CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r27 risk management IFT notes

Risk Management IFT Notes Risk Management Introduction Risk Management as a Process 3 Risk Governance 4 Identifying Risks 5 Measuring Risk 5.1 Measuring Market Risk 5.2 Value at Risk 5.3 The Advantages and Limitations of VaR 11 5.4 Extensions and Supplements to VaR 11 5.5 Stress Testing 11 5.6 Measuring Credit Risk 12 5.7 Liquidity Risk 14 5.8 Measuring Nonfinancial Risks 14 Managing Risk 14 6.1 Managing Market Risk 14 6.2 Managing Credit Risk 15 6.3 Performance Evaluation 15 6.4 Capital Allocation 16 6.5 Psychological and Behavioral Considerations 17 Summary 17 Examples from the Curriculum 23 Example Some Risk Governance Concerns of Investment Firms 23 Example An Analysis of Risk Exposures 23 Example An Operational Risk for Financial Services Companies: The Rogue Trader 24 Example Accounting Risk: The Case of Derivative Contracts 24 Example VaR with Different Probability Levels and Time Horizons 25 Example Calculating VaR Using the Historical Method 26 Example Value at Risk and the Management of Market Risk at Goldman Sachs 27 Example Calculating Credit Risk Exposures 31 Example Basel II—A Brief Overview 32 Example 10 A Fund Management Company and Risk Budgeting 33 IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes Example 11 Repricing a Forward Contract 34 This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA® Program curriculum Some of the graphs, charts, tables, examples, and figures are copyright 2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by IFT CFA Institute, CFA®, and Chartered Financial Analyst® are trademarks owned by CFA Institute IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes Introduction A portfolio manager needs to understand risk management as it relates to his firm He should also understand the risk management process of firms where he invests LO.a: Discuss features of the risk management process, risk governance, risk reduction, and an enterprise risk management system This LO is covered in sections and Risk Management as a Process Risk management is a process that involves:  Recognising the exposures to risk  Creating appropriate ranges for exposures  Constantly measuring these exposures  Performing appropriate adjustments whenever exposure levels fall outside of target ranges This is a constant process and may need adjustments in any of these activities to reflect new policies Exhibit shows the practical application of the process of risk management IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes While applying the risk management process to portfolio management, managers need to measure and price the risks of financial transactions or positions Exhibit demonstrates the process of pricing and measuring risk Risk Governance LO.b: Evaluate strengths and weaknesses of a company’s risk management process Risk governance is an element of corporate governance It is the process of setting overall policies and standards in risk management The two types of risk governance models are:  Decentralized: Here each unit calculates and reports its risk exposures independently The main advantage is that this model allows people who understand risk better to directly manage it  Centralized: Here the risk management is moved closer to senior management The main IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes advantage is that it allows offsetting of risks across units For example, if one unit is exporting goods to Japan and other unit is importing goods from Japan, then the Yen risk exposure can be offset Centralized risk management is now called enterprise risk management (ERM) Refer to Example from the curriculum LO.c: Describe steps in an effective enterprise risk management system 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 Identifying Risks LO.d: Evaluate a company’s or a portfolio’s exposures to financial and nonfinancial risk factors Exhibit shows the main sources of risk Financial risk is the risk derived from events in the external financial markets Non-financial risk refers to all other forms of risk Refer to Example from the curriculum The various types of risks are: 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 IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes 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) Operational Risk: Risk of loss from failures in a company’s systems and procedures or from external events Refer to Example from the curriculum 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 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 Refer to Example from the curriculum Sovereign Risk: A form of credit risk in which the borrower is the government of a sovereign nation 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 Measuring Risk 5.1 Measuring Market Risk Several statistical tools are available to measure market risk:  Volatility of the asset, measured by the standard deviation of asset prices  Volatility relative to a benchmark (active risk, tracking risk) measured by deviation of a portfolio’s returns in excess of a benchmark IFT Notes for the Level III Exam www.ift.world Page Risk Management    IFT Notes For stocks, beta measures the sensitivity to market movements For bonds, duration and convexity measure sensitivity of a bond to a small parallel shift in the yield curve For options: o delta measures an option’s sensitivity to a small change in the value of the underlying o gamma measures the delta’s sensitivity to a change in the value of the underlying o vega measures an option’s sensitivity to a change in the underlying’s volatility o theta measures an option’s sensitivity to a change in the time to expiration 5.2 Value at Risk LO.e: Calculate and interpret value at risk (VaR) and explain its role in measuring overall and individual position market risk VAR is a probability-based measure of loss potential More precisely, 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 Consider the following example of VaR for an investment portfolio: 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:  There is a percent chance that the portfolio will lose at least $1.5 million in a single day  We can say with 95 percent confidence, that the maximum loss will be $1.5 million for one day Elements of measuring VAR 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 0.05 or 0.01  Using 0.01 is more conservative and will give a higher VAR It is recommended to use 0.01 if returns are non-linear 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 Once these key parameters are selected, we can obtain the VAR estimate Exhibit shows the probability distribution for the returns on a portfolio over a specified time period Return on Portfolio Probability Less than –40% 0.010 –40% to –30% 0.010 –30% to –20% 0.030 –20% to –10% 0.050 –10% to –5% 0.100 IFT Notes for the Level III Exam www.ift.world Page Risk Management –5% to –2.5% 0.125 –2.5% to 0% 0.175 0% to 2.5% 0.175 2.5% to 5% 0.125 5% to 10% 0.100 10% to 20% 0.050 20% to 30% 0.030 30% to 40% 0.010 Greater than 40% 0.010 IFT Notes 1.000 The first row in this table tells us that there is a 0.01 probability of a loss of 40% or worse The second row tells us that there is a 0.01 probability of a loss between 30% and 40% The third row tells us that there is a 0.03 probability of a loss between 20% and 30% Adding the three probability numbers we can say there is 0.05 probability of a loss of 20% or worse Assuming a portfolio of $100 million, the VAR with a probability of 0.05 can be calculated as: 20% of $100 million = $20 million Methods to estimate VAR The three standardized methods to estimate VAR are: Analytical variance-covariance method Historical method Monte Carlo simulation method Analytical variance-covariance method: Here we assume that the portfolio returns are normally distributed Exhibit shows the expected annual returns and standard deviation of a portfolio obtained by combining the S&P 500 and NASDAQ S&P 500 NASDAQ Combined Portfolio Percentage invested (w) 0.75 0.25 1.00 Expected annual return (μ) 0.12 0.18 0.135 Standard deviation (σ) 0.20 0.40 0.244 Correlation (ρ) 0.90 Exhibit demonstrates how we can calculate the annual VAR of this portfolio with a probability of 0.05 We start by determining the z-value associated with a cumulative probability of 0.05 This z-value is 1.65 The distribution we are working with has a mean of 0.135 and a standard deviation of 0.244 Given these numbers it can be shown that 5% of the area under the curve is to the left of -0.268 The IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes calculations are outlined in the figure If the portfolio is worth $50 million, we can express VaR as $50,000,000(0.268) = $13.4 million In other words there is a 5% chance that the loss will be $13.4 million or worse in a year To calculate the daily VAR, we can adjust the expected return to its daily average of approximately 0.135/250 = 0.00054 and the standard deviation to its daily value of 0.244 sqrt(250) = 0.01543 This is based on the assumption of 250 trading days in a year and statistical independence between days With these numbers the daily VaR is 0.00054 – 1.65(0.01543) = –0.0249 On a dollar basis, the daily VaR is $50,000,000(0.0249) = $1.245 million Refer to Example from the curriculum Historical method: In this method we calculate the returns for a given portfolio using actual prices from a user-specified period in recent past The advantage of using this method is that the user does not have to make any assumptions about the type of probability distributions that generates returns The disadvantage is that it relies on data from the past and past conditions might not hold in the future Refer to Example from the curriculum Refer to Example from the curriculum Monte Carlo simulation method: In this method we produce random outcomes according to an assumed probability distribution and a set of input parameters For example, consider a $50 million portfolio invested 75% in S&P500 and 25% in NASDAQ The annual expected return is 13.5% and the standard deviation is 24.4% We use a random number generator to IFT Notes for the Level III Exam www.ift.world Page Risk Management IFT Notes produce a series of 300 random values The results are shown in Exhibit To obtain the point in the lower tail with a percent significance, we rank order the data and find the 15th-lowest outcome We use the 15th-lowest outcome because there are 300 iterations and percent of 300 = 15 This corresponds to a portfolio value of $34.25 million – a loss of $15.75 million Based on this information we can say: there is a 5% chance that the loss in one year will be $15.75 million or worse LO.f: Compare the analytical (variance–covariance), historical, and Monte Carlo methods for estimating VaR and discuss the advantages and disadvantages of each The table below compares the three methods Variance-Covariance Method Historical Method Monte Carlo Simulation Advantages: Simple method Advantages: Non-parametric (minimal probability-distribution assumptions) Advantages: Widely used We can assume an appropriate distribution of input data Disadvantages: Relies on simplifying assumptions such as normality of returns If returns are not normally distributed then we cannot rely totally on standard deviation as a measure of risk Consider skewness and kurtosis Portfolios containing options don’t have normal distributions IFT Notes for the Level III Exam Disadvantages: Relies on past events (which might not be good predictors of the future) www.ift.world Disadvantages: Output only as good as our input assumption Monte Carlo simulation software is expensive and requires a lot of computing power Page 10 Risk Management o IFT Notes 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 i evaluate the credit risk of an investment position, including forward contract, swap, and option positions; 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 j demonstrate the use of risk budgeting, position limits, and other methods for managing market risk; 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 k demonstrate the use of exposure limits, marking to market, collateral, netting arrangements, credit IFT Notes for the Level III Exam www.ift.world Page 21 Risk Management IFT Notes standards, and credit derivatives to manage 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  marking to market  use of collateral  netting  minimum credit standards  credit derivatives such as credit default swaps, total return swaps, credit spread options and credit spread forwards l discuss the Sharpe ratio, risk-adjusted return on capital, return over maximum drawdown, and the Sortino ratio as measures of risk-adjusted performance; 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 𝐒𝐡𝐚𝐫𝐩𝐞 𝐫𝐚𝐭𝐢𝐨 = 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 m demonstrate the use of VaR and stress testing in setting capital requirements Methodology Nominal, Notional or Monetary Position Limits VAR-Based Position Limits Maximum Loss Limits Comment 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 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 Establish maximum loss limit for each risk-taking unit IFT Notes for the Level III Exam www.ift.world Page 22 Risk Management Internal Capital Requirements Regulatory Capital Requirements IFT Notes Specify level of capital that will be appropriate for the firm Example: Enough capital such that probability of insolvency over 1-year is 0.01 Many institutions such as banks and security firms must calculate and meet regulatory capital requirements Examples from the Curriculum Example Some Risk Governance Concerns of Investment Firms Regardless of the risk governance approach chosen, effective risk governance for investment firms demands that the trading function be separated from the risk management function An individual or group that is independent of the trading function must monitor the positions taken by the traders or risk takers and price them independently The risk manager has the responsibility for monitoring risk levels for all portfolio positions (as well as for portfolios as a whole) and executing any strategies necessary to control the level of risk To this, the risk manager must have timely and accurate information, authority, and independence from the trading function That is not to say that the trading function will not need its own risk management expertise in order to allocate capital in an optimal fashion and maximize risk-adjusted profit Ideally, the risk manager will work with the trading desks in the development of risk management specifications, such that everyone in the organization is working from a common point of reference in terms of measuring and controlling exposures Effective risk governance for an investment firm also requires that the back office be fully independent from the front office, so as to provide a check on the accuracy of information and to forestall collusion (The back office is concerned with transaction processing, record keeping, regulatory compliance, and other administrative functions; the front office is concerned with trading and sales.) Besides being independent, the back office of an investment firm must have a high level of competence, training, and knowledge because failed trades, errors, and over-sights can lead to significant losses that may be amplified by leverage The back office must effectively coordinate with external service suppliers, such as the firm’s global custodian The global custodian effects trade settlement (completion of a trade wherein purchased financial instruments are transferred to the buyer and the buyer transfers money to the seller), safekeeping of assets, and the allocation of trades to individual custody accounts Increasingly, financial institutions are seeking risk reduction with cost efficiencies through straightthrough processing (STP) systems that obviate manual and/or duplicative intervention in the process from trade placement to settlement Back to Notes Example An Analysis of Risk Exposures Liam McNulty is the risk manager for a large multinational agricultural concern, Agripure The company grows its own corn, wheat, and soybeans but pays large sums to third parties for pesticides, fertilizer, and other supplies For this, it must borrow heavily to finance its purchases Customers typically purchase Agripure’s goods on credit Moreover, Agripure buys and sells its products and raw materials worldwide, often transacting in the domestic currency of its customers and suppliers Finally, to finance its own expansion, Agripure intends to issue stock IFT Notes for the Level III Exam www.ift.world Page 23 Risk Management IFT Notes Recommend and justify the risk exposures that McNulty should report as part of an enterprise risk management system for Agripure Solution: McNulty should report on the following risk exposures:  Market risk, including these subtypes:  Commodity price risk, because Agripure has exposures in raw materials and finished products  Foreign exchange risk, because it buys and sells products world-wide, often transacting in the home currency of the entity on the other side of the transaction  Equity market risk, because Agripure’s expansion financing is affected by the price it receives for its share issuance  Interest rate risk, because Agripure has exposures in financing its raw material purchases and because its customers typically purchase their goods on credit  Credit risk, because Agripure’s customers typically purchase their goods on credit  Operational risk, because as an agricultural producer Agripure is subject to weather-related risk (an external event) Back to Notes Example An Operational Risk for Financial Services Companies: The Rogue Trader Among the more prominent examples of operational risk for financial service companies is that of the so-called rogue trader: an individual who has either assumed an irresponsibly high level of risk, engaged in unauthorized transactions, or some combination of the two The risks associated with this type of activity increase the longer it goes undetected, and often the very lack of controls that creates the opportunity for a rogue trader in the first place renders it difficult to quickly determine that a problem exists In some extreme cases, such as an incident that occurred in the Singapore office of Barings Bank, a rogue trader can cause an entire organization to fold The incidence of high-profile rogue trading episodes has multiplied since the early 1990s, but in nearly all of these episodes, the problem’s major source was a lack of rudimentary corporate controls and oversight Back to Notes Example Accounting Risk: The Case of Derivative Contracts Accounting for derivative contracts has raised considerable confusion When confusion occurs, companies run the risk that the accounting treatment for transactions could require adjustment, which could possibly lead to a need to restate earnings Earnings restatements are almost always embarrassing for a company, because they suggest either a desire to hide information, the company’s failure to fully understand material elements of its business, or some combination of the two Restatements are very detrimental to corporate valuations because they cause investors to lose confidence in the accuracy of corporate financial disclosures Beyond that, if negligence or intent to mislead was involved, the IFT Notes for the Level III Exam www.ift.world Page 24 Risk Management IFT Notes company could face civil and criminal liabilities as well Confusion over the proper accounting for derivatives gives rise to accounting as a source of risk As with regulatory and tax risk, sometimes equivalent combinations of derivatives are not accounted for uniformly The accounting profession typically moves to close such loopholes, but it does not move quickly and certainly does not keep pace with the pace of innovation in financial engineering, so problems nearly always remain The IASB in IAS 39 (International Accounting Standard No 39) requires the inclusion of derivatives and their associated gains and losses on financial statements, as does the FASB in SFAS 133 (Statement of Financial Accounting Standard No 133) These rulings contain some areas of confusion and inconsistency, however, affording considerable room for interpretation Back to Notes Example VaR with Different Probability Levels and Time Horizons Consider a portfolio consisting of stocks as one asset class and bonds as another The expected return on the portfolio’s stock portion is 12 percent, and the standard deviation is 22 percent The expected return on the bond portion is percent, and the standard deviation is percent All of these figures are annual The correlation between the two asset classes is 0.15 The portfolio’s market value is $150 million and is allocated 65 percent to stocks and 35 percent to bonds Determine the VaR using the analytical method for the following cases: a percent yearly VaR a percent yearly VaR a percent weekly VaR a percent weekly VaR Solutions: First, we must calculate the annual portfolio expected return and standard deviation Using S to indicate stocks and B to indicate bonds, we have 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 Solution to 1: For a percent yearly VaR, we have μP – 1.65σP = 0.0955 – 1.65(0.1487) = –0.1499 Then the VaR is $150,000,000(0.1499) = $22.485 million IFT Notes for the Level III Exam www.ift.world Page 25 Risk Management IFT Notes Solution to 2: For a percent yearly VaR, we have μP – 2.33σP = 0.0955 – 2.33(0.1487) = –0.251 Then the VaR is $150,000,000(0.251) = $37.65 million Solution to 3: For weekly VaR, we adjust the expected return to 0.0955/52 = 0.00184 and the standard deviation to 0.1487/Sqrt(52)=0.02062 The percent weekly VaR is then μP – 1.65σ = 0.00184 – 1.65(0.02062) = –0.03218 Then the VaR is $150,000,000(0.03218) = $4.827 million Solution to 4: The percent weekly VaR is μP – 2.33σP = 0.00184 – 2.33(0.02062) = –0.0462 Then the VaR is $150,000,000(0.0462) = $6.93 million Back to Notes Example Calculating VaR Using the Historical Method For simplicity, we use a one-stock portfolio Exhibit shows the 40 worst monthly returns on IBM stock during the last 20 years, in descending order, as of 2011 (minus signs omitted): Exhibit IBM Stock: Worst Monthly Returns 0.26190 0.11692 0.09077 0.07537 0.22645 0.11553 0.08926 0.07298 0.20511 0.10838 0.08585 0.07260 0.19462 0.10805 0.08481 0.07247 0.18802 0.10687 0.08422 0.07075 0.17183 0.10503 0.08356 0.06894 0.16415 0.09873 0.08234 0.06782 0.14834 0.09550 0.08197 0.06746 0.14773 0.09276 0.08143 0.06501 0.12444 0.09091 0.07547 0.06437 For both calculations below, assume the portfolio value is $100,000 Calculate a percent monthly VaR using the historical method Calculate a percent monthly VaR using the historical method Solutions: First, we note that during the last 20 years, there were 240 monthly returns We see here only the worst 40 returns Therefore, although we lack the entire distribution of returns, we have enough to IFT Notes for the Level III Exam www.ift.world Page 26 Risk Management IFT Notes calculate the VaR Solution to 1: Out of 240 returns, the percent worst are the 12 worst returns Therefore, the historical VaR would be about the 12th-worst return From the exhibit, we see that this return is –0.11553 So, the one-month VaR is 0.11553($100,000) = $11,553 Solution to 2: The percent worst returns include 2.4 returns We would probably use the second-worst return, which is –0.22645 The VaR is 0.22645($100,000) = $22,645 Alternatively, we might average the second- and third-worst returns to obtain (–0.22645 + –0.20511)/2 = –0.21578 Then the one-month VaR would be 0.21578($100,000) = $21,578 Back to Notes Example Value at Risk and the Management of Market Risk at Goldman Sachs The following excerpt is from the 2010 Form 10-K of Goldman Sachs: Value-at-Risk VaR is the potential loss in value of inventory positions due to adverse market movements over a defined time horizon with a specified confidence level We typically employ a one-day time horizon with a 95% confidence level Thus, we would expect to see reductions in the fair value of inventory positions at least as large as the reported VaR once per month The VaR model captures risks including interest rates, equity prices, currency rates and commodity prices As such, VaR facilitates comparison across portfolios of different risk characteristics VaR also captures the diversification of aggregated risk at the firmwide level Inherent limitations to VaR include:  VaR does not estimate potential losses over longer time horizons where moves may be extreme  VaR does not take account of the relative liquidity of different risk positions  Previous moves in market risk factors may not produce accurate predictions of all future market moves The historical data used in our VaR calculation is weighted to give greater importance to more recent observations and reflect current asset volatilities This improves the accuracy of our estimates of potential loss As a result, even if our inventory positions were unchanged, our VaR would increase with increasing market volatility and vice versa Given its reliance on historical data, VaR is most effective in estimating risk exposures in markets in which there are no sudden fundamental changes or shifts in market conditions We evaluate the accuracy of our VaR model through daily backtesting (i.e., comparing daily trading net revenues to the VaR measure calculated as of the prior business day) at the firmwide level and for each IFT Notes for the Level III Exam www.ift.world Page 27 Risk Management IFT Notes of our businesses and major regulated subsidiaries VaR does not include:  positions that are best measured and monitored using sensitivity measures; and  the impact of changes in counterparty and our own credit spreads on derivatives as well as changes in our own credit spreads on unsecured borrowings for which the fair value option was elected Stress Testing We use stress testing to examine risks of specific portfolios as well as the potential impact of significant risk exposures across the firm We use a variety of scenarios to calculate the potential loss from a wide range of market moves on the firm's portfolios These scenarios include the default of single corporate or sovereign entities, the impact of a move in a single risk factor across all positions (e.g., equity prices or credit spreads) or a combination of two or more risk factors Unlike VaR measures, which have an implied probability because they are calculated at a specified confidence level, there is generally no implied probability that our stress test scenarios will occur Instead, stress tests are used to model both moderate and more extreme moves in underlying market factors When estimating potential loss, we generally assume that our positions cannot be reduced or hedged (although experience demonstrates that we are generally able to so) Stress test scenarios are conducted on a regular basis as part of the firm's routine risk management process and on an ad hoc basis in response to market events or concerns Stress testing is an important part of the firm's risk management process because it allows us to highlight potential loss concentrations, undertake risk/reward analysis, and assess and mitigate our risk positions Limits We use risk limits at various levels in the firm (including firmwide, product and business) to govern risk appetite by controlling the size of our exposures to market risk Limits are reviewed frequently and amended on a permanent or temporary basis to reflect changing market conditions, business conditions or tolerance for risk The Firmwide Risk Committee sets market risk limits at firmwide and product levels and our Securities Division Risk Committee sets sub-limits for market-making and investing activities at a business level The purpose of the firmwide limits is to assist senior management in controlling the firm's overall risk profile Sub-limits set the desired maximum amount of exposure that may be managed by any particular business on a day-to-day basis without additional levels of senior management approval, effectively leaving day-to-day trading decisions to individual desk managers and traders Accordingly, sub-limits are a management tool designed to ensure appropriate escalation rather than to establish maximum risk tolerance Sub-limits also distribute risk among various businesses in a manner that is consistent with their level of activity and client demand, taking into account the relative performance of each area Our market risk limits are monitored daily by Market Risk Management, which is responsible for identifying and escalating, on a timely basis, instances where limits have been exceeded The businesslevel limits that are set by the Securities Division Risk Committee are subject to the same scrutiny and IFT Notes for the Level III Exam www.ift.world Page 28 Risk Management IFT Notes limit escalation policy as the firmwide limits When a risk limit has been exceeded (e.g., due to changes in market conditions, such as increased volatilities or changes in correlations), it is reported to the appropriate risk committee and a discussion takes place with the relevant desk managers, after which either the risk position is reduced or the risk limit is temporarily or permanently increased Metrics We analyze VaR at the firmwide level and a variety of more detailed levels, including by risk category, business, and region The tables below present average daily VaR and year-end VaR by risk category Average Daily VaR (in millions) Year Ended Risk Categories December 2010 December 2009 November 2008 Interest rates $ 93 $176 $ 142 Equity prices 68 66 72 Currency rates 32 36 30 33 36 44 (92) (96) (108) $134 $218 $ 180 Commodity prices Diversification effect Total a a Equals the difference between total VaR and the sum of the VaRs for the four risk categories This effect arises because the four market risk categories are not perfectly correlated Our average daily VaR decreased to $134 million in 2010 from $218 million in 2009, principally due to a decrease in the interest rates category which was primarily due to reduced exposures, lower levels of volatility and tighter spreads Our average daily VaR increased to $218 million in 2009 from $180 million in 2008, principally due to an increase in the interest rates category and a reduction in the diversification benefit across risk categories, partially offset by a decrease in the commodity prices category The increase in the interest rates category was primarily due to wider spreads The decrease in the commodity prices category was primarily due to lower energy prices Year-End VaR and High and Low VaR (in millions) As of December Year Ended December 2010 Risk Categories 2010 2009 High Low Interest rates $ 78 $ 122 $123 $ 76 Equity prices 51 99 186 39 Currency rates 27 21 62 14 Commodity prices 25 33 62 18 IFT Notes for the Level III Exam www.ift.world Page 29 Risk Management Risk Categories Diversification effect a Total As of December Year Ended December 2010 2010 2009 High Low (70) (122) $111 $ 153 $223 $105 IFT Notes a Equals the difference between total VaR and the sum of the VaRs for the four risk categories This effect arises because the four market risk categories are not perfectly correlated Our daily VaR decreased to $111 million as of December 2010 from $153 million as of December 2009, principally due to a decrease in the equity prices and interest rates categories, partially offset by a decrease in the diversification benefit across risk categories The decreases in the equity prices and interest rates categories were primarily due to reduced exposures and lower levels of volatility During the year ended December 2010, the firmwide VaR risk limit was exceeded on one occasion in order to facilitate a client transaction and was resolved by a reduction in the risk position on the following day Separately, during the year ended December 2010, the firmwide VaR risk limit was reduced on one occasion reflecting lower risk utilization During the year ended December 2009, the firmwide VaR risk limit was exceeded on two successive days It was resolved by a reduction in the risk position without a permanent or temporary VaR limit increase Separately, during the year ended December 2009, the firmwide VaR risk limit was raised on one occasion and reduced on two occasions as a result of changes in the risk utilization and the market environment The chart below reflects the VaR over the last four quarters Daily VaR ($ in millions) The chart below presents the frequency distribution of our daily trading net revenues for substantially all inventory positions included in VaR for the year ended December 2010 IFT Notes for the Level III Exam www.ift.world Page 30 Risk Management IFT Notes Daily Trading Net Revenues ($ in millions) As noted above, daily trading net revenues are compared with VaR calculated as of the end of the prior business day Trading losses incurred on a single day exceeded our 95% one-day VaR on two occasions during 2010 Trading losses incurred on a single day did not exceed our 95% one-day VaR during 2009 Source: Goldman Sachs 2010 Form 10-K, pp 85-87 The Goldman Sachs Group, Inc All rights reserved Back to Notes Example Calculating Credit Risk Exposures Calculate the amount at risk of a credit loss in the following situations: A US party goes long a forward contract on €1 denominated in dollars in which the underlying is the euro The original term of the contract was two years, and the forward rate was $0.90 The contract now has 18 months or 1.5 years to maturity The spot or current exchange rate is $0.862 The US interest rate is percent, and the euro interest rate is percent The interest rates are based on discrete compounding/discounting At the point when the contract has 1.5 years remaining, the value of the contract to the long per $1 notional principal equals the spot exchange rate, $0.862, discounted at the international interest rate for 1.5 years, minus the forward rate, $0.90, discounted at the domestic interest rate for 1.5 years: $0.862/(1.05)1.5−$0.90/(1.06)1.5=−$0.0235 Evaluate the credit risk characteristics of this situation Consider a plain vanilla interest rate swap with two months to go before the next payment Six months after that, the swap will have its final payment The swap fixed rate is percent, and the upcoming floating payment is 6.9 percent All payments are based on 30 days in a month and 360 days in a year Two-month Libor is 7.250 percent, and eight-month Libor is 7.375 percent The present value factors for two and eight months can be calculated as follows: 1/(1+0.0725(60/360))=0.9881 1/(1+0.07375(240/360))=0.9531 IFT Notes for the Level III Exam www.ift.world Page 31 Risk Management IFT Notes The next floating payment will be 0.069(180/360) = 0.0345 The present value of the floating payments (plus hypothetical notional principal) is 1.0345(0.9881) = 1.0222 Given an annual rate of percent, the fixed payments will be 0.07(180/360) = 0.035 The present value of the fixed payments (plus hypothetical notional principal) is, therefore, 0.035(0.9881) + 1.035(0.9531) = 1.0210 Determine the amount at risk of a credit loss and state which party currently bears the risk Assume a $1 notional principal A dealer has sold a call option on a stock for $35 to an investor The option is currently worth $46, as quoted in the market Determine the amount at risk of a credit loss and state which party currently bears the risk Solution to 1: The position has a negative value to the long, so the credit risk is currently borne by the short From the short’s point of view, the contract has a value of $0.0235 per $1 notional principal No payments are due for 18 months, but the short’s claim on the long is worth $0.0235 more than the long’s claim on the short Therefore, this amount is the current value of the amount at risk for a credit loss Of course, the amount could, and probably will, change over the life of the contract The credit risk exposure might even shift to the other party Solution to 2: The market value of the swap to the party paying fixed and receiving floating is 1.0222 – 1.0210 = 0.0012 This value is positive to the party paying fixed and receiving floating; thus this party currently assumes the credit risk Of course, the value will change over the life of the swap and may turn negative, meaning that the credit risk is then assumed by the party paying floating and receiving fixed Solution to 3: All of the credit risk is borne by the investor (the owner of the call), because he will look to the dealer (the seller) for the payoff if the owner exercises the option The current value of the amount at risk is the market price of $46 Back to Notes Example Basel II—A Brief Overview The Basel banking regulations apply only to large international banks, but national governments use them as a guideline in formulating their own financial laws and regulations, so the regulations have much more widespread importance In January 2001, the Basel Committee on Banking Supervision issued a proposal for a New Basel Capital Accord that would replace the 1988 Capital Accord This first accord, “Basel I,” was widely criticized for being too inflexible in applying an across-the-board percent capital adequacy ratio that made no discrimination between a well risk-managed bank and one that was not The Basel II proposal incorporates three mutually reinforcing pillars that allow banks and supervisors to evaluate properly the various risks that banks face: IFT Notes for the Level III Exam www.ift.world Page 32 Risk Management  Pillar 1: Capital Requirements;  Pillar 2: Supervisory Review;  Pillar 3: Market Discipline IFT Notes The first pillar of Basel II moves away from a blanket, one-size-fits-all approach and allows banks to develop their own mathematically based financial models Once these internally developed techniques have been successfully demonstrated to the regulators, banks are able to progress to higher levels of risk management that within the accord are offset by reduced regulatory capital charges Key to these higher levels of risk management are advanced systems for managing credit risk and operational risk The second pillar, supervisory review, requires banks to meet Basel-recommended operational risk requirements that have been tailored by their host country “Risky” banks, whose risk management systems score lowly in the areas of market risk and operational risk, face penalties Better-risk-managed banks will have major competitive advantages over rivals, in that, all else equal, they are likely to be subject to reduced capital requirements per unit of risk The third pillar says that banks must fulfill the Basel requirements for transparency and disclosing company data A key point here is that banks must reveal more detail about their profits and losses, which may lead to a supervisory authority reviewing risk systems and changing the capital allocation under the first pillar Back to Notes Example 10 A Fund Management Company and Risk Budgeting We can readily illustrate the methodology and underlying economics of risk budgeting with the example of a fund management company We choose, for this example, a multistrategy hedge fund, because although mutual funds and other types of institutional money managers certainly face similar risk management issues, they are often bound by strict guidelines that tie their risk budgeting to factors such as the performance of a benchmark index and other mandated fund management protocols For example, the Vanguard family of mutual funds offers a wide range of indexed mutual funds These funds’ associated risk budgets are very narrowly defined, as the managers are called on at all times to track the underlying index very closely in terms of securities held, associated portfolio weightings, and so forth As investor funds flow in and out of these securities, portfolio managers execute trades that little more than reestablish this replication balance Of course, many institutional fund products allow for much broader deviations from market benchmarks; in most cases, however, risk budgeting will be constrained by certain principles associated with benchmarking Hedge funds with multiple portfolio managers (as well as, in some cases, the proprietary trading divisions of banks and broker/dealers) have many fewer risk constraints than indexed mutual funds; they have more freedom, therefore, in establishing risk budgets Because of the absolute return (as opposed to benchmark-driven) nature of their performance, and because of issues such as performance netting risk covered earlier in this reading, it is very much in their interest to ensure that each portfolio in the enterprise operates within a well-conceived risk budget framework Included among the critical components of such a program might be the following: IFT Notes for the Level III Exam www.ift.world Page 33 Risk Management IFT Notes  Performance Stopouts A performance stopout is the maximum amount that a given portfolio is allowed to lose in a period (e.g., a month or a year)  Working Capital Allocations Most funds will allocate a specific amount of working capital to each portfolio manager, both as a means of enforcing risk disciplines and also to ensure the ability to fund all operations  VaR Limits Discussed above  Scenario Analysis Limits The risk manager of the fund company may establish risk limits based on the scenario analysis discussed in the preceding section Under such an approach, the portfolio manager would be compelled to construct a portfolio such that under specified scenarios, it did not produce losses greater than certain predetermined amounts  Risk Factor Limits Portfolio managers may be subject to limits on individual risk factors, as generated by a VaR analysis (e.g., VaR exposure to a certain risk cannot exceed, say, $X or X%) or driven by linear (e.g., duration, beta) or nonlinear (e.g., convexity, gamma) risk estimation methodologies  Position Concentration Limits Many risk managers seek to enforce diversification by mandating a specific maximum amount for individual positions  Leverage Limits A maximum amount of leverage in the portfolio may be specified  Liquidity Limits To help manage liquidity exposure, large funds will often also set position limits as a specified maximum percentage of daily volume, float, or open interest Of course, other types of limits are imposed on portfolio managers in a multistrategy environment, and by the same token, the risk-budgeting strategy of a given enterprise may include only a subset of the examples provided immediately above Nevertheless, some subset of these limit structures is present in nearly every multistrategy fund vehicle, and it is difficult to imagine an effective risk control system that does not set limits Back to Notes Example 11 Repricing a Forward Contract Consider a one-year forward contract established at a rate of $105 The contract is four months into its life The spot price is $108, the risk-free rate is 4.25 percent, and the underlying makes no cash payments The two parties decided at the start that they will mark the contract to market every four months The market value of the contract is $108 – $105/(1.0425)8/12 = $5.873 Determine how the cash flows and resets would work under these circumstances Solution: The contract is positive to the long, so the short pays the long $5.873 The parties then reprice the contract The new price is $108(1.0425)8/12 = $111.04 At this point, the forward price is reset to $111.04 The parties will then mark to market again at the eight-month point and reset the forward price This price will then stay in force until expiration IFT Notes for the Level III Exam www.ift.world Page 34 Risk Management IFT Notes Back to Notes IFT Notes for the Level III Exam www.ift.world Page 35 ... application of the process of risk management IFT Notes for the Level III Exam www .ift. world Page Risk Management IFT Notes While applying the risk management process to portfolio management, managers... offered by IFT CFA Institute, CFA , and Chartered Financial Analyst® are trademarks owned by CFA Institute IFT Notes for the Level III Exam www .ift. world Page Risk Management IFT Notes Introduction... Credit Risk: Risk of loss caused by a counterparty or debtor’s failure to make a promised payment IFT Notes for the Level III Exam www .ift. world Page Risk Management IFT Notes Liquidity Risk: Risk