Temp_store

LO 48.7: Explain challenges in modeling diversification benefits, including aggregating a firms risk capital and allocating economic capital to different business lines.
The overall risk capital for a firm should be less than the total of the individual risk capitals of the underlying business units. That is because the correlation of returns between the business units is likely to be less than +1. Such risk reduction due to diversification effects over risk types and business activities is very difficult to measure in practice. Instead of using an extremely high overall confidence level for the firm, the various business units may use lower confidence levels to avoid an excessively high aggregate risk capital amount.
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For example, assume a firm is subject to only the following four types of risk (risk capital amounts are provided for each risk): Market risk = $400 Credit risk = $300 Liquidity risk = $200 Operational risk = $500 Aggregate risk capital for the firm could be as high as $1,400 assuming a perfect correlation (i.e., sum of the four risk capital amounts). Or it could be as low as $734 assuming zero correlation (square root of the sum of squares of the four risk capital amounts). In taking into account the diversification effects, the firms overall VaR should be computed as some value between $734 and $1,400, which is a very wide range. In addition, there is a lot of subjectivity involved in allocating the diversification benefits back to the business units in a fair manner especially since the allocation will impact the respective business units performance measures (i.e., reduction of risk capital required).
It makes sense that a business unit with earnings or cash flows that are highly correlated to the overall firm would need to be allocated more risk capital than a business unit with earnings or cash flows that are negatively correlated (assuming similar volatility). Having business lines that are countercyclical in nature allows the overall firm to have stable earnings and to attain a given desired credit rating using less risk capital. In practice, the easiest allocation method is a pro-rata allocation based on standalone risk capital amounts.
For example, assume the following information pertaining to a business unit that engages in only two activities, A and B: Activity A alone requires $50 of risk capital Activity B alone requires $60 of risk capital Activities A and B together require a total of $90 of risk capital Stand-alone capital looks at each activity independently and ignores any diversification benefits. Therefore, the stand-alone capital for Activities A and B are $50 and $60, respectively. The stand-alone capital for the business unit is $90. $10.9 is allocated to Activity B. Therefore, Activities A and B have fully diversified capital Fully diversified capital takes into consideration the diversification benefits, which equal $20 ($50 + $60 $90). For simplicity, the diversification benefit can be done on a pro-rata basis as follows: ($20 x $50) / $110 = $9.1 is allocated to Activity A and ($20 x $60) /$ 110 = $10.9 is allocated to Activity B. Therefore, Activities A and B have fully diversified capital of $40.9 and $48.1, respectively. Fully diversified capital should be used to determine a firms solvency and to determine the minimum amount of risk capital required for a given activity.
Marginal capital is the extra capital needed as a result of a new activity added to the business unit. Diversification benefits are fully considered. The marginal risk capital for Activity A is $30 ($90 total $60 for Activity B) and the marginal risk capital for Activity B is $40 ($90 total $50 for Activity A). Total marginal risk capital ($70) is below the full risk capital of the business unit ($90). The general method for computing marginal capital of a new activity is to start with the total risk capital required for the business unit minus all of the risk capital required for the other activities. Marginal capital is useful for making active portfolio management and business mix decisions; such decisions need to fully consider diversification benefits.
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In a performance measurement context, stand-alone risk capital is useful to determine incentive pay and fully diversified risk capital is useful to determine the incremental benefit due to diversification. In allocating the diversification benefits, caution must be taken especially since correlations between the risk factors usually change over time. In a more extreme situation such as a market crisis, correlations could move to 1 or +1, thereby reducing diversification benefits.
RAROC B e s t P r a c t
i c e s

LO 48.6: Compute the adjusted RAROC for a project to determine its viability.
RAROC should be adjusted to consider systematic risk and a consistent hurdle rate.
Adjusted RAROC = RAROC |3p (Rj^ Rp)
where: Rp = risk-free rate = hurdle rate Rm = expected return on market portfolio (3p = firms equity beta (RM Rf ) = excess return over risk-free rate to account for the nondiversifiable systematic risk of the project
Therefore, the revised business decision rules are as follows:

If adjusted RAROC > Rp, then accept the project If adjusted RAROC < Rp, then reject the project
Example: Adjusted RAROC
Suppose RAROC is 12%, the risk-free rate is 5%, the market return is 11%, and the firms equity beta is 1.5. Use ARAROC to determine whether the project should be accepted or rejected.
Answer: Adjusted RAROC RAROC (3p (R m R f ) = 0.12 -1.5(0.11 – 0.05) = 0.12 – 0.09 = 0.03
The project should be rejected because the ARAROC of 3% is less than the risk-free rate of 5%.
R i s k C a p i t a l a n d D i v e r s i f i c a t
i o n

LO 48.5: Calculate the hurdle rate and apply this rate in making business decisions using RAROC.
Similar to internal rate of return (IRR) analysis, the use of a hurdle rate (i.e., after-tax weighted average cost of equity capital) is compared to RAROC in making business decisions. In general, the hurdle rate should be revised perhaps once or twice a year or when it has moved by over 10%.
The hurdle rate, hAT is computed as follows:
hA T
(CE x R c e ) + (PE x R pe )
(CE + PE)
where: CE = market value of common equity PE = market value of preferred equity R^P = cost of common equity [could be derived from the capital asset pricing model (CAPM)] RpE = cost of preferred equity (yield on preferred shares)
Recall, that the CAPM formula is as follows:
R CE = r
f + P c e ( R m r
f )
where: Rp = risk-free rate r m = expected return on market portfolio PCE = firms common equity market beta
Once the hurdle rate and the RAROC are calculated, the following rules apply:
If RAROC > hurdle rate, there is value creation from the project and it should be accepted. If RAROC hurdle rate (accepted projects) also come with high risk that could ultimately result in losses and reduce the value of the firm. In addition, lower return projects that have a RAROC < hurdle rate (rejected projects) also come with low risk that could provide steady returns and increase the value of the firm. As a result, an adjusted RAROC measure should be computed.
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A d j u s t e d RAROC

LO 48.4: Explain challenges that arise when using RAROC for performance measurement, including choosing a time horizon, measuring default probability, and choosing a confidence level.
Time Horizon
In computing RAROC, the focus so far has been on one period (i.e., one-year time horizon) since it is convenient from a business planning cycle perspective and it represents the probable amount of time needed for a firm to recover from a significant unexpected loss. At the same time, it is possible to look at multi-period RAROC to obtain a more accurate RAROC measure for longer-term transactions and loans. One issue that arises is how much economic capital to allocate if the risk of a transaction changes dramatically in subsequent periods. For example, using an averaging method would give rise to periods of overcapitalization and periods of undercapitalization.
Risk capital could be thought of as the firms one-year VaR at a specific confidence level (e.g., 95% or 99%). For both credit risk and operational risk, no adjustments are required from one-year VaR to compute risk capital. For market risk, short time horizons such as one day (risk monitoring) or 10 days (regulatory capital) require adjustments to determine the correct one-year risk capital allocation.
One basic approach is the square root of time rule whereby one-year VaR is estimated by multiplying the one-day VaR by the square root of 252 business days in the year. This approach needs to be fine-tuned by considering that even in a worst-case scenario, the firm might only be able to reduce its risk to a core risk level to retain its status as a financially viable business for the rest of the year. Furthermore, the computation must also factor in the time needed to lower the current risk level to the core risk level (i.e., time to reduce). That amount of time corresponds to the relative liquidity (during difficult market conditions) of the firms investment positions taken. As a result, a large amount of time may be required for a reasonable liquidation of the positions.
Example: Risk capital for market risk
Assume the following information where the core risk level is below the current risk level: Daily value at risk (VaR) = 80 Core risk level = 60 Days needed to reduce current risk level to core risk level =10 (i.e., risk reduction of
2 VaR per day)
Number of business days per year = 252 Compute the required risk capital as a percentage of annualized VaR.
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Answer:
Risk capital = square root
sum of squares + core risk level squared x (number of business days per year days needed to reduce current to core) square root = square root
(802 + 782 + 762 + 742 + 722 + 702 + 682 + 662 + 642 + 622) + 602 x(252 10) ^921,940 = 960.18 square root [50,740 + (3,600 x 242)] = = ^921,940 = 960.18
Note that annualized VaR = 80 x square root of 252 = 1,269.96
Therefore, the risk capital required is approximately 75.6% of annualized VaR (960.18/ 1,269.96).
There is a lot of subjectivity in selecting the time horizon for RAROC calculation purposes. A longer time horizon could be selected to account for the full business cycle; it may not always increase the risk capital required since the confidence level required to maintain a firms solvency will fall as the time horizon is increased. A key consideration with the selection of a time horizon is the fact that risk and return data for periods over one year is likely to be of questionable reliability.
Default Probability
A point-in-time (PIT) probability of default could be used to compute short-term expected losses and to price financial instruments with credit risk exposure. A through-the-cycle (TTC) probability of default is more commonly used for computations involving economic capital, profitability, and strategic decisions.
A firms rating is more likely to change when analyzed under the PIT approach versus the TTC approach. As a result, the TTC approach results in a lower volatility of economic capital versus the PIT approach. From time to time, it is advisable to compare the result of PIT versus TTC for RAROC computations at a stable portion of the economic cycle and at the lowest portion of the cycle.
Confidence Level
In computing economic capital, the confidence level chosen must correspond with the firms desired credit rating. A high rating such as AA or AAA would require a confidence level in excess of 99.95%, for example. Choosing a lower confidence level will reduce the amount of risk capital required/allocated and it will impact the risk-adj usted performance measures. The reduction may be dramatic if the firm is primarily exposed to operational, credit, and settlement risks where large losses are rare.
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H u r d l e R a t e f o r C a p i t a l B u d g e t i n g D e c i s i o n s

LO 48.3: Compute and interpret the RAROC for a project, loan, or loan portfolio, and use RAROC to compare business unit performance.
The necessary amount of economic capital is a function of credit risk, market risk, and operational risk. The RAROC for a project or loan can be defined as risk-adjusted return divided by risk-adj usted capital. The basic RAROC equation is as follows:
RAROC=
after-tax expected risk-adj usted net income
economic capital
There is a tradeoff between risk and return per unit of capital with the numerator acting as return and the denominator acting as risk. For example, a business units RAROC needs to be greater than its cost of equity in order to create shareholder value.
Furthermore, measures such as return on equity (ROE) or return on assets (ROA) are based on accounting book values only, and therefore are unable to account for the relevant risks. RAROC has two specific adjustments to these measures. In the numerator, it deducts expected loss (the risk factor) from the return. In the denominator, it replaces accounting capital with economic capital.
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Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17 standard deviation, and (2) the net present value (NPV), which equals the discounted The underlying principles of the RAROC equation are similar to two other common measures of risk/return: (1) the Sharpe ratio, which equals: (expected return risk-free rate) / standard deviation, and (2) the net present value (NPV), which equals the discounted value of future expected after-tax cash flows. The discount rate for the NPV is a risk- adjusted expected return that uses beta (captures systematic risk only) from the capital asset pricing model (CAPM). In contrast to NPV, RAROC takes into account both systematic and unsystematic risk in its earnings figure.
A more detailed RAROC equation to use for capital budgeting decisions is as follows:
RAROC = taxes + return on economic capital d= transfers exp ected revenues cos ts exp ected losses
taxes + return on economic capital d= transfers
economic capital
Where:
Expected revenues assume no losses and costs refer to direct costs. Taxes are computed
using the firms effective tax rate and transfers include head office overhead cost allocations to the business unit as well as transactions between the business unit and the treasury group, such as borrowing and hedging costs.
Expected losses (EL) consist mainly of expected default losses (i.e., loan loss reserve),
which are captured in the numerator (i.e., higher funding cost) so there is no adjustment required in the denominator. Expected losses also arise due to market, operational, and counterparty risks.
Return on economic capital refers to the return on risk-free investments based on the
amount of allocated risk capital.
Economic capital includes both risk capital and strategic risk capital. Risk capital serves as a buffer against unexpected losses. It is the amount of funds that the firm must hold in reserve to cover a worst-case loss (an amount over the expected loss) at a specific confidence level that is usually 95% or more. Therefore, it is very similar to the annual value at risk (VaR).
Strategic risk capital pertains to the uncertainty surrounding the success and profitability of certain investments. An unsuccessful investment could result in financial losses and a negative reputational impact on the firm. Strategic risk capital includes goodwill and burned-out capital. Goodwill is the excess of the purchase price over the fair value (or replacement value) of
the net assets recorded on the balance sheet. A premium price may exist because of the existence of valuable but unrecorded intangible assets.
Burned-out capital represents the risk of amounts spent during the start-up phase of a venture that may be lost if the venture is not pursued because of low projected risk- adjusted returns. The venture may refer to a recent acquisition or an internally generated project. Burned-out capital is amortized over time as the strategic failure risk decreases. Finally, firms may allocate risk capital to any unused risk limits (e.g., undrawn amounts on a line of credit) because risk capacity could be utilized any time. If risk capacity is utilized, the firm would then have to adjust the risk capital amount.
As mentioned, economic capital is designed to provide a cushion against unexpected losses at a specified confidence level. The confidence level at which economic capital is set can be viewed as the probability that the firm will be able to absorb unexpected losses over
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a specified period. A simple example can help illustrate the concept of unexpected loss and how it is equal to the risk capital allocation. Assume for a given transaction that the expected loss is 20 basis points (bps) and the worst-case loss is 190 bps at a 95% confidence level over one year. Based on this information, the unexpected loss is 170 bps (excess of worst-case loss over expected loss). There is also still a 5% probability that the actual loss will exceed 190 bps.
Example: RAROC calculation
Assume the following information for a commercial loan portfolio: $1.5 billion principal amount
7% pre-tax expected return on loan portfolio Direct annual operating costs of $ 10 million Loan portfolio is funded by $1.5 billion of retail deposits; interest rate = 5% Expected loss on the portfolio is 0.5% of principal per annum Unexpected loss of 8% of the principal amount, or $120 million of economic capital
required) 25% effective tax rate
Assume no transfer pricing issues Compute the RAROC for this loan portfolio.
required
Risk-free rate on government securities is 1% (based on the economic capital
Answer:
First, calculate the following RAROC components:
Expected revenue = 0.07 x $1.5 billion = $105 million Interest expense = 0.05 x $1.5 billion = $75 million Expected loss = 0.005 x $1.5 billion = $7.5 million Return on economic capital = 0.01 x $120 million = $1.2 million
Then, apply the RAROC equation:
RAROC 0 5 – 1 0 – 7 5 – 7 .5 + 1.2 + O)x (1-0.25) =
120
Therefore, maintenance of the commercial loan portfolio requires an after-tax expected rate of return on equity of at least 8.56%.
Note that for capital budgeting projects, expected revenues and losses should be used in the numerator since the analysis is being performed on an ex ante (or before the fact) basis. In contrast, for performance evaluation purposes on an ex post (or after the fact) basis, realized (or actual) revenues and losses should be used.
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RAROC for Performance Measurement

LO 48.2: Describe the RAROC (risk-adjusted return on capital) methodology and its use in capital budgeting.
The risk-adjusted return on capital (RAROC) methodology provides users with information pertaining to the risk-adj usted performance of the firm and its business units as opposed to merely the raw performance numbers. In measuring economic performance, this methodology involves allocating risk capital to the firms business units and to specific transactions.
Benefits of RAROC include: 1. Performance measurement using economic profits instead of accounting profits.
Accounting profits include historical and arbitrary measures such as depreciation, which may be less relevant.
2. Use in computing increases in shareholder value as part of incentive compensation (e.g.,
scorecards) within the firm and its divisions. The flexibility of RAROC may also allow for deferred/contingent compensation or clawbacks for subsequent poor performance.
3. Use in portfolio management for buy and sell decisions and use in capital management in estimating the incremental value-added through a new investment or discontinuing an existing investment.
4. Using risk-based pricing, which will allow proper pricing that takes into account the
economic risks undertaken by a firm in a given transaction. Each transaction must consider the expected loss and the cost of economic capital allocated. Many firms use the marginal economic capital requirement portion of the RAROC equation for the purposes of pricing and determining incremental shareholder value.

LO 48.1: Define, compare, and contrast risk capital, economic capital, and regulatory capital, and explain methods and motivations for using economic capital approaches to allocate risk capital.
Risk capital provides protection against risk (i.e., unexpected losses). In other words, it can be defined as a (financial) buffer to shield a firm from the economic impact of risks taken. Should a disastrous event occur, those impacts could otherwise jeopardize the firms financial security and its ability to remain a going concern. In short, risk capital provides assurance to the firms stakeholders that their invested funds are safe. In most cases, risk capital and economic capital are treated synonymously, although an alternative definition of economic capital exists (discussed further in LO 48.3):
economic capital = risk capital + strategic risk capital
On the other hand, there are at least three distinct differences between risk capital and regulatory capital as follows: 1. Unlike risk capital, regulatory capital is relevant only for regulated industries such as
banking and insurance.
2. Regulatory capital is computed using general benchmarks that apply to the industry.
The result is a minimum required amount of capital adequacy that is usually far below the firms risk capital.
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3. Assuming that risk capital and regulatory capital are the same for the overall firm, the amounts may be different within the various divisions of the firm. From a risk capital allocation perspective, one solution is to allocate the greater of risk capital and regulatory capital to a certain division.
Professors Note: We w ill examine the regulatory capital charges fo r credit, market, and operational risk in the Basel readings later in this book.
Given that Basel III requirements are sufficiently robust, it is probable that in certain areas (e.g., securitization), regulatory capital will be substantially higher than risk/economic capital. Although the two amounts may conflict, risk/economic capital must be computed in order to determine the economic viability of an activity or division. Assuming that regulatory capital is substantially higher than risk/economic capital for a given activity, then that activity will potentially move over to shadow banking (i.e., unregulated activities by regulated financial institutions) in order to provide more favorable pricing.
Using Economic Capital Approaches
>From the perspective of financial institutions, the motivations for using economic capital are as follows:
Capital is used extensively to cushion risk. Compared to most other non-financial institutions, financial institutions can become highly leveraged (i.e., riskier) at a relatively low cost simply by accepting customer deposits or issuing debt. All of this may occur without having to issue equity. Additionally, many of the financial institutions will participate in transactions involving derivatives, guarantees, and other commitments that only require a relatively small amount of funding but always involve some risk. As a result, all of the firms activities must be allocated an economic capital cost.
Financial institutions must be creditworthy. A unique aspect of financial institutions is that their main customers are also their main liability holders. Customers who deposit funds to a financial institution will be concerned about the default risk of the financial institution. With over-the-counter (OTC) derivatives, the concern is counterparty risk. As a result, a sufficient amount of economic capital must be maintained to provide assurance of creditworthiness.
There is difficulty in providing an external assessment o f a financial institutions creditworthiness. It is challenging to provide an accurate credit assessment of a financial institution because its risk profile is likely to be constantly evolving. For example, an institution may engage in complicated hedging and derivatives transactions that could rapidly impact its liquidity. Therefore, having a sufficient store of economic capital could mitigate this problem and provide assurance of financial stability.
Profitability is greatly impacted by the cost o f capital. Economic capital is similar to equity capital in the sense that the invested funds do not need to be repaid in the same manner as debt capital, for instance. In other words, economic capital serves as a reserve or a financial cushion in case of an economic downturn. As a result, economic capital is more expensive to hold than debt capital, thereby increasing the cost of capital and reducing the financial institutions profits. A proper balance between holding sufficient economic capital and partaking in risky transactions is necessary.
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R i s k -A d j u s t e d R e t u r n o n C a p i t a l

LO 47.4: Explain the impact of model risk and poor risk governance in the 2012 London Whale trading loss and the 1998 collapse of Long Term Capital Management.
The impact of model risk has been felt significantly during two specific incidents: the 1997 collapse of Long-Term Capital Management (LTCM) and the 2012 London Whale trading loss at JPMorgan Chase (JPM). Both incidents illustrate the necessity to closely examine and vet models, and the importance of considering model risk within an organizations institutional risk governance framework.
Long-Term Capital Management
Background and Trading Strategies
LTCM was a U.S. hedge fund that existed between 1994 and 1998. The fund raised in excess of $ 1 billion in capital at its inception and grew rapidly over its initial years. LTCMs trading strategy relied on arbitrage positions based on market-neutral and relative-value trading. The fund began primarily as a bond arbitrage hedge fund that sought to make money by exploiting the spread differentials between bonds, including spread differences of European sovereign bonds and spread differences of corporate bonds and government Treasuries in the United States and United Kingdom.
LTCM relied on a combination of extensive empirical research and advanced financial modeling to formulate bets on convergence of prices in bond markets. For example, the fund was long (bought) Spanish and Italian sovereign debt and was short (sold) German
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sovereign debt. The strategy assumed that German sovereign bonds were overpriced relative to the weaker Spanish and Italian bonds, which were expected to increase in value with the imminent membership in the European economic and monetary union.
.Another strategy was based on the expected convergence between the spreads of corporate and government bonds in the United States and United Kingdom, where spreads were expected to return to normal levels. This strategy was designed to make a profit regardless of the movement in price levels, assuming, however, that spreads moved in the appropriate direction and that correlations did not change materially.
Leverage, Correlations, and Volatility
LTCMs strategies were designed to generate only modest profits (around 1%). In order for the fund to generate strong performance, it needed to use extensive leverage of up to 25 times. Such leveraged positions relied on large institutional loans that were collateralized by bond investments. Shortly before the funds collapse in 1998, LTCM had capital of close to $5 billion, assets of over $125 billion, and a notional value of investments in excess of $1.25 trillion. The magnitude of LTCMs leveraged investments was unprecedented in the markets.
LTCMs strategies worked as long as positions converged as anticipated, and as long as correlations did not deviate significantly from historical levels. Volatilities were calculated based on mathematical models to be approximately in line with the risk of investing in the S&P 500. However, at the time of the funds collapse, its one-day volatility exceeded its model predicted volatility by 2.5 times, and the fund suffered losses of more than 3 times its 10-day predicted maximum loss.
Collapse and Lessons
In 1997, Asian markets experienced considerable economic and financial problems that quickly spread to several economies as contagion increased. These troubles ultimately affected Russia, which was forced to devalue its currency, the ruble, and default on its sovereign debt in August 1998. The Asian and Russian crisis triggered a flight-to-quality in European and North American markets with investors seeking the safe and predictable returns of high-quality sovereign bonds. As a result, the yields of the U.S. and German long-term sovereign bonds declined (their prices increased), while at the same time the yields on the riskier corporate bonds and riskier sovereign bonds (for example, Italy and Spain) increased (their prices fell). Credit spreads widened, volatilities increased beyond historical levels, and correlations in the market moved closer to +1 as the contagion effect of the crisis spread across markets.
With higher volatilities and dramatically widening spreads, the profits on LTCMs short positions were no longer sufficient to offset the losses on its long positions. With losses mounting, lenders demanded additional collateral. In order to meet collateral calls, LTCM had to unwind several unprofitable trades that put further downward pressure on markets given the size of the funds trading positions. At the same time, liquidity in the markets quickly began to dry up, leaving many of LTCMs market-neutral positions now directionally exposed on the long side. Ultimately, the fund became insolvent in September 1998 and was bailed out by the Federal Reserve Bank of New York in order to curb a potential global financial crisis.
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LTCMs collapse highlighted several flaws in its regulatory value at risk (VaR) calculations: 1. The funds calculated 10-day VaR period was too short. A time horizon for economic
capital should be sufficiently long enough to raise new capital, which is longer than the 10-day assumption.
2. The funds VaR models did not incorporate liquidity assumptions. The assumption of
perfectly liquid markets proved to be incorrect when the fund experienced liquidity droughts.
3. The funds risk models did not incorporate correlation and volatility risks. This
weakness was especially evident when markets moved to a correlation of close to +1 and volatility increased significantly above historical and model predicted levels.
London Whale
Background and Trading Strategy
JPMorgan Chase & Company (JPM), along with its principal banking subsidiary JPMorgan Chase Bank, is a U.S. financial company and one of the largest derivatives traders in the world. JPM garnered international headlines when in the first half of 2012 it sustained losses in excess of $6 billion due to risky synthetic credit derivatives trades executed by a trader, called the London Whale, in its London office. The London trading desk belonged to JPMs Chief Investment Office (CIO), which was responsible for managing the banks excess deposits.
The CIO was tasked with keeping the banks risk level down and prudently managing the banks $330 billion in excess deposits. Instead, the CIO used the deposits to engage in high- profit potential, high-risk derivatives trading strategies. In 2006, the CIO began a new series of synthetic credit derivatives trading strategies within its Synthetic Credit Portfolio (SCP). Trading focused less on hedging risk and more on earning profits from short positions.
Risk Culture, Model Risk, and Operational Risk
The CIO used various risk metrics for its trading activities, including VaR limits and credit spread widening limits.
In 2011, the CIO was instructed to reduce the banks risk-weighted assets (RWA) in order to reduce regulatory capital requirements. Instead of the common practice of selling high risk assets, the CIO instead launched a trading strategy to offset its outstanding short positions by taking long positions in synthetic credit derivatives. This resulted not only in an increase in the portfolios risk and size, but it also put the portfolio in a net long position, which reduced the hedging protection provided by the SCP.
Concurrently, in early 2012, and in response to breaching its own internal VaR limits as well as the banks VaR limits, the CIO adopted a new VaR model which lowered its calculated VaR by 30%. The revised model allowed the CIO to remain within its VaR limit and at the same time engage in more higher-risk trading activities. However, the bank failed to seek regulatory approval of the new model. In addition, there were manual
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and calculation errors when implementing the model, which led to greater model and operational risk for the bank. Ultimately, the revised VaR model was reversed later in 2012 and the previous model was reinstated.
By 2012, the SCP was losing money on its strategies. In order to minimize its reported losses, the CIO changed its derivatives valuation practices from using midpoint prices (prices at the midpoint of the bid and ask) to using more favorable prices within the bid-ask spread during each day. As the losses in the SCP strategy increased, JPMs counterparties began to dispute the CIOs values, which led to frequent collateral disputes. Ultimately, JPMs positions soured and the bank lost close to $6.2 billion.
The losses from the London Whale trade and the subsequent investigations revealed a poor risk culture at JPM. Risk limits were routinely downplayed or ignored, limit breaches were disregarded, and risk models were altered to favor riskier trading activities.
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Ke y C o n c e pt s
LO 47.1 Model risk becomes important when quantifying the risk exposures of complex financial instruments, including exotic or synthetic derivatives and structured products. Model risk can give rise to losses from model errors, errors in assumptions, carelessness, fraud, or intentional mistakes. These errors can lead to undervaluing risk, overvaluing profit, or both. Six common model errors include: 1. Assuming constant volatility.
2. Assuming a normal distribution of returns.
3. Underestimating the number of risk factors.
4. Assuming perfect capital markets.
3. Assuming adequate liquidity.
6. Misapplying a model.
LO 47.2 Implementation error could occur when models that require complex simulations are not allowed to run a sufficient number of runs. This may result in incorrect output and therefore an incorrect interpretation of results.
For model implementation, considerations include frequency of refreshing model parameters, including volatilities and correlations. Correctly estimating parameters (durations, volatilities, and correlations) is challenging, however, implementing a model with input errors will result in inaccurate results.
Common valuation and estimation errors include: 1.
Inaccurate data.
2.
Incorrect sampling period length.
3. Liquidity and valuation problems.
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LO 47.3 Model risk can be mitigated either through investing in research to improve the model, or through an independent vetting process. Vetting consists of six phases: 1. Documentation.
2. Vetting the soundness of the model.
3. Ensuring independent access to rates.
4. Benchmark selection.
5. Health check and stress testing of the model.
6.
Incorporating model risk into the risk management framework.
LO 47.4 Long-Term Capital Management (LTCM) was a U.S. hedge fund that used arbitrage strategies to exploit spread differentials between bonds, including spread differences of European sovereign bonds and spread differences in corporate bonds and government Treasuries. LTCMs strategy was to make predictable, low returns and then amplify them using extensive leverage.
The collapse of LTCM in 1998 highlights three important lessons: 1. Utilizing a 10-day VaR period as a proxy for the time horizon for economic capital is too short. A time horizon is needed that is sufficiently long enough to model the time to raise new capital.
2. The funds VaR models ignored the possibility that liquidity may decline or even
completely dry up in periods of extreme stress.
3. The funds risk models ignored correlation and volatility risks. Specifically, the fund
did not account for stressed scenarios with material rises in volatility or an increase in positive market correlation as contagion risk spread across international economies.
In 2012, JPMorgan Chase (JPM) and its Chief Investment Office (CIO) sustained severe losses due to risky synthetic credit derivatives trades executed by its London office. The losses from the London Whale trade and the subsequent investigations highlighted a poor risk culture at JPM, giving rise to both model and operational risks across the firm. Risk limits were routinely ignored and limit breaches were disregarded.
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C o n c e pt Ch e c k e r s
1.
2.
3.
4.
3.
A risk analyst for a mid-sized bank believes that two common errors in model building include the assumption of constant volatility of returns and the assumption of a non-normal returns distribution. The analyst is correct with regard to the assumption(s) of: A. volatility of returns only. B. non-normal returns distribution only. C. both volatility of returns and non-normal returns distributions. D. neither volatility of returns nor non-normal returns distributions.
Which of the following scenarios is the best example of a model error? A. Assuming a non-normal distribution of returns. B. Assuming perfectly liquid markets. C. Assuming variable distribution of asset price. D. Assuming imperfect capital markets.
The chief risk officer (CRO) of a European corporation recommends increasing the length of the sampling period in order to minimize model risk. However, increasing the length of the sampling period will most likely: A. B. diminish the power of the statistical test. C. put higher weight on obsolete information. D. diminish the relevance of old data.
increase estimation errors.
Gamma Investments, LLC (Gamma) uses monthly model vetting to mitigate potential model risk. Gammas managers recently accepted the use of a model for valuing short-term options on 30-year corporate bonds, but rejected the same model to value short-term options on three-year government bonds. The managers also frequently test proposed analytical models against a simulation approach. These model vetting techniques are examples of which of the following vetting phases?
Accepting/rejecting a model A. Health check of the model B. Soundness of a model C. Health check of the model D. Soundness of a model
Testing models against simulation Stress testing Stress testing Benchmark modeling Benchmark modeling
Which of the following flaws in Long-Term Capital Managements (LTCM) value at risk (VaR) calculations were most evident following its collapse in 1998? I. The calculated 10-day VaR period was too short. II. The funds VaR model assumed strong positive correlation. A. I only. B. II only. C. Both I and II. D. Neither I nor II.
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C o n c e pt C h e c k e r An s w e r s
1. A The analyst is correct with respect to the assumption of volatility of returns only. Another
common model error is the assumption of a normal distribution of returns. Market participants frequently make the simplifying assumption in their models that asset returns are normally distributed. However, empirical research shows that returns tend to be non- normally distributed.
2. B Six common model errors include: (1) assuming constant volatility, (2) assuming a normal
distribution of returns, (3) underestimating the number of risk factors, (4) assuming perfect capital markets, (5) assuming adequate liquidity, and (6) misapplying a model.
3. C Adding more observations to the model reduces estimation errors and improves the power of statistical tests. However, it gives greater relevance to old and potentially stale data and puts greater weight on obsolete information which may now be irrelevant.
4. D Accepting the model for one use but rejecting it for another (inappropriate) use is an example of vetting the soundness of the model. In other words, the model vetter (in this case the risk managers) should ensure that the mathematical model reasonably represents the asset being valued.
Testing a proposed analytical model against a simulation approach or a numerical approximation technique is an example of benchmark modeling.
Health check of the model ensures that the model contains all of the necessary properties. Stress testing a model uses simulations to check the models reaction to different situations.
5. A LTCM s collapse highlighted several flaws in its regulatory VaR calculations. The fund relied on a VaR model that: (1) used a 10-day horizon, which proved to be too short to sufficiently model the time to raise new capital, (2) did not factor in liquidity risk (in other words, it assumed markets were perfectly liquid), and (3) did not incorporate correlation and volatility risks, where in fact markets exhibited strong positive correlation during periods of stress in 1997 and 1998.
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The following is a review of the Operational and Integrated Risk Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Ri s k Ca pi t a l A t t r i b u t i o n a n d Ri s k -Ad j u s t e d Pe r f o r ma n c e M e a su r e me n t
Topic 48
E x a m F o c u s
This topic covers the application of the risk-adjusted return on capital (RAROC) approach to the allocation of economic capital. The application of a hurdle rate for capital budgeting decisions as well as an adjusted version of the traditional RAROC approach is also presented. For the exam, know the differences between economic capital and regulatory capital, and be able to compute RAROC for capital budgeting as well as adjusted RAROC. Also, be familiar with the qualitative concepts discussed, such as reasons for using economic capital to allocate risk capital, the benefits of RAROC, and best practices in implementing the RAROC approach.
R i s k C a p i t a l
, E c o n o m i c C a p i t a l
, a n d R e g u l a t o r y C a p i t a l

LO 47.3: Explain methods and procedures risk managers can use to mitigate model risk.
Model risk can be mitigated either through investing in research to improve the model or through an independent vetting process. Investing in research leads to developing better and more accurate statistical tools, both internally and externally. Independent vetting includes the independent oversight of profit and loss calculations as well as the model selection and construction process. Vetting consists of the following six phases: 1. Documentation. Documentation should contain the assumptions of the underlying
model and include the mathematical formulas used in the model. It should contain a term sheet to describe the transaction, a mathematical statement of the model (all the variables and processes, payoff function and pricing algorithms, calibrations, and hedge ratios and sensitivities), and the implementation features, including inputs, outputs, and any numerical methods.
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2. M odel soundness. Vetting should ensure that the model used is appropriate for the
financial instrument being valued. For example, a model valuing option-free bonds would not be appropriate to value convertible or callable bonds.
3.
Independent access to rates. To facilitate independent parameter estimation, the model vetter should ensure that the middle office has access to independent financial rates.
4. Benchmark selection. The vetting process should include selecting the appropriate
benchmark based on assumptions made. Results from the benchmark test should be compared with the results from the model test.
3. Health check and stress test. Models should be vetted to ensure they contain all necessary properties and parameters. Models should also be stress tested to determine the range of values for which the model provides accurate pricing.
6.
Incorporate model risk into the risk management framework. Model risk should be considered in the formal risk management governance and framework of an institution. In addition, models need to be periodically reevaluated for relevance and accuracy. Empirical evidence suggests that simple, robust models work better than more complex and less robust models.
C a s e S t u d i e s R e l a t e d t o M o d e l R i s k

LO 47.2: Explain how model risk can arise in the implementation of a model.
In the previous section, we looked at the most common model errors. However, even correct models can be incorrectly implemented. This section looks at the most common implementation issues. Models may be affected by programming bugs or approximation errors, and models that seemed to work under normal conditions may have errors when tested under stressed market conditions.
Common Model Implementation Errors
Implementation error could occur, for example, when models that require Monte Carlo simulations are not allowed to run a sufficient number of simulations. In such a case, even if all the model inputs and assumptions are correct, the results may still be incorrect if insufficient time is given for the computations.
For the implementation of models, important considerations should include how frequently the model parameters need to be refreshed, including volatilities and correlations. Analysts responsible for maintaining models must consider whether adjustments should occur periodically at scheduled dates, or only when material economic events occur. Similarly, the treatment of outliers should also be considered. For example, should outliers be considered extreme outcomes only (that is, not part of the true distribution), or should they be considered part of the true distribution? Correctly answering these questions became especially important in the post-financial crisis period.
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Correctly estimating parameters like durations, volatilities, and correlations is very difficult, and implementing a model with input errors will result in inaccurate results. For example, in the 1970s the investment banking firm Merrill Lynch used incorrect hedge durations for government bonds, which resulted in a considerable loss to the firm. In another example, during the stressed conditions of the financial crisis, default correlations within structured products moved toward the binary extremes of +1 or 1. In other words, the cumulative default rates of collateralized debt obligations (CDOs) either all remained below a threshold with no defaults in any tranches, or all moved above a threshold, leading to defaults of even the AAA-rated tranches.
Common Valuation and Estimation Errors
Models also rely on the accuracy of inputs and values fed into the model, and are therefore subject to human error. Human error is particularly of concern in new or developing markets where adequate controls have not been fully defined and implemented.
Common valuation and estimation errors include: 1.
Inaccurate data. Models may use both internal and external data sources, where the responsibility for data accuracy is not clearly assigned. This could lead to errors from using inaccurate data.
2.
Incorrect sampling period length. Increasing the number of observations is expected to improve data accuracy and reduce estimation errors. Flowever, including old (and therefore obsolete) statistics could put too much weight on stale data.
3. Liquidity and valuation problems. Accurate pricing and valuation may not be possible in all markets. Prices for a particular asset may not exist in certain markets, or the bid-ask spread may be too high to offer accurate valuation.
M i t i g a t i n g M o d e l R i s k