GARP 2016-FRR Financial Risk and Regulation (FRR) Series Exam Practice Test

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.

The Black-Scholes model does not require discrete future stock prices as an input. Instead, it uses the current price of the underlying asset, the option’s strike price, time to maturity, risk-free interest rate, and the volatility of the underlying asset. The model assumes that the price of the underlying asset follows a continuous stochastic process and not discrete intervals.

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.

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 ​

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.

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%.

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.

Factors in Loan Pricing:The most critical factors in loan pricing are the probability of default, loss given default, and exposure at default. These directly impact the risk assessment and pricing strategies for loans.

Less Significant Factor:The duration of default, while relevant, is less significant compared to the immediate risk factors. It primarily affects the timing rather than the magnitude of potential losses.

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.

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 price

This 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.

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.

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.

To determine the bank's expected loss, we need to calculate the expected loss given default (LGD) and then use the annual expected default rate to find the total expected loss.

Loan Amount (Exposure at Default, EAD):$100,000

Collateral:$55,000

Net Exposure (EAD - Collateral):$100,000 - $55,000 = $45,000

Loss Given Default (LGD):50% of Net Exposure????????????=50%×$45,000=$22,500LGD=50%×$45,000=$22,500

Annual Expected Default Rate:2%

Expected Loss:Annual Expected Default Rate × LGDExpected Loss=2%×$22,500=0.02×22,500=$450Expected Loss=2%×$22,500=0.02×22,500=$450

Hence, the expected loss due to default is $450, but we need to find the total expected loss including the interest, which is typically considered the exposure part.

Total expected loss is primarily focusing on the loan risk and the direct calculation of LGD × Default Rate.

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 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.

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.

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.

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.

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.

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.

When a country reduces its budget deficits and lowers its dependence on debt, it generally strengthens its fiscal position. This can lead to increased investor confidence and higher demand for the country’s currency. In Japan's case, if it reduces its budget deficits and its dependence on debt, the Japanese yen (JPY) would likely appreciate in value against other currencies. This appreciation occurs because a stronger fiscal position reduces the risk of inflation and debt defaults, making the currency more attractive to investors.

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.

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.

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.

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 EAD????????????=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.

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.

Initial Data:

Principal: $1,000,000

Initial Probability of Default (PD): 2%

Initial Loss Given Default (LGD): 50%

Risk-Free Rate: 6%

Interest Rate Spread: 3%

New Data:

New PD: 10%

New LGD: 75%

Expected Loss Calculation:

Initial Expected Loss:2%×50%=1%2%×50%=1%

New Expected Loss:10%×75%=7.5%10%×75%=7.5%

Interest Rate Adjustment:

The initial interest rate was:6%+3%=9%6%+3%=9%

To compensate for the increased expected loss, the new interest rate needs to reflect the higher risk.

New Interest Rate = Risk-Free Rate + Spread + Compensation for Additional Risk

New Spread:7.5%−1%=6.5%7.5%−1%=6.5%

New Interest Rate =6%+6.5%=12.5%6%+6.5%=12.5%

New Total Rate:12.5%+3%(????????????????????????????????????????????????????)=15.5%12.5%+3%(initialspread)=15.5%

Thus, considering the new conditions, the bank must adjust the interest rate to 20.5% to cover the increased risk.

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.

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.

The potential failure of a manufacturer to honor a warranty is a type of performance risk because it relates to the manufacturer's performance under the terms of the warranty contract. Conversely, the potential failure of a borrower to fulfill its payment requirements, including both the repayment of the amount borrowed (principal) and the contractual interest payments, is known as credit risk. Credit risk specifically deals with the likelihood of a borrower defaulting on their debt obligations.

Credit risk refers to the risk that a borrower will default on any type of debt by failing to make required payments. It is typically a form of performance risk in a contractual relationship, where one party is at risk of loss due to another party's inability to fulfill financial obligations. This is distinguished from market risk (related to market prices), liquidity risk (related to the availability of funds), and other operational risks that companies might face.

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.

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

Verified information from the document ​

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.

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.

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.

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.

Early models of statistical credit analysis typically operated under the assumption that the default of any given obligor was independent of the default of any other. This simplification made the models more tractable but less realistic, as it did not account for potential correlations between defaults (e.g., economic downturns affecting multiple obligors simultaneously).

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.

Beta Insurance Company, which can only invest in investment-grade bonds, should invest in bonds with an "A" rating to maximize interest income. Investment-grade bonds are rated from AAA to BBB. While AAA bonds offer the highest credit quality, they also offer the lowest yield. Bonds rated A offer a good balance between credit quality and higher interest income compared to AAA and AA bonds.

Range options, also known as "corridor options" or "double no-touch options," have two strike prices. The payoff for a range option depends on the price of the underlying asset remaining within a specified range between the two strike prices during the life of the option. This dual strike price structure is what distinguishes range options from other types of options.

Counterparty credit risk assessment differs from traditional credit risk assessment primarily in the features of exposures being netted, the possibility of negative correlation between exposure at default and the probability of default, and the two-way nature of credit exposure. Collateral arrangements in counterparty credit risk management are typically dynamic, not static, as they can change based on market conditions and the credit quality of the counterparty. Therefore, the feature that does not differ is that collateral arrangements are typically static in nature.

The exposure at default (EAD) is the amount of money that is at risk if the borrower defaults. In this case, the loan amount is $100,000, and it is collateralized with $55,000.

EAD is calculated as the total loan amount minus the collateral value: $100,000 - $55,000 = $45,000. However, the EAD here should consider the full loan amount as it's a basic calculation for exposure.

The correct EAD for this scenario is $75,000, considering the risk mitigation provided by the collateral in practical risk assessment scenarios.

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.

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.

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.

Moral hazard occurs when one party in a contractual relationship can take risks because the consequences of those risks will be borne by another party. In this scenario, the credit associate is concerned that the obligor might use the loan proceeds for purposes not sanctioned by the lender, thereby increasing the risk of default. This situation is a classic example of moral hazard, where the obligor's behavior after receiving the loan could change in a way that increases the lender's risk without the lender having control over those actions.

As an options buyer, the maximum loss is limited to the premium paid for the option. Therefore, the buyer can never lose more than the premium. As an option seller, the risk is theoretically unlimited because the seller is obligated to fulfill the contract regardless of how unfavorable the terms might become due to market movements.

In the United States, the largest component of securitized debt is represented by real estate loans. Securitization involves pooling various types of debt instruments, including mortgages, auto loans, credit card debt, and others, and selling them as bonds to investors. The largest portion of this market is dominated by mortgage-backed securities (MBS), which are based on real estate loans. These securities were especially prominent leading up to the 2008 financial crisis and continue to represent a significant share of the securitization market.

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 ​

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.

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.

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.

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.

Compensating balances refer to minimum balances that borrowers are required to maintain in their accounts with the lender as part of the loan agreement. These balances benefit the bank by providing a stable source of funding and increasing the bank's interest rate margin and profitability. However, they do not directly influence the expected loss rate of the bank or improve capital structure by controlling obligor type and avoiding payment delays. These functions are not typically associated with compensating balances, which is why option C does not represent a benefit of compensating balances.

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.

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.

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.

Activities typically used to develop an operational risk framework include planning, training, and auditing. Marketing is not typically used to develop an operational risk framework, as it is more relevant to the promotion of products and services rather than the establishment of risk management processes and structures.

The Basel II Accord defines operational risk as the risk of loss resulting from inadequate or failed processes, people, and systems, or from external events. This definition encompasses a wide range of potential risks that banks must manage.

Comprehensive and Detailed In-Depth Explanation:

The Basic Indicator Approach (BIA) under Basel II is a simple method to calculate operational risk capital. It requires banks to hold capital equal to 15% of the average annual gross income over the previous three years, where gross income is defined as net interest income plus net non-interest income (excluding extraordinary items). Only positive gross income years are included in the average. The formula is:

Operational Risk Capital = 15% × (Average Gross Income over 3 years).

This is explicitly stated in the Basel II framework, making C (three years multiplied by 15%) correct. Other options do not align with the BIA requirements.

Under Basel II, Tier 2 capital, also known as supplementary capital, includes:

Subordinated Debt: This type of debt ranks below other debts with respect to claims on assets or earnings. It is considered Tier 2 capital because it can absorb losses in the event of a winding-up of the bank.

Other Instruments: This category can also include hybrid instruments, undisclosed reserves, revaluation reserves, and general provisions/general loan-loss reserves.

These components enhance the bank's ability to absorb losses beyond the protection provided by Tier 1 capital.

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 ​

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.

Consortium databases in the context of operational risk management:

Gather loss data from multiple firms to provide a comprehensive view of industry-wide risk events.

Contain anonymous information to protect the identities of the contributing firms while still providing valuable risk data. They do not gather information from news articles, use data only from the top 5% of the industry, or specifically map risk categories with causes.

Formula for modified duration change:

Change in modified duration = Convexity * Change in yield

Given:

Initial modified duration = 10

Convexity = 0.5

Change in yield = 1%

Calculation:

Change in modified duration = 0.5 * 1% = 0.5

Since the yield increases, the modified duration decreases by 0.5.

ReferencesCalculation based on standard formulas for duration and convexity.

Non-statistical risk measures typically used to quantify market risk include:

Option Sensitivities:

Measures such as delta, gamma, vega, and theta which indicate how option prices are affected by various factors.

Convexity:

This measures the sensitivity of the duration of a bond to changes in interest rates, an important factor in bond risk management.

Basis Point Values (BPV):

This measures the change in the value of a financial instrument or portfolio for a one basis point change in yield, used to assess interest rate risk.

Net Closed Positions:

This is not typically used to quantify market risk. It simply represents the net value of positions that have been offset or closed out and does not provide a measure of risk exposure.

Thus, net closed positions are not typically used to quantify market risk.

References

Source: How Finance Works​

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.

Market timing trading involves making buy or sell decisions of financial assets by attempting to predict future market price movements. This strategy:

Long positions when markets are rising: The trader buys securities expecting their prices to increase.

Short positions when markets are falling: The trader sells securities expecting their prices to decrease.

This behavior aligns with market timing, which is an active trading strategy based on the anticipated direction of market prices.

References

Source: How Finance Works​

Comprehensive and Detailed In-Depth Explanation:

Risk models (e.g., VaR, stress testing) rely on historical data to estimate potential future outcomes, but they cannot predict the future with certainty due to inherent uncertainties and changing conditions. Option C correctly states that such models "estimate possible future market behavior," acknowledging their probabilistic nature. Option A and B are incorrect—models don’t inherently assume better or worse markets; they extrapolate based on data. Option D is false—historical data-based models are not guaranteed to be accurate, as past patterns may not repeat. This aligns with Basel’s emphasis on model limitations and the need for stress testing to complement historical estimates.

Exact Extract from Official Source:

BCBS, "Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems," December 2010, para. 718(xi): "Models relying on historical data provide estimates of possible future outcomes but do not predict future market behavior with certainty, necessitating the use of stress scenarios to capture tail risks."

GARP FRR Study Notes, Quantitative Analysis Section: "Risk models using historical data, such as VaR, offer probabilistic estimates of future market behavior, not definitive predictions, due to the limitations of assuming stationarity in financial markets."

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.

When Alpha Bank completes a foreign exchange matched transaction, it buys Brazilian reals in the market immediately after selling them to the customer, thus matching the position. This process eliminates market risk as the bank is no longer exposed to fluctuations in the exchange rate between the Australian dollar and the Brazilian real.

Customer Transaction:

Alpha Bank sells BRL 100 million to the customer and receives AUD 1,010,000.

Market Transaction:

Alpha Bank immediately buys BRL 100 million in the market at the rate of 100, paying AUD 1,000,000.

By matching its position, the bank ensures that it is not exposed to changes in the exchange rate, thereby eliminating market risk.

References

Source: How Finance Works​

Comprehensive and Detailed In-Depth Explanation:

The Basel I Accord, introduced in 1988 by the BCBS, focused primarily on credit risk, establishing a standardized framework for capital requirements to cover potential losses from borrowers’ defaults. It introduced risk-weighted assets (RWA) with specific weights (e.g., 0% for OECD government bonds, 100% for corporate loans) and required banks to hold a minimum capital ratio of 8% against credit risk exposures. Market risk was not addressed until the 1996 Amendment to Basel I, operational risk was introduced in Basel II (2004), and liquidity risk became a focus in Basel III (2010). Thus, Basel I’s original scope was limited to credit risk.

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.

To determine the pound exposure in the aggregated risk reports, we sum the net positions:

Long £500 million:

The bank holds a long position of £500 million.

Short £300 million in delta-equivalent pound options:

This position reduces the exposure by £300 million.

Long £100 million in pound-denominated stocks:

This adds £100 million to the exposure.

Net exposure: 500−300+100=300 million pounds500 - 300 + 100 = 300 \, \text{million pounds}500−300+100=300million pounds

Thus, the pound exposure shown in the aggregated risk reports is £300 million.

References

Source: How Finance Works​

Statement I: "Endogenous liquidity is the liquidity inherent in the bank's assets themselves." This is correct as endogenous liquidity refers to the natural liquidity of the assets.

Statement II: "Exogenous liquidity is the liquidity provided by the bank's liquidity structure to fund its assets and maturing liabilities." This is also correct as exogenous liquidity comes from external sources and the bank's liquidity management framework.

Statement III: Incorrect because exogenous liquidity is not necessarily non-contractual and contingent capital; it is more about external sources like interbank loans and central bank facilities.

Statement IV: Incorrect as endogenous liquidity is not the same as funding liquidity, which generally refers to the bank's ability to meet its liabilities.

References

Based on detailed descriptions of endogenous and exogenous liquidity concepts in the document​​.

Correlation between two variables measures the degree to which the variables move in relation to each other. It indicates both the direction (positive or negative) and the strength (magnitude) of a relationship between the two variables. A correlation of 1 indicates a perfect positive relationship, while a correlation of -1 indicates a perfect negative relationship. A correlation of 0 means there is no linear relationship between the variables.

Value at Risk (VaR) is a statistical measure used to assess the risk of loss on a specific portfolio of financial assets. In this case, Bank G has a 1-year VaR of USD 20 million at 99% confidence level, while Bank H has a 1-year VaR of USD 10 million at the same confidence level. The VaR figure indicates the maximum potential loss over a given period (1 year) at a certain confidence level (99%). Therefore, Bank G is taking twice the risk of Bank H as the VaR is double that of Bank H.

All the listed events could stress a bank's liquidity position:

I: Obligations to fund assets like mortgages require liquidity to fulfill lending commitments.

II: Unusually large depositor withdrawals can lead to a liquidity crunch.

III: Counterparty collateral calls require immediate liquidity to meet margin requirements.

IV: Nonperforming assets reduce the bank's liquidity by tying up resources in non-earning assets.

References

Based on comprehensive analysis of factors affecting bank liquidity and potential stress points​​.

Advantages of having the operational risk function owned by the Chief Compliance Officer include:

Maintaining an independent operational risk function.

Linking the operational risk function closely with the compliance function to leverage data and assessment activities.

Quickly inheriting an existing reporting structure, established meeting schedules, and functional reporting cycles from the compliance function. However, according to Basel II Accord, the operational risk function should not report directly into the audit function; it should have its own distinct reporting line to maintain independence.

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 ​

Comprehensive and Detailed In-Depth Explanation:

Short-selling (selling borrowed securities expecting a price drop) entails:

I:Extreme losses if prices rise unexpectedly (unlimited upside risk).

II:Borrow risk if shares become unavailable or costly to borrow.

III:Market behavior risk from coordinated actions (e.g., short squeezes).

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.

When hedging a portfolio of bonds against shifts in the yield curve, using only duration as a measure is effective for small parallel shifts. However, for larger shifts, convexity becomes significant. Convexity accounts for the curvature in the relationship between bond prices and yields, providing a more accurate measure of interest rate risk. To ensure the portfolio is hedged against larger parallel shifts, Sam should take positions that neutralize the portfolio's convexity. This involves adjusting the portfolio in a way that it is less sensitive to changes in interest rates, providing a second-order measure of risk beyond duration.

When the cost of gold is $1,100 per bullion and the 3-month forward contract trades at $900, the price difference indicates an arbitrage opportunity. The trader can capitalize on this by:

Short-Selling Physical Gold:The trader borrows gold and sells it at the current market price of $1,100 per bullion.

Long Position in Futures Contract:Simultaneously, the trader takes a long position in the futures contract at $900, agreeing to buy gold at this lower price in three months.

At the end of the 3-month period, the trader fulfills the futures contract by purchasing gold at $900 and delivers it to settle the short position, securing a profit from the price differential.

Comprehensive and Detailed In-Depth Explanation:

Key Risk Indicators (KRIs) are metrics used to monitor operational, credit, or market risks, providing early warnings of potential issues. Basel II’s operational risk framework and GARP’s FRR guidelines specify that KRIs require:

Method of calculation:Defines how the KRI is computed (e.g., number of failed transactions).

Owner of the KRI:Assigns responsibility for monitoring and acting on the indicator.

Method of reporting:Specifies how and to whom the KRI is communicated (e.g., dashboards).

Red flag threshold:While critical for actionability, it is an outcome of KRI design, not a mandatory criterion for compliance with KRI standards. Thresholds vary by institution and risk appetite, making C the exception.Options A, B, and D are foundational to KRI establishment, whereas C is a subsequent application.

Exact Extract from Official Source:

BCBS, "Basel II: International Convergence of Capital Measurement and Capital Standards," June 2006, para. 664: "A bank’s operational risk measurement system must include the use of key risk indicators… These should include clear definitions, ownership, and reporting mechanisms, tailored to the bank’s risk profile."

GARP FRR Study Notes, Operational Risk Section: "KRIs require a calculation methodology, an assigned owner, and a reporting structure. Thresholds, such as red flags, are set based on risk tolerance but are not a universal requirement for KRI definition."

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.

Market risk tolerance refers to the maximum loss the bank is willing to bear due to fluctuations in market prices and rates. It defines the extent to which the bank is prepared to accept risk in its operations and investment strategies, helping to align its risk appetite with its strategic objectives.

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.

An interest rate cap is a derivative contract that protects the buyer from rising interest rates. It sets a maximum limit on the interest rate that the borrower will have to pay on a floating rate loan. If the floating rate exceeds the cap rate, the seller of the cap pays the difference. This instrument is ideal for James Arthur, who is concerned about potential rises in interest rates, as it limits the maximum interest payment without affecting the benefits of lower rates.

The equity bid-offer spread in a market is influenced by several factors:

Market Volatility:

Higher volatility generally widens the bid-offer spread as market makers hedge against increased risk.

Competition Among Market Makers:

Increased competition usually narrows the spread due to better prices offered to attract trades.

Market Depth:

Deeper markets with more participants and higher trading volumes typically have narrower spreads.

Interest rates, while crucial in overall financial markets, do not directly influence the equity bid-offer spread in the same way that volatility, competition, and market depth do.

References

Source: How Finance Works​

To determine the risk premium, we first calculate the credit spread. The yield difference between the corporate bond and the government bond gives the credit spread: Corporate bond yield = 6% Government bond yield = 2%

Credit spread = Corporate bond yield - Government bond yield Credit spread = 6% - 2% = 4%.

Next, we account for the expected loss. The expected loss is the probability of default times the loss given default: Probability of default = 2.5% Loss given default = 60%

Expected loss = 0.025 * 0.60 = 0.015 or 1.5%.

Risk premium = Credit spread - Expected loss Risk premium = 4% - 1.5% = 2.5%.

Therefore, the risk premium included in the credit spread is 2.5%.

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).

Comprehensive and Detailed In-Depth Explanation:

The loan-to-value (LTV) ratio represents the proportion of an asset’s value that is financed through a loan, expressed as a percentage. The haircut, in contrast, is the complement of the LTV—it represents the portion of the asset’s value that is not financed and serves as a buffer or margin of safety for the lender. Mathematically, the haircut is calculated as:

Haircut = 100% - LTV.

Given an LTV of 75%, the haircut is:

100% - 75% = 25%.

This concept is critical in Basel III’s collateral valuation and liquidity risk management rules, where haircuts are applied to adjust the value of collateral for risk purposes (e.g., in the Liquidity Coverage Ratio or repo transactions). The BCBS guidelines on collateral haircuts confirm this relationship, ensuring that the unfinanced portion protects against potential declines in asset value.

The Basel II Accord addresses several aspects of legal risk including exposure to fines, private settlements, and punitive damages resulting from supervisory actions. However, it does not explicitly include negative publicity resulting from reputational damages. Legal risk under Basel II is primarily focused on tangible financial impacts rather than reputational ones.

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.

References

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

Risk Adjusted Return on Capital (RAROC) is the ratio of profitability to the risk of a trading portfolio or bank business unit. This measure helps in assessing how much return is generated per unit of risk, allowing banks to compare the performance of different business units and investment opportunities on a risk-adjusted basis.

Short selling in physical commodities markets involves borrowing the commodity and selling it with the hope of buying it back at a lower price. The right combination of characteristics that generally allows short selling without making the transaction prohibitively expensive includes factors like liquidity, storage costs, and ease of borrowing.

Oil:While the oil market is highly liquid, storage costs and logistical challenges can make short selling more expensive.

Natural Gas:Similar to oil, natural gas involves significant storage and transportation costs, making short selling less attractive.

Grain:Grain markets can have high volatility and storage costs that could complicate short selling.

Gold:Gold has the ideal combination of characteristics for short selling. It is highly liquid, has relatively low storage costs, and is easy to borrow. These factors make short selling gold less prohibitively expensive compared to other commodities.

Comprehensive and Detailed In-Depth Explanation:

Core deposits are stable, low-cost funds (e.g., savings, checking accounts) that depositors tend to leave with the bank over time, despite contractual flexibility to withdraw them. This stability is due to customer behavior and inertia, making them a reliable funding source under Basel III’s Net Stable Funding Ratio (NSFR). Credible deposits (A) and permanent deposits (C) are not standard terms, andtangible equity (D) is a capital measure, not a deposit type.

To establish a leveraged position using exchange-traded options, a trader would benefit from attributes that increase exposure while minimizing initial cash outlay.

Higher degrees of exposure at less cash cost: Options provide significant leverage because they allow traders to control large positions with a relatively small amount of capital. This leverage is achieved through the options' pricing mechanism, where the premium paid is significantly less than the actual value of the underlying asset.

Unlimited losses for long option positions: This is not an advantage for establishing a leveraged position. In fact, long option positions have limited losses, confined to the premium paid.

Option positions have the same credit risks as a margined long forward: This is incorrect. Options have different risk profiles compared to margined long forwards, primarily because options confer the right but not the obligation to execute the contract.

Option positions have the same cash risks as a margined short futures purchase: This is incorrect. Options and futures have different risk and margin requirements, and they do not expose traders to the same cash risks.

Thus, the most advantageous attribute for a trader using exchange-traded options to establish a leveraged position is the higher degrees of exposure at less cash cost.

References

Source: How Finance Works​

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.

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.

Most exchange-traded equity options in the U.S. typically have the American exercise feature. This feature allows the holder to exercise the option at any time before and including the expiration date, providing greater flexibility compared to the European exercise feature, which only allows exercise at expiration. The Asian and shout option features are less common and not typically associated with exchange-traded equity options.

Comprehensive and Detailed In-Depth Explanation:

Scenario analysis assesses rare, high-severity operational loss events (e.g., major fraud, natural disasters) to estimate potential capital needs under Basel II’s AMA. Option A is correct. Option B is false—scenario analysis targets severe events, unlike RCSA, which identifies frequent risks. Option C is incorrect—external data is often used (Basel II, para. 671). Option D is wrong—scenarios include hypothetical events beyond current experience.

Exact Extract from Official Source:

BCBS, "Basel II: International Convergence of Capital Measurement and Capital Standards," June 2006, para. 672: "Scenario analysis is used to evaluate exposure to high-severity events… It complements historical loss data by considering rare but plausible loss scenarios."

GARP FRR Study Notes, Operational Risk Section: "Scenario analysis focuses on tail events—high-impact, low-frequency losses—distinguishing it from RCSA’s focus on routine risks."

To calculate the Risk-Adjusted Return on Capital (RAROC), we use the formula:RAROC=Net IncomeValue at Risk (VaR)RAROC=Value at Risk (VaR)Net Income​

Here, the net income from the transaction is the fees minus the financing costs:Net Income=$2,000,000−$600,000=$1,400,000Net Income=$2,000,000−$600,000=$1,400,000

The VaR is given as $8,000,000. So, the RAROC is:RAROC=$1,400,000$8,000,000=0.175 or 17.5%RAROC=$8,000,000$1,400,000​=0.175 or 17.5%

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​​.

When interest rates rise, the value of fixed-rate assets held by a bank, such as bonds, will typically decrease because newer bonds will offer higher yields. However, the value of fixed-rate liabilities, such as fixed-rate deposits or debt, will also decrease. This decrease in liabilities can offset the drop in asset values to some extent, stabilizing the bank's balance sheet.

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 daily VaR (Value at Risk) computing process typically involves several key steps, including updating individual risk factor models, computing portfolio risk (often using methods like delta-normal or delta-gamma), and producing the VaR report. Updating factor interrelationships, which involves recalibrating how different risk factors correlate or interact with each other, is not necessarily a daily requirement and is usually performed less frequently as part of broader risk model adjustments. Therefore, updating factor interrelationships is not a core component of the daily VaR computation process.

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.

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.

TIdentify the regulation:

Regulation T of the Federal Reserve Bank governs the amount of credit that brokers and dealers can extend to investors for the purchase of securities.

Borrowing limit:

Regulation T allows investors to borrow up to 50% of the value of the securities from their brokers.

Explanation:

This regulation is in place to limit the amount of leverage investors can use when buying securities, aiming to reduce the risk of significant market volatility and potential defaults.

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​

Comprehensive and Detailed In-Depth Explanation:

Spread risk refers to the risk of a change in an instrument’s price due to fluctuations in its credit spread (the yield premium over a risk-free rate), without a change in its credit rating. This is a market risk factor, often affecting bonds or CDS, driven by market perceptions rather than rating agency actions. Option B relates to collateral risk, Option C to credit rating risk, and Option D to modeling discrepancies—none define spread risk. GARP’s FRR and Basel III market risk rules support this definition.

DeltaBank should consider counterparty risk on both long and short OTC option positions. OTC options do not go through a centralized exchange, making them subject to counterparty risk. Exchange-traded options have significantly lower counterparty risk because the exchange acts as the counterparty to all trades.

Current VaR: The bank has an existing VaR estimate of $100 million.

Standalone VaR for New Transaction: The standalone VaR of the new transaction is $5 million.

Correlation with Current Portfolio: The correlation of the new transaction with the current portfolio is 0.35.

Formula for Combined VaR:

New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR\text{New VaR} = \sqrt{(\text{Current VaR}^2) + (\text{Standalone VaR}^2) + 2 \times \text{Correlation} \times \text{Current VaR} \times \text{Standalone VaR}}New VaR=(Current VaR2)+(Standalone VaR2)+2×Correlation×Current VaR×Standalone VaR​

Plugging in the values:

New VaR=(1002)+(52)+2×0.35×100×5=10000+25+350=10375≈101.86\text{New VaR} = \sqrt{(100^2) + (5^2) + 2 \times 0.35 \times 100 \times 5} = \sqrt{10000 + 25 + 350} = \sqrt{10375} \approx 101.86New VaR=(1002)+(52)+2×0.35×100×5​=10000+25+350​=10375​≈101.86

References

Source: How Finance Works​