Reading 25 Risk Management

Question 1

Risk management is…

Answer 1

Risk management is a process involving:

• the identification of exposures to risk,
• the establishment of appropriate ranges for exposures (given a clear understanding of an entity’s objectives and constraints),
• the continuous measurement of these exposures (either present or contemplated), and
• the execution of appropriate adjustments whenever exposure levels fall outside of target ranges.

The process is continuous and may require alterations in any of these activities to reflect new policies, preferences, and information.

!A process is continuous and subject to evaluation and revision.

Question 2

Is it possible to operate a successful business or investment program without taking risks?

What exactlty kind of risks the companies should hedge?

Answer 2

It is nearly impossible to operate a successful business or investment program without taking risks.

Companies that succeed in doing the activities they should be able to do well, however, cannot afford to fail overall because of activities in which they have no expertise. Accordingly, many companies hedge risks that arise from areas in which they have no expertise or comparative advantage.

Question 3

If σ is an annual standard deviation and r is annual return, what are monthly standard deviation and return?

Answer 3

σ/(12)^0,5

r/12

Question 4

Qualities of a good ERM?

Answer 4

• Good ERM prectice requires that an individual or group that is independent of the trading function monitor and independently value the positions taken by traders.
• Simply adding VAR estimates from different trading teams together overlooks any diversification effects that may be present, unless the returns of the three teams are perfectly correlated
• Effective risk governance 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 prevent collusion.
• Effective ERM system always feature centralized data warehouses and store all pertinent risk information in a technologically efficient manner.

Question 5

How many weeks in a year?

Answer 5

52

Question 6

Risk governance, governance structure, ERM

Answer 6

The process of setting overall policies and standards in risk management is called risk governance. Risk governance involves choices of governance structure, infrastructure, reporting, and 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).

Governance structure: organizations must determine whether they wish their risk management efforts to be centralized or decentralized.

• Under a centralized risk management system, a company has a single risk management group that monitors and ultimately controls all of the organization’s risk-taking activities.
• By contrast, a decentralized system places risk management responsibility on individual business unit managers. In a decentralized approach, each unit calculates and reports its exposures independently. Decentralization has the advantage of allowing the people closer to the actual risk taking to more directly manage it. 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.
• even when exposures to a single risk factor do not directly offset one another, enterprise-level risk estimates may be lower than those derived from individual units because of the risk-mitigating benefits of diversification
• 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. 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.
• the risk management system of a company that chooses a decentralized risk management approach requires a mechanism by which senior managers can inform themselves about the enterprise’s overall risk exposures.

Question 7

Effective risk governance:

• trading function vs. risk management function?
• back office vs. the front office?

Answer 7

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.

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.

Question 8

What steps typically incorporates an effective ERM system?

Answer 8

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.

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.

Question 9

The source of risk?

Answer 9

Question 10

Market Risk

Answer 10

Market risk is the risk associated with interest rates, exchange rates, stock prices, and commodity prices. It is linked to supply and demand in various marketplaces.

One set of market risk takers with special requirements for market risk are defined-benefit (DB) pension funds, which manage retirement assets generally under strict regulatory regimes. Pension fund risk management necessarily concerns itself with funding the stream of promised payments to pension plan participants. Therefore, a DB plan must measure its market exposures not purely on the basis of its assets but also in terms of the risks of pension assets in relation to liabilities.

Question 11

Credit Risk

Answer 11

Credit risk is the risk of loss caused by a counterparty or debtor’s failure to make a promised payment. This definition reflects a traditional binary concept of credit risk, by and large embodied by default risk (i.e., the risk of loss associated with the nonperformance of a debtor or counterparty). For the last several years, however, credit markets have taken on more and more of the characteristics typically associated with full-scale trading markets. As this pattern has developed, the lines between credit risk and market risk have blurred as markets for credit derivatives have developed.

Question 12

Liquidity risk

Answer 12

Liquidity risk is the 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.

For traded securities, the size of the bid–ask spread (the spread between the bid and ask prices), stated as a proportion of security price, is frequently used as an indicator of liquidity.

However, bid–ask quotations apply only to specified, usually small size, trades, and are thus an imprecise measure of liquidity risk.

One of the best ways to measure liquidity is through the monitoring of transaction volumes, with the obvious rule of thumb being that the greater the average transaction volume, the more liquid the instrument in question is likely to be.

Question 13

Operational risk

Answer 13

Operational risk, sometimes called operations risk, is the risk of loss from failures in a company’s systems and procedures or from external events. These risks can arise from computer breakdowns (including bugs, viruses, and hardware problems), human error, and events completely outside of companies’ control, including “acts of God” and terrorist actions.

Question 14

Model Risk

Answer 14

Model risk is the risk that a model is incorrect or misapplied; in investments, it often refers to valuation models.

Question 15

Settlement (Herstatt) Risk

Answer 15

Settlement risk as the risk that one party could be in the process of paying the counterparty while the counterparty is declaring bankruptcy.

• All transactions on the exchange take place between an exchange member and the central counterparty, which removes settlement risk from the transaction.
• OTC markets, including those for bonds and derivatives, do not rely on a clearing house. Instead, they effect settlement through the execution of agreements between the actual counterparties to the transaction. Netting arrangements, used in interest rate swaps and certain other derivatives, can reduce settlement risk.
  *

Question 16

Regulatory Risk

Answer 16

Regulatory risk is the risk associated with the uncertainty of how a transaction will be regulated or with the potential for regulations to change.

• Regulation is a source of uncertainty. Regulated markets are always subject to the risk that the existing regulatory regime will become more onerous, more restrictive, or more costly. Unregulated markets face the risk of becoming regulated, thereby imposing costs and restrictions where none existed previously. Regulatory risk is difficult to estimate because laws are written by politicians and regulations are written by civil servants;
• Regulatory risk often arises from the arbitrage nature of derivatives and structured transactions. For example, a long position in stock accompanied by borrowing can replicate a forward contract or a futures contract. Stocks are regulated by securities regulators, and loans are typically regulated by banking oversight entities. Forward contracts are essentially unregulated. Futures contracts are regulated at the federal level in most countries, but not always by the same agency that regulates the stock market.

Question 17

Legal/Contract Risk

Answer 17

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.

Derivative transactions often are arranged by a dealer acting as a principal. The legal system has upheld many claims against dealers.

Question 18

Tax Risk

Answer 18

Tax risk arises because of the uncertainty associated with tax laws. Tax law covering the ownership and transaction of financial instruments can be extremely complex, and the taxation of derivatives transactions is an area of even more confusion and uncertainty. Tax rulings clarify these matters on occasion, but on other occasions, they confuse them further.

We noted, in discussing regulatory risk, that equivalent combinations of financial instruments are not always regulated the same way. Likewise, equivalent combinations of financial instruments are not always subject to identical tax treatment. This fact creates a tremendous burden of inconsistency and confusion, but on occasion the opportunity arises for arbitrage gains, although the tax authorities often quickly close such opportunities.

Question 19

Accounting Risk

Answer 19

Accounting risk arises from uncertainty about how a transaction should be recorded and the potential for accounting rules and regulations to change.

• The law demands accurate accounting statements, and inaccurate financial reporting can subject corporations and their principals to civil and criminal litigation for fraud. In addition, the market punishes companies that do not provide accurate accounting statements.
• 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.

Question 20

Sovereign and Political Risks

Answer 20

• Sovereign risk is a form of credit risk in which the borrower is the government of a sovereign nation. Like other forms of credit risk, it has a current and a potential component, and like other forms, its magnitude has two components: the likelihood of default and the estimated recovery rate.
• Political risk is associated with changes in the political environment. Political risk can take many forms, both overt (e.g., the replacement of a pro-capitalist regime with one less so) and subtle (e.g., the potential impact of a change in party control in a developed nation), and it exists in every jurisdiction where financial instruments trade.

Question 21

Other Risks

Answer 21

Other Risks:

• ESG risk
• Performance netting risk
• Settlement netting risk

Question 22

Risk management is best addressed?

1. daily
2. quarterly
3. monthly

Answer 22

Risk management is a continuous process; therefore addressing it more frequently is better.

Question 23

ESG risk

Answer 23

ESG risk is the risk to a company’s market valuation resulting from environmental, social, and governance factors. Environmental risk is created by the operational decisions made by the company managers, including decisions concerning the products and services to offer and the processes to use in producing those products and services. Environmental damage may lead to a variety of negative financial and other consequences. Social risk derives from the company’s various policies and practices regarding human resources, contractual arrangements, and the workplace. Liability from discriminatory workplace policies and the disruption of business resulting from labor strikes are examples of this type of risk. Flaws in corporate governance policies and procedures increase governance risk, with direct and material effects on a company’s value in the marketplace.

Question 24

Performance netting risk

Answer 24

Performance netting risk, which applies to entities that fund more than one strategy, is the 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.

Consider a hedge fund that charges a 20 percent incentive fee of any positive returns and funds two strategies equally, each managed by independent portfolio managers (call them Portfolio Managers A and B). The hedge fund pays Portfolio Managers A and B 10 percent of any gains they achieve. Now assume that in a given year, Portfolio Manager A makes $10 million and Portfolio Manager B loses the same amount. The net incentive fee to the hedge fund is zero because it has generated zero returns. Unless otherwise negotiated, however (and such clauses are rare), the hedge fund remains obligated to pay Portfolio Manager A $1 million. As a result, the hedge fund company has incurred a loss, despite breaking even overall in terms of returns.

Performance netting risk applies not just to hedge funds but also to banks’ and broker/dealers’ trading desks, commodity trading advisors, and indeed, to any environment in which individuals have asymmetric incentive fee arrangements but the entity or unit responsible for paying the fees is compensated on the basis of net results.

Question 25

Settlement netting risk

Answer 25

Distinct from performance netting risk, settlement netting risk (or simply netting risk) refers to the risk that a liquidator of a counterparty in default could challenge a netting arrangement so that profitable transactions are realized for the benefit of creditors. Such risk is mitigated by netting agreements that can survive legal challenge.

! It refers specifically to the liquidator of a counterparty in default changing the terms of expected netting agreements, such that the non-defaulting party now has to make payments (a payment that was expected to have been netted and therefore reduced) to the defaulting party.

Question 26

Volatility as a measure of risk

Answer 26

Over the years, financial theorists have created a simple and finite set of statistical tools to describe market risk. The most widely used and arguably the most important of these is the standard deviation of price outcomes associated with an underlying asset. We usually refer to this measure as the asset’s volatility, typically represented by the Greek letter sigma (σ). Volatility is often an adequate description of portfolio risk, particularly for those portfolios composed of instruments with linear payoffs.

Question 27

Primary sources of risk

Answer 27

• Let us consider measures of 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.
• For options, two other major factors determine price: volatility and time to expiration, both first-order or primary effects. 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.
• 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. 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.

Question 28

Second-order sources of risk

Answer 28

Second-order measures of risk 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.

Question 29

Value at Risk

Answer 29

• 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.
• 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.
• It measures a minimum loss
• VaR is associated with a given probability. Say the VaR is €10,000,000 at a probability of 5 percent for a given time period. All else equal, if we lower the probability from 5 percent to 1 percent, the VaR will be larger in magnitude because we now are referring to a loss that we expect to be exceeded with only a 1 percent probability.
• VaR has a time element and that as such, VaRs cannot be compared directly unless they share the same time interval. There is a big difference among potential losses that are incurred daily, weekly, monthly, quarterly, or annually. 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.
• The VaR for a portfolio is $1.5 million for one day with a probability of 0.05. Recall what this statement says: There is a 5 percent chance that the portfolio will lose at least $1.5 million in a single day. The emphasis here should be on the fact that the $1.5 million loss is a minimum. With due care, it is also possible to describe VaR as a maximum: The probability is 95 percent that the portfolio will lose no more than $1.5 million in a single day. We see this equivalent perspective in the common practice of stating VaR using a confidence level: For the example just given, we would say that with 95 percent confidence (or for a 95 percent confidence level), the VaR for a portfolio is $1.5 million for one day.
• Three standardized methods for estimating VaR: the analytical or variance–covariance method, the historical method, and the Monte Carlo simulation method.

Question 30

Inherent limitations to VaR

Answer 30

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.

VaR is most effective in estimating risk exposures in markets in which there are no sudden fundamental changes or shifts in market conditions.

Question 31

The Analytical or Variance–Covariance Method

Answer 31

• The analytical or variance–covariance method begins with the assumption that portfolio returns are normally distributed.
• To calculate a 5 percent 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.
• For a 1 percent VaR, we would move 2.33 standard deviations in the direction of lower returns.
• 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. 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 $100,000(250)^0.5=$1,581,139 . 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.

Question 32

Number of traiding days in a year? Number of weeks in a year?

Answer 32

Number of days in a year = 250

Number of weeks in a year = 52

Question 33

Pros and cons of the Analytical or Variance–Covariance Method

Answer 33

• The analytical or variance–covariance method’s primary advantage is its simplicity. Its primary disadvantage is its reliance on several simplifying assumptions, including the normality of return distributions.
• 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.
• In addition, 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.
• A related problem that surfaces with the analytical or variance–covariance method is that the normal distribution assumption is inappropriate for portfolios that contain options. The return distributions of options portfolios are often far from normal.
• Therefore, when portfolios contain options, the assumption of a normal distribution to estimate VaR presents a significant problem. One common solution is to estimate the option’s price sensitivity using its delta. Recall that delta expresses a linear relationship between an option’s price and the underlying’s 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. As such, the 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.

Question 34

The Historical Method

Answer 34

• Using historical VaR, we 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.
• With the historical method, however, we are not constrained to using the normal distribution.
• The historical method is also sometimes called the historical simulation 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. In this context, note that a portfolio that an investor might have held in the past might not be the same as the one that investor will have in the future. When using the historical method, one must always keep in mind that the purpose of the exercise is to apply historical price changes to the current portfolio.
• The historical method has the advantage of being nonparametric (i.e., involving minimal probability-distribution assumptions), enabling the user to avoid any assumptions about the type of probability distribution that generates returns. The disadvantage, however, is that this method relies completely on events of the past, and whatever distribution prevailed in the past might not hold in the future.

Question 35

The Monte Carlo Simulation Method

Answer 35

• 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 percent (or 1 percent, if preferred) of return outcomes occur. We then apply this figure to the portfolio value to obtain VaR.
• One advantage of Monte Carlo simulation is that it does not require a normal distribution

Question 36

What is a potential common weakness in the historical and Monte Carlo Simulation approach to VAR estimation?

Answer 36

Both are based on data that may not accurately represent future results.

Both historical and Monte Carlo are similiar in that they are based on selecting from a set of possible outcomes.

Historical uses history for the set and Monte Carlo uses a computer model to simulate possible results (essentially a simulated history). The historical method uses actual returns for the position in question.

• An advantage of the historical method is not having to assume any particular distribution.
• A disadvantage is that it assumes past performance is representative of what can occur in the future, which may not be the case.

The Monte Carlo simulation method for calculation VAR usually involves generating random numbers with a computer. The generated numbers represent possible returns of the asset or portfolio.

• An advantage is that Monte Carlo simulation does not require the normality assumption and can accomodate the required complex relationships.
• A disadvantage is the requirement for many managerial assumptions and a great deal of computer time and calculations.

The historical method and Monte Carlo Simulation both suffer from modeling risk.

Question 37

Surplus at Risk

Answer 37

• The difference between the value of the pension fund’s assets and liabilities is referred to as the surplus, and it is this value that pension fund managers seek to enhance and protect. If this surplus falls into negative territory, the plan sponsor must contribute funds to make up the deficit over a period of time that is specified as part of the fund’s plan.
• In order to reflect this set of realities in their risk estimations, 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.

Question 38

The Advantages and Limitations of VaR

Answer 38

VAR has widely documented imperfections:

• VaR can be difficult to estimate, and different estimation methods can give quite different values.
• VaR can also lull one into a false sense of security by giving the impression that the risk is properly measured and under control.
• VaR often underestimates the magnitude and frequency of the worst returns, although this problem often derives from erroneous assumptions and models.
• VaR for individual positions does not generally aggregate in a simple way to portfolio VaR.
• VaR fails to incorporate positive results into its risk profile, and as such, it arguably provides an incomplete picture of overall exposures.

Users of VaR should routinely test their system to determine whether their VaR estimates prove accurate in predicting the results experienced over time. This process of comparing the number of violations of VaR thresholds with the figure implied by the user-selected probability level is part of a process known as backtesting. It is extremely important to go through this exercise, ideally across multiple time intervals, to ensure that the VaR estimation method adopted is reasonably accurate.

Advantages of VAR:

• VaR is one acceptable method of reporting that information.
• Another advantage of VaR is its versatility. Many companies use VaR as a measure of their capital at risk. They will estimate the VaR associated with a particular activity, such as a line of business, an individual asset manager, a subsidiary, or a division. Then, they evaluate performance, taking into account the VaR associated with this risky activity. In some cases, companies allocate capital based on VaR. For example, a pension fund might determine its overall acceptable VaR and then inform each asset class manager that it can operate subject to its VaR not exceeding a certain amount. The manager’s goal is to earn the highest return possible given its VaR allocation. This activity is known as risk budgeting
• If a risk manager uses VaR with full awareness of its limitations, he should definitely gain useful information about risk. Even if VaR gives an incorrect measure of the loss potential, the risk manager can take this risk measurement error into account when making the key overall decisions—provided, of course, that the magnitude of the error can be measured and adjusted for with some level of precision, e.g., through backtesting a VaR method against historical data. No risk measure can precisely predict future losses. It is important to ensure that the inputs to the VaR calculation are as reliable as possible and relevant to the current investment mix.

Question 39

Extensions and Supplements to VaR

Answer 39

• 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.
• Some variations of VaR are cash flow at risk (CFAR) and earnings at risk (EAR). CFAR and EAR measure the risk to a company’s cash flow or earning, respectively, instead of its market value as in the case of VaR. 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.
• Another useful tool to supplement VaR is the tail value at risk (TVaR), also known as the conditional tail expectation. 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.

Question 40

Stress Testing

Answer 40

Managers often use stress testing (a term borrowed from engineering) 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. Clearly, different scenarios will have attached probabilities of occurring that vary from the highly likely to the almost totally improbable. It is, therefore, the natural complement to VaR analysis. Two broad approaches exist in stress testing: scenario analysis and stressing models.

Question 41

What is the best way to resolve the differences between the stress testing approach to computing capital requirements and the VAR approach?

Answer 41

Where the stress testing approach is weak, the VAR approach is strong and vice versa. A possible way to the two approaches would be to compute the capital requirements using each method and then use the larger of the two values.This ensures that the capital requirements meet the needs of both approaches.

Question 42

Scenario Analysis

Answer 42

• Scenario analysis is the 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. These movements might range from fairly modest changes to quite extreme shifts. Many practitioners use standard sets of stylized scenarios to highlight potentially risky outcomes for the portfolio.
• 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.
• Another approach to scenario analysis involves using actual extreme events that have occurred in the past. 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.
• We might also create scenarios based on hypothetical events—events that have never happened in the markets or market outcomes to which we attach a small probability.

Question 43

Stressing Models

Answer 43

• 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.
• 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.
• 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.
• Other approaches include maximum loss optimization—in which we would try to optimize mathematically the risk variable that will produce the maximum loss—and worst-case scenario analysis—in which we can examine the worst case that we actually expect to occur.

Question 44

Measuring Credit Risk

Answer 44

• We must assess first the risk associated with immediate credit events and second the risk associated with events that may happen later. With respect to credit, the risk of events happening in the immediate future is called current credit risk (or, alternatively, jump-to-default risk); it relates to the risk that amounts due at the present time will not be paid. For example, some risk exists that the counterparty could default on an interest or swap payment due immediately. Assuming, however, that the counterparty is solvent and that it will make the current payment with certainty, the risk remains that the entity will default at a later date. This risk is called potential credit risk, and it can differ quite significantly from current credit risk; the relationship between the two is a complex one.
• 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 (this is known as a cross-default provision). Creditors stipulate this condition as one means of controlling credit exposure; in particular, it allows them to act quickly to mitigate losses to counterparties unable to meet any of their obligations. For example, suppose Party A owes Party B, but no payments are due for some time. Party A, however, currently owes a payment to Party C and is unable to pay. A is, therefore, in default to Party C. Depending on what actions C takes, A may be forced into bankruptcy. If so, then B’s claim simply goes into the pool of other claims on A. In that case, A has technically defaulted to B without actually having a payment due.
• 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. A company might, for example, quote a credit VaR of €10 million for one year at a probability of 0.05 (or a confidence level of 95 percent). In other words, the company has a 5 percent chance of incurring default-related losses of at least €10 million in one year. Note that credit VaR cannot be separated from market VaR because 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 percent upper tail of the market risk distribution is €5 million. The credit VaR can be roughly thought of as €5 million, but this thinking assumes that the probability of loss is 100 percent and the net amount recovered in the event of a loss is zero.
• Credit risk is less easily aggregated than market risk; the correlations between the credit risks of counterparties must be considered.

Question 45

Option-Pricing Theory and Credit Risk

Answer 45

• The stock of a company with leverage can be viewed as a call option on its assets. This approach will lead to the result that a bond with credit risk can be viewed as a default-free bond plus an implicit short put option written by the bondholders for the stockholders.
• The stock of a company with a single zero-coupon bond issue is a call option on the assets.
• The bondholders’ claim, which is subject to default, can thus be viewed as a default-free bond and a short put on the assets. In other words, the bondholders have implicitly written the stockholders a put on the assets. From the stockholders’ perspective, this put is their right to fully discharge their liability by turning over the assets to the bondholders, even though those assets could be worth less than the bondholders’ claim. In legal terminology, this put option is called the stockholders’ right of limited liability.

Question 46

The Credit Risk of Forward Contracts

Answer 46

• Prior to expiration, no current credit risk exists, because no current payments are owed, but there is potential credit risk in connection with the payments to be made at expiration.
• The market value at a given time reflects the potential credit risk. This is another reason why the calculation of market value is important: It indicates the amount of a claim that would be subject to loss in the event of a default.

Question 47

The Credit Risk of Swaps

Answer 47

The credit risk of swaps can vary greatly across product types within this asset class and over a given swap’s lifetime.

For interest rate and 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, typically we would assume that the credit risk is small because, presumably, the involved counterparties have performed sufficient current credit analysis on one another to be comfortable with the arrangement or otherwise they would not engage in the transaction. At the end of the life of the swap, the credit risk is diminished because most of the underlying risk has been amortized through the periodic payment process. There are fewer payments at the end of a swap than at any other time during its life; hence, the amount a party can lose because of a default is smaller. This leaves the greatest exposure during the middle period, a point at which

1) the credit profile of the counterparties may have changed for the worse and
2) the magnitude and frequency of expected payments between counterparties remain material.

One exception to this pattern involves currency swaps, which often provide for the payment of the notional principal at the beginning and at the end of the life of the transaction. 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, whereas interest rate swaps have their greatest credit risk midway during the life of the swap, currency swaps have their greatest credit risk between the midpoint and the end of the life of the swap.

Question 48

The Credit Risk of Options

Answer 48

• Forward contracts and swaps have bilateral default risk. Although only one party will end up making a given payment, each party could potentially be the party owing the net amount. Options, on the other hand, have unilateral credit risk. The buyer of an option pays a cash premium at the start and owes nothing more unless, under the buyer’s sole discretion, he decides to exercise the option. Once the premium is paid, the seller assumes no credit risk from the buyer. Instead, credit risk accrues entirely to the buyer and can be quite significant.
• 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.
• Derivatives’ credit risk can be quite substantial, but this risk is considerably less than that faced by most lenders. With the exception of currency swaps, the notional principal is never exchanged in a swap. Even with currency swaps, however, 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 notional principal and to the credit risk on a bond or loan of equivalent principal.

Question 49

Liquidity Risk

Answer 49

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 or lower volatility. This dynamic is counterintuitive, because we would expect instruments that are illiquid to have a higher bid–ask spread and higher volatilities.

Question 50

Measuring Nonfinancial Risks

Answer 50

Nonfinancial risks are intrinsically very difficult to measure.

Question 51

Managing Market Risk

Answer 51

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. As we noted at the beginning of this reading, companies are in business to take risk and taking too little risk will more than likely reduce the possible rewards; it could even make the company vulnerable to takeover. In a more extreme scenario, insufficient risk-taking may lead to situations in which the expected return stands little chance of covering variable (let alone fixed) costs.

Question 52

Risk Budgeting

Answer 52

• Risk budgeting: It focuses on questions such as, “Where do we want to take risk?” and “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.
• To take an organizational perspective first, 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. As an example, the foreign exchange (FX) trading desk of a bank could be allocated capital of €100 million and permitted a daily VaR of €5 million. In other words, the desk is granted a budget, expressed in terms of allocated capital and an acceptable level of risk, expressed in euro amounts of VaR.
• The point about risk budgeting is that it is a comprehensive methodology that empowers management to allocate capital and risk in an optimal way to the most profitable areas of a business, taking account of the correlation of returns in those business areas.

Question 53

Managing Credit Risk

Answer 53

Credit risk is not easily analyzed or controlled using such measures as standard deviation and VaR. Creditors need to regularly monitor the financial condition of borrowers and counterparties.

1. Reducing Credit Risk by Limiting Exposure

Limiting the amount of exposure to a given party is the primary means of managing credit risk. Just as a bank will not lend too much money to one entity, neither will a party engage in too many derivatives transactions with one counterparty.

2. Reducing Credit Risk by Marking to Market

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: Some OTC contracts are marked to market periodically during their lives.

OTC options usually are not marked to market because their value is always positive to one side of the transaction. Option credit risk is normally handled by collateral.

3. Reducing Credit Risk with Collateral

4. Reducing Credit Risk with Netting

Payment netting, reduces the credit risk by reducing the amount of money that must be paid.

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. 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.

5. Reducing Credit Risk with Minimum Credit Standards and Enhanced Derivative Product Companies

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. 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. Transferring Credit Risk with Credit Derivatives

Credit derivatives include such contracts as credit default swaps, total return swaps, credit spread options, and credit spread forwards. These transactions are typically customized, although the wording of contract provisions is often standardized. 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. 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. 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); by contrast, a credit spread forward is a forward contract on a yield spread. 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.

Question 54

Sharpe Ratio

Answer 54

The seminal measure for risk-adjusted return, the Sharpe ratio has become the industry standard. The traditional definition of this measure is as follows:

Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return

The Sharpe ratio calculation is the most widely used method for calculating risk-adjusted return. Nevertheless, it can be inaccurate when applied to portfolios with significant nonlinear risks, such as options positions. In part for these reasons, alternative risk-adjusted return methodologies have emerged over the years.

Question 55

Risk-Adjusted Return on Capital (RAROC)

Answer 55

This concept divides the expected return on an investment by a measure of 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.

Question 56

Return over Maximum Drawdown (RoMAD)

Answer 56

• 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—particularly as associated track records become longer—for investors who believe that observed loss patterns over longer periods of time are the best available proxy for actual exposure.
• 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 percent and Y = 15 percent (RoMAD = 1.5) would be more attractive than an investment with X = 40 percent and Y = 10 percent (RoMAD = 0.25).

Question 57

Sortino Ratio

Answer 57

One school of thought concerning the measurement of risk-adjusted returns argues, with some justification, that 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). 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

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 of whether 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.

Question 58

Capital Allocation

Answer 58

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:

1. Nominal, Notional, or Monetary Position Limits Under this approach, 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. It has the advantage of being easy to understand, and, in addition, it lends itself very nicely to the critical task of calculating a percentage-based return on capital allocated. Such limits, however, may not capture effectively the effects of correlation and offsetting risks. Furthermore, an individual may be able to work around a nominal position using other assets that can replicate a given position. For these reasons, although it is often useful to establish notional position limits, it is seldom a sufficient capital allocation method from a risk control perspective.
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. This approach has a number of distinct advantages, most notably the fact that it allocates capital in units of estimated exposure and thus acts in greater harmony with the risk control process. This approach has potential problems as well, however. Most notably, the limit regime will be only as effective as the VaR calculation itself; when VaR is cumbersome, less than completely accurate, not well understood by traders, or some combination of the above, it is difficult to imagine it providing rational results from a capital allocation perspective. In addition, the relation between overall VaR and the VaRs of individual positions is complex and can be counterintuitive.56 Nevertheless, VaR limits probably have an important place in any effective capital allocation scheme.
3. Maximum Loss Limits Irrespective of other types of limit regimes that it might have in place, 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.
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. 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. If the company can assume a normal return distribution, the 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). 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.
5. Regulatory Capital Requirements 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.

Question 59

Comparability of VAR in measuring performance

Answer 59

VAR measures risk comparably across asset classes. The result is that with VAR the risk of a bond portfolio can be compared against the risk of an equity portfolio.

There is no need in normal distributions of volatility! Embedded options can be included in the portfolio.

On the other hand, VAR is relatively incomparible across managers due to its inherent model risk. For example, two people can be given an assignment to compute the VAR for the same underlying asset and the result will likely be different due to the use of different methodologies and model assumptions.

Question 60

As a risk measurement, VAR may be superior to standard deviation because

Answer 60

VAR, which measures downside risk, may capture market participant`s attitudes towards risk more completely

Question 61

Which of the following risk measures does not assume a normal distribution of returns?

Sortino ratio, Standard deviation, RoMAD

Answer 61

The RoMAD (return over maximum drawdown) is the average return divided by the maximum drawdown. Drawdown refers to the percentage difference between the highest and the lowest portfolio values during a period. This measure does not make the assumption of normality in the returns.

Question 62

What is not an appropriate application of VAR for portfolio manager?

Answer 62

Peer group evaluation

VAR is useful to compare performance of different business units with different asset classes and risk characteristics because VAR is interpreted the same regardless of the assets in question. VAR can be used in risk budgeting units and the goal is to maximize return for the allocated VAR. Comparing managers based on return for a given level of risk utilizes the Sharpe ratio and not VAR.

Question 63

Beta Portfolio Managers (Beta) has a variety of bonds in thier portfolio of differing durations, call features, and coupons. Beta is worried about the impact on the firm’s bond portfolio from simultaneous changes in interest rates, the shape of the yield curve, and interest rate volatilities. Wich form of stress testig is Beta most likely to utilize?

Answer 63

In stylized scenarios, one or more risk factors are changed to measure their impact on the portfolio.

Question 64

What is the best way to deal with temporary problems according to risk management?

Answer 64

In most cases, when there is a risk management problem that is viewed temporary, the best course of action is often take no action at all.

Question 65

The final step in the implementation phase of risk management process is?

Answer 65

• Identify and price the appropriate tools for achieving the objectives

After setting goals and assessing the current level of risk, the firm needs to see if the goals can be achieved cost-effectively.

There is no “waiting” in risk management because it is an ongoing procedure. The Monte Carlo simulation may be involved in risk management, but it is certainly not the final step.