Reading 26 - Risk Management

6.2.6. Transferring Credit Risk with *Credit Derivatives* Final

*Credit derivatives* may be used not only to *eliminate credit risk* but also to *assume credit risk* For example, an *investor may be well positioned to assume a credit risk* because it is *uncorrelated with other credit risks in her portfolio*

Advantages of Descentralized

1. Allowing the people closer to the actual risk taking to more directly manage it.

Advantages of Centralized

1. Centralization permits economies of scale and allows a company to recognize the offsetting nature of distinct exposures that an enterprise might assume in its day-to-day operations. 2. Enterprise-level risk estimates MAY BE LOWER than THOSE DERIVED FROM INDIVIDUAL UNITS because of the RISK-MITIGATING BENEFITS OF DIVERSIFICATION 3. CENTRALIZED RISK MANAGEMENT puts the responsibility on a level closer to senior management, where we have argued it belongs. It gives an overall picture of the company's risk position, and ultimately, the overall picture is what counts.

*CROSS-DEFAULT PROVISION* Important

*Another element of credit risk*, which *blends current and potential credit risk*, is the possibility that a counterparty will default on a *CURRENT PAYMENT to a DIFFERENT CREDITOR* Most direct lending or derivative-based credit contracts stipulate that if a *borrower defaults ON ANY outstanding credit obligations*, the *borrower is in DEFAULT ON THEM ALL* (a CROSS-DEFAULT PROVISION)

Correlation

*Correlation is a source of risk for certain types of options—for example, options on more than one underlying (when the correlations between the underlyings' returns constitute a risk variable).

6. *Managing Risk*

Having established methods for the *identification* & *measurement* of risk, we turn our attention to a critical stage of any solid risk management program: *managing risk*

NON FINANCIAL RISKS • POLITICAL RISKS:

associated with changes in the political environment o Overt: replace PRO CAPITALIST with LESS SO o SUBTLE: i.e. The potential for party control change in a developed nation

NON FINANCIAL RISKS • ACCOUNTING RISKS:

o Uncertainty of how a transaction should be recorded or accounting rules to change Accounting for Derivatives Contracts (Blue Box)

NON FINANCIAL RISKS Regulatory risk

o Uncertainty of how transaction will be regulated or with the potential that regulations will change o Equity, bonds, futures, and ETFs are all much more regulated o OTC and Alternatives: less regulated

*DERIVATIVE Credit Risk* vs *Credit Risk on REGULAR LOANS*

*Credit risk for derivatives* is *considerably LESS than that faced by most lenders* When a *lender makes a loan*, the *interest and principal are at risk* *The loan principal* corresponds closely to the NP of most derivative contracts With the exception of CURRENCY SWAPS, the *NP is never exchanged in a swap* Even with CURRENCY SWAPS the *risk is much SMALLER than on a LOAN* *If a counterparty defaults on a currency swap*, the amount owed to the defaulting counterparty serves as a *type of collateral because the creditor is not required to pay it to the defaulting party* Therefore, *the credit risk on derivative transactions tends to be quite small relative to that on LOANS* *On forward and swap transactions*, the *NETTING OF PAYMENTS* makes the *risk extremely SMALL relative to the NP* and *to the credit risk on a BOND or LOAN of equivalent principal*

6.3. Performance Evaluation l. Discuss: 1. Sharpe ratio 2. Risk-adjusted return on capital (RAROC) 3. *Return over maximum drawdown* 4. Sortino ratio as measures of risk-adjusted performance

*Drawdown*, in the field of *hedge fund* management, is defined as the *difference between a portfolio's maximum point of return* (known in industry parlance as its *high-water mark*), and any *subsequent low point of performance* Maximum drawdown is the *largest difference between a high-water and a subsequent low* Maximum drawdown is a *preferred way of expressing the risk of a given portfolio* for investors who *believe that observed loss patterns over longer periods of time are the best available proxy for actual exposure*

*CHERRY PICKING*

*During this BANKRUPTCY PROCESS*, netting plays an important role in *REDUCING a practice known* as *CHERRY PICKING*, which in this case would involve a *bankrupt company* attempting to *enforce contracts that are favorable to it* while *walking away from those that are unprofitable* In our example, without netting, *A could default on the contracts in which it owes more to B than B owes to A*, but *B could be forced to pay up on those contracts in which it owes more to A than A owes to B*

i. *Evaluate the credit risk of an investment position, including forward contract, swap, and option positions* .6.2. The *Credit Risk of Forward Contracts*

*Forward contracts* involve *commitments on the part of each party* *NO CASH IS DUE AT THE START* *NO CASH IS PAID UNTIL EXPIRATION*, at which time *one party owes the greater amount to the other* The *party that owes the larger amount could default*, leaving the other with a claim of the defaulted amount. Each *party assumes the other's credit risk* Current credit risk arises when the contract is at its expiration

*Credit Risk for options*

*If the buyer exercises the option*, the seller must meet certain terms embedded in the contract *If the option is a CALL*, the *seller must deliver the underlying* or *pay an equivalent cash settlement* *If the option is a PUT*, the *seller must accept delivery of the underlying* and *pay for it* or meet these obligations in the form of cash payments If the *seller fails to fulfill her end of the obligation*, *it is in default* Like forward contracts, *EUROPEAN OPTIONS have no payments due UNTIL EXPIRATION*. Hence, they have *NO CURRENT CREDIT RISK* until expiration, although significant *POTENTIAL CREDIT RISK exists*

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 4. *Internal Capital Requirements*

*Internal capital requirements* specify the *level of capital that management* believes to be appropriate for the firm Some *regulated financial institutions*, such as *banks and securities firms*, typically also have *REGULATORY CAPITAL REQUIREMENTS* that, if they are higher, *overrule internal requirements*

5.8. *Measuring Nonfinancial Risks*

*Nonfinancial risks* are intrinsically *very difficult to measure* Some of these risks could be thought of as *more suitable for INSURANCE* than *measurement and hedging* *Insurance companies* usually have *sufficient assets and are capitalized to withstand these uncertain events*. Where it is possible to model a source of risk, actuaries often use techniques like *EXTREME VALUE THEORY*, but even these techniques *are only as good as the historical data on which they are based*

i. *Evaluate the credit risk of an investment position, including forward contract, swap, and option positions* 5.6.4. The Credit Risk of Options

*OPTIONS*, on the other hand, *have unilateral credit risk* (vs *forward and swaps* which have *bilateral credit risk*) *The buyer* of an option *pays a cash premium at the start* and *owes nothing more* unless he decides to exercise the option *Once the PREMIUM is paid*, the SELLER *assumes no CREDIT RISK* from *the BUYER OF THE OPTION Instead, *CREDIT RISK is assumed entirely TO THE BUYER* & *can be quite significant*

6.2.2. Reducing Credit Risk *by marking to market* k. *Demonstrate the use of: 1. Exposure limits 2. *Marking to market* 3. Collateral 4. Netting arrangements, 5. Credit standards, 6. Credit derivatives to manage credit risk

*One device that the FUTURES MARKET uses to control credit risk* is *marking tradable positions to market* The *OTC derivatives market also uses MARKING TO MARKET* to deal with credit risk: *OTC contracts are marked to market periodically during their lives*. Recall that a forward contract or swap has a market value that is positive to one party and negative to another. When a *contract calls for marking to market*, the *party for which the value is negative pays* the MV to the *party for which the value is positive* Then the *fixed rate on the contract* is *recalculated*, taking into account the new spot price, interest rate, and time to expiration.

5.7. *Liquidity Risk* The last major type of financial risk...(DB note)

*One of the implicit assumptions in risk management* with VAR is *that positions can be LIQUIDATED* when they approach or move outside risk limits In practice, *some assets are far more liquid than others* and *practitioners will often LIQUIDITY-ADJUST VAR* estimates accordingly *Wide bid-ask spreads* in proportion to price are an obvious measure of the *cost of trading an illiquid* instrument or underlying security But some instruments simply *trade very infrequently* at any price—a far more complex problem, because *infrequently quoted prices often give the statistical ILLUSION OF LOW VOLATILITY* *This dynamic is counterintuitive*, because we would expect instruments that are *ILLIQUID to have a HIGHER bid-ask SPREAD & HIGHER VOLATILITIES*

For example Continued (2)

*Without netting*, B would need to send €40,000 to A, which would send €100,000 to B *Suppose B was in the process of sending its €40,000 to A* but was *unaware that A was in default* and *unable to send the €100,000 to B. If the €40,000 is received by A, B might be unable to get it back until the bankruptcy court decides what to do, which could take years. *Using netting*, only the *€60,000 owed by A to B is at risk*

Blue Box Risk Budgeting Examples from Fund Management Company and Hedge Funds: LOTS of Definitions

*Performance Stop outs*: maximum amount that a given portfolio is allowed to lose in a period (e.g., a month or a year). Working Capital Allocations: 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. Scenario Analysis Limits: PM 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 PM 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*: RM seek to enforce diversification by mandating a specific maximum amount for individual positions. *Leverage Limits* Max amount of leverage in the portfolio may be specified Liquidity Limits: To help manage liquidity exposure, funds set position limits as a specified maximum % of daily volume, float, or open interest

5.6.3. The *Credit Risk of Swaps* Example

*Plain vanilla IR swap* with a *1-yr life* & *quarterly payments at Libor* Swap has a *fixed rate of 3.68%*, leading to *quarterly fixed payments of $0.0092 per $1 NP* *Move forward 60 days* and *we can determine that the swap's MV is $0.0047 per $1 NP* *To the party that is long* (i.e., *paying fixed and receiving floating*), the *swap has a positive market value* *To the counterparty*, which pays floating and receives fixed, *the claim has a market value of -$0.0047* *NO CURRENT CREDIT RISK* (you are only 30 days away from next pmt date) There is, however, *POTENTIAL CREDIT RISK* ($0.0047)

6.3. Performance Evaluation l. Discuss: 1. Sharpe ratio 2. Risk-adjusted return on capital (RAROC) 3. *Return over maximum drawdown* 4. Sortino ratio as measures of risk-adjusted performance

*Return over maximum drawdown* is simply the *average return in a given year that a portfolio generates*, expressed as a percentage of this drawdown figure It enables investors to ask the following question: Am I willing to accept an occasional *drawdown of X percent* in order to generate an *average return of Y percent*? An investment with X=10% & Y=15% (RoMAD = 1.5) would be *more attractive* than an investment with X=40% and Y=10% (RoMAD = 0.25)

*ORGANIZATIONAL PERSPECTIVE* The *key here* is that *enterprise allocates risk capital BEFORE the fact* in order to provide guidance on the acceptable amount of risky activities that a given unit can undertake

*Risk budgeting* involves *establishing objectives for individuals, groups, or divisions of an organization* that take into account the allocation of an acceptable level of risk Example: The *foreign exchange trading desk* of a bank could be *allocated capital of €100M & *permitted a daily VAR of €5M In other words, *the desk is granted a budget*, expressed in *terms of allocated capita*l and *an acceptable level of risk*

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements*

*Risk management* has become a *vital*, if not central, *component in the process of allocating capital* across units of a *risk-taking enterprise* As part of the task of allocating capital across business units, organizations *must determine how to measure such capital* Here there are multiple methodologies, and we will discuss five of them in further detail:

6.2.5. Reducing Credit Risk with *Minimum Credit Standards* and *Enhanced Derivative Product Companies* Continued

*Some companies will not do business with an enterprise* UNLESS its *rating from these agencies meets a prescribed level of credit quality* This *practice can pose a problem for some derivatives dealers*, most of which engage in other lines of business that expose them to a variety of other risks; for example, *banks are the most common derivatives dealers*

6.5. Psychological and Behavioral Considerations

*The main factor to consider from a risk management perspective* is the importance of *establishing a risk governance framework* that *anticipates the points in a cycle* when the *incentives of risk takers* diverge from those of *risk capital allocators* One *common example* occurs when *portfolio managers who are paid a percentage of their profits in a given year* fall into a negative performance situation.

*Risk Budgets*

*The sum of risk budgets for individual units* will typically *exceed the risk budget for the organization* as a whole *because of the IMPACTS OF DIVERSIFICATION*

If one of the party defaults...

*This claim has a probability of not being paid* and *also has the potential for recovery of a portion of the loss* in the event of default *If the counterparty declares bankruptcy* before the contract expires, *the claim of the non-defaulting counterparty* is the *forward contract's market value at the time of the bankruptcy*, assuming this value is positive So, if the short declares bankruptcy at this time, *the long has a claim worth $0.7728* If the *long declares bankruptcy*, the *long holds an asset worth $0.7728*

Example

*To an end user* considering *engaging in a derivative contract with a dealer*, the *potential for the dealer's other business* to cause the dealer to default is a serious concern *Banks*, in particular, are *involved in consumer and commercial lending*, which can be quite risky. *The possibility that bad loans* will cause a *bank to default on its derivatives transactions is quite real*, and *credit ratings often reflect this possibility* In turn, *ratings are a major determinant in business flows for banks* that act as dealers Hence, *many derivatives dealers have taken action to control their EXPOSURE TO RATING DOWNGRADES*

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 4. *Internal Capital Requirements*

*Traditionally*, internal capital requirements have been specified heuristically in terms of the capital ratio (the *ratio of capital to assets*). *Modern tools* permit a more *rigorous approach* If the *value of assets declines* by an amount that *exceeds the value of capital*, the *firm will be insolvent* Say a *0.01 probability of insolvency over a one-year horizon is acceptable* By *requiring capital* to *equal at least one-year aggregate VAR* at the *1 percent probability* level*, the *capital should be adequate in terms of the firm's risk tolerance*.

6.3. Performance Evaluation l. Discuss: 1. Sharpe ratio 2. Risk-adjusted return on capital* (RAROC) 3. Return over maximum drawdown 4. *Sortino ratio* as measures of risk-adjusted performance

*portfolio managers should not be penalized for volatility deriving from outsized positive performance* The *Sortino ratio adopts this perspective* *The numerator of the Sortino Ratio* is the *return in excess of the investor's minimum acceptable return (MAR)* (Return of portfolio - MAR) *The denominator is the downside deviation* using *the MAR as the target return* *Downside deviation* computes *volatility using only rate of return data points below the MAR* Thus the expression for the Sortino ratio is Sortino ratio = (Mean portfolio return - MAR)/(Downside deviation)

Explaining the Chart Exhibit 2 illustrates this process of pricing and measuring risk

1. In pricing the transaction, we first identify the source(s) of uncertainty 2. Then we select the appropriate pricing model and enter our desired inputs to derive our most accurate estimate of the instrument's model value. 3. Look to the marketplace for an indication of where we can actually execute the transaction. If the execution price is "attractive" (i.e., the market will buy the instrument from us at a price at or above, or sell it to us at a price at or below, the value indicated by our model), it fits our criteria for acceptance; If not, we should seek an alternative transaction. After executing the transaction, we would then return to the process of measuring risk

5% VAR and the 1% VAR formula

5% VAR: More Aggressive Formula: VP x [ Mean return - 1.65 x stdev] 1.65 = used when asked for the 5% VAR value 1% VAR: More Conservative Formula: VP x [ Mean return - 2.33 x stdev] 2.33 = used when asked for the 1% VAR value

5. Regulatory Capital Requirements

A *capital requirement based on aggregate VAR* has an *advantage over regulatory capital requirements* in that it takes *account of correlations*. Furthermore, to *account for extraordinary shocks*, we *can stress test the VAR-based recommendation* In addition, *many institutions (e.g., securities firms and banks) must calculate and meet regulatory capital requirements* *Wherever and whenever this is the case*, it of course *makes sense to allocate this responsibility to business units* *Meeting regulatory capital requirements can be a difficult process*, among other reasons *because such requirements are sometimes inconsistent with rational capital allocation schemes* that have capital preservation as a primary objective Nevertheless, when regulations demand it, firms must include regulatory capital as part of their overall allocation process.

i. *Evaluate the credit risk of an investment position, including forward contract, swap, and option positions* 5.6.3. The *Credit Risk of Swaps*

A *swap is similar to a series of forward contracts* The *periodic payments associated with a swap imply, however, that *CREDIT RISK will be PRESENT* at a *series of points during the contract's life* As with *forward contracts*, the *swap's market value can be calculated at any time* and *reflects the present value of the amount at risk for a credit loss* (i.e., the *potential credit risk*)

6.2.6. Transferring Credit Risk with *Credit Derivatives* *CREDIT SPREAD OPTION*

A CREDIT SPREAD OPTION is an *option on the yield spread of a reference obligation* and *over a referenced benchmark* Such as the yield on a specific default-free security of the same maturity

CREDIT VAR Example

A company might quote: Credit VAR OF €10M For ONE YEAR At a PROBABILITY OF 5% (confidence level of 95%) *Credit VAR CANNOT BE SEPARATED from MARKET VAR* bc *credit risk arises from gains on market positions held* Therefore, to accurately measure *credit VAR*, a *risk manager must focus* on the *UPPER TAIL* of the distribution of market returns, where the *return to the position is POSITIVE*, in contrast to *market risk VAR*, which *focuses on THE LOWER TAIL* Suppose the 5% upper tail of the market risk distribution is €5M *The credit VAR can be roughly thought of as €5M*, but this *thinking assumes that the probability of loss is 100%* and the *net amount recovered in the event of a loss is ZERO*

f. Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR and discuss the advantages and disadvantages of each* HISTORICAL METHOD: • Actual daily prices from user specified period Advantages and Disadvantages

Advantages: NON-PARAMETRIC (involves minimum probability assumptions) which means the user does not have to make assumptions about the type of the probability distributions (normal distribution, log normal distribution etc) Disadvantages: Relying completely on the events of the past • However this flaw is also present in the analytical method and Monte Carlo methods

g. *Discuss advantages and limitations of VAR and its extensions, including cash flow at risk, earnings at risk, and tail value at risk* VAR: • Advantages:

Advantages: o Quantify the potential loss in simple terms & easily understood by senior management o Regulatory bodies use VAR as a risk measure and require firms to use it in their reports o Versatility: many use VAR as a measure of capital at risk. Also can be used in risk budgeting process to allocate capital

c. *Describe steps in an effective enterprise risk management system*

An effective ERM system typically incorporates the following steps: 1. Identify each risk factor to which the company is exposed. 2. Quantify each exposure's size in money terms. 3. Map these inputs into a risk estimation calculation. 4. Identify overall risk exposures as well as the contribution to overall risk deriving from each risk factor. 5. 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. 6. Monitor compliance with policies and risk limits.

6.2.6. Transferring Credit Risk with *Credit Derivatives* k. *Demonstrate the use of: 1. Exposure limits 2. Marking to market 3. Collateral 4. Netting arrangements 5. Credit standards 6. *Credit derivatives to manage credit risk*

Another mechanism for managing credit risk is to *TRANSFER IT TO ANOTHER PARTY* Credit derivatives provide ways for such transfers Credit derivatives include such contracts as: 1. Credit default swaps 2. Total return swaps 3. Credit spread options 4. Credit spread forwards These *transactions are typically customized*, although the *wording* of contract provisions is often *standardized*

Last point on ERM Storage and Technology

As a final note, effective ERM systems always feature centralized data warehouses, where a company stores all pertinent risk information, including position and market data, in a technologically efficient manner. Depending on the organization's size and complexity, developing and maintaining a high-quality data warehouse can require a significant and continuing investment. In particular, the process of identifying and correcting errors in a technologically efficient manner can be enormously resource intensive—especially when the effort requires storing historical information on complex financial instruments. It is equally clear, however, that the return on such an investment can be significant.

Enhanced Derivative Products Companies EDPCs or SPVs (Special Purpose Vehicles)

As a result of these features, *these subsidiaries almost always receive the highest credit quality* rating by the rating agencies In the event that the *parent goes bankrupt*, the *EDPC is not liable for the parent company's debts*; if the *EDPC goes under*, however, *the parent is liable for an amount up to its equity investment* and may find it necessary to provide even more protection Hence, an *EDPC would typically have a HIGHER CREDIT RATING* than its *PARENT*. In fact, it is *precisely for the purpose of obtaining the highest credit rating*, and thus the most favorable financing terms with counterparties, that banks and broker dealers go through the expense of putting together EDPCs

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 2. *VAR-Based Position Limits*

As an alternative or supplement to *NOTIONAL LIMITS*, enterprises often assign a *VAR LIMIT* as a *proxy for allocated capital* Advantages: 1. *Allocates capital in units of estimated exposure* and thus acts in greater harmony with the risk control process Limitations: 1. *The limit regime will be only as effective as the VAR calculation itself*; *When VAR is complex, less than completely accurate, not well understood by traders*, it is difficult to imagine it providing rational results from a capital allocation perspective. 2. In addition, the *relation between overall VAR and the VARs of individual positions* is complex and can be counter intuitive

f. *Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR* The analytical or variance-covariance method

Assumes that portfolio returns are normally distributed. Example: 5% VAR for a portfolio (i.e., VAR at a probability of 0.05), we would estimate its expected return and subtract 1.65 times its estimated standard deviation of returns

b. *Evaluate strengths and weaknesses of a company's risk management process*

Be prepared to analyze a case

*Credit Risk for IR SWAP* versus *Credit Risk for a Currency Swap*

Because the *notional principal* tends to be a *large amount relative to the payments*, the *potential for loss* caused by the counterparty defaulting on the *FINAL NOTIONAL PRINCIPAL PAYMENT IS GREAT* Thus, *CURRENCY SWAPS* have their *greatest credit risk* between the *MIDPOINT & THE END OF THE LIFE OF THE SWAP*

g. *Discuss advantages and limitations of VAR and its extensions, including cash flow at risk, earnings at risk, and tail value at risk* CASH FLOW AT RISK (CFAR) EARNINGS AT RISK (EAR)

CFAR is the minimum cash flow loss that we expect to be exceeded with a given probability over a specified time period. EAR is defined analogously to CFAR but measures risk to accounting earnings *CFAR and EAR can be used when a company (or portfolio of assets) generates cash flows or profits but cannot be readily valued in a publicly traded market, or when the analyst's focus is on the risk to cash flow and earnings, for example, in a valuation. CFAR and EAR can complement VAR's perspective on risk.

6.2.6. Transferring Credit Risk with *Credit Derivatives* *CREDIT SPREAD FORWARD*

CREDIT SPREAD FORWARD is a *forward contract on a yield spread*

f. *Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR* 5.2.3. The Historical Method This term is somewhat misleading because the approach involves not a simulation of the past returns but rather what actually happened in the past

Calculate returns for a given portfolio using actual daily prices from a user-specified period in the recent past, graphing these returns into a histogram. Example: The year examined here contains 248 returns. Having 5% of the returns in the distribution's lower tail would mean that about 12 return observations should be less than the VAR estimate If THE HISTORICAL RETURN IS BETWEEN 2ND AND 3RD WORST YOU CAN EITHER PICK ON OR DO THE AVERAGE OF THE TWO.

1. CENTRALIZED

Company has a single risk management group that monitors and ultimately controls all of the organization's risk-taking activities. This centralized type of risk management is now called ENTERPRISE RISK MANAGEMENT (ERM) or sometimes firmwide risk management because its distinguishing feature is a firmwide or across-enterprise perspective. In ERM, an organization must consider each risk factor to which it is exposed—both in isolation and in terms of any interplay among them.

*Risk Budgeting* in the second perspective ALLOCATING FUNDS TO PORTFOLIO MANAGERS

Consider an active investor who wants to allocate funds optimally to several domestic and non-domestic equity and fixed-income investment managers Such an investor *might focus on tracking risk as the primary risk* measure and decide on an overall maximum acceptable level for it, such as 200bp *The expected information ratio (IR)* for each manager is one possible measure of each manager's ability to add value, considering the managers in isolation

6.2.5. Reducing Credit Risk with *Minimum Credit Standards* and *Enhanced Derivative Product Companies* k. *Demonstrate the use of: 1. Exposure limits 2. Marking to market 3. Collateral 4. Netting arrangements 5. *Credit standards* 6. Credit derivatives to manage credit risk

Ensure that all *credit-based business* is done with entities that have *ADEQUATE LEVELS OF CREDIT QUALITY* The *historical standard measures* for such credit quality come from *rating agencies* such as MOODY'S & Standard & Poor's

6.2. Managing *Credit Risk*

Credit is a *ONE-SIDED RISK* *IF PARTY B OWES PARTY A* the amount of £1,000, *B will end up paying A either £1,000 or some amount ranging from zero to £1,000* *A's rate of return is certainly not normally distributed and not even symmetric*. *All of the risk is downside*

5.6. *Measuring Credit Risk*

Credit risk is present when there is a *positive probability that one party owing money to another will not pay on the obligation* (i.e., the *counterparty could default*) Credit losses have *TWO DIMENSIONS*: 1. *LIKELIHOOD OF LOSS* 2. *THE ASSOCIATED AMOUNT OF LOSS* (*amount of credit* outstanding & the associated *recovery rate*)

SECOND-ORDER MEASURES

Deal with the change in the price sensitivity of a financial instrument and include convexity for fixed-income portfolios and gamma for options. CONVEXITY measures how interest rate sensitivity changes with changes in interest rates. GAMMA measures the delta's sensitivity to a change in the underlying's value. Delta and gamma together capture first- and second-order effects of a change in the underlying. For options, TWO OTHER MAJOR FACTORS determine price: volatility and time to expiration, both first-order or primary effects.

Final

Depending on such factors as the *type of enterprise, its corporate culture, fiduciary obligations*, the *most effective approach to capital allocation* probably involves a *combination of most of the above methodologies* The trick, of course, is to *combine the appropriate ones* in a rational and consistent manner that creates the proper *incentives for balance between the dual objectives of profit maximization and capital preservation*

Example from Blue Box 2 Lot of definition Cut all the fat and keep only the important points

Effective risk governance for investment firms demands that THE TRADING FUNCTION be separated from the RISK MANAGEMENT FUNCTION Effective risk governance for an investment firm ALSO requires that the back office be fully independent from the front office. The back office must coordinate with external service suppliers, such as the firms GLOBAL CUSTODIANS (trade settlement) Increasingly investment firms are seeking risk reduction with cost efficiencies via *STRAIGHT THROUGH PROCESSING SYSTEMS* that obviate manual and duplicative intervention in the process from trade placement to settlement

Explanation of steps in the RM process c. *Describe steps in an effective enterprise risk management systems*

Establishing a series of risk management policies & procedures 1. *Defines its risk tolerance*, which is the level of risk it is willing and able to bear. 2. *Identifies the risks*, drawing on all sources of information 3. *Measure these risks* using information or data related to all of its identified exposures *Risk measurement more often than not it involves expertise in the practice of modeling and sometimes requires complex analysis Now the firm is in the position to *ADJUST ITS RISK EXPOSURES*

6.2. Managing *Credit Risk*

Estimating *default probabilities* is *DIFFICULT because of the infrequency of losses* for many situations where credit risk exists Credit losses differ considerably from losses resulting from market moves

*European option* Example

European call option Underlying security has a price of 52.75 Standard deviation of 0.35 The exercise price is 50 Risk-free rate is 4.88% continuously compounded Option expires in 9 months Using the *Black-Scholes-Merton model*, we find that the *value of the option is 8.5580* The holder (buyer) thus has *potential credit risk* represented by a *present claim of 8.5580* This amount can be thought of as the *amount that is at risk*, even though *at expiration the option will probably be worth a different amount*

Another method for scenario analysis Scenarios based on HYPOTHETICAL EVENTS

Events that have NEVER HAPPENED in the markets or market outcomes to which we attach a small probability. These types of scenarios are very difficult to analyze and may generate confusing outcomes, so it is important to carefully craft hypothetical analyses if they are to generate information that adds value to the risk management processes.

Financial Risks: 1. Market Risk 2. Credit Risk 3. Liquidity Risk Market Risk: I have Interest in Equity of Foreign Commodities

FINANCIAL: • *MARKET RISK*: Linked to supply & demand in various market places 1. Interest rate Risk 3. Equity Market Risk: Stock prices 2. Foreign Exchange Risk: Exchange rates 4. Commodity Price Risk: • *CREDIT RISK*: Risk of loss caused by counterparty failure to make payment • *LIQUIDITY RISK*: o Present in both initiating and liquidating position o Can also be present with short sellers on a short squeeze * EOC: Derivatives CANNOT be used to reduce liquidity risk as the liquidity risk on the spot transfer to the derivative markets as well.

Example:

FX trading desk made a *quarterly profit of €20M from its allocation* The bank's fixed-income trading desk: Allocated capital of €200M Permitted a daily VAR of €5 million; Made €25M in quarterly trading profits *DAILY VARs for the two business areas are the same*, so each area has the *same risk budget*, and that the *fixed-income desk generated better returns on the VAR allocation*, but *worse on the allocation of actual capital* The FX desk €20/€100 = 20% return The FI desk €25/€200 = 12.5%

Credit risk for different type of asset and different time periods

For *INTEREST RATE* & *EQUITY SWAPS*, the *POTENTIAL CREDIT RISK* is largest during the *MIDDLE period of the swap's life* During the *BEGINNING of a swap's life*, credit risk is *SMALL* *At the END of the life of the swap*, the credit risk is *diminished* (*fewer payments left*)

PRIMARY SOURCES OF RISK first

For a stock or stock portfolio, BETA measures sensitivity to market movements and is a linear risk measure. For bonds, DURATION measures the sensitivity of a bond or bond portfolio to a small parallel shift in the yield curve and is a linear measure, as is DELTA for options, which measures an option's sensitivity to a small change in the value of its underlying. These measures all reflect the expected change in price of a financial instrument for a unit change in the value of another instrument.

Example of converting between time periods

For example, if the daily VAR is estimated at $100,000, the annual VAR will be This simple conversion of a shorter-term VAR to a longer-term VAR (or vice versa) does not work, however, if the average return is NOT ZERO In these cases, one would have to convert the average return and standard deviation to the different time period and compute the VAR from the adjusted average and standard deviation.

Risk Governance

For the risk management process to work, managers need to specify thoughtfully the BUSINESS PROCESSES THEY USE TO PUT RISK MANAGEMENT INTO PRACTICE. We refer to these processes collectively as RISK GOVERNANCE, the subject of the next section.

*How potential credit risk changes* during the life of the contract as the value of the underlying changes

From the perspective of a given party, a forward contract's market value can be easily calculated as the: *PV of amount OWED * (-) *PV of amount it OWES* So, the *MARKET VALUE at a given time* reflects the *POTENTIAL CREDIT RISK*

5.5.2. Stressing Models

Given the difficulty in estimating the sensitivities of a portfolio's instruments to the scenarios we might design, ANOTHER APPROACH might be to use an existing model and apply shocks and perturbations to the model inputs in some mechanical way. This approach might be considered more scientific because it emphasizes a range of possibilities rather than a single set of scenarios, but it will be more computationally demanding

*CLOSEOUT NETTING*

If *A declares bankruptcy*, the *parties can use netting to solve a number of problems*. *If A and B agree to do so BEFORE THE BANKRUPTCY*, they can *net the market values of ALL of their derivative contracts to determine one overall value owed by one party to another*. It could well be the case that *even though A is bankrupt*, *B might owe more to A than A owes to B*. Then, *rather than B being a creditor to A*, *A's claim on B* becomes one of *A's remaining assets*. This process is referred to as *CLOSEOUT NETTING*

6.2.3. Reducing Credit Risk *with Collateral* k. *Demonstrate the use of: 1. Exposure limits 2. Marking to market 3. *Collateral* 4. Netting arrangements 5. Credit standards 6. Credit derivatives to manage credit risk

If a given *derivatives contract has a positive value to Party A* and a *negative value to Party B*, Party B owes more than Party A Party B must put collateral into an account designated for this purpose As the *contract's market value changes*, the *amount of collateral that must be maintained will vary*, increasing as the market value increases & vice versa At some point, if the *market value of the transaction changes sign*, the *collateral position will typically reverse itself*, with the *entity previously posting collateral seeing a release of these assets* and *the other participant in the transaction experiencing a collateral obligation*. In addition to *market values*, collateral *requirements are sometimes also based* on factors such as *participants' credit ratings*

For example

If a payment is due and *Party A owes more to Party B than B owes to A*, the difference between the amounts owed is calculated and *Party A pays the net amount owed* This procedure, called *PAYMENT NETTING*, *reduces the credit risk* by *reducing the amount of money that must be paid* *If Party A owes €100,000 to Party B, which owes €40,000 to A*, then *the net amount owed is €60,000, which A owes to B*

Conversion between Times 1. From Year to Monthly 2. From Year to Weekly 3. From Month to Weekly Daily VAR use 20 trading days convention

If given 1 year: Monthly Return = 1 Year Return/12 Monthly Stdev = 1 Year / √12 If given 1 year: Weekly Return = 1 Year Return/52 Weekly Stdev = 1 Year / √52 If given 1 month: Weekly Return = 1 month x 12 = Year / 52 Weekly Stdev = 1 month x ( √12) / (√52)

6.3. Performance Evaluation l. Discuss: 1. Sharpe ratio 2. Risk-adjusted return on capital* (RAROC) 3. Return over maximum drawdown 4. *Sortino ratio*

If the *MAR is set at the RISK-FREE RATE*, the *Sortino ratio is IDENTICAL to the SHARPE RATIO*, save for the fact that it *uses downside deviation instead of the standard deviation* in the denominator. A *side-by-side comparison of rankings of portfolios* according to the *Sharpe and Sortino ratios* can *provide a sense* if *OUTPERFORMANCE* may be affecting assessments of risk-adjusted performance* Taken together, the two ratios can tell a more detailed story of risk-adjusted return than either will in isolation, but the *Sharpe ratio is better grounded in financial theory* and *analytically more tractable* Furthermore, *departures from normality of returns* can *raise issues for the Sortino ratio as much as for the Sharpe ratio*

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 4. *Internal Capital Requirements*

If the *company can assume a normal return distribution*, *required amount of capital* can be stated in *standard deviation units* (e.g., 1.96 standard deviations would reflect a 0.025 probability of insolvency)

*American Option* Example

If the OPTION WERE AMERICAN, the *value could be GREATER* With *American options*, *CURRENT credit risk* could arise if the *option holder decides to exercise the option early* This alternative *creates the possibility of the SHORT DEFAULTING before expiration*

*ORGANIZATIONAL PERSPECTIVE* Continued...

In VARIATION on this theme, instead of using VAR units an organization might allocate risk based on: 1. Individual *transaction size* 2. *Amount of working capital* needed to support the portfolio 3. *Amount of losses acceptable for any given time period* (e.g., one month)

6.2.6. Transferring Credit Risk with *Credit Derivatives* *CREDIT DEFAULT SWAP*

In a *CREDIT DEFAULT SWAP*, *the protection buyer pays the protection seller* in return for the *right to receive a payment from the seller* in the event of a specified *CREDIT EVENT*

6.2.6. Transferring Credit Risk with *Credit Derivatives* *TOTAL RETURN SWAP*

In a *TOTAL RETURN SWAP*, the *protection buyer pays the total return on a reference obligation* (or basket of reference obligations) in *return for floating-rate payments* If the *reference obligation has a CREDIT EVENT*, the *total return on the reference obligation should FALL*; the *total return should also fall in the event of an INCREASE IN INTEREST RATES*, so the *protection seller* (total return receiver) in this contract is actually exposed to *both credit risk and interest rate risk*

Discuss with Baba....

In addition, instruments such as bonds and most derivatives behave differently at different times in their lives, and any accurate historical VAR calculation must take this into account by adjusting current bond/derivative pricing parameters to simulate their current characteristics across the period of analysis. For example, a historical VAR calculation that goes back one year for a portfolio that contains bonds that mature in the year 2027 should actually use otherwise identical bonds maturing in 2026 as proxies; these bonds are the most accurate representations of the current risk profile because they would have presented themselves one year ago in time. When a company uses a different portfolio composition to calculate its historical VAR than the one it actually had in the past, it may be more appropriate to call the method a historical simulation.

Volatility for indexing

In some applications, such as INDEXING, volatility relative to a benchmark is paramount. In those cases, our focus should be on the volatility of the deviation of a portfolio's returns in excess of a stated benchmark portfolio's returns, known as ACTIVE RISK, TRACKING RISK, tracking error volatility, or by some simply as tracking error.

Example continued (3)

In the examples we have seen so far, *netting is applied on the PAYMENT DATE* *The concept of netting* can be extended to the events and conditions *surrounding a bankruptcy* *Suppose A and B are counterparties to a number of derivative contracts* On some of the contracts, *the market value to A is positive*, while on others, the *market value to B is positive*

*Current Credit Risk* vs *Potential Credit Risk*

In the risk management business, exposure must often be viewed from *TWO DIFFERENT TIME PERSPECTIVES* We must assess: 1. *the risk associated* with *IMMEDIATE credit events*: *CURRENT CREDIT RISK* or *JUMP-TO-DEFAULT RISK* 2. *the risk associated* with *events that may happen LATER*: *POTENTIAL CREDIT RISK* Regardless of which risk is greater, however, a creditor *must assess credit risk* at different points in time In doing so, the *creditor must understand how different financial instruments* have *different patterns of credit risk*, both *across instruments* and *across time within a given instrument*

Continued

In this application, however, it is *appropriate for the investor to adjust each manager's IR to eliminate the effect of asset class correlations*; *CORRELATION-ADJUSTED IRs* will capture each manager's *incremental ability to add value in a portfolio* context. Using such *CORRELATION-ADJUSTED IRs*, we can determine the *OPTIMAL TRACKING RISK ALLOCATION* for *EACH INVESTMENT MANAGER* (which, intuitively, is positively related to his CORRELATION-ADJUSTED IR) For many portfolio managers, *risk budget allocations* should be measured in *relation to risk to the SURPLUS*—that is, the difference between the *values of assets and liabilities*

6.1.1. *Risk Budgeting*

It focuses on questions such as: *"Where do we want to take risk?"* *"What is the efficient allocation of risk across various units of an organization or investment opportunities?"* *Risk budgeting* is *relevant in both an organizational* and a *portfolio management context*

6.2.1. Reducing Credit Risk *by Limiting Exposure* k. *Demonstrate the use of: 1. *Exposure limits* 2. Marking to market 3. Collateral 4. Netting arrangements, 5. Credit standards, 6. Credit derivatives to manage credit risk

LIMITING THE AMOUNT OF EXPOSURE to a given party is the *PRIMARY means of managing credit risk* *Experienced risk managers* often have a *good sense of when and where to limit their exposure*, and they *make extensive use of quantitative credit exposure measures* to guide them in this process. *Banks* have *regulatory constraints* on the amount of *credit risk they can assume*

5.1. Measuring Market Risk

MARKET RISK refers to the exposure associated with actively traded financial instruments, typically those whose prices are exposed to the changes in interest rates, exchange rates, equity prices, commodity prices, or some combination thereof. The most common tool to MEASURE market risk is: Standard Deviation or Volatility. Volatility is often an adequate description of portfolio risk, particularly for those portfolios composed of instruments with LINEAR PAYOFFS.

5.5.2. Stressing Models: other models MAXIMUM LOSS OPTIMIZATION WORST-CASE SCENARIO ANALYSIS

MAXIMUM LOSS OPTIMIZATION: In which we would try to optimize mathematically the risk variable that will produce the maximum loss WORST-CASE SCENARIO ANALYSIS: in which we can examine the worst case that we actually expect to occur.

h. *Compare alternative types of stress testing and discuss advantages and disadvantages of each* 5.5. Stress Testing

Managers often use stress testing to SUPPLEMENT VAR as a risk measure. The MAIN PURPOSE OF VAR analysis is to quantify potential losses under normal market conditions. Stress testing, by comparison, SEEKS TO IDENTIFY UNUSUAL CIRCUMSTANCES THAT COULD LEAD TO LOSSES IN EXCESS OF THOSE TYPICALLY EXPECTED. Two broad approaches exist in stress testing: 1. SCENARIO ANALYSIS 2. STRESSING MODELS

Risk Reduction

Many companies hedge risks that arise from areas in which they have no expertise In areas in which they do have an edge, they tend to hedge only tactically. They hedge when they think they have sufficient information to suggest that a lower risk position is appropriate. They manage risk, increasing it when they perceive a competitive advantage and decreasing it when they perceive a competitive disadvantage (they EFFICIENTLY ALLOCATE RISK) RM involves far more than RISK REDUCTION or HEDGING (one particular risk-reduction method) RM is a general practice that INVOLVES RISK MODIFICATION (e.g., risk reduction or risk expansion) as deemed necessary and appropriate by the custodians of capital and its beneficial owners.

LEPTOKURTOSIS Distributions can deviate from normality because of SKEWNESS and KURTOSIS.

Many observed distributions of returns have an ABNORMALLY LARGE NUMBER OF EXTREME EVENTS. This quality is referred to in statistical parlance as LEPTOKURTOSIS but is more commonly called the property of FAT TAILS Using a normality assumption to estimate VAR for a portfolio that features fat tails could understate the actual magnitude and frequency of large losses. VAR would then fail at precisely what it is supposed to do: measure the risk associated with large losses.

g. *Discuss advantages and limitations of VAR and its extensions, including cash flow at risk, earnings at risk, and tail value at risk* 5.4. Extensions and Supplements to VAR INCREMENTAL VAR

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. We can also use IVAR to assess the incremental effect of a subdivision on an enterprise's overall VAR. Although IVAR gives an extremely limited picture of the asset's or portfolio's contribution to risk, it nonetheless provides useful information about how adding the asset will affect the portfolio's overall risk as reflected in its VAR

NON FINANCIAL RISKS Model risks

Model is not correct or misapplied o Present in any attempts to identify fair value of financial instruments but most prevalent in derivative markets

CREDIT VAR Harder to estimate bc of lack of data...

Nevertheless, estimating *CREDIT VAR is MORE COMPLICATED* than estimating *MARKET VAR* because *credit events are RARE and RECOVERY RATES are hard to estimate* *CREDIT RISK is less easily aggregated* than *MARKET RISK*; the *CORRELATIONS between the credit risks of counterparties* must be considered

6.2.4. Reducing Credit Risk with Netting k. *Demonstrate the use of: 1. Exposure limits 2. Marking to market 3. Collateral 4. *Netting arrangements* 5. Credit standards 6. Credit derivatives to manage credit risk

One of the *most common features used in two-way contracts* with a credit risk component, such as *FORWARDS & SWAPS*, is *NETTING* This process, which we have already briefly discussed, involves the *reduction of all obligations owed between counterparties* into a *single cash transaction* that *eliminates these liabilities*

Enhanced Derivative Products Companies EDPCs or SPVs (Special Purpose Vehicles)

One such action is the *formation of a type of subsidiary* that is *separate from the dealer's other activities* These subsidiaries are referred to as ENHANCED DERIVATIVES PRODUCTS COMPANIES (EDPCs), sometimes known as special purpose vehicles (SPVs). These companies are usually *completely separate from the parent organization and are not liable for the parent's debts* They tend to be *very heavily capitalized* and are *committed to hedging all of their derivatives positions*

THETA

Option prices are also sensitive to changes in time to expiration, as measured by THETA, the change in price of an option associated with a one-day reduction in its time to expiration. Theta, like vega, is a risk that is associated exclusively with options.

6.1. Managing *Market Risk*

Our *enterprise risk management system* will be INCOMPLETE *without a well-thought-out approach to setting appropriate RISK TOLERANCE levels* and *identifying the proper corrective behavior* to take if our actual risks turn out to be significantly higher or lower than is consistent with our risk tolerance Note here that in many circumstances, it *could cause as many problems to take too little risk* as to take too much risk *Corrective behavior* in the case of excessive market risk will almost always result in the *need for additional HEDGING* or *the scaling back of tradable positions* Quite often, however, *liquidity and other factors will prevent perfect hedging*, perhaps exacerbating risk concerns rather than mitigating them

6.5. Psychological and Behavioral Considerations

Over the past several years, a body of research has emerged that seeks to model the behavioral aspects of portfolio management. This concept has *IMPORTANT IMPLICATIONS* for risk management for *TWO reasons* 1. *Risk takers may behave differently at different points* in the portfolio management cycle, *depending on such factors as their recent performance*, the risk characteristics of their portfolios, and market conditions* 2. On a related note, *risk management would improve* if these dynamics *could be modeled*

5.2.5. "Surplus at Risk": VAR as It Applies to Pension Fund Portfolios

Pension funds face a slightly different set of challenges in the measurement of market exposures BC of the fact that the assets must fund pension obligations whose PV is itself subject to IR & other risks. Pension fund managers typically apply VAR methodologies not to their portfolio of assets but TO THE SURPLUS. To do so, they simply express their LIABILITY PORTFOLIO as a set of SHORT securities and calculate VAR on the NET POSITION. VAR handles this process quite elegantly, and once this adjustment is made, all three VAR methodologies can be applied to the task.

2. DECENTRALIZED

Places risk management responsibility on individual business unit managers. Each unit calculates and reports its exposures independently.

h. *Compare alternative types of stress testing and discuss advantages and disadvantages of each* 5.5.1. *Scenario Analysis*

Process of evaluating a portfolio under different states of the world. Quite often it involves designing scenarios with deliberately large movements in the key variables that affect the values of a portfolio's assets and derivatives. ONE TYPE of scenario analysis, that of STYLIZED SCENARIOS, involves simulating a movement in at least one interest rate, exchange rate, stock price, or commodity price relevant to the portfolio

NON FINANCIAL RISKS Settlement risk

o One party in the process of paying and the other in the process of declaring bankruptcy

DELTA SOLUTION use of delta to estimate the option's price sensitivity for VAR purposes has led some to call the analytical method (or variance-covariance method) the DELTA-NORMAL METHOD.

Recall that delta expresses a LINEAR relationship between an option's price and the underlying price (i.e., Delta = Change in option price/Change in underlying). A linear relationship lends itself more easily to treatment with a normal distribution. That is, a normally distributed random variable remains normally distributed when multiplied by a constant. In this case, the constant is the delta. The change in the option price is assumed to equal the change in the underlying price multiplied by the delta. This trick converts the normal distribution for the return on the underlying into a normal distribution for the option return

Marking to market Example

Recall that we examined a *one-year forward contract* with an *initial forward price of $105* 3 MO later: Asset price was $102 Its *value was $0.7728 to the long* If the contract were marked to market at that time, the *short would pay the long $0.7728* Then, the *two parties would enter into a new contract expiring in 9MO* with a new forward price, which would be $102 x (1.05)^0.75 = $105.80

NON FINANCIAL RISKS • SETTLEMENT NETTING RISK:

Refers to the risk of a liquidator of a counter party in default could challenge a net arrangement so that profitable transactions are realized to the benefit of creditors o Mitigated by the use of netting agreement that survive legal challenges

3. Risk Governance

Risk governance begins with CHOICES CONCERNING GOVERNANCE STRUCTURE. RISK GOVERNANCE is an element of CORPORATE GOVERNANCE Organizations must determine whether they wish their risk management efforts to be: 1. CENTRALIZED 2. DECENTRALIZED

VEGA

Sensitivity to volatility is reflected in VEGA, the change in the price of an option for a change in the underlying's volatility. Most early option-pricing models (e.g., the Black-Scholes-Merton model) assume that volatility does not change over the life of an option, but in fact, volatility does generally change. Volatility changes are sometimes easy to observe in markets: Some days are far more volatile than others. Moreover, new information affecting the value of an underlying instrument, such as pending product announcements, will discernibly affect volatility. Because of their nonlinear payoff structure, options are typically very responsive to a change in volatility. Swaps, futures, and forwards with linear payoff functions are much less sensitive to changes in volatility.

6.3. Performance Evaluation l. Discuss: 1. *Sharpe ratio* 2. Risk-adjusted return on capital 3. Return over maximum drawdown 4. Sortino ratio as measures of risk-adjusted performance

Sharpe ratio = (Mean port return − RF ) / St Dev of port return The Sharpe ratio is the *mean return earned in excess of the risk-free rate per unit of volatility or total risk* By subtracting a risk-free rate from the mean return, *we can isolate the performance associated with risk-taking activities* SR *can be INACCURATE when applied to portfolios with significant NONLINEAR RISKS*, such as *options positions*.

SKEWNESS Distributions can deviate from normality because of SKEWNESS and KURTOSIS.

Skewness is a measure of a distribution's deviation from the perfect symmetry (the normal distribution has a skewness of zero). A positively skewed distribution is characterized by relatively many small losses and a few extreme gains and has a long tail on its right side. A negatively skewed distribution is characterized by relatively many small gains and a few extreme losses and has a long tail on its left side. When a distribution is positively or negatively skewed, the variance-covariance method of estimating VAR will be INACCURATE.

NON FINANCIAL RISKS • TAX RISK: uncertainty associated with taxes

o Fails to keep with innovations in financial instruments: investor are left to guess work and possible back taxes

g. *Discuss advantages and limitations of VAR and its extensions, including cash flow at risk, earnings at risk, and tail value at risk* TAIL VALUE AT RISK (TVAR) Also known as conditional tail expectation *With some difficulty, VAR can be extended to handle CREDIT RISK, the risk that a counterparty will not pay what it owes

TVAR is defined as the VAR plus the EXPECTED LOSS IN EXCESS OF VAR, when such excess loss occurs. For example, given a 5 percent daily VAR, TVAR might be calculated as the average of the worst 5 percent of outcomes in a simulation.

6.2.3. Reducing Credit Risk *with Collateral* k. *Demonstrate the use of: 1. Exposure limits 2. Marking to market 3. *Collateral* 4. Netting arrangements 5. Credit standards 6. Credit derivatives to manage credit risk

The *POSTING OF COLLATERAL is a widely accepted credit exposure mitigant* in both *lending and derivatives transactions* An common example of its use *comes from futures markets*, which *require that all market participants post margin collateral* Many *OTC derivative markets have collateral posting provisions*, with the *collateral* usually taking the form of *cash or highly liquid*, *low-risk securities* A typical arrangement involves the *routine, periodic posting of values sufficient to cover mark-to-market deficiencies*

6.5. Psychological and Behavioral Considerations

The *trader's situation does not deteriorate from a compensation perspective with incremental losses at this point* (i.e., *the trader is paid zero, no matter how much he loses*), *but of course the organization as a whole suffers from the trader's loss* Moreover, the *risks at the enterprise level* can be *nonlinear* under these circumstances because of *concepts of netting risk* covered earlier in this reading. These and other behavioral issues can be handled best by *RISK CONTROL* and *GOVERNANCE PROCESSES* that contemplate them. One such example is *LIMIT SETTING*, which can, with some thought, *easily incorporate many of these issues*

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 1. *Nominal, Notional, or Monetary Position Limits*

The enterprise simply *defines the amount of capital that the *individual portfolio* or *business unit* can *use in a specified activity*, based on the *actual amount of money exposed* in the markets Advantages: 1. easy to understand 2. it lends itself very nicely to the critical task of calculating a percentage-based return on capital allocated Limitations: 1. MAY NOT capture effectively the effects of CORRELATION & OFFSETTING RISKS 2. An *individual may be able to work around a nominal position* using other assets that can replicate a given position. For these reasons it is *rarely a sufficient capital allocation method* from a risk control perspective

The problem with options

The normal distribution assumption is inappropriate for portfolios that CONTAIN OPTIONS The return distributions of options portfolios are often far from normal (normal distribution has an unlimited upside and an unlimited downside) The distribution of returns for a call, put, covered call and protective put is HIGHLY SKEWED. One COMMON SOLUTION is to estimate the option's price sensitivity using its DELTA

3. Risk Governance

The process of setting overall policies and STANDARDS IN RISK MANAGEMENT IS CALLED RISK GOVERNANCE. Risk governance involves choices of: 1. governance structure 2. infrastructure, reporting 3. methodology The quality of risk governance can be judged by its TRANSPARENCY, ACCOUNTABILITY, EFFECTIVENESS (achieving objectives), and EFFICIENCY (economy in the use of resources to achieve objectives).

h. *Compare alternative types of stress testing and discuss advantages and disadvantages of each* SCENARIO ANALYSIS Potential problem...

The results, of course, are only as good as implied by the accuracy of the scenarios devised. ONE PROBLEM with the STYLIZED SCENARIO APPROACH is that the shocks tend to be applied to variables in a sequential fashion. In reality, these shocks often HAPPEN AT THE SAME TIME, have much different CORRELATIONS THAN NORMAL, or have some causal relationship connecting them.

5.5.2. Stressing Models FACTOR PUSH

The simplest form of STRESSING MODEL is referred to as FACTOR PUSH. The basic idea of which to is to push the prices and risk factors of an underlying model in the most disadvantageous way and to work out the combined effect on the portfolio's value. This exercise might be appropriate for a wide range of models, including OPTION-PRICING MODELS such as Black-Scholes-Merton, MULTIFACTOR EQUITY RISK MODELS, and TERM STRUCTURE FACTOR models But factor push also has its limitations and difficulties, principally the enormous model risk that occurs in assuming the underlying model will function in an extreme risk climate.

Delta Solution (2)

The use of delta is appropriate only for SMALL CHANGES in the underlying. As an alternative, some users of the delta-normal method add the second-order effect, captured by GAMMA. Unfortunately, as these higher-order effects are added, the relationship between the option price and the underlying's price begins to approximate the true nonlinear relationship

Volatility for individual positions

The volatility associated with individual positions can be combined with other simple statistics, such as correlations, to form the building blocks for the portfolio-based risk management systems that have become the industry standard in recent years

4. Identifying Risks d. *Evaluate a company's or a portfolio's exposures to financial and nonfinancial risk factors* Effective risk management demands the separation of risk exposures into specific categories that reflect their distinguishing characteristics.

These risks may be grouped into financial risks and nonfinancial risks as shown in Exhibit 3 FINANCIAL RISK refers to all risks derived from events in the EXTERNAL FINANCIAL MARKETS; NONFINANCIAL RISK refers to all other forms of risk

Especial case: Expected return of ZERO Some approaches to estimating VAR using the analytical method assume an expected return of ZERO.

This assumption is generally thought to be ACCEPTABLE FOR *DAILY VAR* calculations because expected daily return will indeed tend to be close to zero. Because expected returns are typically positive for longer time horizons, shifting the distribution by assuming a zero expected return will result in a *larger projected loss*, so the VAR estimate will be *greater*. Therefore, this small adjustment offers a slightly more conservative result and avoids the problem of having to estimate the *expected return*, a task typically much harder than that of estimating associated *volatility*. Another advantage of this adjustment is that it makes it easier to *adjust the VAR* for a *different time period*. For example, if the daily VAR is estimated at $100,000, the annual VAR will be

Credit risk for different type of asset and different time periods

This leaves the greatest exposure during the *MIDDLE PERIOD*, a point at which: 1) the *credit profile* of each party *may have changed for the worse* 2) the *magnitude* and *frequency of expected payments* between parties *remain material* * One exception is *CURRENCY SWAPS*, which often provide for the *payment of the NP at the beginning* and at the *end of the life of the transaction*

6.2. Managing *Credit Risk*

Thus *credit risk is not easily analyzed* or controlled using such measures as *standard deviation & VAR* Creditors *need to regularly monitor the financial condition of borrowers* and *counterparties* In ADDITION, *they can use the risk management techniques* for credit discussed below

To be supported through the bankruptcy process, Netting must be Recognized by Legal System

To be supported through the bankruptcy process, however, *NETTING MUST BE RECOGNIZED BY THE LEGAL SYSTEM* and *works best* when each party's obligations are *specified at the time BEFORE* or at the sames time to the executions of transactions. *MOST, but not all*, legal jurisdictions recognize netting

5.6.1. Option-Pricing Theory and Credit Risk (complicated stuff; unlikely in the exam)

Tough subject...I just skipped this... Look at the main points in the schweser book...

Example:

Underlying asset price = $100 Risk-free interest rate is 5% So forward price = $100 x (1.05) = $105 3MO later: Asset price is $102 Long forward contract's value at that time is $102 - [ ($105 / (1.05)^0.75 ] = $0.7728 This is the *value to the long* because the *contract is a claim on the ASSET*, which is *currently worth $102*, and *an obligation to pay $105 for it in nine months*. To the holder of the *long position*, this contract is worth *$0.7728*, and to the *holder of the short position*, it is worth *-$0.7728* The *LONG'S CLAIM IS POSITIVE*; the short's claim is negative. So, *LONG CURRENTLY has CREDIT risk*. This is *POTENTIAL credit risk*

5.8.1. *Operational Risk* Getting more important and attention from regulators...

Until a few years ago, the *subject of operational risk received little attention*, and *ideas about actually measuring operational risk* were practically *unheard of* But a *number of well-publicized losses* at *financial institutions*, ranging from a *breakdown of internal systems* to *rogue employees* and in some cases employee theft, have put *operational risk justifiably into the forefront* Furthermore, the *explicit mention of operational risk requirements in the Basel II banking regulations* has created *real advantages for banks that can credibly measure their operational risks*. This, in turn, has *led to an explosion in the academic literature* relating to the *measurement of operational risk* and its *role in enterprise risk systems*

5.2. Value at Risk e. *Calculate and interpret value at risk (VAR) and explain its role in measuring overall and individual position market risk*

VALUE AT RISK (VAR) is an estimate of the loss (in money terms) that we EXPECT TO BE EXCEEDED with a GIVEN LEVEL OF PROBABILITY over a SPECIFIED TIME PERIOD. Implications: 1. VAR is an estimate of the loss that we expect to be exceeded (measures a minimum loss; actual loss may be much worse) 2.VAR is associated with a given probability (All else equal, if we lower the probability from 5% to 1%, the VAR will be LARGER bc we now are referring to a loss that we expect to be exceeded with only a 1% prob) 3. VAR has a time element and that as such, VARs cannot be compared directly unless they share the same time interval *Potential losses over LONGER periods should be LARGER than those over SHORTER periods, but in most instances, longer time periods will not increase exposure in a linear fashion.

5.2. Value at Risk

VAR is a probability-based measure of loss potential for a company, a fund, a portfolio, a transaction, or a strategy. It is usually expressed either as a percentage or in units of currency. Any position that exposes one to loss is potentially a candidate for VAR measurement VAR is most widely and easily used to measure the loss from MARKET RISK, but it can also be used—subject to much greater complexity—to measure the loss from credit risk and other types of exposures

*CREDIT VAR*

VAR is also used, albeit with greater difficulty, to *MEASURE CREDIT RISK* This measure is sometimes called: *CREDIT VAR*, *DEFAULT VAR*, or *CREDIT AT RISK* Like *ordinary VAR*, it reflects the *minimum loss* with a *given probability during a period of time*

5.2.1. Elements of Measuring Value at Risk

VAR may be implemented in several forms. You need to make a few decisions before calculating: a. probability level (1% vs 5%, leads to a more CONSERVATIVE VAR estimate) If LINEAR risk characteristics, the two probability levels will provide essentially identical information. If optionality or NON-LINEAR risks, may need to select the more conservative probability threshold b. selecting the time period over which to measure VAR (the longer the period, the greater the VAR number will be) c. choosing the specific approach to modeling the loss distribution (next slides)

Another approach to scenario analysis ACTUAL EXTREME EVENTS that have occurred in the past

We might want to put our portfolio through price movements that simulate for example the stock market crash of October 1987; This type of scenario analysis might be *particularly useful* if we think that the *occurrence of extreme market breaks *has a *higher probability* than that given by the probability model or historical time period being used in developing the VAR estimate.

f. *Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR* 5.2.4. The Monte Carlo Simulation Method

When estimating VAR, we use Monte Carlo simulation to produce random portfolio returns. We then assemble these returns into a summary distribution from which we can determine at which level the lower 5%(or 1% , if preferred) of return outcomes occur We then apply this figure to the portfolio value to obtain VAR.

6.4. Capital Allocation m. *Demonstrate the use of VAR and stress testing in setting capital requirements* 3. *Maximum Loss Limits*

it is crucial for any risk-taking enterprise to establish a maximum loss limit for each of its risk-taking units In order to be effective, this *figure must be large enough* to *enable the unit to achieve performance objectives* but *small enough* to be *consistent with the preservation of capital* This *limit must represent a firm constraint on risk-taking activity* Nevertheless, *even when risk-taking activity is generally in line with policy*, management should *recognize that extreme market discontinuities can cause such limits to be breached*

NON FINANCIAL RISKS Operational risks

o *Failure of systems* or from *external events* (acts of Gods or terrorist attack, weather related exposures)

f. Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR and discuss the advantages and disadvantages of each* MONTE CARLO METHOD: • Type of probability distribution for each variable • We can make any distributional assumption o Inappropriate to use normality assumption for some markets Derivatives for example

o Advantages: Is often the only practical means of generating the information needed to manage the risk (DOES NOT REQUIRE A NORMAL DISTRIBUTION) o Disadvantages: Extensive commitment of computer resources (tens of thousands of transactions)

NON FINANCIAL RISKS • PERFORMANCE NETTING RISK (NETTING RISK):

o Applies to entities that fund more than one strategy o Potential for a loss resulting from failure of fees based on net performance to fully cover contractual payout obligations to individual portfolio managers that have positive performance when other had losses You may make money from performance in one manager (i.e. $10m) but you lost money on the other manager (i.e. $10m). You are obligated to pay a performance fee to the first manager of 20% (i.e. $2m) but net net you did not make any money because you made $10m in one manager but the other lost you $10m. You are now down $2m even though you could be only breakeven if that structure was not in place.

g. *Discuss advantages and limitations of VAR and its extensions, including cash flow at risk, earnings at risk, and tail value at risk* VAR: • Limitations:

o Difficult to estimate; different methods can yield different results o VAR can also give a FALSE SENSE OF SECURITY o VAR underestimates the MAGNITUDE and FREQUENCY of worst returns This problem often derives from the erroneous assumptions in the model o Individual VAR does not generally aggregate to PORTFOLIO VAR o Fails to incorporate POSITIVE RESULSTS into risk profile, so gives an incomplete picture of overall risks • Users should apply BACKTESING to improve and test VAR results

NON FINANCIAL RISKS Legal and Contract risk

possibility of loss arising from the legal system's failure to enforce a contract o Nearly every transaction subject to contract law o In a dispute over a contract between two parties, the losing party cold claim the other party was fraudulent and ask for the contract to be void The possibility of such claim being upheld in court creates a form of legal risk

NON FINANCIAL RISKS • ESG (ENVIROMENTAL, SOCIAL, GOVERNMANCE):

risk of company market valuations resulting from environmental, social and governance factors

NON FINANCIAL RISKS • SOVEREIGN RISK:

type of credit risk but the borrower is a government o Current or potential risks o Magnitude: the likelihood of default and the estimated recovery rate

6. *Managing Risk* The *key components*

• An *effective risk governance model*, which *places overall responsibility at the senior management level*, *allocates resources effectively* and *features the appropriate separation of tasks between revenue generators* and those on the control side of the business • *Appropriate systems and technology to combine information analysis* in such a way as to *provide timely and accurate risk information* to decision makers • *Sufficient and suitably trained personnel to evaluate risk information* and *articulate it to those who need this information for the purposes of decision making

f. Compare the analytical (variance-covariance), historical, and Monte Carlo methods for estimating VAR and discuss the advantages and disadvantages of each* Analytical (variance-covariance) Advantages and Disadvantages

• Assumes normal distributions! o Advantages: Simple o Disadvantages: Relying on simplifying assumptions, including normality assumptions Normality assumptions is inappropriate for portfolios that contains OPTIONS There is no reason why the calculation has to have a *normal distribution*, but if we move away from the normality assumption, we *cannot rely on variance as a complete measure of risk*

6.3. Performance Evaluation l. Discuss: 1. Sharpe ratio 2. *Risk-adjusted return on capital* (RAROC) 3. Return over maximum drawdown 4. Sortino ratio as measures of risk-adjusted performance

• Risk-Adjusted Return on Capital (RAROC) This concept divides the *expected return on an investment by a measure of *CAPITAL AT RISK*, Capital at Risk: a measure of the investment's risk that can take a *number of different forms* and can be *calculated in a variety of ways* that may have proprietary features The *company may require* that an investment's *expected RAROC* exceed a *RAROC benchmark* level for capital to be allocated to it

A portfolio's exposure to losses because of market risk typically takes ONE OF TWO FORMS:

• Sensitivity to adverse movements in the value of a key variable in valuation (primary or first-order measures of risk) • Risk measures associated with changes in sensitivities (secondary or second-order measures of risk) Primary measures of risk often reflect linear elements in valuation relationships; secondary measures often take account of curvature in valuation relationships. Each asset class (e.g., bonds, foreign exchange, equities) has specific first- and second-order measures.