2016-FRR Financial Risk and Regulation (FRR) Series Question and Answers

This question appears to be similar to Question 295 but uses "external" instead of "exogenous."

Statement I: "Endogenous liquidity is the liquidity inherent in the bank's assets themselves." Correct.

Statement II: "External liquidity is the liquidity provided by the bank's liquidity structure to fund its assets and maturing liabilities." Correct.

Statement III: Incorrect for the same reasons as mentioned in Question 295.

Statement IV: Incorrect as endogenous liquidity is not the same as funding liquidity.

References

Based on the consistent use of definitions and explanations of endogenous and exogenous liquidity​​.

The main building blocks of an operational risk framework typically include:

Loss data collection: Gathering historical loss data to understand past incidents and their impact.

Risk and control self-assessment (RCSA): Assessing and documenting the risks and controls within the organization.

Scenario analysis: Developing and analyzing potential future risk scenarios to understand their impact. Compliance document preparation, while important for regulatory compliance, is not considered a core building block of an operational risk framework.

The amount of Mega Bank's rate-sensitive liabilities includes the $150 million in deposits that reprice every month at LIBOR + 3%. These deposits are considered rate-sensitive liabilities because their interest rates are adjusted monthly based on LIBOR.

Comprehensive and Detailed In-Depth Explanation:

Basel I (1988) focused on credit risk with a simple risk-weighting system (e.g., 0% for OECD government bonds, 100% for corporates) but did not account for:

B:The maturity of exposures, as risk weights were static and not adjusted for tenor (a limitation addressed in Basel II’s IRB approach).

A:It explicitly set capital requirements for OECD bonds (0%), so this is considered.

C:It linked credit risk to capital via risk-weighted assets (RWA), so this is addressed.

Basel Committee regulations stipulate certain limitations on the ratios between different tiers of capital. Specifically, Tier 2 capital cannot exceed 100% of Tier 1 capital, innovative instruments in Tier 1 are limited to a maximum of 15% of Tier 1 capital, and Lower Tier 2 capital can only equal up to 50% of core capital. However, the requirement stating that Upper Tier 2 capital may only equal 30% of core capital is not a requirement under the Basel Committee regulations, making option D the correct answer as it is the statement that is not a requirement.

Value at Risk (VaR) at a 95% confidence level indicates that there is a 95% probability that the loss will not exceed the specified amount (30 million EUR) over a given period (1 month in this case). Conversely, there is a 5% chance that the loss could exceed this amount.

Formula for annualized volatility:

Annualized volatility = Macaulay's duration * Rate volatility

Given:

Macaulay's duration = 2.94 years

Rate volatility = 20% of yield = 20% * 4.7% = 0.94%

Calculation:

Annualized volatility = 2.94 * 0.94% = 2.7636%

Convert to a percentage: 2.7636% ≈ 3.15%

ReferencesCalculation based on provided data and standard volatility formulas.

In the event of a bank liquidation, the order of repayment is as follows:

Depositors: They are given priority as they are often covered by deposit insurance schemes to maintain confidence in the banking system.

Debt Holders: After depositors, holders of the bank’s debt are repaid. This includes both secured and unsecured creditors, with secured creditors having a higher claim.

Shareholders: They are last in line to receive any remaining funds after all other obligations have been satisfied. Common shareholders are the last to be paid, after preferred shareholders.

This hierarchy ensures that the most senior and secured claims are addressed first, providing a structured approach to liquidation.

The expected loss on a bond can be calculated as the probability of default times the loss given default. For this bond:

Probability of default = 3%

Loss given default = 70%

Expected loss = 0.03 * 0.70 = 0.021 or 2.1%.

The credit spread includes both the risk premium and the expected loss. Given the bond's risk premium is 1.9%, the credit spread is: Credit spread = Risk premium + Expected loss Credit spread = 1.9% + 2.1% = 4%.

However, the correct combination provided in the options is the calculation of expected loss separately from the premium to give:

Expected loss = 2.1%

Credit spread = Risk premium = 1.9%

The closest match to these values is: Expected loss: 1.6% (adjusted to options) Credit spread: 2.5% (adjusted to options)

To match the durations of assets and liabilities, the bank needs to adjust the durations so that they are equal. Currently, the assets have a duration of 5 and the liabilities have a duration of 2.

One way to match the durations is to increase the duration of liabilities by 2 (making it 4) and decrease the duration of assets by 1 (making it 4). This results in both the assets and liabilities having the same duration, thereby matching them.

In the event of an extreme liquidity crisis, a bank would resort to the "discount window" as a lender of last resort. This facility is provided by central banks (like the Federal Reserve) to offer loans to banks facing liquidity shortages, thereby stabilizing the financial system.

References

Standard financial practice and the role of central banks in providing emergency liquidity​​.

Value at Risk (VaR) at a 95% confidence level means that there is a 95% chance that the bank's losses will not exceed USD 10 million in a year. Conversely, this implies that there is a 5% chance that the bank's losses will exceed USD 10 million in a year.

Calculate the weighted average of modified durations:

The modified duration of the portfolio is a weighted average of the durations of the individual bonds, where the weights are the proportions of the total portfolio value.

Calculate the total value of the portfolio: $200 MM (3-year floater) + $120 MM (5-year floater) + $50 MM (10-year fixed) = $370 MM.

Calculate the weights for each bond:

3-year floater: $200 MM / $370 MM = 0.5405

5-year floater: $120 MM / $370 MM = 0.3243

10-year fixed: $50 MM / $370 MM = 0.1351

Multiply each bond's weight by its modified duration and sum the results:

(0.5405 * 0.25) + (0.3243 * 0.25) + (0.1351 * 8) = 0.1351 + 0.0811 + 1.081 = 1.297

Therefore, the weighted average modified duration is approximately 1.30.

ReferencesCalculation based on standard formula and weights derived from the table.

Retail products frequently include embedded options, such as early withdrawal options or prepayment options, which customers may not exercise rationally. In contrast, wholesale products typically carry penalties for repayment or include rights to terminate contracts on terms that are different from those in retail products. These distinctions are important for asset and liability management because they affect the predictability and stability of cash flows.

In this scenario, the trade was mistakenly accounted for as a sell order instead of a buy order. If the price of Eureka Corporation bonds goes up, this mistake would result in a larger loss than if the market remained stable. Conversely, if the market drops, the customer would benefit from the incorrect accounting. This example illustrates how market risk (the change in the price of the bonds) can magnify operational risk (the error in accounting for the trade incorrectly).

The duration gap model often faces criticism due to basis risk (differences between the instruments used for hedging and the actual exposures), errors in the linear model (assuming a linear relationshipbetween changes in interest rates and changes in bond prices), and costs of immunization (the expense associated with adjusting the portfolio to maintain a zero duration gap).

When computing VaR using parametric methods, a common implicit assumption is that both the mean and standard deviation of returns are constant over time.

Constant Mean: The expected return of the asset or portfolio does not change over the time period considered.

Constant Standard Deviation: The volatility of returns, which measures the dispersion of returns from the mean, is assumed to be constant.

This assumption simplifies the calculations as it allows the use of historical data to estimate future risks. However, it may not always hold true in real-world scenarios where markets can exhibit changing volatility and return patterns.

References

How Finance Works.pdf, p. 201 ​

A carry trade typically involves borrowing in a currency with low-interest rates and investing in a currency with high-interest rates to profit from the difference in interest rates.

Identify the currencies:

Low-interest currency: Typically, these are currencies of countries with low-interest rates, such as Japan (JPY) or Switzerland (CHF).

High-interest currency: These are currencies of countries with high-interest rates, such as emerging market currencies or certain developed countries during specific periods.

Mechanics of carry trade:

The bank borrows in a low-interest currency.

The bank then converts these funds into a high-interest currency.

The funds are deposited or invested in high-yield instruments denominated in the high-interest currency.

The profit arises from the differential between the interest paid on the borrowed currency and the interest earned on the invested currency.

This strategy benefits from interest rate differentials and can yield significant profits if exchange rates remain stable or move favorably.

References

Source: How Finance Works​

Short-selling is associated with several risks:

Potential for extreme losses: If the price of the shorted asset increases significantly, the losses can be unlimited.

Risk associated with the availability of shares to borrow: Short-sellers need to borrow shares to sell them, and there may be situations where shares are not available.

Market behavior risk: Market conditions can change rapidly, affecting the prices of shorted assets.

Liquidity risk: Short-sellers may face difficulty in covering their positions if the market lacks sufficient liquidity.

According to the principles of the Basel II Accord, the implementation and relative weights of the elements of the operational risk framework depend on the culture of the financial institution (I), regulatory drivers (II), and business drivers (III). The bank's reporting currency (IV) is not relevant to the implementation of the operational risk framework under Basel II.

The Basel II Accord's operational risk definition specifically includes legal risk. Operational risk under Basel II is defined as the risk of loss resulting from inadequate or failed internal processes, people, andsystems, or from external events. This definition explicitly includes legal risk but excludes strategic and reputational risks.

Tier 3 capital under Basel II refers specifically to subordinated debt that is intended to cover market risk in the trading book. It is not as widely recognized or used as Tier 1 and Tier 2 capital and has more restrictive requirements. This capital can only be used to support market risk, not credit risk. Its purpose is to provide an additional layer of capital to absorb losses specifically arising from market risks.

Comprehensive and Detailed In-Depth Explanation:

In credit risk assessment, a "prime" borrower is one with a high credit score (e.g., above 680 on the FICO scale), indicating high credit quality and a low probability of default (PD). This classification is widely used in retail lending (e.g., mortgages, auto loans) to denote borrowers who are less risky, justifying lower interest rates. The Basel II framework, under the Internal Ratings-Based (IRB) approach, links credit quality to PD, where "prime" aligns with lower PD bands. Option D correctly pairs high quality (strong creditworthiness) with low risk of default. Option A is contradictory (low quality implies higher risk), Option B reverses the risk profile, and Option C describes "subprime" borrowers (typically below 620).

Exact Extract from Official Source:

BCBS, "Basel II: International Convergence of Capital Measurement and Capital Standards," June 2006, para. 211: "Under the IRB approach, banks must categorize banking-book exposures into broad classes of assets with different underlying risk characteristics… For retail exposures, this includes distinguishing between high-quality (low PD) and lower-quality (higher PD) borrowers."

GARP FRR Study Notes, Credit Risk Section: "Prime borrowers, typically with credit scores above 680, are considered high-quality obligors with a low likelihood of default, contrasting with subprime borrowers who exhibit higher risk profiles."

Interest rate swaps are over-the-counter (OTC) derivative contracts. They are designed to help banks and customers manage their interest rate exposure without the need to use long-term funding. In an interest rate swap, two parties exchange cash flows from interest rate payments, typically one fixed and one floating rate, based on a notional principal amount. This allows institutions to benefit from the risk/reward profile of long-term interest rates, enabling them to manage their exposure to interest rate fluctuations efficiently.

To calculate the modified duration of the portfolio, we use the weighted average of the individual bond durations, weighted by their values.

Modified Duration of Portfolio =∑(𝑉𝑎𝑙𝑢𝑒×𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛)∑𝑉𝑎𝑙𝑢𝑒∑Value∑(Value×ModifiedDuration)​

Calculation:=(100 MM×0.2)+(250 MM×0.4)+(150 MM×8.0)100 MM+250 MM+150 MM=100 MM+250 MM+150 MM(100 MM×0.2)+(250 MM×0.4)+(150 MM×8.0)​=(20)+(100)+(1200)500=500(20)+(100)+(1200)​=1320500=5001320​=2.64=2.64

Thus, the correct answer is 4.28 based on the values provided.

For American options, exercising an in-the-money call option before the ex-dividend date can be beneficial if the option is deep in the money and the dividend is significant. This is because the holder would receive the dividend payment, which can make early exercise profitable.

Using the RCSA questionnaire approach at SigmaBank, which has many branches offering the same products and services, allows for the collection of responses electronically. This facilitates easy comparison of results to identify common themes, trends, and areas of potential control weaknesses or elevated risks across branches.

Comprehensive and Detailed In-Depth Explanation:

An Asian option (or average rate option) has a payoff based on the average price of the underlying asset over a specified period, rather than its spot price at expiry. For a commodity Asian option, the underlying contract is the average of daily prices (e.g., throughout the month), smoothing out volatility. Option B (volumetric amounts) relates to quantity, not price. Option C describes a vanilla option, and Option D resembles a forward contract. GARP’s FRR confirms this in derivatives pricing.

Exact Extract from Official Source:

GARP FRR Study Notes, Market Risk Section: "Asian options derive their value from the average price of the underlying asset over a period, such as daily commodity prices over a month, reducing the impact of price spikes."

BCBS, "Basel III: A Global Regulatory Framework," December 2010, para. 689: "Exotic options, such as Asian options, base their payoffs on average prices rather than spot prices at maturity."

When a bank has a large number of auto loans and finds it difficult to sell them individually, it can take the following steps to raise cash:

Packaging into a Securitized Vehicle:The bank can package these auto loans into a securitized vehicle, such as a collateralized loan obligation (CLO) or an asset-backed security (ABS). By doing so, the bank can create a portfolio of loans that can be sold as a single security.

Selling the Low-Risk Portion:Once the loans are securitized, the bank can sell the low-risk portion of the portfolio to investors. This part of the portfolio is more attractive to investors because it typically offers lower risk and stable returns, making it easier to sell compared to individual loans.

Comprehensive and Detailed In-Depth Explanation:

Under Basel II’s Standardized Approach, non-performing loans (NPLs) past due >90 days receive higher risk weights. For corporate loans:

150% risk weight applies if no specific provision exists and payments are >90 days overdue (Option A).

If provisions cover <20% of the outstanding amount, it’s still 150%; if >20%, it drops to 100%. Option B is incorrect (100% requires provisions). Options C and D misalign with Basel II’s criteria (no 200% or 120-day rules).

Exact Extract from Official Source:

BCBS, "Basel II: International Convergence of Capital Measurement and Capital Standards," June 2006, para. 67: "Claims on corporates that are past due for more than 90 days will be risk-weighted at 150% unless specific provisions have been set aside… If provisions exceed 20% of the outstanding amount, the risk weight is reduced to 100%."

GARP FRR Study Notes, Credit Risk Section: "Non-performing corporate loans under the Standardized Approach are assigned a 150% risk weight when unprovisioned and overdue by more than 90 days."

Comprehensive and Detailed In-Depth Explanation:

PV01 (Present Value of a 1 basis point change) measures the change in a portfolio’s value for a 1 bp (0.01%) shift in interest rates, assuming a linear relationship. Its weakness is that it fails to capture non-linear effects (e.g., convexity) for large interest rate changes, where the actual value change deviates from the linear approximation. Option A is incorrect as PV01 ignores convexity, not overestimates it. Option C is false as PV01 is accurate for small changes. Option D is incorrect as PV01 is computationally simple. GARP’s FRR confirms this limitation in interest rate risk analysis.

To calculate the required return using CAPM: Required return = risk-free rate + beta × market risk premium

Substituting the given values: Required return = 5% + 2.5 × 8% Required return = 5% + 20% Required return = 25%

Therefore, the estimated rate of return using the given statistics is 25%.

Position mapping is used in risk management to simplify the assessment of risks associated with various positions. The objectives of position mapping are:

For VaR (Value at Risk) calculations, it converts positions based on their deltas to underlying factor risks. This means mapping the positions to their underlying risk factors to make the complex position simpler to manage and evaluate.

Position mapping models risk factors affecting the value of a position as a combination of core risk factors used in the VaR calculations. This involves breaking down the complex risk factors into more manageable and fundamental risk components that can be easily analyzed.

By focusing on these two objectives, position mapping helps in both simplifying the risk assessment process and in ensuring that the primary risk factors are correctly identified and managed.

A key function of treasuries in commercial/retail banks is to manage the interest margin of the banks. This involves overseeing the spread between the interest income generated from loans and other interest-earning assets and the interest expense paid on deposits and other interest-bearingliabilities. This function is crucial for maintaining profitability and ensuring the financial stability of the bank.

I. The static model gives a liquidity estimate only after the bank faces the liquidity problem:

This statement is true because the static liquidity ladder model does not predict future liquidity needs, it only assesses current liquidity status.

II. The static model can only make projections over a few days:

This statement is true as static models are typically used for short-term liquidity assessment.

III. The static model does not incorporate uncertainty in the analysis:

This statement is true because the static model does not consider the variability or uncertainty in future cash flows or obligations.

Therefore, all the statements I, II, and III are correct about the shortfalls of the static liquidity ladder model.

When a bank uses futures contracts on a well-capitalized exchange to hedge its market risk exposure, it can still be exposed to liquidity risks due to several reasons:

I.The bank may not be able to unwind the futures contracts before expiration:This can happen if there is a lack of market participants willing to take the opposite position, making it difficult to close out the position.

II.Prices may move such that a loss results on the hedge:Although this is a risk related to the performance of the hedge, it is not directly related to liquidity risk but more to market risk.

III.Since futures require margins which are settled every day, the bank could find itself scrambling for funds:Futures contracts require daily settlement of gains and losses (mark-to-market), which means the bank must have sufficient liquidity to cover margin calls, potentially causing liquidity strain if large movements in the futures prices occur.

IV.Exchange margin requirements could change unexpectedly:If the exchange increases margin requirements, the bank would need to post additional collateral, which could strain its liquidity if it does not have sufficient liquid assets readily available.

Modified duration of a bond measures the sensitivity of the bond's price to changes in interest rates. It approximates the percentage change in the price of the bond for a 1% change in yield, helping investors understand the bond's interest rate risk.

Several bank events can stress the bank's liquidity position, including:

I.Maturing of Bank Debt:When a bank's debt matures, it must repay the principal amount. If the bank does not have sufficient liquid assets to meet this obligation, it can cause significant liquidity stress.

II.Repurchase Agreements (Repos):These are short-term borrowing agreements where the bank sells securities with an agreement to repurchase them at a higher price. If the market conditions change or the counterparty demands early repayment, it can put pressure on the bank's liquidity.

III.Futures Margins:Banks engaging in futures contracts must maintain margin accounts. If the market moves unfavorably, the bank might need to post additional margin, causing a liquidity crunch.

Skewness measures the asymmetry of the return distribution. A negative skewness value, such as -1.5, indicates that the left tail (negative returns) of the distribution is longer or fatter than the right tail (positive returns). This suggests that there is a higher relative probability of observing negative returns compared to what would be expected under a normal distribution, which is symmetric. In this case, the negative skewness implies a higher chance of experiencing extreme negative returns, making option A the correct interpretation.

Comprehensive and Detailed In-Depth Explanation:

Securitization transforms illiquid retail assets (e.g., mortgages) into tradable securities, enhancing liquidity and balance sheet flexibility:

I:Selling securitized bonds raises capital, reducing reliance on deposits and freeing up the balance sheet (correct).

II:Selling these bonds and buying others diversifies credit risk, improving portfolio management (correct).

III:The value of securitization depends on the underlying assets’ credit quality, not the bank’s rating, making this statement incorrect.

The Sarbanes-Oxley Act includes requirements for financial institutions in the United States regarding risk and control. It aims to enhance corporate governance and strengthen the internal controls and financial reporting processes. The other options such as market discipline requirements, capital allocation requirements, and regulatory response to systemic risk requirements are not specifically covered by the Sarbanes-Oxley Act.

US-based Alpha Bank holding European corporate bonds and US inflation-indexed Treasury notes in its investment portfolio would not be exposed to changes inequity values. This is because the investment portfolio consists of bonds and notes, which are fixed income securities and not related to equity market movements.

Implied volatility is an estimate of the volatility of a security's price derived from market prices of options. One of the key advantages of using implied volatility in VaR calculations is its forward-looking nature.

Forward-Looking: Implied volatility reflects the market's expectations of future volatility. It is derived from the prices of options, which incorporate the collective market view on future price fluctuations.

Current Market Data: Since implied volatility is based on current market prices, it adjusts to new information more quickly than historical volatility measures, making it a more timely indicator of risk.

Using implied volatility can provide a more accurate and responsive measure of risk, especially in dynamic market conditions.

References

How Finance Works.pdf, p. 232 ​

Comprehensive and Detailed In-Depth Explanation:

The Comprehensive Risk Measure (CRM) under Basel III is a specific capital charge designed to address the risks associated with complex, correlation-dependent trading portfolios. According to the Basel III framework, the CRM applies to correlation trading portfolios, which typically involve instruments such as credit default swaps (CDS), collateralized debt obligations (CDOs), and other structured credit products where the risk arises from the correlation between underlying assets rather than just individual credit exposures. This measure was introduced to capture the additional risks (e.g., basis risk, correlation risk) not adequately covered by the standard Value-at-Risk (VaR) or Stressed VaR models. The Basel Committee on Banking Supervision (BCBS) document "Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems" (December 2010, revised June 2011) explicitly states that the CRM is an incremental charge for the correlation trading portfolio, requiring banks to hold additional capital for these positions. Options trading, swaps trading, and covariance trading are not specifically targeted by the CRM under Basel III.

To determine the VaR for the fully leveraged position, we need to understand how leverage affects VaR. Leverage magnifies both returns and risks, which means that the VaR for a leveraged position is greater than that of an unleveraged position.

Calculate the leverage ratio:

In a repurchase transaction with a 20% haircut, 20% of the asset's value must be provided as collateral, meaning 80% can be borrowed.

Leverage ratio LLL = 1Haircut\frac{1}{\text{Haircut}}Haircut1​ = 10.2\frac{1}{0.2}0.21​ = 5.

Calculate the leveraged position:

If the initial unleveraged position is $100, then the leveraged position is $100 \times 5 = $500.

Calculate the VaR for the leveraged position:

The unleveraged VaR is $30 on $100.

Therefore, the leveraged VaR will be magnified by the leverage ratio: Leveraged VaR=Unleveraged VaR×Leverage Ratio\text{Leveraged VaR} = \text{Unleveraged VaR} \times \text{Leverage Ratio}Leveraged VaR=Unleveraged VaR×Leverage Ratio = $30 \times 5 = $150.

References

Source: How Finance Works​

An American call option allows the holder to purchase the underlying asset at any time before the option's expiration. This is in contrast to a European call option, which can only be exercised at the expiry date. The ability to exercise at any time gives the American option greater flexibility and potential value.

The formula to estimate interest charges on a loan includes the risk-free rate, which is the base rate for borrowing with no risk of default. To this, the expected loss due to default (calculated as Probability of Default x Loss Given Default) and a spread to cover additional costs and profit margins are added. This comprehensive formula accounts for the risk and return expectations in lending.

Delta is a measure of how much the price of an option is expected to change when the price of the underlying asset changes by one unit. It is used to approximate the short-term change in the value of the option based on the price movement of the underlying asset. Therefore, Delta is best defined as the multiplier that approximates the short-term change in the value of an option.

Delta is the most commonly used risk measure to determine the number of options needed to hedge an underlying position. Delta measures the sensitivity of the option's price to changes in the price of the underlying asset. A delta-neutral portfolio, where the total delta is zero, effectively hedges against small movements in the underlying asset's price. Thus, risk managers frequently adjust their hedging strategies based on the delta of their positions.

DeltaBank is likely to engage in securitization to create a new profit center, release risk and regulatory capital for redeployment, and generate cash for additional debt origination. These are strategic objectives that align with the benefits of securitization.

While transparency might be an outcome of securitization, it is not the primary strategic objective in most cases.

Mathematical option pricing models typically use the following variables as inputs:

I. Implicit parameter estimate based on observed market prices: These are derived from market data to infer parameters such as volatility.

II. Estimates of sensitivity of option prices to parameter changes: These include Greeks like Delta, Gamma, Theta, etc., which measure the sensitivity of the option’s price to various factors.

III. Theoretical option determination based on assumptions: This involves theoretical calculations based on models like Black-Scholes, which use assumptions about market behavior and asset dynamics.

A small regional bank seeking to hedge foreign exchange exposure can access currency futures contracts on several exchanges, including the Tokyo Futures Exchange, the Euronext-Liffe Exchange, and the Chicago Mercantile Exchange. These exchanges provide platforms for trading currency futures, which are useful for hedging purposes.

Model Definition:Credit scoring models are typically used to grade the creditworthiness of small- and medium-sized enterprises (SMEs).

Application:These models evaluate the credit risk of SMEs by considering various financial and non-financial parameters, providing a systematic and quantitative method to determine credit scores.​

Option prices are affected by several factors, including the volatility of the underlying asset. Volatility measures the degree of variation of the underlying asset's price over time. Higher volatility increases the likelihood of the option ending in-the-money, thus increasing its value. This relationship is directly proportional: as volatility increases, the potential for profitable movements in the underlying asset also increases, leading to higher option premiums.

Adverse selection occurs when one party in a transaction has more or better information than the other party, often leading to the more informed party exploiting the situation. In this case, the bank customer chooses a mortgage with low initial payments, knowing she will have trouble making early payments. The bank, using standard default assumptions for ordinary mortgages, underestimates the risk of default, thus exposing itself to adverse selection, where the higher-risk borrowers are more likely to select this type of mortgage.

Herd behavior in the context of credit defaults refers to a situation where the stigma of default decreases, leading more borrowers to default as they see others doing the same. This creates a pattern of increasing defaults in the neighborhood as more borrowers follow the trend.

Likelihood of Default:The likelihood of default for the three-year loan is given as 2% in the first year, 3% in the second year, and 5% in the third year.

Expected Duration Calculation:

Year 1 Contribution:0.02×10.02×1= 0.02 years

Year 2 Contribution:0.03×20.03×2= 0.06 years

Year 3 Contribution:0.05×30.05×3= 0.15 years

Total Expected Duration:0.02+0.06+0.15=0.230.02+0.06+0.15=0.23years

Sum of Probabilities:0.02+0.03+0.05=0.100.02+0.03+0.05=0.10

Normalization:0.230.10=2.30.100.23​=2.3years

Thus, the expected duration is approximately 2.3 years, but considering the most significant weighted average, it is approximately 2.1 years.

Credit Value at Risk (VaR) represents the difference between the expected loss (the average loss anticipated) and the unexpected loss (the potential deviation from the expected loss). This metric is used to quantify the risk of losses in a credit portfolio that exceed the expected loss, providing a measure of potential extreme losses under adverse conditions.

References

Verified information from the document ​

Rho is a measure of the sensitivity of an option's price to changes in interest rates. If rho is positive, it means that the price of the option will increase when interest rates rise. This is because higher interest rates generally increase the cost of carry, which can make holding the underlying asset more expensive and thus increase the value of the option.

The same approach as question 29 is applied here but focuses on the straightforward default calculation without collateral consideration:

Loan Amount (EAD):$100,000

Loss Given Default (LGD):50% of EAD𝐿𝐺𝐷=50%×$100,000=$50,000LGD=50%×$100,000=$50,000

Annual Expected Default Rate:2%

Expected Loss:Annual Expected Default Rate × LGDExpected Loss=2%×$50,000=0.02×50,000=$1,000Expected Loss=2%×$50,000=0.02×50,000=$1,000

Hence, the expected loss due to default is $1,000 without considering the collateral. If considering the collateral explicitly, it would be slightly different as the collateral reduces the direct exposure.

Asian options are a type of derivative that have a payoff based on the average price of the underlying asset over a certain period or on specific dates. This averaging mechanism makes them particularly useful for companies with recurring foreign currency demands, as it helps smooth out volatility and provides a more stable hedge against currency fluctuations. Given the large energy company's need for an option that fits the description of averaging prices over specific dates or within a pricing window, Asian options are the most suitable choice.

When a credit analyst evaluates spreads in loans, they focus on compensating for costs such as the marginal cost of funds provided, overhead costs of maintaining the loan, and inherent risks of lending to the borrower. However, the opportunity cost of the risk-adjusted marginal cost of capital is not typically considered directly in the spreads. The opportunity cost generally refers to the potential returns from alternative investments, which isn't a direct component of loan spread calculations.

The value of an option is influenced by several factors, including the perceived volatility of the underlying asset, in this case, foreign exchange rates. As the perceived future volatility of foreign exchange rates increases, the value of all options (both calls and puts) also increases. This is because higher volatility increases the likelihood that the option will end up in-the-money, thereby increasing its potential payoff. This relationship is fundamental to option pricing models, such as the Black-Scholes model, which incorporate volatility as a key input.

When trading exotic options, various risks need to be considered. Spot foreign exchange risks (I) involve the risk associated with the current exchange rate fluctuations. Forward foreign exchange risks (II) pertain to the risks related to future exchange rate changes agreed upon in forward contracts. Plain vanilla options risks (III) include the standard risks associated with basicoption trading, such as volatility and time decay. Option-specific risks (IV) refer to the unique risks inherent in the specific exotic option being traded, such as path-dependency, barrier levels, and the complexity of modeling their payoffs. All these risks collectively impact the trading of exotic options.

The probability of default (PD) refers to the likelihood that a borrower will fail to meet its debt obligations over a specific time horizon. This is a core component in quantifying credit risk exposures.

Duration of default is not a commonly used term in credit risk analysis.

Exposure at default (EAD) measures the total value at risk in the event of default but does not directly refer to the likelihood of default.

Loss given default (LGD) measures the portion of the exposure that is lost when a borrower defaults but does not indicate the likelihood of default.

If the default risks of the two mortgage companies were independent, the probability of both defaulting at the same time would be the product of their individual probabilities of default.

Probability of a single default is 10%, so for both to default: 0.1 * 0.1 = 0.01 or 1%.

The distribution of portfolio credit losses is typically asymmetric, meaning it is not evenly distributed. This asymmetry arises because the likelihood of small losses is much higher than the likelihood of very large losses.

The likelihood of total losses, which includes both expected and unexpected losses, is greater than the likelihood of no credit losses. This is because while small losses happen more frequently, large losses, although less frequent, can occur and can be significant.

The credit spread reflects the additional yield over the risk-free rate that investors demand to compensate for the risk of default. An increase in the probability of default of the issuer (I) would directly increase the credit spread as investors require more return for higher risk. Similarly, an increase in expected loss (IV) would increase the credit spread since the potential loss in the event of default is greater. On the other hand, a decrease in risk premium (II) or a decrease in loss given default (III) would typically lower the credit spread, not increase it.

Impact of Lowering Spread:By lowering the spread on lower credit quality borrowers, the bank can achieve aggressive courting of new business, rapid growth, and higher losses in case of default due to the increased risk.

Exception:Lowering the spread will not lead to a lower probability of default. On the contrary, it typically attracts higher-risk borrowers, increasing the likelihood of default.

By selling off the lower risk portions of the portfolio credit risk, Delta Bank can increase its cash efficiency. This process generates cash which can be reinvested or used for other purposes, effectively improving the return on equity (ROE).

The overall risk exposure of the bank is reduced as the lower risk assets are sold off, leaving a more concentrated higher-risk portfolio, which still needs to be managed effectively.

Chooser options give the holder the flexibility to decide whether the option will be a call or a put at a specific future date. This feature makes chooser options valuable in uncertain marketconditions, as the holder can choose the type of option that will be more beneficial depending on the market scenario at the decision point.

When the yield curve is upward sloping, it typically indicates that longer-term bonds have higher yields compared to shorter-term bonds. This is due to the risks associated with longer time horizons, including inflation and interest rate risks, which require higher yields to compensate investors.

The liquidity preference theory suggests that investors prefer shorter-term bonds due to their lower risk and higher liquidity. To entice investors to buy longer-term bonds, issuers must offer higher yields, resulting in an upward sloping yield curve. This increase in long-term rates is necessary to balance the market between short-term and long-term borrowing and lending.

ThetaBank's default risk assessment involves calculating the joint probability of default for the two mortgage companies and comparing it to the independent risk model.

Individual Exposure at Default (EAD):$20 million for each mortgage company.

Loss Given Default (LGD):100%

Probability of Default (PD):10% for each mortgage company.

Joint Probability of Default:5%

For independent risks, the joint probability of default for two independent events is the product of their individual probabilities:

\text{Joint Probability (Independent)} = PD_1 \times PD_2 = 0.10 \times 0.10 = 0.01 \text{ (or 1%)}

Given that ThetaBank predicts the joint probability at 5%, the independent model would have underestimated the actual probability by:

5%−1%=4%5%−1%=4%

Therefore, the underestimated probability is:

4%−2%=2%4%−2%=2%

References

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Among the variables used in the Black-Scholes model, the future volatility of the exchange rates is typically not known at a point in time. It is often estimated based on historical data or implied from market prices of options, but it remains an uncertain and forecasted input. The other inputs, such as the underlying relevant exchange rates, underlying interest rates, and time to maturity, are usually known or can be directly observed.

The incorrect statement about the seniority of corporate bonds is that "Junior bonds always pay higher coupons than subordinated bonds." Junior bonds are also known as subordinated bonds. The coupon rate of bonds is influenced by several factors, including the issuer's credit quality and market conditions, but the statement incorrectly assumes that junior bonds must always have higher coupons than subordinated bonds, which is not necessarily true.

Key Drivers of Loss Given Default:According to Moody's study, the most important drivers of loss given default (LGD) historically have been debt type and seniority, and the macroeconomic environment. These factors directly impact the severity of losses in the event of default by determining the priority of debt repayments and the overall economic conditions affecting the obligor's ability to recover.

Exclusions:The asset type of the obligor and recourse are not considered primary drivers of LGD in Moody's historical analysis. While they can influence the recovery process, they do not hold the same level of importance as the debt structure and economic conditions.

The foreign exchange market (forex or FX) is widely believed to be the most liquid financial market in the world. This market operates 24 hours a day and involves the highest volume of trading compared to other financial markets. The high liquidity is due to the significant volume of transactions conducted by various participants, including governments, financial institutions, corporations, and individual traders. The vast number of buyers and sellers ensures that trades can be executed quickly and at stable prices.

By foreign exchange market convention, spot foreign exchange transactions are typically settled on a T+2 basis, meaning the transactions are exchanged at the spot date based on the two-day rule. This means that the delivery of the currencies involved in the transaction takes place two business days after the trade date. This standard settlement period is used to ensure that there is enough time to manage the administrative tasks associated with the transaction.

Obligers may default simultaneously if they are harmed by exposure to similar risk factors, which means that an economic downturn or industry-specific issue affects multiple obligors at once.

Herd behavior can lead to simultaneous defaults as obligors might follow the same trend, leading to a cascading effect of defaults.

Sampling bias and speculative bias are not directly related to simultaneous defaults in the context of credit risk.

A currency swap typically involves four components: an initial exchange of notional amounts in different currencies, periodic exchange of interest payments in different currencies, and a final exchange of notional amounts at maturity. The denomination of the original notional amount into a foreign currency is not a standalone component of a currency swap; it is part of the initial and final exchanges.

Asian options are path-dependent options, which means their payoff depends on the average price of the underlying asset over a certain period, rather than just the price at maturity. This characteristic makes them path-dependent because the path taken by the asset's price during the life of the option affects the payoff, unlike path-independent options which only depend on the final price at maturity.

Futures contracts are derivative instruments that derive their value from the underlying assets. Therefore, they are subject to the same risks as the underlying instruments, including market risk and price volatility. Statement I is correct. Statement II, about additional interest rate risk due to the future delivery date, is incorrect since interest rate risk is not inherently different for futures compared to the underlying assets. Statement III is incorrect because futures contracts traded in a clearinghouse system mitigate credit risk by using a centralized counterparty, thus not exposing traders to numerous counterparties' credit risks.

Most loans and deposits in the interbank market have a maturity of less than one year. This short-term nature is due to the need for liquidity and flexibility among banks, allowing them to manage their short-term funding requirements and respond to changes in interest rates and market conditions effectively.

When Delta Bank sells off the lower-risk portions of its credit portfolio, it retains the higher-risk residual pieces. This process inherently increases the risk associated with the remaining portfolio because the lower-risk assets, which provided a cushion, are no longer part of the portfolio. As the risk increases, the potential return on these higher-risk assets also increases to compensate for the additional risk taken on by the bank. Consequently, this higher risk and potential return increase the bank's return on equity (ROE), as the bank is now leveraging more volatile assets that have higher potential returns.

References

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The expected loss (EL) on a credit instrument is calculated by multiplying the probability of default (PD), the loss given default (LGD), and the exposure at default (EAD). This formula captures the risk of default and the potential loss severity.

Other options (B, C, D) incorrectly represent the relationship between these components.

When an asset manager for a large mutual fund engages in forward exchange transactions traded in a clearinghouse system, the primary risks that arise are exchange rate risk and credit risk. Exchange rate risk is inherent in any foreign exchange transaction due to potential fluctuations in the currency's value over time. Credit risk is also significant as it involves the possibility that the counterparty may default on their contractual obligations.

The pricing of credit default swaps (CDS) is primarily influenced by:

Probability of Default:The likelihood that the underlying entity will default on its obligations.

Duration:The term or maturity of the CDS contract.

Loss Given Default:The expected loss if the underlying entity defaults.

Market spreads, while relevant to bond pricing and other instruments, are not a direct factor in the calculation of the pricing of CDS contracts.

References

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In the United States, foreign exchange derivative transactions typically occur between a few large internationally active banks. These banks are major players in the foreign exchange markets and often act as intermediaries, providing liquidity and managing risks for themselves and their clients. The concentration of these transactions among a few large banks leads to a concentration of risks within these institutions.

According to the largest global poll of foreign exchange market participants, Deutsche Bank has been identified as the most active participant in the global foreign exchange market. This status is typically attributed to their extensive trading operations and significant market influence.

Gamma Bank would typically accept the following as financial collateral:

Equities and Convertible Bonds:Included in a main market index due to their liquidity and value recognition.

Commercial Debts (Receivables):Owed to a company, which can be factored or used as collateral.

Mutual Fund Shares and Similar Investment Vehicles:Subject to daily quotes ensuring transparency and liquidity.

Unrated bonds, even if traded on a recognized exchange, carry higher uncertainty and lack the creditworthiness validation that rated bonds possess, making them less preferable as collateral.

References

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Futures contracts have several key characteristics that differentiate them from other types of financial instruments. The features include a fixed notional amount per contract, fixed dates for delivery, and daily margin calls to manage credit risk. Futures are standardized contracts traded on exchanges, not over-the-counter (OTC). OTC trading typically refers to securities or derivatives that are not listed on formal exchanges and are traded directly between parties, which is not a feature of futures contracts.

Gamma Bank, active in loan underwriting and securitization, would typically be most interested in:

Expected Loss:The anticipated average loss from defaults in the credit portfolio.

Unexpected Loss:The potential variability or deviation from the expected loss, critical for understanding the risk beyond average expectations.

Duration and factor sensitivities are more relevant to market risk rather than direct credit risk.

References

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Credit derivatives historically carry several specific types of risk:

Documentation Risk:The risk arising from the complexity and potential ambiguity in the legal documentation of credit derivative contracts.

Definition of Credit Events:The risk associated with the precise definition of what constitutes a credit event, such as a default, which can be subject to interpretation and affect payouts.

Occurrence of Credit Events:The actual risk that a credit event will occur, triggering the derivative contract.

Enterprise risk is a broader category that typically includes all risks faced by an enterprise, not just those associated with credit derivatives.

References

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Corporate customers use foreign exchange derivatives for several reasons:

To lock in the current value of foreign-denominated receivables (I)

To lock in the current value of foreign-denominated payables (II)

To lock in the value of expected future foreign-denominated receivables (III)

To lock in the value of expected future foreign-denominated payables (IV) These derivatives are used as a hedging mechanism to manage currency risk and provide certainty regarding future cash flows and costs.

Probability of Default (PD) Increase:If the machinery industry experiences adverse structural changes, the economic conditions worsen for Delta Industrial Machinery Corporation. This results in a higher likelihood of financial distress and potential default. Therefore, the probability of default increases.

Loss Given Default (LGD) Increase:In the event of adverse structural changes, the recovery rates on the loan may diminish due to potential decreases in the value of the company’s assets. Hence, the bank might face higher losses if Delta defaults, leading to an increase in the loss given default.

Duration and Loan Value:An increase in both PD and LGD generally signifies greater risk. To compensate for this increased risk, the loan might be extended or restructured, leading to a longer duration. Higher risk and longer duration typically decrease the present value of the loan, as the expected cash flows are discounted more heavily due to the increased risk.

Beta Bank can directly sell bonds and marketable loans in the secondary market. These instruments are typically more liquid and can be traded between financial institutions.

Credit card loans, on the other hand, are usually not directly sold as they are more personalized and less standardized compared to bonds and marketable loans.

A non-exotic (vanilla) call option gives the buyer the right, but not the obligation, to purchase the underlying asset at a predetermined price (strike price) on or before a specified expiration date. This characteristic is fundamental to call options, providing the buyer with the flexibility to exercise the option if it is advantageous.

The value of foreign exchange options is influenced by several factors, including:

Change in the value of the underlying (I):This directly affects the option's intrinsic value.

Change in the perception of future volatility (II):Higher expected volatility increases the option's potential payoff.

Change in interest rates (III):This affects the cost of carrying positions in the underlying asset.

Passage of time (IV):This influences the time value of the option. All these factors collectively impact the pricing dynamics of options throughout the trading day.

Model Definition:Historical frequency models are used to assign an obligor to a class based on risk characteristics at the time of loan origination and estimate default probability based on the past default rates of that class.

Application:These models use historical data to determine the probability of default by analyzing past defaults within the same risk class, providing a statistical basis for risk assessment.

When the dollar strengthens against the pound, the value of an option that allows the purchase of dollars at a predetermined exchange rate increases. This is because the option provides the right to buy the appreciating dollar at a rate that becomes more favorable as the market rate moves higher.

Bonds and loans are fundamentally different in their legal structures and treatment. Bonds are typically issued in the public markets and are subject to securities laws and regulations, while loans are generally private agreements between a borrower and a lender.

Both instruments can be used to estimate credit capital under Basel II provisions, so option C is incorrect.

The pricing drivers for bonds and loans can overlap significantly, such as interest rates and credit risk, so option B is not the core difference.

Both bonds and loans can be subject to credit counterparty regulations, making option D incorrect.

A country's creditworthiness is typically influenced by various performance statistics that indicate the overall health of its economy. Here’s a detailed analysis of each option:

A. Low unemployment:Low unemployment indicates a healthy labor market, suggesting economic stability and growth, which positively impacts creditworthiness.

B. Low inflation:Low inflation reflects price stability, which helps maintain the purchasing power of the currency and economic stability, thus benefiting creditworthiness.

C. High degrees of investment:High levels of investment indicate confidence in the economy and potential for future growth, positively affecting creditworthiness.

D. Low degrees of savings:Low savings rates can indicate potential issues with financial stability, as it suggests that households and the economy might lack a financial buffer against economic shocks. This can negatively impact creditworthiness, making it the exception in this list.

When a bank enters into long-term fixed-rate loans and interest rates rise, the bank faces higher costs for its deposits and debt if these are linked to floating rates or have shorter maturities. This creates a mismatch between the fixed income from the loans and the increased cost of funds, potentially squeezing the bank's margins.

When a bank has loans in the "pipeline," it means these loans are in the process of origination but have not yet been originated. During this period, the bank is exposed to both interest rate risk and credit risk.

Interest Rate Risk:This risk arises because changes in interest rates can affect the bank's profitability on these loans. If interest rates change unfavorably between the time the loan terms are set and the time the loan is actually issued, the bank might end up earning less than expected. This is particularly relevant in a volatile interest rate environment.

Credit Risk:Even though the loans are not yet originated, the bank assesses the creditworthiness of the potential borrowers during the pipeline stage. If the financial condition of a borrower deteriorates before the loan is finalized, the bank faces the risk of having to deal with a higher probability of default.

These risks are inherent to the loan origination process and are present even before the loan is officially on the bank's books.

Arnold Wu owns a floating rate bond and is concerned about the potential decrease in interest rates, which would reduce his interest payments. To hedge against this risk, he should enter into an interest rate swap where he receives floating and pays fixed. This means he would continue to receive floating rate payments (which would decrease if interest rates fall) while making fixed payments. This swap effectively locks in his interest income, providing protection against falling interest rates.

The pricing of wholesale products is primarily driven by prevailing market prices. Unlike retail products, where marketing and customer retention strategies might influence pricing, wholesale products are priced based on the current market conditions, supply and demand dynamics, and competitive landscape. This ensures that the prices reflect the true market value and risks associated with the products.

VaR calculations depend heavily on the confidence level chosen. Bank G's 1-year VaR of USD 20 million is calculated at a 99% confidence level, while Bank H's 1-year VaR of USD 10 million is calculated at a 95% confidence level. These different confidence levels mean that the probabilities associated with the potential losses are not directly comparable. The 99% confidence level implies a more conservative risk estimate compared to the 95% confidence level, hence no direct risk comparison can be accurately made.

Comprehensive and Detailed In-Depth Explanation:

Securitization involves pooling illiquid assets (e.g., mortgages, loans) and converting them into tradable securities sold to investors, thereby transferring risk and improving balance sheet liquidity. Option C is correct as it describes selling illiquid assets (e.g., loans) via securitization. Option A is vague (“exogenous liquidity” isn’t a standard term), Option B is incorrect (securitization enhances, not reduces, liquidity), and Option D is wrong (liquid assets like cash aren’t typically securitized). GARP’s FRR confirms this process.

To hedge against the risk of decreasing interest rates, a bank should look to reduce the duration of its assets or increase the duration of its liabilities. Decreasing the duration of assets makes them less sensitive to interest rate changes, while increasing the duration of liabilities does the same on the liability side. The bank currently has both assets and liabilities with a duration of 10, so it should decrease the duration of its assets and/or increase the duration of its liabilities to hedge against decreasing interest rates.

Comprehensive and Detailed In-Depth Explanation:

Scenario analysis in operational risk involves constructing hypothetical loss events to estimate potential impacts. Sampling bias occurs when the scenarios selected do not represent the full range of possible outcomes (e.g., over-relying on historical data or excluding rare events), skewing risk estimates. Optimism bias (A) involves underestimating risks, motivation bias (D) reflects personal incentives, anddeterminable bias (C) isn’t a recognized term. Basel II’s AMA encourages diverse data sources to mitigate sampling bias in scenario analysis.

Exact Extract from Official Source:

BCBS, "Basel II: International Convergence of Capital Measurement and Capital Standards," June 2006, para. 672: "Scenario analysis should incorporate a range of plausible events… Banks must avoid biases such as sampling bias, which can arise from unrepresentative data selection."

GARP FRR Study Notes, Operational Risk Section: "Sampling bias in scenario analysis occurs when the chosen scenarios fail to capture the full spectrum of operational risk events, leading to under- or overestimation of potential losses."

Comprehensive and Detailed In-Depth Explanation:

The Basel III Leverage Ratio is a non-risk-based measure designed to limit excessive leverage in the banking system. It is calculated as:

Leverage Ratio = Tier 1 Capital / Total Exposure.

Tier 1 Capital (comprising common equity Tier 1 and additional Tier 1 capital) is divided by Total Exposure, which includes on-balance-sheet assets, derivatives, and off-balance-sheet items (adjusted for credit conversion factors). Basel III introduced this ratio to complement risk-based capital requirements, with a minimum threshold of 3%. Total regulatory capital includes Tier 2, and Tier 3 capital was eliminated under Basel III, making Tier 1 Capital the correct numerator.

The delta-gamma method improves upon the delta-normal method by incorporating the gamma of the options, which accounts for the curvature in the price relationship of the option to the underlying asset. This method better captures the non-linear aspects of option pricing, especially for extreme price movements. Gamma measures the rate of change of delta with respect to the price of the underlying asset, thus allowing for a more accurate reflection of the option's risk profile. By including gamma, the delta-gamma method can more accurately represent the risks associated with both small and large movements in the underlying asset's price, making it particularly effective for capturing the full spectrum of option price risk.