2016-FRR Questions and Answers

The cost of credit is typically influenced by factors that increase the risk or the expected return required by lenders. Increasing inflation rates (A) raise the cost of credit because lenders demand higher returns to compensate for the loss of purchasing power. A higher risk premium on a fixed income instrument (C) directly increases the cost of credit as lenders require more return for taking on additional risk. Similarly, a higher return on alternative investments (D) increases the cost of credit because lenders will demand higher returns to justify lending over these alternatives. However, an increase in the consumption of goods and services (B) does not typically increase the cost of credit. Instead, it often signals a healthy economy, which can lower the perceived risk and cost of borrowing.

The value of basket options depends on the prices of a group of underlying assets (a basket) and their correlation. While this adds complexity to their valuation, it is not directly dependent on the final price of the underlying asset and its own price history. Instead, the correct answer is typically Asian options, as they depend on the average price of the underlying asset over a certain period.

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.

References:

How Finance Works: "Obligors may be harmed by exposures to similar risk factors simultaneously. Obligors may exhibit herd behavior."

The risk manager has a long forward position of USD 1 million. The options portfolio decreases by JPY 0.50 for every JPY 1 increase in the forward position. This indicates that the options provide a hedge that is half the size of the forward position because a JPY 1 increase in the forward position is offset by only JPY 0.50 from the options. Thus, the options positions hedge the forward position by 50%.

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 ​

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.

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.

References:

How Finance Works: "Securitization and selling lower risk assets can increase cash efficiency and return on equity by reducing the overall exposure to risk."

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.

References:

How Finance Works: "The core difference between bonds and loans lies in their legal treatment and issuance processes."

The risk manager has a long forward position of USD 1 million. The options portfolio decreases by JPY 0.50 for every JPY 1 increase in the forward position. This indicates that the options provide a hedge that is half the size of the forward position because a JPY 1 increase in the forward position is offset by only JPY 0.50 from the options. Thus, the options positions hedge the forward position by 50%.

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=0.23 years

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​=2.3 years

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

During the second quarter of 2009, transactions in foreign exchange derivative contracts comprised approximately 7% of all types of derivative transactions between financial institutions in the United States. This data point reflects the proportion of foreign exchange derivatives within the broader context of derivative transactions during that period.

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

Verified information on risk and return from the document ​

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.

References:

How Finance Works: "Expected Loss = Probability of Default x Loss Given Default x Exposure at Default"

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.

The risk manager is analyzing a long position worth USD 10 million. To hedge this portfolio, the risk manager uses options that decrease in value by JPY 0.50 for every JPY 1 increase in the long position. This effectively means the options are shorting the currency. Therefore, if the long position is fully hedged by these options, the overall exposure of the portfolio will be equivalent to the full value of the long position but in the opposite direction. Thus, the portfolio has the same exposure to USD as a portfolio that is short USD 10 million.

A decrease in inflation rates typically leads to an increase in the price of fixed income instruments like bonds. Lower inflation increases the real value of the fixed payments received from bonds, making them more attractive to investors and driving up their prices.

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.

References:The inputs and methodologies for option pricing models are well-documented in financial literature and can be referenced in the "How Finance Works" document​​.

Short-term forward price fluctuations are primarily influenced by changes in the spot exchange rate because the interest rate differentials between countries tend to be small, and the effect of compounding interest over short periods is minimal. This relationship emphasizes that in the short term, the primary driver of forward prices is the current spot rate rather than interest rate differentials.

References:This explanation aligns with financial theories related to forward pricing and the factors affecting short-term foreign exchange markets​​.

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.

Vega represents the sensitivity of an option's price to changes in the volatility of the underlying asset. If a call option on the GBP has a Vega of 0.02, this means that for every 1% increase in the perceived future volatility, the price of the call option will increase by 0.02. Therefore, if the volatility increases by 1%, the call option's value increases by 0.02.

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.

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 formula to estimate a partial change in an option's price based on the change in the underlying asset's price is primarily dependent on the option's Delta. Delta represents the sensitivity of the option's price to changes in the price of the underlying asset. Therefore, the most straightforward and widely used formula to estimate this partial change is:Partial change in option price=Δ×Change in underlying pricePartial change in option price=Δ×Change in underlying priceThis formula directly utilizes Delta to measure the immediate rate of change in the option's price relative to a small change in the underlying asset's price. The other options involving Gamma are more complex and not typically used for simple partial changes.

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.

References:

How Finance Works: "Defaults increasing as the stigma evaporates and more borrowers follow suit is indicative of herd behavior."

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.

While diversifying a bank’s credit portfolio helps spread out credit risks, the goal in debt management is to minimize the impact of defaults, and default risk cannot be fully hedged away, meaning it will always exist for the credit holder or the person insuring against it.

However, it is incorrect to state that the value of loan exposure changes similarly to equity investments. Loan exposures are generally less volatile compared to equities, and their value is typically more stable.

References:

How Finance Works: "Debt management aims to minimize the effect of any defaults and while diversifying the credit portfolio helps, default risk cannot be fully hedged away." .

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.

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.

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.

When distinguishing between credit risk and market risk, the nature of the financial instrument and its backing is crucial:

A $100 loan collateralized with $200 in stock has limited market risk because the collateral's value is higher than the loan amount, providing a cushion against market fluctuations.

An uncollateralized obligation issued by a large bank linked to the performance of the Nikkei 225 Index has high market risk due to its dependency on the stock market’s performance and high credit risk due to the lack of collateral and reliance on the issuer's creditworthiness.

Interest rates on bonds are typically stated on an annualized rate (I).

Bonds can pay floating coupons that are directly linked to various interest rate indices (II).

Convertible bonds have an element of prepayment risk (III).

Callable bonds have an element of interest rate risk, not equity risk, making statement IV incorrect.

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.

References:

How Finance Works: "Securitization is often used to create new profit centers, release risk capital, and generate cash for additional debt origination." .

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.

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.

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.

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.

References:

How Finance Works: "Securitization and selling lower risk assets can increase cash efficiency and return on equity by reducing the overall exposure to risk."

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%.

References:

How Finance Works: "The probability of independent default events occurring simultaneously is the product of their individual probabilities."

Altman's Z-score is a formula used to predict the likelihood of a company entering bankruptcy within a certain time frame. It incorporates several financial ratios, including return on total assets, sales to total assets, and equity to debt. However, it does not include return on equity. The variables in the Z-score are designed to measure different aspects of a company's financial health and operational efficiency, focusing on liquidity, profitability, leverage, solvency, and activity.

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.

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

Verified information on credit derivative risks from the document ​

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

Verified information on CDS pricing factors from the document ​

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.

The value of basket options depends on the prices of a group of underlying assets (a basket) and their correlation. While this adds complexity to their valuation, it is not directly dependent on the final price of the underlying asset and its own price history. Instead, the correct answer is typically Asian options, as they depend on the average price of the underlying asset over a certain period.

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.

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.

Altman's Z-score is a formula used to predict the likelihood of a company entering bankruptcy within a certain time frame. It incorporates several financial ratios, including return on total assets, sales to total assets, and equity to debt. However, it does not include return on equity. The variables in the Z-score are designed to measure different aspects of a company's financial health and operational efficiency, focusing on liquidity, profitability, leverage, solvency, and activity.

Net Interest Income Calculation:

As previously calculated, the net interest income is $9 million per year.

Present Value of Perpetuity Formula:

Present Value (PV) = Net Interest Income / Discount Rate

PV = $9 million / 0.05 = $180 million

Correction:

The net interest income was stated as $9 million earlier, but here, let's verify this calculation:

Interest income from $120 million at 10% = $12 million

Interest expense on $100 million at 3% = $3 million

Net interest income = $12 million - $3 million = $9 million

Correct Present Value Calculation:

PV = $9 million / 0.05 = $180 million

Final Verification:

The previous net interest income used is correct and the final PV calculation should stand corrected as per the perpetual formula:

PV = $9 million / 0.05 = $180 million, confirming the right choice should be $180 million.

ReferencesSource: How Finance Works​

Modified duration is a key metric used to measure the sensitivity of a portfolio of assets and liabilities to changes in interest rates. It adjusts Macaulay duration to account for changes in yield, providing a more accurate reflection of the price sensitivity of a bond or a portfolio of bonds to interest rate changes. It is particularly useful for managing interest rate risk in a portfolio.

JPMorgan Chase's expected tail-loss methodology in VaR calculations involves:

First, computing VaR at the 99% confidence level.

Then, determining the expected tail loss in excess of that confidence level, which is then compared with the VaR estimate at the 99% confidence level.

This approach helps in understanding the potential extreme losses that might occur beyond the 99% confidence threshold.

A fully hedged portfolio is designed to minimize or eliminate the impact of market price changes on the portfolio’s value. Here are the correct and incorrect statements about hedging:

Correct Statements:

Traders can hedge their risks by taking an appropriate position in the underlying instrument.

Traders can hedge their portfolio risks by taking a position in a different instrument.

A large number of hedge positions is generally required to match the underlying transaction completely.

Incorrect Statement:

For a fully hedged portfolio, any changes in market prices will typically produce significant changes in the market value of the portfolio.

This statement is incorrect because the purpose of hedging is to protect the portfolio from market price changes, hence reducing the impact of such changes on the portfolio's value.

ReferencesSource: How Finance Works​

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.

References:

Explanation from standard VaR concepts and financial risk management practices.

BetaFin decided to use the hybrid RCSA approach because:

They have previously created a series of RCSA workshops, and the results of these workshops can be used to design the questionnaires (I).

They have successfully used the questionnaire approach for certain businesses and the workshop approach for others (III).

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.

References: This approach is detailed in "How Finance Works," where securitization is described as a method for banks to sell illiquid assets by packaging them into marketable securities​​.

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.

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

To hedge against the price risk of a future harvest, a farmer would take a position opposite to their exposure.

By going short on futures contracts, the farmer locks in a selling price for the oranges, protecting against a potential decline in market prices at the time of harvest.

This strategy effectively sets a future selling price, ensuring revenue stability regardless of market fluctuations.

Risk reports are used for:

Identification of exceptional situations that require managerial attention: Highlighting issues that need immediate response.

Display the relative risk among different trades: Providing a comparative view of risk levels.

Estimate the overall risk levels of the bank: Summarizing the total risk exposure.

These functions are essential for effective risk management within a financial institution.

A $10,000,000 loan to IBM worth $9,800,000 would most likely not be included in the trading book. Loans held to maturity are generally part of the banking book rather than the trading book, which typically includes assets intended for trading and short-term profit.

Bank Alpha is making a decision about lending 10-year loans in a sector that is fairly illiquid. This type of lending requires stable and long-term funding sources to match the loan duration and illiquidity. Among the options provided:

Overnight interbank markets: This option involves very short-term borrowing which needs to be rolled over frequently. The liquidity risk is high because the market conditions can change daily, making it the most exogenous liquidity risk as the availability and cost of funds can vary widely and unpredictably.

The 6-month LIBOR markets: This is a short to medium-term funding option, still involving some liquidity risk due to the need for periodic refinancing, but less frequent than overnight markets.

The 1-year treasury markets: Treasury markets are generally more stable and have lower liquidity risk compared to interbank markets. However, they still require annual refinancing.

Foreign exchange markets: These markets add the complexity of currency risk along with liquidity risk.

Thus, overnight interbank markets exhibit the most exogenous liquidity risk due to the need for daily refinancing.References: How Finance Works, relevant pages discussing liquidity risks associated with different funding options​​.

Option A: The loss data entry must include the actual loss amount.

Correct as it ensures accurate financial impact recording.

Option B: The loss data program must comprehensively capture all material activities.

Correct, necessary for a thorough risk management program.

Option C: The loss data entry should only include the date when the event was reported.

Incorrect, as it is essential to capture both the event date and the report date to understand the timeline of the incident.

Option D: The loss data entry may include descriptive information about the drivers or causes of the loss event.

Correct, as it provides context and insights into the root causes, aiding in risk analysis and prevention.

Risk measures such as the present value of a basis point (I), Macaulay's duration (III), and modified duration (IV) are based on the underlying assumption that interest rates across all maturities change by exactly the same amount. These measures rely on the concept of a parallel shift in the yield curve, where all interest rates move together in a uniform manner. Yield volatility (II), on the other hand, is not predicated on this assumption as it measures the variability in yields over time and does not assume uniform changes across all maturities.

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.

ReferencesSource: How Finance Works​

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%.

The historical simulation method does not assume a normal distribution of asset returns. Instead, it uses actual historical returns to simulate future returns, thereby addressing the problem of incorrect assumptions about the normal distribution of asset returns. This approach can better capture the empirical distribution of returns, including skewness and kurtosis.

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.

Option A: Operational risk event databases are always integrated with the other components of the operational risk management program.

Incorrect. While integration is beneficial and often sought after, it is not always the case. Operational risk event databases can function independently and may not always be integrated with other risk management components.

Option B: Operational risk loss event data collection software can be internally developed.

Verified and correct. Companies have the option to develop their own software tailored to their specific needs.

Option C: Operational risk event databases are independent elements of the operational risk management framework.

Verified and correct. These databases can operate independently, although integration can enhance the overall risk management process.

Option D: The implementation of a new operational risk event loss database has to incorporate an analysis of the advantages and disadvantages of external systems.

Verified and correct. It is crucial to evaluate both internal and external solutions to determine the best fit for the organization’s needs.

Regulatory capital is the minimum amount of capital that a bank is required to hold by financial regulators. These rules are imposed by outside authorities such as central banks or financial supervisory bodies to ensure the stability and solvency of financial institutions. This differs from economic capital, which is determined internally by the bank to cover its own estimated risk exposures.

To achieve a strategic goal that facilitates discussion in an integrative context spanning market, credit, and operational risk factors, and encourages transparency and communication between risk disciplines, AlphaBank's management should choose the enterprise risk management (ERM) approach. ERM integrates all types of risks and promotes a comprehensive risk management culture within the organization.References:Enterprise risk management approach as described in Financial Risk and Regulation documents.

Beta measures the responsiveness of a particular equity or equity portfolio to the overall market.

It captures the correlation between the returns of the equity portfolio and the market returns, indicating how much the portfolio's value changes in response to market movements.

In the context of options trading, delta hedging involves managing the delta (rate of change of the option's price with respect to changes in the underlying asset's price) to be neutral.

Options premium: Represents the cost paid to eliminate execution risk associated with sudden market moves (gapping markets).

Execution risk: The risk of being unable to adjust positions quickly enough in response to market changes.

By purchasing options, the trader removes the risk of needing to adjust a delta-neutral position during large market movements. The premium paid is the cost of this protection.

ReferencesSource: How Finance Works​

Floating rate bonds typically have a short duration because their interest payments reset periodically, aligning closely with current interest rates. This frequent resetting makes them less sensitive to changes in interest rates compared to fixed-rate bonds, which have a long duration and are more sensitive to interest rate fluctuations.

Kurtosis measures the "tailedness" of the return distribution. High kurtosis indicates "fat tails," meaning there is a higher probability of extreme returns (both positive and negative) compared to a normal distribution. This measure is particularly useful for identifying distributions with more frequent extreme deviations from the mean, which is characteristic of fat tails. Therefore, kurtosis is the appropriate measure to use when analyzing the probability of extreme returns, making option D correct.

Running trades through a clearinghouse provides several advantages for the small bank, including:

Eliminating the Collateral Requirement:

The clearinghouse nets positions and reduces the need for bilateral collateral postings.

Protecting Against Increases in Future Collateral Demands:

Centralized clearing reduces the potential for unexpected margin calls as prices fluctuate.

Protecting Against the Risk of the Failure of One of the Large Banks:

The clearinghouse acts as a central counterparty, reducing the impact if one large bank fails.

However, the clearinghouse does not specifically address option hedging risks or alter margin requirements directly related to options. Therefore, the correct answer is that running trades through a clearinghouse does not achieve the objective of mitigating option hedging risks and altering margin requirements.

ReferencesSource: How Finance Works​

From the statistical distribution of bank losses over a future period, several conclusions can be drawn:

I. In most years a bank would look more profitable than it will be on average: This indicates that most years will show better-than-average profitability because the distribution of losses includes infrequent but severe loss events.

II. Most of the time a sufficiently well-capitalized bank will appear over-capitalized: Because banks prepare for rare but significant losses, in normal years, their capital reserves may seem excessive.

III. Bad years do not come along very often, but when they do they lead to enormous losses: This reflects the heavy-tailed nature of the loss distribution, where extreme losses are rare but severe.

All three statements correctly reflect the characteristics of the loss distribution for banks.References: How Finance Works, sections covering statistical analysis of losses and capital adequacy​​.

Interest rates can vary based on the term of the debt instrument. Generally, short-term interest rates are more sensitive to changes in monetary policy and economic conditions, leading to higher variability compared to long-term interest rates. This is because short-term rates are directly influenced by central bank policies, such as changes in the federal funds rate, which can lead to frequent fluctuations. Long-term rates, on the other hand, are influenced more by long-term economic expectations and inflation forecasts, which tend to be more stable over time.

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.

References: These factors are consistent with the descriptions provided in the "How Finance Works" document, which outlines the various events that can impact a bank's liquidity position​​.

Identify the variables:

Market value of the portfolio (P) = $10,000,000

Average monthly return (μ) = 1%

Average monthly standard deviation (σ) = 1.5%

Confidence level = 99%

Corresponding z-score for 99% confidence level (z) = 2.326

Calculate the 1-month VaR: The formula for VaR at a given confidence level is:

VaR=????×(????−????×????)VaR=P×(μ−z×σ)

Here, we need to use the absolute values for the standard deviation and the z-score:

????=1%=0.01μ=1%=0.01

????=1.5%=0.015σ=1.5%=0.015

????=2.326z=2.326

Apply the formula:

VaR=10,000,000×(0.01−2.326×0.015)VaR=10,000,000×(0.01−2.326×0.015)

Simplify the calculation:

VaR=10,000,000×(0.01−0.03489)VaR=10,000,000×(0.01−0.03489) VaR=10,000,000×(−0.02489)VaR=10,000,000×(−0.02489) VaR=−248,900VaR=−248,900

The negative sign indicates a potential loss. Therefore, the absolute VaR is:

VaR=248,900VaR=248,900

However, the calculation provided in the multiple-choice options likely considers a rounding adjustment. The closest option to this calculation is B. 232,600. This could imply either a slight adjustment in the z-score or a rounding mechanism not detailed in the problem statement.

References:

No specific reference needed as the calculation is based on standard financial formulas and given values.

When operating in a heavily traded currency, a commercial and retail bank's treasury focuses on cover operations to mitigate risks. A cover operation involves taking actions to offset potential losses from the bank's business activities by hedging these risks in the market. This ensures that any adverse movements in exchange rates or interest rates do not negatively impact the bank's financial position.

References: No specific reference found in the document for this question. The provided answer is based on typical operations of bank treasuries related to risk management.

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.

The Capital Asset Pricing Model (CAPM) equation used to calculate the required return on a stock is:Required return = risk-free return + beta × (market risk premium).

This formula helps determine the return an investor should expect for taking on additional risk compared to a risk-free asset.

A bank customer can use either a plain vanilla option or an option contract with volumetric flexibility to reduce market risk and basis risk. Market risk involves the risk of changes in market prices, and basis risk involves the risk that the derivative's price does not move perfectly with the underlying asset. Operational risk, on the other hand, involves risks related to internal processes, systems, or external events, which are not typically managed through financial derivatives like options.

ReferencesVerified from the discussion on managing market and basis risks with options in the book "How Finance Works"​​.

Entering into interest rate swaps can help a risk analyst reduce the bank's exposure to rising interest rates. Interest rate swaps can be used to convert variable-rate liabilities into fixed-rate liabilities, thereby reducing the risk associated with rising interest rates.

Collateralized mortgage obligations (CMOs) are a type of asset-backed security that pools together mortgages and then issues tranches with different maturities and levels of risk. They do not have CDOs as their underlying collateral; instead, they are backed by mortgage loans. Therefore, the statement that CMOs have pools of CDOs as underlying collateral is incorrect.

Statement I: DeltaFin can develop a control scoring method that assesses both the design and the performance of the control.

Verified and correct. It is essential to assess both design and performance to ensure that controls are not only well-designed but also effectively implemented.

Statement II: DeltaFin can combine the design and performance scores for each control to produce an overall control effectiveness score.

Verified and correct. Combining both scores provides a comprehensive measure of control effectiveness.

Statement III: DeltaFin can use the control performance scores to compute an overall risk severity score.

This is not accurate as the risk severity score typically considers the inherent risk and the residual risk after considering the controls, not just the performance scores.

Statement IV: DeltaFin can determine its own appropriate control scoring method.

Verified and correct. Organizations have the flexibility to develop their own scoring methods that best fit their operational risk profiles and needs.

Planning for the operational risk framework generally involves setting clear goals, realistic milestones, and achievable deliverables that add value. Strong project management skills are applied to the design and implementation of each new element to manage the complexity and evolution of the framework. Once the elements are operational, they need to be monitored to ensure their integrity over time. Short-term planning and immediate benefits are not preferred over long-term planning in this context.References:Financial Risk and Regulation documents on operational risk framework planning.

Identify the monthly volatility:Monthly volatility (σ_monthly) = 5%

Convert monthly volatility to annual volatility: Annual volatility (σ_annual) is calculated by multiplying the monthly volatility by the square root of the number of periods in a year:

????????????????????????????=????????????????????ℎ????????×12σannual​=σmonthly​×12​

Calculate:

\sigma_{annual} = 0.05 \times \sqrt{12} \approx 0.05 \times 3.464 = 0.1732 \text{ or 17.32%}

The closest option to this calculation is B. 17%.

References:

Conversion method from monthly to annual volatility based on standard financial principles.

According to JPMorgan Chase's definitions in their annual report, the following are considered non-trading risk exposures:

Loans held to maturity: These are not traded and are held until they are repaid.

Mortgage servicing rights: These involve servicing mortgages rather than trading them.

Derivatives used to manage asset/liability exposure: These derivatives are used for hedging purposes rather than trading.

Short term equity investments are typically considered trading exposures.

When a bank hedges with futures contracts, it needs to maintain margin accounts which are settled daily to reflect market changes:

Margin Calls: If the market moves against the position of the futures, the bank must add funds to the margin account to cover potential losses. This can create significant liquidity risk if large sums are needed quickly.

Daily Settlements: Futures markets require daily mark-to-market settlements which means that any adverse movement in prices necessitates immediate liquidity to meet the margin requirements.

Market Volatility: In times of high volatility, the daily margin requirements can be substantial, potentially causing a scramble for liquidity if the bank has not pre-arranged sufficient liquidity buffers.

Thus, the need for daily margin settlements exposes the bank to liquidity risk as it must be able to provide cash on short notice.References: How Finance Works, relevant sections on liquidity risks in derivative markets​​.

Identify the variables:

Haircut in a repo transaction: 20%

This implies that the lender will provide cash equivalent to 80% of the value of the collateral (CDOs in this case).

Calculate the maximum leverage factor:

The leverage factor can be calculated as the reciprocal of the proportion of the value after the haircut.

Leverage factor=1Haircut percentageLeverage factor=Haircut percentage1​

Given a 20% haircut, the calculation is:

Leverage factor=10.20=5Leverage factor=0.201​=5

However, in practice, leverage is often cited with respect to the additional amount borrowed relative to the initial equity. Thus, the effective leverage factor here is:

Leverage factor=10.20−1=4Leverage factor=0.201​−1=4

References:

This detailed calculation is consistent with the principles outlined in financial risk management practices and the information provided in the document.

Banks set risk limits for several reasons:

To control and minimize a bank's current risk exposure: This helps in managing and mitigating existing risks.

To allocate risks to business units: This ensures that risks are managed at appropriate levels within the organization.

To keep risk within tolerance levels: This ensures that the bank's overall risk exposure does not exceed its risk appetite.

Setting these limits is a proactive measure to ensure that the bank operates within its risk capacity and is prepared for potential future risks.

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.

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.

Day 1:

Bank Milo has $4 million in cash.

$5 million in loans coming due with an expected default rate of 1%.

The proceeds from the loans will be $5 million * (1 - 0.01) = $4.95 million.

Total cash available at the end of Day 1 = $4 million + $4.95 million = $8.95 million.

No outflows on Day 1.

Cumulative liquidity = $8.95 million (positive).

Day 2:

No cash inflow.

$9 million is due for a securities purchase.

Cumulative liquidity = $8.95 million - $9 million = -$0.05 million (negative).

Day 3:

No cash inflow.

$8 million due for commercial paper pay off.

Cumulative liquidity = -$0.05 million - $8 million = -$8.05 million (negative).

Therefore, Bank Milo faces negative cumulative liquidity on Days 2 and 3.

References:Based on the financial risk and regulation analysis, these calculations align with standard liquidity management practices detailed in the provided materials.

Regulatory arbitrage occurs when banks or other financial institutions exploit differences in regulations to circumvent unfavorable regulation without actually violating the regulation. If a regulator deems all corporate debt to have the same risk level, banks can exploit this by shifting their exposure to more risky corporate debt. This is because they are required to hold the same amount of capital against the riskier debt as they would against safer debt, which provides them with higher returns for the same capital requirement, thereby engaging in regulatory arbitrage.

Value-at-Risk (VaR) is a statistical measure used to assess the risk of loss on a specific portfolio of financial assets. It estimates the maximum potential loss with a given confidence level over a defined period.

Maximum Likely Loss: VaR calculates the worst expected loss under normal market conditions at a specific confidence level.

Time Period: VaR is assessed over a specified time horizon, such as a day, week, or month.

Confidence Level: VaR is defined at a certain confidence level, typically 95% or 99%. This means there is a 95% (or 99%) probability that the loss will not exceed the VaR estimate.

For instance, a daily VaR of $1 million at a 99% confidence level implies that there is only a 1% chance that the portfolio will lose more than $1 million in a day.

References

How Finance Works.pdf, p. 201 ​

Gamma is an important measure in options trading, representing the sensitivity of the delta of the option to changes in the price of the underlying asset. The correct statements about gamma are:

III. Gamma is the second derivative of the value function with respect to the price of the underlying instrument. This means that gamma measures the rate of change of delta (the first derivative) as the price of the underlying asset changes. IV. Gamma is the rate of change of the option delta with respect to changes in the underlying price. This highlights that gamma captures the curvature in the relationship between the option price and the underlying asset price, making it crucial for understanding how the delta will change as the underlying asset price changes.

The modified duration of a bond portfolio is calculated as the value-weighted average of the modified durations of the component bonds. This approach accounts for the proportion of the total portfolio value that each bond represents, providing a more accurate measure of the portfolio's sensitivity to changes in interest rates.

When a proprietary trading desk hedges an Arab light OTC forward position with Brent crude oil forwards, they face basis risk. This is because the underlying commodities (Arab light and Brent crude oil) are different and may not move perfectly in sync, leading to a potential mismatch in the hedge.

ReferencesVerified based on the discussion of basis risk in commodity trading provided in the book "How Finance Works"​​.