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Level III Risk Management Summary Graphs, charts, tables, examples, and figures are copyright 2016, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved Risk Management, Risk Governance and ERM Risk management process: Recognise exposures to risk  create appropriate ranges for exposures Constantly measure these exposures Risk governance (subset of corporate governance): process of setting overall policies and standards in risk management  Decentralized: Each unit calculates and reports its risk exposures independently; allows people who understand risk better to directly manage it  Centralized: Risk management is moved closer to senior management The main advantage is that it allows offsetting of risks across units Centralized risk management is now called enterprise risk management (ERM) Those responsible for risk management should be independent of the trading function; back office should be independent of front office An effective ERM system usually includes the following steps: Identify each risk factor to which the company is exposed Quantify each exposure’s size in money terms Map these inputs into a risk estimation calculation Identify overall risk exposures as well as the contribution to overall risk deriving from each risk factor Set up a process to report on these risks periodically to senior management, who will set up a committee of division heads and executives to determine capital allocations, risk limits, and risk management policies Monitor compliance with policies and risk limits Financial and Non-financial Risk Factors (1/2) Financial risks Market Risk: Risk associated with interest rates, exchange rates, stock prices and commodity prices Credit Risk: Risk of loss caused by a counterparty or debtor’s failure to make a promised payment Liquidity Risk: Risk that a financial instrument cannot be purchased or sold without a significant concession in price because of the market’s potential inability to efficiently accommodate the desired trading size (large bid-ask spread) Sovereign Risk: A form of credit risk in which the borrower is the government of a sovereign nation Non-financial risks Operational Risk: Risk of loss from failures in a company’s systems and procedures or from external events Model Risk: Risk that a model is incorrect or misapplied; in investments, it often refers to valuation models Settlement (Herstatt) Risk: Risk that one party could be in the process of paying the counterparty while the counterparty is declaring bankruptcy Regulatory Risk: Risk associated with how a transaction will be regulated or with the potential for regulations to change Legal/Contract Risk: The possibility of loss arising from the legal system’s failure to enforce a contract in which an enterprise has a financial stake 2008 Q A Financial and Non-financial Risk Factors (1/2) Non-financial risks (continued…) Tax Risk: Risk associated with uncertainty in tax laws Accounting Risk: Risk associated with uncertainty about how a transaction should be recorded and the potential for accounting rules and regulations to change Political Risk: Risk associated with changes in political environment ESG Risk: Risk to a company’s market valuation resulting from environmental, social and governance factors Performance Netting Risk: Potential for loss resulting from the failure of fees based on net performance to fully cover contractual payout obligations to individual portfolio managers that have positive performance when other portfolio managers have losses and when there are asymmetric incentive fee arrangements with the portfolio managers Settlement Netting Risk: Risk that a liquidator or a counterparty in default could challenge a netting arrangement so that profitable transactions are realized for the benefit of creditors Calculate and Interpret VaR VAR is an estimate of the loss (in money terms) that we expect to exceed with a given level of probability over a specified time period Example: The VaR for a portfolio is $1.5 million for one day with a probability of 0.05 This statement can be interpreted in the following two ways:  percent probability that the portfolio will lose at least $1.5 million in a single day  95 percent probability, that the maximum loss will be $1.5 million for one day VAR measures requires the user to make the following decisions about the calculation’s structure Picking a probability level: • The probability chosen is typically either 0.01 or 0.05 • Using 0.01 is more conservative and will give a higher VAR; it relates to losses that can be expected less frequently Selecting the time period over which to measure VAR: • The choices are: day, week, two-week, month, etc • If the portfolio has a high turnover it is recommended to use a shorter period • Using a longer period results in a higher VAR Choosing the specific approach to modeling the loss distribution VaR Methods Three methods: analytical variance-covariance method, historical method and Monte Carlo simulation method Analytical variance-covariance method: Consider a portfolio with 65% allocation to stocks (μ=12%, σ=22%) and 35% allocation to bonds (μ=5%, σ=7%) 𝜇𝑝 = 𝑤𝑠 𝜇𝑠 + 𝑤𝐵 𝜇𝐵 = 0.65 0.12 + 0.35 0.05 = 0.0955 𝜎𝑃2 = 𝑤𝑆2 𝜎𝑆2 + 𝑤𝐵2 𝜎𝐵2 + 2𝜌𝑤𝑆 𝑤𝐵 𝜎𝑆 𝜎𝐵 = (0.65)2(0.22)2+(0.35)2(0.07)2+2(0.15)(0.65)(0.35)(0.22)(0.07) = 0.0221 𝜎𝑃 = 0.0221 = 0.1487 For a percent yearly VaR, we have μP – 1.65σP = 0.0955 – 1.65(0.1487) = –0.1499 5% yearly VaR is $150,000,000(0.1499) = $22.485 million For weekly VaR, we adjust the expected return to 0.0955/52 and the standard deviation to 0.1487/Sqrt(52) Historical method: In this method we calculate the returns for a given portfolio using actual prices from a user-specified period in the recent past Monte Carlo simulation method: In this method we produce random outcomes according to an assumed probability distribution and a set of input parameters Advantages and Disadvantages of VaR Methods Variance-Covariance Method Historical Method Advantages: Simple Advantages: Advantages: Non-parametric (does not rely on Widely used probability-distribution assumptions) We can assume an appropriate distribution of input data Disadvantages: Relies on past events which might Disadvantages: not be good predictors of the Output only as good as our input future assumption Disadvantages: Relies on normality of returns; doesn’t consider skewness and kurtosis If returns are not normally distributed then we cannot rely totally on standard deviation as a measure of risk Portfolios containing options don’t have normal distributions Monte Carlo Simulation Monte Carlo simulation software is expensive and requires a lot of computing power Advantages and Limitations of VaR Advantages Quantifies potential loss in simple terms Limitations One sided Entire focus is on the left tail Most regulatory authorities accept VAR as an acceptable risk measure Lulls into false sense of security Gives the incorrect impression that risk is properly understood and quantified Some companies use VAR as a measure of Often underestimates magnitude and frequency of worst returns capital at risk across different lines of business Extremely difficult to calculate VAR for large organizations Extensions of VaR Incremental VAR (IVAR) measures the incremental effect of an asset on the VAR of a portfolio by measuring the difference between the portfolio's VAR while including a specified asset and the portfolio's VAR with that asset eliminated Cash flow at risk (CFAR) is the minimum cash flow loss that we expect to be exceeded with a given probability over a specified time Earnings at risk (EAR) is the minimum earnings loss that we expect to be exceeded with a given probability over a specified time Tail value at risk (TVAR) is VAR plus the expected loss in excess of VAR when such excess loss occurs Stress Testing Stress testing supplements VaR by identifying unusual circumstances that could lead to losses in excess of those typically expected The two broad approaches are: 1) scenario analysis and 2) stress modeling Scenario analysis is the process of evaluating a portfolio under different states of the world Stylized scenarios involves simulating a movement in at least one interest rate, exchange rate, stock price, or commodity price relevant to the portfolio One approach to scenario analysis is to use actual extreme events that have occurred in the past We can also create scenarios based on hypothetical events – i.e events that have never happened but might happen Stress modeling: It is difficult to estimate sensitivity of a portfolio to scenarios we design; so another approach is to use an existing model and apply shocks and perturbations to the model inputs in some mechanical way Stressing models can take several forms:  Factor push: Here we push the prices and risk factors of an underlying model in the most disadvantageous way to calculate the combined effect on the portfolio’s value  Maximum loss optimization: Here we try to optimize mathematically the risk variables that will produce the maximum loss  Worst case scenario analysis: Here we examine the worst case that we actually expect to occur 2008 Q 7B Credit Risk Credit risk: risk that the party that owes the larger amount could default Credit losses have two dimensions: likelihood of loss and associated amount of loss Credit risk exposure has two time perspectives: current credit risk and potential credit risk Forward contracts Credit risk exposure is based on the market value: PV of amount to be received – PV of amount to be paid Swaps Swap’s market value is the PV of amounted to be received – PV of amount to be paid For interest rate and equity swaps the potential credit risk is the largest during the middle period of the swap’s life: Risk is low at the start because both counterparties will have performed sufficient current credit analysis Risk is low at the end because few payments remain Currency swaps have greatest credit risk closer to the end of swap’s life This is because the notional principal needs to be swapped at the end of the currency swap Options Forward contracts and swaps have bilateral default risk This means that either party could face credit risk Options have unilateral credit risk Only the long party faces credit risk 2015 Q 6A 10 Risk Budgeting To manage risk, we need to: identify sources of market risk, define how these risks will be measured, set appropriate risk tolerance levels, identify corrective action if actual risk is outside tolerance levels Risk budgeting focuses on where to take risk and how to efficiently allocate risk Example: consider a bank with an FX unit and a fixed income unit The allocation of capital and risk budget for each unit is shown below:  FX desk: allocated capital = 100 million and permitted daily VAR = million  Fixed income desk: allocated capital = 200 million and permitted daily VAR = million  Permitted daily VAR for both desks combined = million The fixed income desk has twice the allocated capital (200 million) but the same daily VAR limit of million In percentage terms the FX desk is allowed to take more risk This simple example illustrates how the risk is budgeted across the two desks Note that the sum of risk budgets for individual units (5 million + million = 10 million) exceeds the risk budget for the organization (9 mm) because of the diversification effect 11 Reducing Credit Risk Credit risk is one sided and returns are not symmetric; hence, not easily measured using standard deviation and VAR The various methods to reduce credit risk are: • • • • • • • using exchange traded rather than OTC derivatives limiting exposure 2015 Q 6B marking to market 2009 Q 9A use of collateral netting minimum credit standards credit derivatives such as credit default swaps, total return swaps, credit spread options and credit spread forwards 12 Measures of Risk-Adjusted Performance 𝐒𝐡𝐚𝐫𝐩𝐞 𝐫𝐚𝐭𝐢𝐨 = Mean portfolio return − Risk free rate Standard deviation of portfolio return Sharpe ratio is inaccurate when applied to portfolios with significant nonlinear risks such as option positions Risk-Adjusted Return on Capital (RAROC) = Expected return on an investment / measure of capital at risk A company may require that an investment’s expected RAROC exceed a RAROC benchmark level for capital to be allocated to it Return over Maximum Drawdown (RoMAD) = average annual return / drawdown Drawdown is the difference between a portfolio’s maximum point (known as high water mark) and any subsequent low point of performance Sortino ratio = (Mean portfolio return – MAR)/Downside deviation Unlike Sharpe ratio, Sortino ratio only measures downside deviation below the minimum acceptable rate (MAR) Thus it does not penalize portfolio managers for volatility due to extreme positive performance 13 Capital Allocation Methods Methodology Comment Nominal, Notional or Monetary Position Limits Enterprise defines capital for each business unit Simple and allows us to calculate percentage return on capital allocated Does not capture effects of correlation and offsetting risks VAR-Based Position Limits Use VAR limit as alternative or supplement to notional limit Limit regime only as effective as VAR calculation Relation between overall VAR and individual VARs is complex Maximum Loss Limits Internal Capital Requirements Establish maximum loss limit for each risk-taking unit Specify level of capital that will be appropriate for the firm Regulatory Capital Requirements Many institutions such as banks and security firms must calculate and meet regulatory capital requirements Example: Enough capital such that probability of insolvency over 1-year is 0.01 14 ... senior management The main advantage is that it allows offsetting of risks across units Centralized risk management is now called enterprise risk management (ERM) Those responsible for risk management. .. allocations, risk limits, and risk management policies Monitor compliance with policies and risk limits Financial and Non-financial Risk Factors (1/2) Financial risks Market Risk: Risk associated... appropriate risk tolerance levels, identify corrective action if actual risk is outside tolerance levels Risk budgeting focuses on where to take risk and how to efficiently allocate risk Example: