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LO 69.4: Describe risk monitoring and its role in an internal control environment.
Within an entitys internal control environment, risk monitoring attempts to seek and investigate any significant variances from budget. This is to ensure, for example, that there are no threats to meeting its ROE and RORC targets. Risk monitoring is useful in that it should detect and address any significant variances in a timely manner.

LO 69.3: Describe risk budgeting and the role of quantitative methods in risk budgeting.
The risk budget quantifies the risk plan. There needs to be a structured budgeting process to allocate risk capital to meet the entitys objectives and minimize deviations from the plan. Each specific allocation from the risk budget comes with a reasonable return expectation. The return expectation comes with an estimate of variability around that expectation.
With risk budgets, an amount of VaR could be calculated for each item on the income statement. This allows RORC to be calculated individually and in aggregate.
Quantitative methods (i.e., mathematical modeling) may be used in risk budgeting as follows: 1. Set the minimum acceptable levels of RORC and ROE over various time periods. This is to determine if there is sufficient compensation for the risks taken (i.e., risk-adjusted profitability).
2 . Apply mean-variance optimization (or other quantitative methods) to determine the
weights for each asset class.
3. Simulate the portfolio performance based on the weights and for several time periods.
Apply sensitivity analysis to the performance by considering changes in estimates of returns and covariances.
Ris k M o n it o r in g

LO 69.2: Describe risk planning, including its objectives, effects, and the participants in its development.
There are five risk planning objectives for any entity to consider. 1. Setting expected return and expected volatility goals.
Examples of an entitys goals could include specifying the acceptable amounts of VaR and tracking error for a given period of time. Scenario analysis could be employed to determine potential sources of failure in the plan as well as ways to respond should those sources occur.
2. Defining quantitative measures of success or failure.
Specific guidelines should be stated. For example, one could state an acceptable level of return on equity (ROE) or return on risk capital (RORC). This would help regulatory agencies assess the entitys success or failure from a risk management perspective.
3. Generalizing how risk capital will be utilized to meet the entitys objectives.
Objectives relating to return per unit of risk capital need to be defined. For example, the minimum acceptable RORC should be defined for each activity where risk is allocated from the budget. The correlations between the RORCs should also be considered within an entity-wide risk diversification context.
4. Defining the difference between events that cause ordinary damage versus serious
damage. Specific steps need to be formulated to counter any event that threatens the overall long- term existence of the entity, even if the likelihood of occurrence is remote. The choice between seeking external insurance (i.e., put options) versus self-insurance for downside portfolio risk has to be considered from a cost-benefit perspective, taking into account the potential severity of the losses.
3.
Identifying mission critical resources inside and outside the entity and discussing what should be done in case those resources are jeopardized. Examples of such resources would include key employees and financing sources. Scenario analysis should be employed to assess the impact on those resources in both good and bad times. Specifically, adverse events often occur together with other adverse (and material) events.
In general, the risk planning process frequently requires the input and approval of the entitys owners and its management team. An effective plan requires very active input from the entitys highest level of management so as to ensure risk and return issues are addressed, understood, and communicated within the entity, to key stakeholders, and to regulatory agencies.
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Ris k Bu d g e t in g

LO 69.1: Define, compare, and contrast VaR and tracking error as risk measures.
Value at risk (VaR) is defined to be the largest loss possible for a certain level of confidence over a specific period of time. For example, a firm could express its VaR as being 95% certain that they will lose a maximum of $5 million in the next ten days. Delta-normal VaR assumes a normal distribution, and its calculation reflects losses in the lower tail of the returns distribution.
Tracking error is defined as the standard deviation of excess returns. Excess return is defined as the portfolio return less the benchmark return (i.e., alpha). Assuming a normal distribution of excess returns, 95% of the outcomes will fall within the mean benchmark return plus or minus roughly two standard deviations.
VaR and tracking error are both measures of risk. An organizations objective is to maximize profits for a given level of risk taken. Too much risk taken (in comparison with budget) suggests a VaR level that is too high and a willingness to accept large losses to produce unnecessarily high returns. Too little risk taken suggests that there is not enough active management, and actual returns will fall short of budgeted returns.
VaR may be used to suggest the maximum dollar value of losses for a specific level of confidence over a specific time. From a portfolio management perspective, VaR could be determined for each asset class, and capital allocation decisions could be made amongst the asset classes depending on risk and return preferences. This will help to achieve targeted levels of dollar VaR. In contrast, tracking error may be used to determine the relative amount of discretion that can be taken by the portfolio manager (away from benchmark returns) in his or her attempts at active management.
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Ris k Pl a n n in g

LO 68.8: Describe the risk budgeting process and calculate risk budgets across asset classes and active managers.
Risk budgeting should be a top down process. The first step is to determine the total amount of risk, as measured by VaR, that the firm is willing to accept. The next step is to choose the optimal allocation of assets for that risk exposure. As an example, a firms management might set a return volatility target equal to 20%. If the firm has $100 million in assets under management and assuming the returns are normally distributed, at a 95% confidence level, this translates to:
VaR = (1.65) x (20%) x ($100 million) = $33 million
The goal will be to choose assets for the fund that keep VaR less than this value. Unless the asset classes are perfectly correlated, the sum of the VaRs of the individual assets will be greater than the actual VaR of the portfolio. Thus, the budgeting of risk across asset classes should take into account the diversification effects. Such effects can be carried down to the next level when selecting the individual assets for the different classes.
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Example: Budgeting risk across asset classes (part 1)
A manager has a portfolio with only one position: a $500 million investment in W. The manager is considering adding a $500 million position X or Y to the portfolio. The current volatility of W is 10%. The manager wants to limit portfolio VaR to $200 million at the 99% confidence level. Position X has a return volatility of 9% and a correlation with W equal to 0.7. Position Y has a return volatility of 12% and a correlation with W equal to zero. Determine which of the two proposed additions, X or Y, will keep the manager within his risk budget.
Answer:
Currently, the VaR of the portfolio with only W is:
VaR^ = (2.33)(10%)($500 million) = $116.5 million
When adding X, the return volatility of the portfolio will be:
8.76% = V (0.52)(10%)2 +(0.52)(9%)2 + (2)(0.5)(0.5)(0.7)(10%)(9%)
VaRW+X = 2.33(8.76%)($ 1,000 million) = $204 million
When adding Y, the return volatility of the portfolio will be:
7.81% = V (0.52 )(10% )2 +(0.52)(12% )2
VaRw+y = (2.33)(7.81 %)($ 1,000 million) = $182 million
Thus, Y keeps the total portfolio within the risk budget.
Example: Budgeting risk across asset classes (part 2)
In the previous example, demonstrate why focusing on the stand-alone VaR of X and Y would have led to the wrong choice. Answer:
Obviously, the VaR of X is less than that of Y.
VaRx = (2.33)(9%)($500 million) = $104.9 million
VaRy = (2.33)(12%)($500 million) = $139.8 million
The individual VaRs would have led the manager to select X over Y; however, the high correlation of X with W gives X a higher incremental VaR, which puts the portfolio of W and X over the limit. The zero correlation of W and Y makes the incremental VaR of Y much lower, and the portfolio of W with Y keeps the risk within the limit.
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The traditional method for evaluating active managers is by measuring their excess return and tracking error and using it to derive a measure known as the information ratio. Excess return is the active return minus the benchmark return. The information ratio of manager i is:
(expected excess return of the manager)
(the managers tracking error)
For a portfolio of funds, each managed by a separate manager, the top management of the entire portfolio would be interested in the portfolio information ratio:
(expected excess return of the portfolio)
(the portfolios tracking error)
If the excess returns of the managers are independent of each other, it can be shown that the optimal allocation across managers is found by allocating weights to managers according to the following formula:
IRj x (portfolios tracking error) weight of portfolio managed by manager i = ————————————— – IRP x (managers tracking error)

1

One way to use this measure is to budget portfolio tracking error. Given the IRp, the IRp and the managers tracking error, top management can calculate the respective weights to assign to each manager. The weights of the allocations to the managers do not necessarily have to sum to one. Any difference can be allocated to the benchmark itself because, by definition, IRbenchmark = 0.
Determining the precise weights will be an iterative process in that each selection of weights will give a different portfolio expected excess return and tracking error. Figure 2 illustrates a set of weights derived from the given inputs that satisfy the condition.
Figure 2: Budgeting Risk Across Active Managers
Tracking Error
Information Ratio
Manager A Manager B Benchmark Portfolio
5.0% 5.0% 0.0% 3.0%
0.70 0.50 0.00 0.82
Weights 51% 37% 12% 100%
Although we have skipped the derivation, we can see that the conditions for optimal allocation hold true:
For A: 51% =
For B: 37% =
(3%) (0.70) (5%) (0.82)
(3%) (0.50) (5%)(0.82)
The difference between 100% and the sum of the weights 51% and 37% is the 12% invested in the benchmark.
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Ke y Co n c e pt s
LO 68.1 Risk budgeting is a top-down process that involves choosing and managing exposures to risk.
LO 68.2 Compared to banks on the sell side, investors on the buy side have a longer horizon, slower turnover, and lower leverage. They have tended to use historical risk measures and focus on tracking error, benchmarking, and investment guidelines. Banks use forward- looking VaR risk measures and VaR limits. Investors seem to be using VaR more and more, but they have to adapt it to their needs.
LO 68.3 Investors are relying more on VaR because of increased globalization, complexity, and dynamics of the investment industry. They have found simply measuring risk from historical measures is no longer adequate.
LO 68.4 Hedge funds have risk characteristics that make them more similar to the sell side of the industry like the use of leverage and high turnover. In addition to that, they have other risks such as low liquidity and low transparency. Low liquidity leads to problems in measuring risk because it tends to put a downward bias on volatility and correlation measures.
LO 68.3 Absolute or asset risk refers to the total possible losses over a horizon. Relative risk is measured by excess return, which is the dollar loss relative to a benchmark. VaR measures can apply to both.
The risk from the policy mix is from the chosen portfolio weights, and active risk is from individual managers deviating from the chosen portfolio weights.
Funding risk is the risk that the value of assets will not be sufficient to cover the liabilities of the fund. It is important for pension funds. In applying VaR, a manager will add the expected increase in the surplus to the surplus and subtract the VaR of the assets from it. The difference between the expected surplus and the portfolio VaR is the shortfall associated with the VaR.
Two components of sponsor risk are cash-flow risk, which addresses variations of contributions to the fund, and economic risk, which is the variation of the earnings.
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LO 68.6 Risk monitoring is important in large firms to catch rogue traders whose activities may go undetected with simple periodic statements. It is also needed for passive portfolios because the risk characteristics of the benchmarks can change. Risk monitoring can also determine why changes in risk have occurred (e.g., individual managers exceeding their budget, different managers taking on the same exposures, or the risk characteristics of the whole market changing).
There is a trend toward using a global custodian in the risk management of investment firms. It is an easy means to the goal of centralized risk management. The custodians can combine reports on changes in positions with market data to produce forward-looking risk measures. Those that choose not to use a global custodian have done so because they feel they have tighter control over risk measures and can better incorporate VaR systems into operations.
LO 68.7 There is a trend of investment managers incorporating VaR systems into their investment management process. There is evidence that money managers are differentiating themselves with respect to their risk management systems, and those that do not use such systems are at a competitive disadvantage.
VaR techniques can help move away from the ad hoc nature and overemphasis on notionals and sensitivities that characterize the guidelines many managers now use. Such guidelines are cumbersome and ineffective in that they focus on individual positions and can be easily circumvented.
VaR is useful for the investment process. When a trader has a choice between two new positions for a portfolio, the trader can compare the marginal VaRs to make the selection. When deciding whether to increase one existing position over another, the trader can compare the excess-return-to-MVaR ratios and increase the position in the one with the higher ratio.
LO 68.8 Budgeting risk across asset classes means selecting assets whose combined VaRs are less than the total allowed. The budgeting process would examine the contribution each position makes to the portfolio VaR.
For allocating across active managers, it can be shown that the optimal allocation is achieved with the following formula:
IR: x (portfolios tracking error) weight of portfolio managed by manager i = —————————- ;———– IRp x (managers tracking error)
.
For a given group of active managers, the weights may not sum to one. The remainder of the weight can be allocated to the benchmark, which has no tracking error.
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Co n c e pt Ch e c k e r s
1.
With respect to the buy side and sell side of the investment industry:
the sell side has relied more on VaR measures.
I. the buy side uses more leverage. II. A. I only. B. II only. C. Both I and II. D. Neither I nor II.
2.
3.
Compared to policy risk, which of the following is not a reason that management risk is not much of a problem? A. There will be diversification effects across the deviations. B. Managers tend to make the same style shifts at the same time. C. For well-managed funds, it is usually fairly small for each of the individual
D. There can be diversification with the policy mix VaR to actually lower the total
funds.
portfolio VaR.
Using VaR to monitor risk is important for a large firm with many types of managers because: A. it can help catch rogue traders and it can detect changes in risk from changes in it can help catch rogue traders and it can detect changes in risk from changes in benchmark characteristics.
B. although it cannot help catch rogue traders, it can detect changes in risk from
changes in benchmark characteristics.
C. although it cannot detect changes in risk from changes in benchmark
characteristics, it can help detect rogue traders.
D. of no reason. VaR is not useful for monitoring risk in large firms.
4.
VaR can be used to compose better guidelines for investment companies by:
focusing more on overall risk.
I. relying less on notionals. II. A. I only. B. II only C. Both I and II. D. Neither I nor II.
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In making allocations across active managers, which of the following represents the formula that gives the optimal weight to allocate to a manager denoted z, where IRj and IRp are the information ratios of the manager and the total portfolio respectively?
a A.
IR P x (portfolios tracking error) —————————————- . IRi x (managers tracking error)
IRi x (managers tracking error) IRp x (portfolios tracking error)
IRi x (portfolios tracking error) IRp x (managers tracking error)
IRp x (managers tracking error) IRi x (portfolios tracking error)
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Co n c e pt Ch e c k e r An s w e r s
1. B Compared to banks on the sell side, investors on the buy side have a longer horizon,
slower turnover, and lower leverage. Banks use forward-looking VaR risk measures and VaR limits.
2. B
If managers make the same style shifts, then that would actually increase management risk. All the other reasons are valid.
3. A
4. C
5. C
Both of these are reasons large firms find VaR and risk monitoring useful.
Investment companies have been focusing on limits on notionals, which is cumbersome and has proved to be ineffective.
r
r
. IRs X (portfolios tracking error) weight or portfolio managed by manager i = —————————————- IRP x (managers tracking error) ,
,
, ,
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Ri s k M o n i t o r i n g a n d Pe r f o r m a n c e M e a s u r e m e n t
Topic 69
Ex a m Fo c u s
Most of this topic is qualitative in nature, however, it does contain several testable concepts. Many of the concepts covered here are also covered in other assigned readings, so this topic should serve as reinforcement of those concepts. For the exam, focus on the three pillars of effective risk management: planning, budgeting, and monitoring. Understand the concept of a risk management unit (RMU) and be able to discuss its appropriate role within a company. Always keep in mind while reviewing this topic that it is the amount of risk taken that ultimately drives the level of returnsrisk is the cost of returns.
Ris k M e a s u r e s

LO 68.7: Explain how VaR can be used in the investment process and the development of investment guidelines.
Investment Guidelines
VaR can help move away from the ad hoc nature and overemphasis on notionals and sensitivities that characterize the guidelines many managers now use. Clearly, ad hoc procedures will generally be inferior to formal guidelines using established principles. Also, limits on notionals and sensitivities have proven insufficient when leverage and positions in derivatives exist. The limits do not account for variations in risk nor correlations. VaR limits include all of these factors.
The problem with controlling positions and not risk is that there are many rules and restrictions, which in the end may not achieve the main goal. There is no measure of the possible losses that can occur in a given time perioda good quantity to identify in order to know how much capital to have on hand to meet liquidity needs. Furthermore, simple restrictions on certain positions can be easily evaded with the many instruments that are now available. As a wider range of products develop, obviously, the traditional and cumbersome position-by-position guidelines will become even less effective.
Investment Process
VaR can help in the first step of the investment process, which is the strategic asset- allocation decision. Since this step usually uses mean-variance analysis, as does the most basic VaR measures, VaR can help in the portfolio allocation process. Furthermore, VaR can
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measure specific changes in risk that can result as managers subjectively adjust the weights from those recommended by pure quantitative analysis.
VaR is also useful at the trading level. A trader usually focuses on the return and stand-alone risk of a proposed position. The trader may have some idea of how the risk of the position will affect the overall portfolio, but an adequate risk management system that uses VaR can give a specific estimate of the change in risk. In fact, the risk management system should stand ready to automatically calculate the marginal VaR of each existing position and proposed position. When the trader has the choice between adding one of two positions with similar return characteristics, the trader would choose the one with the lower marginal VaR. VaR methodology can help make choices between different assets too. The optimal portfolio will be the one that has the excess-return-to-marginal VaR ratios equal for all asset types, as seen in the previous topic. Thus, when a trader is searching for the next best investment, the trader will look at securities in the asset classes that currently have the higher returns-to-marginal-VaR ratios.
Bu d g e t in g Ris k

LO 68.6: Apply VaR to check compliance, monitor risk budgets, and reverse engineer sources of risk.
There are many types of risks that can increase dramatically in a large firm. For example, the rogue trader phenomenon is more likely in a large firm. This occurs when a manager of one of the accounts or funds within the larger portfolio deviates from her guidelines
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in terms of portfolio weights or even trades in unauthorized investments. Such deviations from compliance can be very short-term, and regular reporting measures may not catch the violations.
Risk management is necessary for all types of portfolioseven passively managed portfolios. Some analysts erroneously believe that passive investing, or benchmarking, does not require risk monitoring. This is not true because the risk profiles of the benchmarks change over time. In the late 1990s, a portfolio benchmarked to the S&P 500 would clearly have seen a change in risk exposures (e.g., an increase in the exposure to risks associated with the high- tech industry). A forward-looking risk measurement system would pick up on such trends.
Monitoring the risk of actively managed portfolios should help identify the reasons for changes in risk. Three explanations for dramatic changes in risk are (1) a manager taking on more risk, (2) different managers taking similar bets, and (3) more volatile markets. Thus, when there is an increase in the overall risk of a portfolio, top management would want to investigate the increase by asking the following questions.
Has the manager exceeded her risk budget? VaR procedures and risk management can allocate a risk budget to each manager. The procedures should give an indication if and why the manager exceeds the risk budget. Is it a temporary change from changes in the market? Has the manager unintentionally let the weights of the portfolio drift so as to increase risk? Or, more seriously, has the manager engaged in unauthorized trades?
Are managers taking too many of the same style bets? If the managers are acting independently, it is possible that they all start pursuing strategies with the same risk exposures. This could happen, for example, if all managers forecast lower interest rates. Bond managers would probably begin moving into long-term bonds, and equity managers would probably begin moving into stocks that pay a high and stable dividend like utility companies and REITs. This would drastically increase the interest rate risk of the overall portfolio.
Have markets become more volatile? If the risk characteristics of the entire market have changed, top management will have to decide if it is worth accepting the volatility or make decisions to reduce it by changing the target portfolio weights.
VaR can also be reverse engineered by utilizing the VaR tools outlined in the previous topic, such as component VaR and marginal VaR. These tools provide insight on how the overall portfolio will be affected by individual position changes. This method can be used provided that all relevant risks have been identified within the risk management system.
In the risk management process, there is a problem with measuring the risk of some unique asset classes like real estate, hedge funds, and venture capital. Also, there may be limited information on investments in a certain class (e.g., emerging markets and initial public offerings).
There is a trend in the investment industry toward management choosing a global custodian for the firm. Such a choice means an investor aggregates the portfolios with a single custodian, which more easily allows a consolidated picture of the total exposures of the fund. The custodian can combine reports on changes in positions with market data to produce forward-looking risk measures. Thus, the global custodian is an easy choice in pursuing centralized risk management. Along with the trend toward global custodians,
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there has been a trend in the custodian industry toward fewer custodians that can provide more services. Large custodian banks such as Citibank, Deutsche Bank, and State Street are providing risk management products.
Those that choose not to use a global custodian have done so because they feel that they have a tighter control over risk measures and can better incorporate VaR systems into operations. There are often economies of scale for larger firms in that they can spread the cost of risk management systems over a large asset base. Also, they can require tighter control when their assets are partly managed internally.
Increasingly, clients are asking money managers about their risk management systems. The clients are no longer satisfied with quarterly performance reports. Many investment managers have already incorporated VaR systems into their investment management process. Widely used risk standards for institutional investors recommend measuring the risk of the overall portfolio and measuring the risk of each instrument. It may be the case that those who do not have comprehensive risk management systems will soon be at a significant disadvantage to those who do have such systems. There also seems to be some attempt by managers to differentiate themselves with respect to risk management.
Va R Appl ic a t io n s

LO 68.5: Distinguish among the following types of risk: absolute risk, relative risk, policy-mix risk, active management risk, funding risk, and sponsor risk.
Absolute or asset risk refers to the total possible losses over a horizon. It is simply measured by the return over the horizon. Relative risk is measured by excess return, which is the dollar loss relative to a benchmark. The shortfall is measured as the difference between the fund return and that of a benchmark in dollar terms. VaR techniques can apply to tracking error (i.e., standard deviation of excess return) if the excess return is normally distributed.
Professors Note: The authors definition o f tracking error differs from the definition of tracking error in other assigned readings. Jorion defines tracking error as active return minus the benchmark return. In other readings, this value is simply the excess return and tracking error is the volatility (i.e., standard deviation) of the excess return. Throughout this topic, we have expressed excess return as portfolio return minus benchmark return and tracking error as the volatility of the excess return. This methodology follows the definition of tracking error on previous FRM exams.
Distinguishing policy mix from active risk is important when an investment firm allocates funds to different managers in various asset classes. This breaks down the risk of the total portfolio into that associated with the target policy (i.e., the weights assigned to the various funds in the policy) and the risk from the fact that managers may make decisions which lead to deviations from the designated weights. VaR analysis is especially useful here because it can show the risk exposure associated with the two types of risk and how they affect the overall risk of the entire portfolio. Often, active management risk is not much of a problem for several reasons:
For well-managed funds, it is usually fairly small for each of the individual funds.
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There will be diversification effects across the deviations. There can be diversification effects with the policy mix VaR to actually lower the total
portfolio VaR.
Fu n d in g Ris k
Funding risk refers to being able to meet the obligations of an investment company (e.g., a pensions payout to retirees). Put another way, funding risk is the risk that the value of assets will not be sufficient to cover the liabilities of the fund. The level of funding risk varies dramatically across different types of investment companies. Some have zero, while defined benefit pension plans have the highest.
The focus of this analysis is the surplus, which is the difference between the value of the assets and the liabilities, and the change in the surplus, which is the difference between the change in the assets and liabilities:
Surplus = Assets Liabilities
ASurplus = AAssets – ALiabilities
Typically, in managing funding risk, an analyst will transform the nominal return on the surplus into a return on the assets, and break down the return as indicated:
R surplus
ASurplus Assets
AAssets Assets
f ALiabilities) Liabilities ^ _ D , Liabilities , , Assets
,
asset
D . .
liabilities
Liabilities , Assets
,
Evaluating this expression requires assumptions about the liabilities, which are in the future and uncertain. For pension funds, liabilities represent accumulated benefit obligations, which are the present value of pension benefits owed to the employees and other beneficiaries. Determining the present value requires a discount rate, which is usually tied to some current level of interest rates in the market. An ironic aspect of funding risk is that assets for meeting the obligations like equities and bonds usually increase in value when interest rates decline, but the present value of future obligations may increase even more. When assets and liabilities change by different amounts, this affects the surplus, and the resulting volatility of the surplus is a source of risk. If the surplus turns negative, additional contributions will be required. This is called surplus at risk (SaR).
One answer to this problem is to immunize the portfolio by making the duration of the assets equal that of the liabilities. This may not be possible since the necessary investments may not be available, and it may not be desirable because it may mean choosing assets with a lower return.
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Example: Determining a funds risk profile
The XYZ Retirement Fund has $200 million in assets and $180 million in liabilities. Assume that the expected return on the surplus, scaled by assets, is 4%. This means the surplus is expected to grow by $8 million over the first year. The volatility of the surplus is 10%. Using a Z-score of 1.65, compute VaR and the associated deficit that would occur with the loss associated with the VaR.
Answer:
First, we calculate the expected value of the surplus. The current surplus is $20 million (= $200 million – $180 million). It is expected to grow another $8 million to a value of $28 million. As for the VaR:
VaR= (1.65)(10%)($200 million) = $33 million
If this decline in value occurs, the deficit would be the difference between the VaR and the expected surplus value: $33 million – $28 million = $5 million.
Professors Note: According to the assigned reading, the surplus at risk (SaR) is the VaR amount calculated previously. Note that SaR on previous exams has been approached differently, as illustrated in the following example. Be prepared for either approach on the actual exam. In the example to follow, we will illustrate how to calculate the volatility o f surplus growth. On previous FRM exams, this value has not been provided.
Example: Surplus at risk (via computing volatility of surplus)
The XYZ Retirement Fund has $200 million in assets and $180 million in liabilities. Assume that the expected annual return on the assets is 4% and the expected annual growth of the liabilities is 3%. Also assume that the volatility of the asset return is 10% and the volatility of the liability growth is 7%. Compute 95% surplus at risk assuming the correlation between asset return and liability growth is 0.4.
Answer:
First, compute the expected surplus growth:
200 x (0.04) – 180 x (0.03) = $2.6 million
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Next, compute the volatility of the surplus growth. To compute the volatility you need to recall one of the properties of covariance discussed in the FRM Part I curriculum. The variance of assets minus liabilities [i.e., Var(A-L)] = Var(A) + Var(L) – 2 x Cov(A,L). Where covariance is equal to the standard deviation of assets times the standard deviation of liabilities times the correlation between the two. The asset and liability amounts will also need to be applied to this formula.
Variance(A-L) = 2002 x 0.102 + 1802 x 0.072- 2 x 200 x 180 x 0.10 x 0.07 x 0.4
= 400+ 158.76-201.6 = $357.16 million
Standard deviation = V357.16 = $18.89
Thus, SaR can be calculated by incorporating the expected surplus growth and standard deviation of the growth.
95% SaR = 2.6 – 1.65 x 18.89 = $28.57 million
Professors Note: Like VaR, SaR is a negative value since it is the surplus amount that is at risk. As a result, the negative sign is usually not presented since a negative amount is implied.
Pl a n Sp o n s o r Ris k
The plan sponsor risk is an extension of surplus risk and how it relates to those who ultimately bear responsibility for the pension fund. We can distinguish between the following risk measures: Economic risk is the variation in the total economic earnings of the plan sponsor. This
takes into account how the risks of the various components relate to each other (e.g., the correlation between the surplus and operating profits).
Cash-flow risk is the variation of contributions to the fund. Being able to absorb
fluctuations in cash flow allows for a more volatile risk profile.
Ultimately, from the viewpoint of the sponsor, the focus should be on the variation of the economic value of the firm. The management should integrate the various risks associated with the movement of the assets and surplus with the overall financial goals of the sponsor. This is aligned with the current emphasis on enterprise-wide risk management.
M o n it o r in g Ris k W it h VaR

LO 68.4: Describe the risk management challenges associated with investments in hedge funds.
Hedge funds are a very heterogeneous class of assets that include a variety of trading strategies. Since they often use leverage and trade a great deal, their risk characteristics may be more similar to the sell side of the industry. Hedge funds have some other risks like liquidity and low transparency. Liquidity risk has many facets. First, there is the obvious potential loss from having to liquidate too quickly. Second, there is the difficulty of measuring the exact value of the fund to be able to ascertain its risk. Furthermore, the low liquidity tends to lower the volatility of historical prices as well as the correlations of the positions. These properties will lead to an underestimation of traditional measures of risk. In addition to these risks, there is the low level of transparency. This makes the risk measurement difficult with respect to both the size and type. Not knowing the type of risk increases the difficulty of risk management for the entire portfolio in which an investor might include hedge funds.
Ab s o l u t e v s . Re l a t iv e Ris k a n d P o l ic y M ix v s . Ac t iv e Ris k

LO 68.3: Describe the investment process of large investors such as pension funds.
‘The first step in the investment process is to determine the long-term, strategic asset allocations. Usually, the goal of the first step is to balance returns and risks using methods like mean-variance portfolio optimization. This step determines the allocations to asset classes such as domestic and foreign stocks, domestic and foreign bonds, and alternative investments such as real estate, venture capital, and hedge funds. Making this allocation relies on passive indices and other benchmarks to help measure the properties of the investment, and the availability of passive indices helps make the allocations feasible.
The second step in the investment process is to choose the managers who may either passively manage the fund (i.e., simply track the benchmarks) or actively manage the fund in an effort to outperform the benchmarks. The investors should review the managers activities and performance periodically. Their activities should conform to a list of guidelines, which includes the types of investments and risk exposure restrictions such as beta and duration. Managers performance can be evaluated by analyzing their tracking error.
VaR risk management systems are beginning to become more important because of the globalization of available investments and the increased complexity of investments. Also, investment companies are becoming more dynamic, which makes it more difficult to assess risk. With many managers, for example, each of the managers may make changes within his constraints, but the collective changes could be difficult to gauge with historical measures. In sum, because of increased globalization, complexity, and the dynamic nature of the investment industry, simply measuring risk using historical measures is no longer adequate, which has increased the need for VaR.
2018 Kaplan, Inc.
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Topic 68 Cross Reference to GARP Assigned Reading – Jorion, Chapter 17
H e d g e Fu n d Is s u e s