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

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.

Counterparty credit risk refers to the risk that the counterparty to a financial contract will default before the final settlement of the contract's cash flows, resulting in a financial loss. This is correctly stated in option A.

The exposure at default (EAD) is indeed variable due to fluctuations in the underlying valuations, such as swaps, as mentioned in option B.

The EAD can be negatively correlated with the probability of default (PD) because as the credit quality of a counterparty deteriorates, their exposure may also decline, correctly stated in option C.

However, dynamic collateral provisions are typically designed to reduce counterparty risk by adjusting collateral requirements based on changes in exposure and credit quality, not to increase it. Therefore, option D is incorrect.

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.

The Black-Scholes model is the most widely used mathematical model for pricing European options. Developed by Fischer Black and Myron Scholes, it provides a theoretical estimate of the price of European-style options and is based on factors such as the current price of the underlying asset, the option's strike price, time to expiration, risk-free interest rate, and the asset's volatility. This model is particularly popular because of its relative simplicity and the accuracy of its predictions under a wide range of market 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.

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.

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.

To determine the appropriate interest rate to charge, Alpha Bank needs to cover the risk-free rate, the spread, and the expected loss due to default. The formula used is: Risk-free rate + Spread + (Probability of Default x Loss Given Default). Substituting the given values: 6% (risk-free rate) + 3% (spread) + (0.02 x 0.50) = 6% + 3% + 1% = 10%.

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 ​

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.

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.

As of April 2007, the three most widely traded currencies on the global foreign exchange market in decreasing order of market share were the United States dollar (USD), the European euro (EUR), and the Japanese yen (JPY). This ranking reflects the liquidity and trading volume associated with each currency, with the USD being the most traded, followed by the EUR and then the JPY.

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.

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 nottypically increase the cost of credit. Instead, it often signals a healthy economy, which can lower the perceived risk and cost of borrowing.

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

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.

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.

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 relationship that approximates the yield on a risk-free instrument, excluding the credit quality of the Credit Default Swap (CDS) protection seller, is given by the combination of a bond and a CDS. The bond provides the base yield, and the CDS offers protection against default, together creating an instrument that mimics the characteristics of a risk-free yield by hedging against credit risk.

References

Verified information on risk-free yield approximation from the document ​

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

The 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 ​

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.

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

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

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.

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

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.

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.

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

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.

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.

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.

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

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

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

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

References

Verified information from the document ​

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.

Gamma Bank would typically accept the following as financial collateral:

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

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

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

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

References

Verified information on acceptable financial collateral from the document ​

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.

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.

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.

Market-linked credit risk drivers often face specific disadvantages:

Need to supply a large number of input parameters to the model:Complex models require numerous data inputs, which can be challenging to obtain and maintain.

Slow computation speed due to higher simulation complexity:The complexity of these models can lead to slower computation times, making them less efficient for real-time analysis.

Non-linear nature of models and the need to estimate unknown variables are also relevant but are not as primary disadvantages as the first two mentioned.

References

Verified information from the document ​

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.

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 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 value of the USD against other foreign currencies is influenced by various factors. An increase in the US current account surplus (D) would likely strengthen the value of the USD. This is because a current account surplus indicates that the US is exporting more goods and services than it is importing, leading to higher demand for the USD by foreign buyers who need it to pay for US exports. This increased demand for the USD relative to other currencies results in an appreciation of the USD.

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

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

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.

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.

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.

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.

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.

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.

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

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

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

The most convenient approach for a credit analyst to quantify the credit risk exposure for the bank would be to analyze the distribution of the bank's credit losses and map credit risks at various statistical levels. This method provides a comprehensive view of potential losses and the probabilities associated with different loss levels, which is crucial for effective risk management and regulatory compliance.

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

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.

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 ​

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.

From the bank's point of view, repricing the retail debt portfolio introduces risks primarily related to fluctuations in interest rates and bank spreads. When interest rates change, the cost of funds for the bank can fluctuate, which affects the interest margins (bank spreads). Additionally, the repricing of existing debt to match current market rates introduces direct exposure to interest rate volatility. Therefore, the risks associated with fluctuations in these areas are III. Interest rates and IV. Bank spreads.

Market risk typically involves risks that affect the entire market or market segment. These include:

Unexpected changes in the term structure of interest rates:

This affects the prices of bonds and other interest-rate-sensitive securities.

The JPY depreciating against the USD:

This is an example of foreign exchange risk, which is a type of market risk.

Changes in the oil price due to the discovery of new oil fields:

This affects commodities markets and can have broader economic implications.

Increased default rate on commercial mortgages due to higher interest rates:

This is more of a credit risk than market risk. It specifically relates to the creditworthiness of borrowers rather than the overall market movements.

Thus, the increased default rate on commercial mortgages due to higher interest rates is not a typical source of market risk.

References

Source: How Finance Works​​

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.

The TED spread is the difference between the interest rates on interbank loans and short-term U.S. government debt (T-bills). A decrease in the TED spread suggests that the perceived credit risk in the banking sector has decreased. This is because the lower spread indicates that banks are more confident in lending to each other, reflecting lower default risk on interbank loans. This typically happens in response to improved economic conditions or increased confidence in the banking system's stability.

Option A:Use of benchmarked data reflects similar data collection standards.

Incorrect. Benchmarking ensures that data is collected using similar standards, enhancing comparability and reliability.

Option B:External events are usually not of interest to senior management.

Incorrect. External events provide valuable insights and lessons that are often of significant interest to senior management.

Option C:If the external data is gathered from news sources, it may only reflect events that are interesting to the press.

Verified and correct. Data sourced from news can be biased towards more sensational events, potentially missing out on less newsworthy but equally important incidents.

Option D:They provide a source of data on what operational loss events will occur.

Incorrect. External databases provide historical data that can inform risk assessments but do not predict future events directly.

Comprehensive and Detailed In-Depth Explanation:

The recovery rate is the percentage of the original exposure recovered, adjusted for the time value of money and recovery costs. Here, the exposure at default (EAD) is USD 20 million, the gross recovery after one year is USD 10 million, and the recovery cost is USD 1 million. The recovery discount rate is 10%, reflecting the time value of money over one year.

Step-by-step calculation:

Net Recovery Amount:Gross recovery - Recovery costs = USD 10 million - USD 1 million = USD 9 million.

Present Value of Recovery:Since the recovery occurs after one year, discount the net recovery at 10%:PV = USD 9 million / (1 + 0.10) = USD 9 million / 1.1 ≈ USD 8.1818 million.

Recovery Rate:Divide the present value of the recovery by the original exposure:Recovery Rate = (USD 8.1818 million / USD 20 million) × 100 ≈ 40.91%, which rounds to 41%.

This aligns with Basel II/III definitions of Loss Given Default (LGD = 1 - Recovery Rate) and the discounting approach for recovery cash flows in credit risk models.

The delta-normal method, which uses the delta to approximate the change in the price of an option, has limitations when dealing with options. This method can significantly misrepresent the risks associated with options, particularly because it only considers the linear component of the price change (delta) and ignores the convexity (gamma). Specifically, it tends to understate the risks of long positions in calls because it does not fully account for the increasing delta as the underlying asset price rises, leading to potential underestimation of the risk. Conversely, it overstates the risks of short positions in puts, as the delta of puts decreases less dramatically when the price of the underlying asset falls.

Economic capital is a risk measure used by banks to determine the amount of capital they need to hold to remain solvent and cover potential losses:

Internal Risk Estimates: Unlike regulatory capital, which is determined by external regulatory requirements, economic capital is based on the bank's own risk assessment models and internal estimates of potential losses.

Risk Types: It considers a range of risks including credit risk, market risk, operational risk, and other financial risks that the bank might face.

Purpose: The goal is to ensure the bank has enough capital to absorb unexpected losses and to maintain confidence among depositors and investors.

Therefore, economic capital is a measure of the potential losses based on the bank's internal risk estimates.

Collecting internal operational risk event and loss information serves several purposes:

Assessing the risk of specific areas of concern (I).

Evaluating risk events and outcomes (II).

Collecting data for capital modeling (III). Getting insight into risk events in other firms in the industry (IV) typically involves external data collection rather than internal event collection.

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.

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.

References

Source: How Finance Works​

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.

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.

The modified duration of a bond can be estimated using the following formula:Modified Duration=Δ????/????Δ????Modified Duration=ΔyΔP/P​whereΔ????ΔPis the change in the bond's price,????Pis the initial price, andΔ????Δyis the change in yield.

Given:

Initial price (P) = $87,000

New price after yield change (P') = $84,500

Change in price (ΔP) = $87,000 - $84,500 = $2,500

Change in yield (Δy) = 5.7% - 4.7% = 1% = 0.01

Modified Duration =2,500/87,0000.01=0.0287350.01=2.8735≈2.880.012,500/87,000​=0.010.028735​=2.8735≈2.88

The Chief Risk Officer (CRO) should report to the CEO or the Board of Directors. This ensures that the CRO maintains independence from the business units whose activities they are monitoring and managing, which is critical for unbiased risk assessment and management.

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​

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.

References

Source: How Finance Works​

The TED spread is calculated as the difference between the interest rates on interbank loans and short-term U.S. government debt (T-bills). Specifically, the TED spread = LIBOR - Treasury bill rate. In this case, the 3-month LIBOR rate is 2.5% and the yield on the 3-month U.S. Treasury bill is 0.5%. Thus, the TED spread is 2.5% - 0.5% = 2.0%.

Back testing VaR models involves comparing the predicted losses (VaR estimates) with the actual daily profits and losses to assess the accuracy and reliability of the VaR model. This process helps in validating whether the model is effective in predicting risk and in identifying any discrepancies between predicted and actual outcomes. Therefore, the correct statement about back testing the VaR models is option B.

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.

To convert annualized volatility to daily volatility, we can use the formula:????daily=????annual252σdaily​=252​σannual​​

Given the annualized standard deviation (volatility) of the portfolio returns is 30%, we calculate the daily volatility as follows:????daily=30%252≈30%15.87≈1.89%σdaily​=252​30%​≈15.8730%​≈1.89%

This value is closest to 1.0%, making option A the correct answer.

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.

References

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

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.

When a bank looks to issue new capital to increase its Tier 1 capital levels, the following instrument is most likely considered:

Convertible Preferred Shares: These shares can be converted into common stock. They are considered part of Tier 1 capital because they have characteristics of equity, such as absorbing losses while the bank remains a going concern.

Long-term and callable debt, short-term callable debt, and short-term debt convertible to non-cumulative preferred shares do not typically qualify as Tier 1 capital because they do not provide the same level of loss absorption as equity instruments.

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

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.

To calculate the 12-month futures price for Unico Delta stock, we use the formula for pricing equity futures, considering the current stock price, dividend yield, and the risk-free rate (LIBOR in this case):

????=????×????(????−????)????F=S×e(r−d)t

Where:

????Fis the futures price

????Sis the current stock price ($20)

????ris the risk-free rate (3% or 0.03)

????dis the dividend yield (5% or 0.05)

????tis the time to maturity (1 year)

Plugging in the values:

????=20×????(0.03−0.05)×1F=20×e(0.03−0.05)×1????=20×????−0.02F=20×e−0.02????≈20×0.9802F≈20×0.9802????≈20.04F≈20.04

Therefore, the 12-month futures contract will trade at approximately $20.04.

References

How Finance Works.pdf, p. 206 ​

Commercial banking can be viewed as a fixed-income carry trade because banks typically engage in maturity transformation, where they borrow short-term and lend long-term.

Short-term floating-rate deposits:

Banks often attract deposits with short-term maturities and floating interest rates.

These deposits are generally considered stable and low-cost sources of funds.

Long-term fixed-rate loans:

Banks use these short-term deposits to fund long-term loans, such as mortgages or business loans, which typically have fixed interest rates.

This creates a mismatch between the interest rates and maturities of assets and liabilities.

Carry trade analogy:

The bank earns the spread between the interest it pays on short-term deposits and the interest it earns on long-term loans.

This process is similar to a carry trade, where profits are derived from the difference between borrowing costs and investment returns.

Thus, commercial banking inherently involves aspects of a carry trade through the practice of borrowing short-term to lend long-term.

References

Source: How Finance Works​

Covariance is a measure of the degree to which two variables move together. It is calculated as the average product of the deviations of each pair of observations from their respective means. If the covariance is positive, the variables tend to move in the same direction. If it is negative, they move in opposite directions.

Funding liquidity risk and trading liquidity risk are two distinct types of liquidity risks faced by financial institutions, particularly banks.

Funding Liquidity Risk:This type of risk pertains to a bank's ability to meet its financial obligations as they come due without incurring unacceptable losses. It primarily concerns the bank's ability to fund withdrawals, meet depositor demands, and other liabilities when they come due. If a bank cannot manage its funding liquidity, it may be forced to sell assets at fire sale prices, which can further deteriorate its financial condition.

Trading Liquidity Risk:This risk, on the other hand, deals with the market liquidity of the bank's assets. It involves the risk of being unable to buy or sell assets at or near their market value due to inadequate market depth or market disruptions. It is more concerned with the bid-offer spreads and the ability to execute trades without significantly impacting the market price of the asset.

Calculate the weighted average of modified durations:

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

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

Calculate the weights for each bond:

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

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

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

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

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

Therefore, the weighted average modified duration is approximately 1.30.

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

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

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.

Implementing a successful RCSA program requires thorough preparation. This includes interviewing participants, stakeholders, and support functions before launching the RCSA to ensure it is well designed and effectively addresses all relevant risks and controls.

Comprehensive and Detailed In-Depth Explanation:

In a single-name Credit Default Swap (CDS), the protection seller (who assumes the credit risk) often posts collateral to the buyer to mitigate counterparty risk. The amount of collateral is typically determined by:

Credit standing of the protection seller:If the seller’s creditworthiness declines (e.g., lower credit rating), more collateral is required to secure the buyer against the seller’s potential default.

Derivatives have several advantages over cash instruments in hedging transactions. These include:

Lower Credit Risk:

Derivatives, especially exchange-traded ones, often have lower credit risk because the clearinghouse guarantees the performance of the contract.

Lower Funding Requirements:

Derivatives typically require lower upfront capital than buying or selling the underlying cash instruments directly. This is due to the leverage they offer, where only a margin is required instead of the full value of the position.

Lower Dealing Costs:

Trading derivatives can be cheaper in terms of transaction costs compared to trading the underlying cash instruments. This is especially true for large positions or frequent trading.

Lower Capital Charges:

Regulatory capital requirements for derivatives can be lower compared to cash instruments because derivatives can be used to hedge and reduce overall portfolio risk, thereby reducing capital charges under regulatory frameworks.

References

Source: How Finance Works​

The market risk management function within a bank encompasses several key roles:

Establish a comprehensive market risk policy framework: This ensures that there are clear guidelines and procedures for managing market risk.

Define, approve, and monitor risk limits: This involves setting boundaries on the levels of risk that can be taken and continuously overseeing them.

Perform stress tests and other qualitative risk assessments: These are conducted to evaluate the bank's resilience to extreme market conditions and to identify potential vulnerabilities.

These activities are crucial for maintaining the bank's overall market risk exposure within acceptable levels.

Asian options are a type of option where the payoff depends on the average price of the underlying asset over a certain period.

This characteristic makes them suitable for consumers who want to hedge against price fluctuations over a period rather than at a single point in time.

For a natural gas consumer concerned with the average price over the course of a month, Asian options provide the necessary hedging mechanism.

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.

To minimize the variability of net interest income, Gamma Bank should aim to have a duration gap of zero. This means that the weighted average duration of assets matches the weighted average duration of liabilities, thus immunizing the bank’s net interest income against changes in interest rates.

Under Basel II, Tier 1 capital, also known as core capital, includes:

Equity Capital: This includes common stock and retained earnings. It is the highest quality of capital because it is fully available to cover losses.

Accrued Profits to Reserves: Profits that are retained and not distributed as dividends are added to reserves, increasing the bank's capital base.

This combination of equity capital and retained earnings ensures that Tier 1 capital is robust and able to absorb significant losses, thereby providing a strong financial cushion.

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

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

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

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

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

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

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

Comprehensive and Detailed In-Depth Explanation:

Mark-to-market (MtM) involves valuing positions at current market prices daily, primarily for the trading book (e.g., securities, derivatives). Option C—obtaining and verifying market prices for trading book instruments—is the core MtM activity under Basel III’s market risk rules. Option A applies to the banking book (not typically MtM), Option B describes settlement, and Option D is a profitability analysis, not MtM.

Exact Extract from Official Source:

BCBS, "Basel III: A Global Regulatory Framework," December 2010, para. 688: "Mark-to-market requires banks to obtain current market prices and verify them daily for all trading book positions to reflect fair value."

GARP FRR Study Notes, Market Risk Section: "The MtM process entails collecting and validating market prices for trading book instruments to determine their current value."

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

The PVBP (Present Value of a Basis Point) can be calculated by taking the change in the bond's price and dividing it by the change in yield (expressed in basis points). Here, the bond's price drops from $1,000 to $976 when the yield increases from 4.7% to 4.71%, which is a 1 basis point increase. The change in price is $1,000 - $976 = $24. Therefore, the PVBP is $24 / 1 = $24.

To hedge a bond portfolio against small parallel shifts in the term structure, you need to take a position in an instrument with an equal and opposite duration. John has a bond portfolio worth $2 million with a duration of 10. To hedge this, he should take a short position in bonds worth $20 million with a duration of 1. This is because the product of the value and duration of the hedge position should equal the product of the value and duration of the original portfolio (2 million * 10 = 20 million * 1).

Option delta (Δ) is a measure used in finance to indicate the sensitivity of an option's price to the price of the underlying asset. Specifically, it represents the rate of change of the option's value with respect to changes in the price of the underlying instrument. It is a fundamental concept in options trading and risk management.

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.

I. Selling or securitizing assets:

This is a common method to quickly generate liquidity during stressed conditions by converting non-liquid assets into cash.

II. Obtaining additional credit lines:

This method provides immediate access to additional funds when required, enhancing liquidity.

III. Securing a better credit rating:

While important for long-term financial health, this is not a direct method to increase liquidity in stressed conditions.

Thus, the most common methods to increase liquidity in stressed conditions are selling or securitizing assets and obtaining additional credit lines.

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​

An operational risk policy should include:

The firm's definition of risk: Clearly defining what constitutes operational risk for the organization.

The governance of operational risk including who owns it, what it owns, and how issues should be escalated: Establishing roles and responsibilities for managing operational risk.

The main activities and elements that are managed by the operational risk function: Outlining the key processes and controls that are in place to manage operational risks.

Comprehensive and Detailed In-Depth Explanation:

Under Basel II’s Foundation Internal Ratings-Based (FIRB) Approach for non-retail exposures (e.g., corporate loans), banks are required to estimate the Probability of Default (PD) internally, while the Basel framework provides supervisory estimates for Loss Given Default (LGD), Exposure at Default (EAD), and Maturity (M). PD represents the likelihood of an obligor defaulting within a year and is a key input into the risk-weighted asset (RWA) calculation. The FIRB approach balances bank-specific inputs with standardized parameters, distinguishing it from the Advanced IRB approach, where banks also estimate LGD and EAD.

In practice, financial institutions often sum the economic capital required for market, credit, and operational risks to arrive at an aggregate economic capital estimate. This is done because:

Difficulty in Estimating Correlations: Estimating the correlations between different types of risks is complex and data-intensive. These correlations can change over time and under different market conditions, making it challenging to arrive at accurate estimates.

Conservatism: To avoid underestimating the total risk, a conservative approach is often taken by adding up the individual risk capitals. This ensures that the institution holds sufficient capital to cover potential losses from all types of risks, even if they were to occur simultaneously.

Regulatory Guidance: Although regulations encourage a more integrated approach, the lack of precise data often leads banks to use simpler, more conservative methods in practice.

Thus, option B correctly reflects the practical approach taken due to the difficulty in estimating correlations between different risk categories.

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.

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.

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 ​

Regulatory standards impose formulaic capital calculations for all of the bank's activities to ensure:

Comparability Across Banks: Different models used by banks would make it difficult for regulators to compare results across banks.

Comprehensive Risk Assessment: Standardized calculations help ensure that banks are not missing key risks in their calculations.

Avoiding Gaming of the System: Standardized calculations prevent banks from using capital calculations to game the banking regulation system, ensuring consistency and fairness.

References

Source: How Finance Works​

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.

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).