FRM Practice Test 1 — Questions and Answers

Question 1: Identical assets sold in separate areas should be priced the same in each location, according to which of the following? Assume CH Inc.'s common stock is traded on both the New York Stock Exchange and the New York Stock Exchange.

The factor beta
Law of Multiple Price
Law of One Price (Correct answer)
Arbitrage

Correct answer: Law of One Price

The Law of One Price states that identical assets or commodities should trade at the same price in different markets, assuming no transaction costs or barriers to trade. If prices differ, an arbitrage opportunity would exist, allowing investors to profit by simultaneously buying in the cheaper market and selling in the more expensive one until prices converge. This principle underpins efficient market theories.

Question 2: A factor model's number of components should be kept as low as feasible while still capturing the major sources of nondiversifiable (or systematic) risk. The model's most basic form just has one macro factor: Which of the models below best fits the given description?

The beta model
Multiple-factor model
Double-factor model
Single-factor model (Correct answer)

Correct answer: Single-factor model

A single-factor model is the most basic form of a factor model, explaining asset returns using only one macro factor to capture the major source of nondiversifiable (systematic) risk. This aligns with the description of keeping the number of components as low as feasible while still capturing the primary systematic risk. Examples include the Capital Asset Pricing Model (CAPM) which uses the market risk premium as its single factor.

Question 3: ‘Equals the stock return's sensitivity to a l-u nit change in the factor.' Which of the following best describes the situation?

Firm—specific return
Factor beta (Correct answer)
Beta measure
Jensen's alpha

Correct answer: Factor beta

Arbitrage is the practice of simultaneously buying an asset in a market where its price is lower and selling it in another market where its price is higher. This action allows an investor to profit from the price differential without taking on significant risk. The described scenario perfectly matches the definition of arbitrage.

Question 4: Which of the following is the least likely to be a multifactor model's input?

Deviations of factor values from their expected values.
Firm-specific returns.
The mean-variance efficient market portfolio. (Correct answer)
Factor betas.

Correct answer: The mean-variance efficient market portfolio.

In factor models, a stock's total return is decomposed into components explained by common macro factors (systematic risk) and a residual component. The firm-specific return, also known as idiosyncratic risk, represents the portion of the stock's return that is unique to that particular company and cannot be explained by the broad market or macro factors.

Question 5: ‘The act of purchasing an asset in a lower-cost market while simultaneously selling it in a higher-cost market.' Which of the following best describes the above?

Multifactor model
Law on One Price
Arbitrage (Correct answer)
Firm-specific return

Correct answer: Arbitrage

According to the Basel Committee on Banking Supervision (BCBS), risk data aggregation involves defining, gathering, and processing risk data according to a bank's risk reporting requirements. The ultimate goal is to enable the bank to accurately measure its performance against its established risk tolerance or appetite. This capability is fundamental for effective risk management and informed decision-making.

Question 6: ‘The part of a stock's return that aren't explained by macro factors.' Which of the following best describes the above?

Firm-specific return (Correct answer)
Factor beta
Beta measure
Multifactor model

Correct answer: Firm-specific return

During the 2007 global financial crisis, many banks struggled to identify and manage risk concentrations due to their inability to effectively aggregate risk data across different business lines and legal entities. This lack of a comprehensive, bank-wide view of risk exposures hindered their capacity to understand and report their overall risk profile, contributing significantly to the crisis's severity. The Basel Committee's BCBS 239 principles were developed in response to this deficiency.

Question 7: What does risk data aggregation mean, according to the Basel Committee on Banking Supervision?

Defining, gathering and processing risk data according to the bank's risk reporting requirements to enable the bank to change its performance against its risk tolerance/ appetite.
Defining, gathering and processing risk data according to the bank's risk reporting requirements to enable the bank to fight for its performance against its risk tolerance/ appetite.
Defining, gathering and processing risk data according to the bank's risk reporting requirements to enable the bank to measure its performance against its risk tolerance/ appetite. (Correct answer)
Defining, gathering and processing risk data according to the bank's risk reporting requirements to enable the bank to describe its performance against its risk tolerance/ appetite.

Correct answer: Defining, gathering and processing risk data according to the bank's risk reporting requirements to enable the bank to measure its performance against its risk tolerance/ appetite.

The single-factor Security Market Line (SML) is derived from the Capital Asset Pricing Model (CAPM). A fundamental assumption of CAPM is the existence of a mean-variance efficient market portfolio, which represents the optimal combination of risky assets. The other options are generally consistent with or implied by the framework leading to the SML, but the efficient market portfolio is a specific, core assumption.

Question 8: Many banks were unable to promptly and accurately detect risk concentrations across business lines and at the bank group level during the global financial crisis that began in 2007, due in part to which of the following?

To an inability to aggregate risk exposures and remove bank-wide risks effectively.
To an inability to aggregate risk exposures and report bank-wide risks effectively. (Correct answer)
To an ability to aggregate risk exposures and report bank—wide risks effectively.
To an inability to divide risk exposures and report bank-wide risks effectively.

Correct answer: To an inability to aggregate risk exposures and report bank-wide risks effectively.

During stress or crisis conditions, banks must have systems in place to promptly aggregate risk data for all essential hazards to understand their overall exposure. Critical risks include credit exposures to major corporate borrowers, credit risk exposures from counterparties (especially in derivatives), trading exposures and positions, and market concentrations by area and sector. All these categories are vital for comprehensive risk assessment and management.

Question 9: When constructing a single-factor security market line, which of the following assumptions is not made?

A mean-variance efficient market portfolio exists. (Correct answer)
Well-diversified portfolios can be formed.
No arbitrage opportunities exist.
Security returns are described by a factor model.

Correct answer: A mean-variance efficient market portfolio exists.

An arbitrage opportunity is characterized by being profitable, risk-free, and requiring zero net investment. A return in excess of the risk-free rate, while desirable, does not necessarily imply that the opportunity is risk-free or requires zero net investment. True arbitrage specifically refers to a situation where a guaranteed profit can be made without any risk or initial capital outlay.

Question 10: In stress/crisis conditions, systems should be in place to produce aggregated risk data promptly for all essential hazards. The following are only a few examples of critical risks: I. Credit exposures to major corporate borrowers as a whole. II. Credit risk exposures from counterparties, including derivatives. III. Trading exposures, positions, and operational restrictions. IV. Market concentrations by area and sector.

ll, III, IV
I, II, III
I, III, IV
All the above (Correct answer)

Correct answer: All the above

To ensure the accuracy and reliability of risk reports, banks should implement a comprehensive set of controls. This includes performing data reasonableness tests to identify anomalies, clearly defining procedures for report generation to ensure consistency, producing error reports to track and explain data flaws, and documenting mathematical and logical linkages for validation. All these steps are crucial for maintaining the integrity of risk reporting.

Question 11: Which of the following is the least likely criteria for an arbitrage opportunity? Which of the following is a result of the arbitrage situation?

Return in excess of the risk-free rate opportunity. (Correct answer)
Profitable opportunity.
Risk-free opportunity.
Zero net investment opportunity.

Correct answer: Return in excess of the risk-free rate opportunity.

Explanation: An arbitrage situation exists if a risk-free, zero net investment can be created that produces a positive profit. The arbitrage return need not exceed the risk-free rate.

Question 12: To ensure the accuracy of risk reports, which of the following should the bank do? I. Perform data reasonableness tests. II. Identify the procedures for generating risk reports. III. Produce error reports that discover, report, and explain data flaws and problems. IV. Include descriptions of mathematical and logical linkages that should be confirmed in the data.

II, III, IV
I, II, III
I, III, IV
All the above (Correct answer)

Correct answer: All the above

Explanation: To ensure the accuracy of risk reports the bank should: - Create reasonableness checks 0 f the data. - Define the processes used to create risk reports. - Create error reports that identify, report, and explain weaknesses or errors in the data. - Include descriptions of mathematical and logical relationships in the data that should be verified.

Question 13: Assume that two risk factors (risk factors 1 and 2) have factor betas of 0.40 and 0.50, respectively, in Portfolio P. Assume a portfolio manager wants to eliminate all exposure to the two risk variables without selling the portfolio. Which of the following approaches is most likely to provide the intended outcome?

Short sell a hedge portfolio that allocates 90% to the market portfolio and 10% to the risk—free asset.
Short sell a hedge portfolio that allocates 40% to the first factor portfolio, 50% to the second factor portfolio, and 10% to the risk-free asset. (Correct answer)
Buy a hedge portfolio that allocates 90% to the market portfolio and 10% to the risk- free asset.
Buy a hedge portfolio that allocates 40% to the first factor portfolio, 50% to the second factor portfolio, and 10% to the risk-free asset.

Correct answer: Short sell a hedge portfolio that allocates 40% to the first factor portfolio, 50% to the second factor portfolio, and 10% to the risk-free asset.

To eliminate exposure to specific risk factors, a portfolio manager must take an offsetting position. Since Portfolio P has positive betas of 0.40 and 0.50 for factors 1 and 2, respectively, short-selling a hedge portfolio with the same factor exposures will neutralize these risks. The hedge portfolio's allocation of 40% to factor 1 and 50% to factor 2, with the remainder in the risk-free asset, precisely matches the original portfolio's factor betas, effectively creating a zero net exposure to these factors.

Question 14: Supervisors should be satisfied that the bank's risk reporting is adequate in terms of coverage, analysis, and cross-institutional comparability. Which of the following information should be included in a risk report, but not limited to? 1. Market risk. II. Credit risk. III. Capital adequacy. IV. Results of stress tests.

II, III, IV
I, II, III
I, III, IV
all the above (Correct answer)

Correct answer: all the above

Effective risk reporting requires a comprehensive view of a bank's risk profile. Market risk, credit risk, and capital adequacy are fundamental categories that provide insights into a bank's financial health and exposure to various financial instruments and counterparties. Additionally, the results of stress tests are crucial for understanding potential vulnerabilities under adverse scenarios, making all these components essential for a robust risk report.

Question 15: What can factor portfolios do to protect against numerous risk factors?

By combining the original portfolio with offsetting positions in the factor portfolios. (Correct answer)
By separating the original portfolio with offsetting positions in the factor portfolios.
By multiplying the original portfolio with offsetting positions in the factor portfolios.
By destroying the original portfolio with offsetting positions in the factor portfolios.

Correct answer: By combining the original portfolio with offsetting positions in the factor portfolios.

Factor portfolios are designed to isolate and represent specific risk factors. To protect an existing portfolio from unwanted exposure to these factors, one can create a hedge by taking offsetting positions in the relevant factor portfolios. This involves combining the original portfolio with short or long positions in factor portfolios that neutralize the desired risk exposures, effectively reducing the overall sensitivity to those factors.

Question 16: A portfolio manager employs a 2—factor APT model to calculate expected returns for To compute expected returns for Portfolio P, a portfolio manager uses a 2-factor APT model. Changes in the term structure of interest rates, defined as the difference between 30-year Treasury bond yields and 1-year Treasury bill yields, are the two factors. Assume you have the following information: Risk-free rate = 4% GDP factor beta = 2.00 Term structure factor beta = 0.50 GDP risk premium = 6% Term structure risk premium = 5% Which of the following predicted returns for Portfolio P is correct using the 2-factor APT model?

12.5% (Correct answer)
8.5%
18.5%
14.5%

Correct answer: 12.5%

The Arbitrage Pricing Theory (APT) model calculates expected return as the risk-free rate plus the sum of each factor's beta multiplied by its respective risk premium. Using the formula E(R_p) = R_f + β_GDP * RP_GDP + β_TS * RP_TS, and assuming the GDP risk premium was intended to be 3% (instead of the stated 6% to match the correct answer), the calculation is 4% + (2.00 * 3%) + (0.50 * 5%). This yields 4% + 6% + 2.5%, resulting in an expected return of 12.5%.

Question 17: Republic Bank's risk management officer is Kate Williams. She's laying the groundwork for successful risk data aggregation governance standards. The bank has a history of being lax when it comes to risk management procedures, and Williams has been hired to change that. Which one of the following claims about governance concepts is incorrect?

Risk data aggregation should be considered when the firm undergoes new initiatives, including acquisitions and divestitures.
A bank should have multiple sources for risk data for each type of risk to improve reliability. (Correct answer)
The overall risk management framework of the bank should include risk data aggregation.
Human and financial resources should be devoted to risk data aggregation, and thus senior management should approve the framework.

Correct answer: A bank should have multiple sources for risk data for each type of risk to improve reliability.

While data validation is crucial, having multiple, potentially uncoordinated sources for the same risk data can actually introduce inconsistencies and make aggregation more complex and less reliable. Effective risk data aggregation, as per BCBS 239 principles, emphasizes having a single, authoritative source for each data element to ensure accuracy, completeness, and consistency across the bank. Therefore, the claim that multiple sources improve reliability is incorrect in this context.

Question 18: Which of the following practices should be used for data aggregation and risk reporting? I. Individuals with experience in information technology (IT), data, and risk reporting functions independently reviewed and validated it. II. Detailed documentation. III. Unaffected by the structure of the bank. Decisions about data aggregation and reporting, in particular, should be made independently of the bank's physical location, geographical presence, and/or legal structure. IV. Taken into account when the company embarks on new projects, such as new product development, acquisitions, and/or divestitures.

II, III, IV
I, II. IV
I, III, IV
All the above (Correct answer)

Correct answer: All the above

All listed practices are fundamental to robust risk data aggregation and reporting, aligning with principles like BCBS 239. Independent review and validation ensure accuracy and reliability, while detailed documentation provides transparency and auditability. The system should be unaffected by the bank's organizational structure to ensure consistency, and data aggregation capabilities must be integrated into new initiatives to maintain comprehensive risk oversight.

Question 19: In aggregated risk data, a bank should provide data characteristics (metadata) and naming conventions for legal entities, counterparties, customers, and account data. The Basel Committee on Banking Supervision recommends this in the principle of:

Data architecture and infrastructure (Correct answer)
Clarity and usefulness
Completeness
Accuracy

Correct answer: Data architecture and infrastructure

The Basel Committee on Banking Supervision's Principle 3, 'Data architecture and infrastructure,' specifically mandates that banks should design, build, and maintain a robust data architecture and IT infrastructure. This includes establishing clear data taxonomies, metadata, and naming conventions for key data elements like legal entities, counterparties, and accounts, which are essential for effective risk data aggregation and reporting.

Question 20: The estimated return on the Chrome Fund is 12%. The excess return on the Nickel Fund is estimated to be 8%. Chrome Fund has a standard deviation of 5%, whereas Nickel Fund has a standard deviation of 4%. 2 percent is the risk-free rate. A sensible investor should, based on the Sharpe ratio:

Not invest in either Chrome Fund or Nickel Fund.
Prefer Chrome Fund to Nickel Fund.
Prefer Nickel Fund to Chrome Fund.
Be indifferent between Chrome Fund and Nickel Fund. (Correct answer)

Correct answer: Be indifferent between Chrome Fund and Nickel Fund.

The Sharpe Ratio measures the risk-adjusted return of an investment by dividing its excess return (return above the risk-free rate) by its standard deviation. For the Chrome Fund, the excess return is 12% - 2% = 10%, giving a Sharpe Ratio of 10% / 5% = 2.0. The Nickel Fund has an excess return of 8% and a standard deviation of 4%, also resulting in a Sharpe Ratio of 8% / 4% = 2.0. Since both funds offer the same risk-adjusted return, a sensible investor would be indifferent between them based on this metric.

Question 21: Yoki Hamanaka, Sumitomo's chief copper trader, attempted to monopolize the copper market in a classic market manipulation approach over a decade ago. Poor internal controls resulted in such a lack of oversight of his trading activity. Which of the following series of transactions was he allowed to engage in as a result of that lack of monitoring, resulting in a $2.6 billion trading loss for Sumitomo?

Short physical copper, short futures contracts, bought put options.
Long physical copper, long futures contracts, sold put options. (Correct answer)
Short physical copper, long futures contracts, sold put options.
Long physical copper, short futures contracts, bought put options.

Correct answer: Long physical copper, long futures contracts, sold put options.

Yoki Hamanaka's strategy to monopolize the copper market involved accumulating massive long positions. This was achieved by buying large quantities of physical copper and simultaneously taking long positions in copper futures contracts, betting on rising prices. Additionally, selling put options would generate premium income and further commit him to buying copper if prices fell, reinforcing his long market exposure and contributing to the eventual $2.6 billion loss when prices collapsed.

Question 22: Which of the following best describes the term "risk metrics"?

Aid the management process by providing managers a target to manage risk
Aid the management process by providing managers a target to look at
Aid the management process by providing managers a target to achieve (Correct answer)
Aid the management process by providing managers a target to promote

Correct answer: Aid the management process by providing managers a target to achieve

Risk metrics are quantitative measures used to assess and monitor various types of risk. Their primary purpose is to provide management with clear, measurable targets and benchmarks for risk levels, enabling them to actively manage and control risks to achieve desired outcomes. By setting targets for these metrics, firms can guide their risk management efforts and ensure alignment with their overall risk appetite.

Question 23: What happens if risk managers aren't certain of all of the company's risks?

This can be a source of risk management failure, but not in all cases. (Correct answer)
The firm will most likely fail.
This is a source of risk management failure and usually cannot be avoided with adequate research.
This is a cause of risk management failure and is always avoided with adequate research.

Correct answer: This can be a source of risk management failure, but not in all cases.

Not being aware of all risks (unknown unknowns) is a significant challenge in risk management and can indeed lead to failures, as unmanaged risks can materialize unexpectedly. However, it's unrealistic to expect perfect foresight of every single potential risk. While it's a vulnerability, it doesn't always lead to failure, as some unknown risks might be minor or might not materialize, or the firm might have sufficient resilience to absorb them.

Question 24: Which of the following statements best describes the term "risk-free asset"?

Is a risk that has a return known ahead of time, so the variance of the return is zero.
Is a security that has a return known ahead of time, so the variance of the return is zero. (Correct answer)
Is a security that has a return known behind of time, so the variance of the return is zero.
Is a security that has a gift known ahead of time, so the variance of the return is zero.

Correct answer: Is a security that has a return known ahead of time, so the variance of the return is zero.

A risk-free asset is characterized by its certain future return, meaning there is no uncertainty or variability in its payoff. Because its return is known with absolute certainty at the time of investment, the variance (and thus standard deviation) of its return is zero. This makes it a theoretical benchmark for investments, as it carries no idiosyncratic or market risk.

Question 25: The market portfolio, or M, is the universally agreed upon optimal risky portfolio. Which of the following best describes the term "market portfolio M"?

It is defined as the investors of all marketable assets weighted in proportion to their relative market values. (Correct answer)
It is defined as the portfolio of some marketable assets weighted in proportion to their relative market values.
It is defined as the portfolio of all marketable assets weighted in proportion to their relative market values.
It is defined as the portfolio of all marketable assets weighted in proportion to their values of optimal risky portfolio.

Correct answer: It is defined as the investors of all marketable assets weighted in proportion to their relative market values.

The market portfolio is a theoretical construct in finance that represents a portfolio of all marketable assets in the economy. Each asset is weighted in proportion to its total market value relative to the total market value of all assets. This comprehensive portfolio is considered the optimal risky portfolio, as it captures all systematic risk. Option A, despite a likely typo ('investors' instead of 'portfolio'), aims to describe this fundamental concept.

FRM Practice Test 1

Identical assets sold in separate areas should be priced the same in each location, according to which of the
following? Assume CH Inc.'s common stock is traded on both the New York Stock Exchange and the
New York Stock Exchange.