Reading 25 Risk Management Flashcards
Scenario Analysis
- 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.
The Credit Risk of Swaps
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.
Risk management is…
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.
Risk Budgeting
- 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.
Liquidity risk
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.
Effective risk governance:
- trading function vs. risk management function?
- back office vs. the front office?
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.
Risk governance, governance structure, ERM
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.
Surplus at Risk
- 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.
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. 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.
Is it possible to operate a successful business or investment program without taking risks?
What exactlty kind of risks the companies should hedge?
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.
If σ is an annual standard deviation and r is annual return, what are monthly standard deviation and return?
σ/(12)0,5
r/12
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?
In stylized scenarios, one or more risk factors are changed to measure their impact on the portfolio.
Legal/Contract Risk
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.
Tax Risk
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.
What is a potential common weakness in the historical and Monte Carlo Simulation approach to VAR estimation?
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.
Other Risks
Other Risks:
- ESG risk
- Performance netting risk
- Settlement netting risk
Capital Allocation
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:
- 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.
- 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.
- 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.
- 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.
- 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.
Which of the following risk measures does not assume a normal distribution of returns?
Sortino ratio, Standard deviation, RoMAD
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.
Settlement (Herstatt) Risk
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.
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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.
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Sortino Ratio
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.
The Advantages and Limitations of VaR
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.
As a risk measurement, VAR may be superior to standard deviation because
VAR, which measures downside risk, may capture market participant`s attitudes towards risk more completely
Risk-Adjusted Return on Capital (RAROC)
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.
Regulatory Risk
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.
Primary sources of risk
- 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.
The Credit Risk of Forward Contracts
- 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.
The source of risk?
Option-Pricing Theory and Credit Risk
- 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.
