GARP 2016-FRR Dumps

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

Probability of default = 3%

Loss given default = 70%

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

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

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

Expected loss = 2.1%

Credit spread = Risk premium = 1.9%

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

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.

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

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

First, computing VaR at the 99% confidence level.

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

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

A clearinghouse serves several vital functions in trading activities, mainly focusing on reducing various types of risk:

Counterparty Risk:

The clearinghouse acts as an intermediary between buyers and sellers, ensuring that each party fulfills its contractual obligations. This reduces the risk that one party will default.

Liquidity Risk:

By centralizing and standardizing transactions, the clearinghouse enhances market liquidity, making it easier to buy and sell without causing significant price changes.

Operational Risk:

The clearinghouse standardizes and streamlines the clearing and settlement processes, reducing the risk of errors and delays.

Credit Risk:

The clearinghouse requires margin deposits and marks positions to market daily, minimizing credit risk.

Thus, the primary purpose of a clearinghouse is to reduce counterparty and liquidity risk.

ReferencesSource: How Finance Works​

Present Value of a Basis Point (PVBP) measures the change in the value of a bond when the yield changes by one basis point (0.01%). This measure helps quantify the interest rate risk of a bond by indicating how much its price will fluctuate with small changes in yield.

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

Calculate the leverage ratio:

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

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

Calculate the leveraged position:

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

Calculate the VaR for the leveraged position:

The unleveraged VaR is $30 on $100.

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

ReferencesSource: How Finance Works​

To 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).

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.

T Identify 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.

References:

From the search results and standard financial regulations knowledge, the limit specified in Regulation T is consistent with 50% of the value of the securities.

opic 3, Volume C

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.

When evaluating a diversified equity portfolio, an endowment asset manager should consider:

Company-specific projected earnings and earnings risk to understand the performance potential and variability of individual assets.

Aggregate earnings expectations to gauge the overall market outlook and economic conditions affecting the portfolio.

Individual asset volatility to assess the risk and potential fluctuations in the value of specific investments within the portfolio.

Market liquidity, while important, is not typically a primary concern for long/short equity strategies focused on diversified portfolios.

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).

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

Equity indices are numerical calculations that reflect the performance of hypothetical equity portfolios.

They are designed to track the overall performance of an equity market and do not trade in cash form.

Capitalization-weighted indices, which weight stocks by their market capitalization, are generally considered effective in tracking the performance of the overall market. Therefore, the statement that they are not generally considered better is incorrect.

Price-weighted indices give greater weight to shares trading at high prices, reflecting their price movements more heavily in the index.

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

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

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

Calculate:

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

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

References:

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

Identify the transaction details:

Initial value of CDOs = $100

Haircut = 20%

Repo transaction:

With a 20% haircut, the trader can use the CDOs to obtain 80% of their value in cash:

Cash obtained=100×(1−0.20)=80Cash obtained=100×(1−0.20)=80

Explanation:

The trader buys $100 worth of CDOs and then uses these CDOs in a repo transaction to get back $80 (less interest). This fully utilizes the leverage provided by the repo transaction under the specified conditions.

References:

This explanation aligns with standard financial practices for repo transactions and the leverage principles outlined in the document .

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.

Standard operational risk definitions typically include human errors (I), process failure (II), and systems failure (III). Unexpected events (IV) are generally considered in broader risk categories but are not standard elements of operational risk definitions.References:Standard operational risk definitions from Financial Risk and Regulation documents.

Areas that typically report into a central operational risk function include business continuity planning, information security, and embedded operational risk coordinators or specialists or managers. Geopolitical and strategic planning, while important, does not typically report into the central operational risk function but rather into separate strategic or planning departments.References:Operational risk function organizational structure.

To hedge against potential declines in aluminum prices, Omega Bank should take a position that benefits from a price drop. Here are the steps and strategies:

Current Position:

Omega Bank has bought 100 metric tons of aluminum for delivery in six months.

Hedging Strategy:

To protect against a decline in aluminum prices, the bank should take a short position in the aluminum futures market. This involves selling aluminum futures contracts.

Execution:

By selling an aluminum futures contract, Omega Bank locks in a price for selling aluminum in the future, thus offsetting the risk of price declines.

The correct strategy is to sell an aluminum futures contract, which effectively hedges the bank’s exposure to a potential drop in aluminum prices.

ReferencesSource: How Finance Works​

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.

ReferencesSource: How Finance Works​​

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.

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

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

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

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

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.

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.

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

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

References: No specific reference found in the document for this question. The provided answer is based on common practices in treasury management within banks.

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.

References:The references align with the documented limitations of static liquidity models in financial risk management literature.

When evaluating a diversified equity portfolio, an endowment asset manager should consider:

Company-specific projected earnings and earnings risk to understand the performance potential and variability of individual assets.

Aggregate earnings expectations to gauge the overall market outlook and economic conditions affecting the portfolio.

Individual asset volatility to assess the risk and potential fluctuations in the value of specific investments within the portfolio.

Market liquidity, while important, is not typically a primary concern for long/short equity strategies focused on diversified portfolios.

Risk reports are used for:

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

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

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

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

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

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

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

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

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

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

To determine the frequency score for an event likely to happen once in 2 years:

Frequency score can be calculated as the reciprocal of the event frequency.

For an event likely to happen once in 2 years: Frequency=12Frequency=21​ per year.

Thus, the frequency score = 1.

This statement is incorrect because it is generally observed that longer-term contracts can be less volatile due to the smoothing effect over time, whereas short-term contracts can be more sensitive to immediate market conditions and supply-demand imbalances.

ReferencesVerified with information on the volatility of term contracts in commodity derivatives discussed in the book "How Finance Works"​​.

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.References: How Finance Works, sections explaining the structure and components of Tier 2 capital under Basel II​​.

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

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

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

Securitization is a financial process used by banks to improve their liquidity and manage risk. The process involves the following steps:

I. Issuing Bonds: Banks issue bonds where the payment of interest and repayment of principal on the bonds depend on the cash flow generated by a pool of bank assets. This means that the assets (like loans) are used to back the bonds, and the revenue from these assets is used to pay bondholders.

II. Transfer of Legal Rights: When banks issue these bonds, they transfer their legal right to payment of interest and repayment of principal to bondholders. This transfer ensures that bondholders have a claim on the cash flows generated by the pooled assets, reducing the bank's risk exposure.

III. Selling Illiquid Assets: By securitizing assets, banks can sell off illiquid assets (like loans) and convert them into liquid securities (like bonds) that can be traded in the financial markets. This improves the bank's liquidity position by turning assets that are difficult to sell individually into marketable securities.

References: Based on "How Finance Works" document, securitization involves issuing bonds backed by asset pools, transferring legal payment rights, and selling illiquid assets to improve liquidity​​.

To estimate the forward price of gold, the cost of holding physical gold and the cost of shorting it must be considered. The formula to calculate the forward price (F) is:

????=????×(1+????????−????????)F=S×(1+rf​−rl​)

where ????S is the spot price, ????????rf​ is the risk-free rate, and ????????rl​ is the lease rate.

Given:

Physical gold spot price (????S) = $1,000

Annual risk-free rate (????????rf​) = 5% or 0.05

Gold lease rate (????????rl​) = 2% or 0.02

Plugging in the values:

????=1000×(1+0.05−0.02)=1000×1.03=1030F=1000×(1+0.05−0.02)=1000×1.03=1030

Therefore, the best estimate of the gold forward price is $1030.

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

Correct Statements:

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

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

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

Incorrect Statement:

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

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

ReferencesSource: How Finance Works​

When evaluating the upward reporting governance structure in the context of operational risk, critical features include independence, importance, and relevance. Security is not typically considered a critical feature of the upward reporting governance structure. The focus is on ensuring that the governance structure is independent, important, and relevant to the organization's operational risk management.References:Upward reporting governance structure guidelines.

Endogenous liquidity risk refers to the risk arising from the inherent characteristics of the asset itself, which can affect its liquidity under stress conditions.

A 2-year U.S. Treasury bond (Option A) and a 10-year U.S. Treasury bond (Option C) are both highly liquid because they are backed by the U.S. government and have deep, well-functioning markets.

A 1-week corporate loan with a AAA-rated company (Option B) has high credit quality and a short duration, making it relatively liquid.

A 3-year subprime mortgage (Option D), however, carries significant credit risk and is less liquid due to its lower credit quality and the potential for higher default rates, particularly under stress conditions. This makes it the asset with the greatest endogenous liquidity risk.

ReferencesBased on information on liquidity risks and the inherent risk characteristics of various assets as discussed in the document​​.

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%.

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

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.

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

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

Interest Expense on Deposits:

Deposits = $100 million, interest rate = 3%

Interest expense = $100 million * 0.03 = $3 million

Interest Income from Loans:

Loan portfolio = $120 million, interest rate = 10%

Interest income = $120 million * 0.10 = $12 million

Net Interest Income Calculation:

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

ReferencesSource: How Finance Works​

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

ReferencesSource: How Finance Works​

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.

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

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

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

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

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

Profit and loss (P&L) calculations in trading are typically made by comparing the current market value to the purchase price or the previous day's closing price, not the intrinsic value. Here are the correct statements:

Cash settled instruments: The final market value is used to settle the transaction with the counterparty.

Margin calls: Futures exchanges base margin calls on the current market value.

Credit risk calculations: Analyzing the current values of all deals with the same counterparty is crucial for assessing counterparty credit risk.

The incorrect statement is that P&L calculations are made by comparing current values to intrinsic values, which are theoretical and not always reflective of market conditions.

ReferencesSource: How Finance Works​

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

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

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

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

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

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.

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%.

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.

References:The extensive use and details of the Black-Scholes model for European options are elaborated in the "How Finance Works" document​​.

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.

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

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.

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.

References:The inherent uncertainty in predicting future volatility is discussed in the context of option pricing in the "How Finance Works" document​​.

Compound options are exotic options that have another option as their underlying asset, making them particularly complex to model. The complexity arises because the value of a compound option is derived from another option, which is already a derivative with its own set of valuation challenges. This nested structure introduces multiple layers of volatility and dependencies that are difficult to predict and model accurately using standard option pricing models.

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.

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 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.

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

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

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

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 × LGD Expected Loss=2%×$50,000=0.02×50,000=$1,000Expected Loss=2%×$50,000=0.02×50,000=$1,000

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

Asian options are 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.

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.

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.

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

Expected Duration Calculation:

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

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

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

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

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

Normalization: 0.230.10=2.30.100.23​=2.3 years

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

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

References

Verified information from the document ​

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

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

References:

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

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 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.

References:

How Finance Works: "Gamma Bank provides a $100,000 loan to Big Bath retail stores at 5% interest rate (paid annually). The loan is collateralized with $55,000. The loan also has an annual expected default rate of 2%, and loss given default at 50%. In this case, what will the bank's exposure at default (EAD) be?"

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.

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.

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

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

References:

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

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 ​

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

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.

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 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.

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 ​

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

References:

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

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

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

References:

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

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.

References:The inherent uncertainty in predicting future volatility is discussed in the context of option pricing in the "How Finance Works" document​​.

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

Expected Duration Calculation:

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

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

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

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

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

Normalization: 0.230.10=2.30.100.23​=2.3 years

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

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

References

Verified information from the document ​

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 ​

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.

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.

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

To quantify the aggregate average loss for the credit portfolio and its possible constituent subportfolios, a credit portfolio manager should use the expected loss metric. This measure captures the average anticipated loss due to defaults and is essential for understanding the baseline risk of the portfolio.

References

Verified information from the document ​

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 ​

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.

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

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

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

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

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

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.

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

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

References:

How Finance Works: "Banks can directly sell bonds and marketable loans to manage their credit portfolios." .

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

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

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.

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.

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.

References:Details on the risks associated with forward exchange transactions can be found in the "How Finance Works" document, which discusses the implications and risks of financial instruments, including forward contracts​​.

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.