Enron!).,Liquidity risk is the uncertainty of being able to easily and without undue cost avail oneself of cas
14、h either through converting financial assets to cash(“liquidate a position”)or through credit.A person or institution might be exposed to liquidity risk if sudden unexpected cash outflows occurs and the markets on which it depends are subject to loss of liquidity,or if a financial asset it holds los
15、ses“marketability”or if the credit rating of the institution falls.A position can be hedged against market risk but still entail liquidity risk.Accordingly,liquidity risk has to be managed in addition to market,credit and other risks.Cash flow exercises and stress testing(along with asset-liability
16、matching)cab be applied to assess liquidity risk.However,Comprehensive metrics of liquidity risk due to systemic failures are not easily available.Remember James Thompsons comment about matching assets and liabilities,this reduces exposure to liquidity risk!.,Liquidity Risk,Risk that a localized pro
17、blem in the financial markets could cause a chain of events which ultimately cripple the market.A default by a major market participant(i.e.Government default,and even maybe foreign currency depletion and/or inability to access international markets)might cause liquidity problems for a number of tha
18、t institutions counterparties.This might cause those counterparties to fail to make payment on their own obligations,and a liquidity crisis could spread throughout the market.One of the purposes of financial regulation is to ensure that the market operates in a manner that minimizes systemic risk.Th
19、is issue might be discussed by Edgardo Podjarny for the Argentina case.,Systemic Risk,“Risk management”as it is understood today,largely emerged during the early 1990s.It is different from earlier forms(it is more oriented to financial solutions using derivatives).The four approaches to risk managem
20、ent are:Risk Transfer:through the purchase of traditional insurance products,or through the acquisition of derivative products to“hedge”exposures.Termination(or mitigation)of risks:via safety measures,quality control and hazard education.Risk transformation:also through the use of derivatives.Tolera
21、te risks:alternative risk financing,including self-insurance and captive insurance(assume expected value of impact or loss is lower than cost of hedging,transferring risk or preventive measures).,Basic Risk Management Concepts,Basic Concepts of Modern Portfolio Theory,Markowitz(1952)“Portfolio Selec
22、tion”Harry Markowitz proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios form securities that have(individually)attractive risk-reward characteristics.MPT treats volatility and expected return as proxies for
23、risk and reward.Out of the entire set of possible portfolios,a certain sub-set will optimally balance risk and reward.(sub-set=efficient frontier of portfolios)An investor should select a portfolio that lies on the efficient frontier.MPT provides a broad context for understanding the structuring of
24、a portfolio.,Modern Portfolio Theory(MPT),Today,it is possible to monitor daily the values(reflecting price changes,coupon payments,dividends,stock splits,etc.)for most of the traded financial instruments.However,their future values behave in what seems a random pattern.Observing their past behavior
25、 and using several algorithms we may estimate their future returns and volatilities and correlations(for each pair of instruments).With these inputs(expected returns,volatilities and correlations)we may calculate the expected return and volatility of any portfolio.The notion of“optimal”portfolio can
26、 be defined in one of two ways:For any expected return,consider all the portfolios which have that expected return and select the one which has the lowest volatility.For any level of volatility,consider all the portfolios which have that volatility and select the one which has the highest expected r
27、eturn.,Efficient Frontier,Efficient Frontier,The green region corresponds to set of achievable risk-return portfolios(basket of instruments).Portfolios on the efficient frontier are optimal in both the sense that they offer maximal expected return for some given level of risk and minimal risk for so
28、me given level of expected return.Typically,the portfolios which comprise the efficient frontier are the ones which are most highly diversified.,A corollary of MPT.Diversification(“dont put all your eggs in one basket”)A portfolio that is invested in multiple instruments whose returns are uncorrelat
29、ed will have an expected simple return which is the weighted average of the individual instruments returns,but its expected volatility(risk)will be less than the weighted average of the individual instruments volatilities.Expected behavior need to be uncorrelatedTo diversify it is not sufficient to
30、add instruments to a portfolio.Suitable diversification requires reduction of risk concentrations and unrelated risks taken on.,Diversification,Capital Market Line,James Tobin(1958)added the notion of leveraging the“efficient”portfolio by combining it with a risk-free asset.Investors who hold the su
31、per-efficient portfolio using the risk-free asset may:Leverage their position by shorting the risk-free asset and investing the proceeds in additional holdings in the super-efficient portfolio.De-leverage their position by selling some of their holdings in the super-efficient portfolio and investing
32、 the proceeds in the risk-free asset.,Risk-Free Rate,CML,Borrow at risk free rateand purchase more efficientportfolio,Loan at risk free rateand sell efficientportfolio,William Sharpe(1964)extended MPT by introducing notions of systematic and specific risk.CAPM demonstrates that(given simplifying ass
33、umptions),the super-efficient portfolio must be the market portfolio.All investors should hold the market portfolio(leveraged or de-leveraged to achieve whatever level of risk they desire).CAPM decomposes a portfolios risk into:Systematic risk:risk of holding the market portfolio for which an invest
34、or is compensated.Specific risk:risk which is unique to an individual asset and can be diversified(the investor doesnt receive compensation for it).When an investor holds the market portfolio,each individual asset in that portfolio entails specific risk,but through diversification the risk may be nu
35、llified(the net exposure ends up as only systematic risk of the market portfolio).,Capital Asset Pricing Model(CAPM),Beta measures the volatility of a security relative to the asset class(or to the market portfolio).If a securitys Beta is known,then CAPM can establish the required return(a higher Be
36、ta that is higher expected risk-requires higher expected returns).CAPM simplifies the task of finding the efficient frontier because it is necessary to calculate the correlations of every pair of asset classes(proxies of the market)instead of every pair of instruments in the entire universe.Investin
37、g in the asset class is possible and simple via investing in index funds that effectively replicate the market.,Capital Asset Pricing Model(CAPM),Metrics,Duration,Duration is a weighted measure of when an investor will get his money back from a fixed income investment.Duration considers coupon payme
38、nts.The duration of a zero-coupon bond equals its maturity.For two bonds that mature at the same time,the bond with the higher coupon payment will have lower duration.Duration is also a metric of interest rate sensitivity.With a single number duration summarizes an instruments sensitivity to changes
39、 in interest rates.Of the many risks facing investors(in fixed income),interest rate is probably the most worrisome.Duration is one of the key metrics that allows identifying,measuring and controlling interest rate risk.The value of the instrument will decline if interest rates rise and rise if inte
40、rest rates fall.Bonds with higher duration face higher interest rate risk.,Duration,A good rule of thumb regarding duration and changes in interest rates:,Geometrically,duration is defined to be the slope of that tangent line,multiplied by negative one.,Volatility,Example:Time series of prices of tw
41、o assets,The asset on the left is more risky(more volatile of the two),Volatility may be defined as the uncertainty surrounding an expected value Volatility usually refers to movements in financial prices and rates.Fluctuations(of prices or rates in financial markets)are generally random and indepen
42、dent from one period to the next(there are no serial correlations or other dependencies).Usually,we refer to volatility as the mean of the standard deviation of expected returns.,Variance and Standard Deviation,The variance is a metric of the spread of random variables probability distribution(aroun
43、d the arithmetic mean average).The most commonly used measure of spread is the standard deviation(which is calculated as the square root of the variance).,Example:High vs.Low Variance,Probability density functions(PDFs)are indicated for two random variables.The one on the left is more dispersed(it h
44、as a higher variance)than the one on the right.,Value at Risk(VaR),Value at Risk(VaR)is metric that summarizes in a single number the portfolios market risk.VAR measures the maximum loss over an established time horizon(i.e.worst case scenario of losses in one month).VaR is applicable to any liquid
45、portfolio(any portfolio that can reasonably be marked to market on a regular basis and that its assets may be readily converted to cash).VaR uses standard deviation and statistical analysis(of price and volatilities)to determine the worst loss scenario for a given probability(confidence level).If th
46、e returns are normally distributed(bell-shaped curve distribution),approx.68%of the outcomes will fall within one standard deviation on either side of the expected value(mean)and approximately 95%will fall within 2 standard deviations on either side of it.The higher the variance and standard deviati
47、on,the greater the variability of possible returns from the investment(the greater the risk).,Credit VaR is similar to“market”VaR,but it refers specifically to the maximum exposure and expected maximum loss(through default or price change)a firm is willing to take in an investment(or loan)portfolio.
48、This approach is based on the credit transition matrix,which defines the probability of one asset”migrating”or“transiting”to lower credit ratings.Industry limits,country and counterparty limits may be established to limit the credit exposure.,Credit VaR,Source:CONSAR.March 2005,Credit rating transit
49、ion matrix,Alpha is a measure of the incremental reward(or loss)that an investor gained in relation to the market.This is measured as performance of a selected portfolio relative to a market benchmark.Alpha can be used to directly measure the value added or subtracted by a a funds manager.It is calc
50、ulated by measuring the difference between a funds actual returns and its expected performance.Tracking error is the standard deviation of the excess return.The information ratio(IR)is one measure of volatility-adjusted return.IR is defined as alpha divided by tracking error.,Alpha()and Information
