Estimated reading time: 33 minutes

## FRM Sample Questions

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Below, you will find over three dozen sample questions to help you in your journey to become a Financial Risk Manager. These exam questions (and much more) are offered as downloadable PDF files…all at absolutely no cost on our Shop Page.

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## Part I Samples

**Question 001 **

Of the following statements, select the one(s) that is (are) most likely true with regards to a loan portfolio:

i) Lowering the recovery rate + Increasing the default probability = an increase expected loss

ii) Increasing the recovery rate + Increasing the default probability = an increase expected loss

iii) Lowering the recovery rate + Lowering the default probability = an increase expected loss

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) i, ii and iii

**ANSWER**

All three will result in an increase in expected loss!

Lowering the recovery rate + Increasing the default probability = an increase expected loss

Increasing the recovery rate + Increasing the default probability = an increase expected loss

Lowering the recovery rate + Lowering the default probability = an increase expected loss

**Thus, the correct answer is F.**

Note:

Increasing the recovery rate + Decreasing the default probability will result in a decrease in the expected loss.

**Question 002**

Which of the following, if any, are true?

i) Value-at-Risk, VaR, is a not measure of downside risk

ii) Value-at-Risk, VaR, is the minimum loss at a given confidence level over a given period of time

iii) Value-at-Risk, VaR, does not capture catastrophic losses that have a small probability of occurring

A) i only

B) i and ii only

C) i and iii only

D) ii and iii only

E) iii only

F) None of the above

**ANSWER**

Remember to read and re-read questions in your test! Here, we are being asked to determine the options that are **true.**

Value-at-Risk, VaR, **is** a measure of downside risk. It may also be considered as the **maximum** loss at a given confidence level over a given period of time.

VaR, does **not** capture catastrophic losses that have a small probability of occurring.

It is also true that since most firms are more concerned about unexpected loss, the frequently used risk measure is Value-at-Risk.

Daily VaR becomes meaningless if there is illiquidity

**Thus, the correct answer is E.**

**Question 003**

You are being asked to consider the following statement:

A comprehensive and integrated framework for managing keys risks achieving business objectives, minimizing unexpected earnings volatility and maximizing firm value.

This statement may be described as one that is addressing:

A) Trading Risk Management

B) Enterprise Risk Management

C) Systematic Risk Management

D) Unsystematic Risk Management

E) Volatility Risk Management

F) None of the above

**ANSWER**

On your way to becoming a Financial Risk Manager, several topics and definitions will pop up repeatedly over time. Enterprise Risk Management (ERM) is a comprehensive and integrated framework for managing keys risks in order to achieve business objectives, minimize unexpected earnings volatility and maximize firm value.

**Thus, the correct answer is B.**

**Question 004**

From your knowledge of arbitrage opportunities select which of the following are false:

i) Riskless profits can be made with arbitrage

ii) Trades are essentially made simultaneously

iii) Arbitrageurs aren’t required to have capital

iv) Arbitrage involves the simultaneous buying and selling of securities, currency, or commodities in different markets or in derivative forms in order to take advantage of differing prices for the same asset.

A) i and ii only

B) ii and iii only

C) i, ii and iv only

D) i and iv only

E) i, ii and iii only

F) None of the above

**ANSWER**

Remember, you are being asked to select the **false** answer(s). And it is true that:

- Riskless profits can be made with arbitrage
- Trades are essentially made simultaneously
- Arbitrageurs aren’t required to have capital

**Thus, the correct answer is F.**

By definition: Arbitrage involves the simultaneous buying and selling of securities, currency, or commodities in different markets or in derivative forms in order to take advantage of differing prices for the same asset.

**Question 005**

Of the presented options below, which, if any, would you say is/are the most accurate statement/s?

i) The capital market line can only be applied to efficient portfolios.

ii) The capital allocation line can only be applied to efficient portfolios.

iii) The capital market line can be applied to an investor’s individual assets

iv) The capital allocation line can be applied to an investor’s individual assets

A) i only

B) i and iii only

C) ii only and iv only

D) ii and iii only

E) i and iv only

F) i and ii only

**ANSWER**

Remember, you are being asked to find the **most accurate** statement/s, GARP will certainly test your limits on definitions and comprehension, so you must be keen at all times in your FRM test.

The capital market line (CML) is a line used in the capital asset pricing model to illustrate the rates of return for efficient portfolios depending on the risk-free rate of return and the level of risk (standard deviation) for a particular portfolio. The CML can only be applied to efficient portfolios (i.e. no unsystematic risk) and not to an investor’s individual assets.

The capital allocation line (CAL) is a line created in a graph of all possible combinations of risky and risk-free assets. Also known as the “reward-to-variability ratio”. The CAL can only be applied to efficient portfolios (i.e. no unsystematic risk) and not to an investor’s individual assets.

**Thus, the correct answer is F.**

**Question 006**

If you are told that the daily, 90% confidence level, value at risk of a portfolio is $100,000, then you would anticipate that:

i) 9 out of 10 times, the value of the portfolio will lose more than $100,000.

ii) 1 out of 10 times, we would expect the portfolio to lose $100,000 or less.

iii) 9 out of 10 times, the value of the portfolio will lose less than $100,000.

iv) 1 out of 10 times, we would expect the portfolio to lose $100,000 or more.

A) i only

B) ii only

C) iii only

D) i and ii only

E) iii and iv only

F) iv only

**ANSWER**

We are told that the daily, 90% confidence level, value at risk of a portfolio is $1,000,000. Hence, we would expect that:

9 out of 10 times (i.e. 90% of the time) the value of the portfolio will lose less than $100,000.

**Put another way;**

1 times out of 10 (i.e. 10% of the time), we would expect the portfolio to lose $100,000 or more.

**Thus, the correct answer is E.**

We note:

- Value-at-Risk, VaR,
**is**a measure of downside risk. It may also be considered as the**maximum**loss at a given confidence level over a given period of time. - VaR, does
**not**capture catastrophic losses that have a small probability of occurring. - It is also true that since most firms are more concerned about unexpected loss, the frequently used risk measure is Value-at-Risk.
- Daily VaR becomes meaningless if there is illiquidity

**Question 007**

Consider your knowledge of Value-at-Risk ( VaR ) and select the statements that are most likely true.

i) Value-at-Risk will increase once holdings periods become longer

ii) Value-at-Risk will decrease once probability levels become lower

iii) Value-at-Risk cannot be calculated by using the historical returns of a portfolio

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following is considered to be correct:

- Value-at-Risk will increase once holdings periods become longer
- Value-at-Risk will
**increase**once probability levels become**lower** - Value-at-Risk
**can**be calculated by using the historical returns of a portfolio

**Thus, the correct answer is A.**

**Question 008**

Consider your knowledge of the Student’s t-Distribution and select the most accurate statements below:

i) The Student’s t-Distribution’s shape will become less similar to that of a Standard Normal Distribution as the Degrees of Freedom increases

ii) The Student’s t-Distribution’s shape is considered to be less-peaked compared to a Normal Distribution

iii) The Student’s t-Distribution’s has a greater area under its tails compared to a Normal Distribution

iv) There are three factors to choose from when selecting the appropriate Distribution: 1) Whether the Population Variance is Known, 2) Whether the Distribution is Normal and 3) What is the Sample Size

A) i and ii only

B) i and iii only

C) i, ii and iii only

D) i, ii and iv only

E) i, iii and iv only

F) ii, iii and iv only

G) i, ii, iii and iv

H) None of the above

**ANSWER**

The following are considered to be correct:

- The Student’s t-Distribution’s shape will become
**more**similar to that of a Standard Normal Distribution as the Degrees of Freedom increases - The Student’s t-Distribution’s shape is considered to be less-peaked compared to a Normal Distribution
- The Student’s t-Distribution’s has a greater area under its tails compared to a Normal Distribution
- There are three factors to choose from when selecting the appropriate Distribution: 1) Whether the Population Variance is Known, 2) Whether the Distribution is Normal and 3) What is the Sample Size

**Thus, the correct answer is F.**

**Question 009**

Consider your knowledge of Regression Analysis. From your knowledge, determine which of the following is (are) most likely correct:

i) Having Positive Serial Correlation will result in t-values becoming larger

ii) Having a Negative Serial Correlation will happen once a -ve Error in one given observation increase the probability of a +ve Error occurring for another

iii) Type-II Errors may be developed as a result of having Positive Serial Correlation

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- Having Positive Serial Correlation will result in t-values becoming larger
- Having a Negative Serial Correlation will happen once a
**+ve Error**in one given observation increase the probability of a**–ve Error occurring for another** **Type-I Errors**may be developed as a result of having Positive Serial Correlation

**Thus, the correct answer is A.**

**Question 010**

You are being asked to determine whether one particular stock that is trading frequently on the market is of a greater volatility than another given stock that also trades frequently. As a result of this request, you collect data on both securities, using their respective prices to create their Sample Variance. Under these circumstances, determine which of the following would be considered as the most appropriate means to conduct such a testing.

A) The F-Test

B) The t-Test

C) The q-Test

D) The Z-Test

E) The Chi Square Test

F) The Binomial Test

G) Unable to determine from given information

**ANSWER**

We will utilize the ‘ F-Test ‘ in testing dissimilarity of two samples’ variance.

**Thus, the correct answer is A.**

**Question 011**

From the following given options, determine those that may be classified as ‘ linear ‘ or even ‘ near linear ‘.

i) Swaps

ii) Forwards

iii) Futures

iv) Options

A) i and ii only

B) i and iii only

C) i, ii and iii only

D) i, ii and iv only

E) i, iii and iv only

F) ii, iii and iv only

G) i, ii, iii and iv

H) None of the above

**ANSWER**

The following are considered to be linear ( or near linear ):

- Swaps
- Forwards
- Futures

**Thus, the correct answer is C.**

Please note that Options are typically non-linear.

**Question 012**

Consider your knowledge of the Central Limit Theorem. Assuming that the Population Variance is not known and the size of the sample taken is 31, an appropriate test for determining the Sample Mean will be:

i) The t-test

ii) The z-test

iii) The f-test

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

Assuming that the Population Variance is not known and the size of the sample taken is 31, an appropriate test for determining the Sample Mean will be:

- The t-test
**OR**the Z-test

**Thus, the correct answer is D.**

We Note:

- According to the Central Limit Theorem, the z-test may be employed if the population is sufficiently large ( i.e. n ≥ 30 ),
**even if the Variance is unknown** - As the size of the sample gets larger, both t- and z- distributions will converge ( so either test will suffice )
- Nevertheless, the t-test will be considered a more conservative estimation

**Question 013**

Determine which of the following options below may be considered as reasons for causing a yield curve to slope upwards.

i) Expectations of higher inflation rates

ii) Expectations of higher interest rates

iii) Expectations of improving outlook for credit risk

iv) Investors favoring maturities with short terms

A) i and ii only

B) i and iii only

C) i, ii and iii only

D) i, ii and iv only

E) i, iii and iv only

F) ii, iii and iv only

G) i, ii, iii and iv

**ANSWER**

The following may be considered as reasons for causing a yield curve to slope upwards:

- Expectations of higher inflation rates
- Expectations of higher interest rates
- Expectations of improving outlook for credit risk
- Investors favouring maturities with short terms

**Thus, the correct answer is G.**

**Question 014**

Consider your knowledge of FRAs (Forward-Rate-Agreements). Of the given options presented below, select that which is mostly likely correct:

A) A Forward-Rate-Agreement will not settle in cash. It will have interest rate risk only. FRAs may employed to hedge risks regarding uncertainty around receiving payments from a (floating-rate) loan.

B) A Forward-Rate-Agreement will settle in cash. It will have both interest rate risk as well as default risk. FRAs may not be used to hedge risks regarding uncertainty around receiving payments from a (fixed-rate) loan.

C) A Forward-Rate-Agreement will settle in cash. It will have both interest rate risk as well as default risk. FRAs may employed to hedge risks regarding uncertainty around receiving payments from a (floating-rate) loan.

D) A Forward-Rate-Agreement will not normally settle in cash. It will have default risk only. FRAs may employed to hedge risks regarding uncertainty around receiving payments from a (fixed-rate) loan.

E) A Forward-Rate-Agreement will not settle in cash. It will have both interest rate risk as well as default risk. FRAs may employed to hedge risks regarding uncertainty around receiving payments from a (floating-rate) loan.

F) A Forward-Rate-Agreement will settle in cash. It will have both interest rate risk only. FRAs may be employed to hedge risks regarding uncertainty around receiving payments from a (fixed-rate) loan.

**ANSWER**

A Forward-Rate-Agreement **will** settle in **cash**. It will have **both** interest rate risk as well as default risk. FRAs may employed to hedge risks regarding uncertainty around receiving payments from a (**floating**-rate) loan. While it may seem tedious to go through all these details, it is understood that Financial Risk Managers are expected to be experts at several topical issues in their field and you must always remember that you are being judged against a very high international standard.

**Thus, the correct answer is C.**

**Question 015**

Consider the scenario of a pension fund that owns a portfolio of bonds (fixed rate in nature). You are told that the duration of the portfolio is 4 years however the duration of the liabilities of the pension fund amounts to 8 years. If the fund manager thinks that interest rates will have a good chance of dropping within the next few months, which of the following strategies will he want to pursue to nullify the duration disparity?

A) Participate in a swap, receiving fixed while paying floating.

B) Participate in a swap, receiving floating while paying fixed.

C) Participate in a swap, receiving fixed while paying fixed.

D) Sell USD futures contracts

E) Sell GBP futures contracts

F) None of the above

**ANSWER**

In this example, we are faced with a fund that has the duration of its liabilities exceeding that its assets (i.e. their investment portfolio). As a result, if interest rates go down, then the fund’s liabilities will continue to overshadow their assets, making the situation worse.

Remember: A swap’s duration will be the difference in the duration of the fixed and the duration of the floating.

Knowing this, by participating in a swap that will **receive fixed** the fund can then have its portfolio duration increased up to the point where it is even equal to its liabilities, thereby reducing the risk of interest rates going down.

If we entered a pay fixed, such an action will lower the assets’ duration (making the situation worse when rates go down).

If we sold futures, this action will also lower the portfolio’s duration (and increase the present duration mis-match).

**Thus, the correct answer is A.**

**Question 016**

Consider your knowledge of option strategies. Of the following given options, select the ones that are most likely correct.

i) The strategy of purchasing both a put & call with strike prices that are different is known as a “long strangle”

ii) A “vertical spread” is a term synonymous with having strike prices that are different.

iii) The strategy of selling a call at a relatively lower strike price & buying a call at a relatively higher strike price is known as a “short bull”

A) i only

B) ii only

C) iii only

D) i and ii only

E) ii and iii only

F) i, ii, and iii

**ANSWER**

The following are correct:

- The strategy of purchasing both a put & call with strike prices that are different is known as a “long strangle”
- A “vertical spread” is a term synonymous with having strike prices that are different.
- The strategy of selling a call at a relatively lower strike price & buying a call at a relatively higher strike price is known as a “short bull”

**Thus, the correct answer is F.**

**Question 017**

You are told that an investment manager sold 500 call-option contracts each on 300 share units within Firm X, having a 60-day maturity at a price of $3.00. Assuming that the option’s delta on a single share unit is 0.42, determine the most appropriate action necessary towards the firm’s shares so as to achieve a hedge of the option’s exposure and have it remain delta-neutral.

A) 15,000 shares to be sold

B) 15,000 shares to be bought

C) 19,500 shares to be sold

D) 19,500 shares to be bought

E) 25,200 shares to be sold

F) 25,200 shares to be bought

G) Unable to determine from given information

**ANSWER**

Firstly, determining the actual number of calls for the given sale action:

# of Calls = ( 200 contracts ) X ( 300 units )

= 60,000 calls

As a result, this amount has to be hedged by: 60,000 X 0.42 = **25,200 share units**

Meaning, 25,200 shares will have to be purchased to keep a delta-neutral position.

**Thus, the correct answer is F.**

**Question 018**

Consider your knowledge how the price of an option varies with the change in price of the underlying security and determine which of the following statements is correct:

A) Gamma will be at its lowest ( i.e. when delta is the most sensitive ) for short term options that are at-the-money. Gamma will be the same for both calls as well as puts in the Black Scholes pricing environment

B) Gamma will be at its highest ( i.e. when delta is the least sensitive ) for short term options that are in-the-money. Gamma will be the same for both calls as well as puts in the Black Scholes pricing environment

C) Gamma will be at its highest ( i.e. when delta is the most sensitive ) for short term options that are at-the-money. Gamma will be the same for both calls as well as puts in the Black Scholes pricing environment

D) Gamma will be at its lowest ( i.e. when delta is the most sensitive ) for long term options that are at-the-money. Gamma will be different for both calls as well as puts in the Black Scholes pricing environment

E) Gamma will be at its highest ( i.e. when delta is the most sensitive ) for short term options that are at-the-money. Gamma will be different for both calls as well as puts in the Black Scholes pricing environment

F) Gamma will be at its highest ( i.e. when delta is the least sensitive ) for long term options that are at-the-money. Gamma will be different for both calls as well as puts in the Black Scholes pricing environment

**ANSWER**

The following is considered to be correct:

Gamma will be at its **highest** ( i.e. when delta is the **most sensitive** ) for **short** term options that are **at-the-money**. Gamma will be **the same** for both calls as well as puts in the Black Scholes pricing environment. Be sure to pay keen attention to these topics in your FRM books- don’t let simple concepts cost you valuable points in your exam!

**Thus, the correct answer is C.**

**Question 019**

Consider your knowledge of duration. From the following given options, determine which of the following is (are) most likely correct:

i) We consider effective duration to be an approximation. This, as the calculation does not take into account the price-yield graph’s curvature.

ii) Interest rate risk and price volatility have a direct relationship

iii) Above the line, the formula with respect to effective duration will assume that rates go up and down by the same basis point (bps) amounts

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

**ANSWER**

The following are considered to be correct:

- We consider effective duration to be an approximation. This, as the calculation does not take into account the price-yield graph’s curvature.
- Interest rate risk and price volatility have a direct relationship
- Above the line, the formula with respect to effective duration will assume that rates go up and down by the same basis point (bps) amounts

**Thus, the correct answer is G.**

**Question 020**

Consider your knowledge of stress testing and determine which of the following are most likely correct with respect to this financial tool:

i) Stress testing is considered to be very objective

ii) Stress testing is unable to compliment Value-at-Risk computations

iii) Having more scenarios presented will better aid in understanding a portfolio’s risk exposures

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered correct with respect to stress testing:

- Stress testing is considered to be very
**subjective** - Stress testing is
**able**to compliment Value-at-Risk computations - Having more scenarios presented will
**not**aid in understanding a portfolio’s risk exposures (too many scenarios will cause problems in interpretation)

**Thus, the correct answer is H.**

## Part II Samples

**Question 021**

From your knowledge of Term Structure Models, select which of the following is not likely to incorporate negative interest rates:

i) The Cox-Ingersoll-Ross ( CIR ) Model

ii) The Merton Model

iii) The Ho-Lee Model

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

- Under the
**Cox-Ingersoll-Ross ( CIR )**Model, we will not see negative interest rates - The Vasicek Model and the Ho-Lee Model can
*theoretically*give negative interest rates

**Thus, the correct answer is A.**

**Question 022**

As the Chief Risk Officer within your organization, you are asked to explain the meaning of what exactly is a Copula. You correctly state that:

i) Copula is a statistical measure that represents a multivariate uniform distribution

ii) Copula will only examine the dependence between two variables each time

iii) As a singular function, Copula will be able to correlate several securities

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- Copula is a statistical measure that represents a multivariate uniform distribution
- Copula will examine the dependence or association between multiple variables.
- As a singular function, Copula will be able to correlate several securities

**Thus, the correct answer is E.**

“ Copula “ is a statistical measure that represents a multivariate uniform distribution, which examines the association or dependence between multiple variables. Although the statistical calculation of a copula was invented in 1957, it was not applied to financial markets and finance until the late 1990s. The FRM test will not stress you too much on certain origin dates, however it will be off no harm to know a few of these in your professional career.

**Question 023**

Consider a scenario where trading frequently occurs in a particular commodity that is considered to be ‘seasonal’ in its nature. From the given selections, determine which statement/s is/are most likely to be correct:

i) By employing an Equally Weighted Estimated Shortfall ( ES ) tactic, the given commodity’s seasonality will not be adequately captured

ii) By employing an Equally Weighted Value at Risk ( VaR ) tactic, the given commodity’s seasonality will not be adequately captured

iii) By employing an Equally Weighted Estimated Shortfall ( ES ) tactic, the given commodity’s seasonality will be adequately captured

iv) By employing an Equally Weighted Value at Risk ( VaR ) tactic, the given commodity’s seasonality will be adequately captured

A) i only

B) ii only

C) iii only

D) iv only

E) i and ii only

F) iii and iv only

G) i and iv only

H) ii and iii only

I) None of the above

**ANSWER**

Equal Weighting will present the same problem in both Estimated Shortfall and Value at Risk, as there will be different risks associated with the different seasons.

The following are considered to be correct:

- By employing an Equally Weighted Estimated Shortfall ( ES ) tactic, the given commodity’s seasonality
**will not**be adequately captured - By employing an Equally Weighted Value at Risk ( VaR ) tactic, the given commodity’s seasonality
**will not**be adequately captured

**Thus, the correct answer is E.**

**Question 024**

From your knowledge of the various Simulation methodologies, select which of the following is/are disadvantages of Historical Simulation:

i) The results of Historical Simulation may include ghosting effects

ii) The results of Historical Simulation may include shadow effects

iii) Historical Simulation is considered to be simplistic in its nature

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be **disadvantages**:

- The results of Historical Simulation may include ghosting effects
- The results of Historical Simulation may include shadow effects

**Thus, the correct answer is D.**

**Question 025**

Consider your knowledge of the international credit crisis, particularly as it relates to the ‘originate-to-distribute’ model approach of many banks during that period, and determine which of the following statement/s is/are correct.

i) By using the originate-to-distribute model, systematic risks could have been reduced as fewer risks would be within the banks

ii) Mortgage originators were faced with warehouse risk and lost funds from this type of exposure. This was due to the fact that loans had to be kept on the company balance sheets before securitization could take place

iii) Many mortgage originators escaped going bankrupt during the financial crisis

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- By using the originate-to-distribute model, systematic risks could have been reduced as fewer risks would be within the banks. This is a true statement, however, many banking institutions decided to keep the risks during the period.
- Mortgage originators were faced with warehouse risk and lost funds from this type of exposure. This was due to the fact that loans had to be kept on the company balance sheets before securitization could take place.
- Many mortgage originators
**experienced going bankrupt**during the crisis due to the large amount of losses suffered over the period.

**Thus, the correct answer is D.**

**Question 026**

Limitations of Quantitative Credit Analysis include:

i) Reliance on Historical Data

ii) Quality of Data

iii) Over-Modelling

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

Limitations of Quantitative Credit Analysis include:

- Reliance on Historical Data
- Quality of Data
- Over-Modelling
- Under-Modelling
- Difficulty of future credit predictions based on historical data

**Thus, the correct answer is G.**

**Question 027**

Consider the following definition:

The Recovery Rate, calculated as ( 1 – Loss Rate ), is the extent to which principal and accrued interest on defaulted debt can be recovered, expressed as a percentage of face value. The Recovery Rate can also be defined as the value of a security when it emerges from default. It is also noted that the Loss Rate is generally swayed by the volatility of the underlying assets or securities.

In consideration of the aforementioned, determine which of the following would most likely carry the highest Recovery Rate.

A) A hedge fund that is highly leveraged

B) A hedge fund that is lowly leveraged

C) A company operating in a volatile emerging market

D) A specialized tech company in the Americas

E) A high-demand asset manufacturing company

F) A specialized tech company in the emerging market

G) None of the above

**ANSWER**

The highest Recovery Rate will be held by that institution whose assets are considered to be:

- Tangible and
- May be easily resold in the event of a default

**Thus, the best answer is E.**

**Question 028**

Consider your knowledge of the Merton Model as developed by Robert C. Merton and determine which of the following is/are most likely correct:

Employing the use of the Merton Model, if all other parameters are constant, the value of credit-sensitive debt will decrease as:

i) The firm’s valuation increases

ii) The firm’s volatility increases

iii) The maturity increases

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

Employing the use of the Merton Model, if all other parameters are constant, the value of credit-sensitive debt will decrease as:

- The firm’s valuation increases
- The firm’s volatility increases
- The maturity increases

**Thus, the correct answer is G.**

**Question 029**

*The financial practice of pooling various types of contractual debt such as residential mortgages, commercial mortgages, auto loans or credit card debt obligations (or other non-debt assets which generate receivables) and selling their related cash flows to third party investors as securities, which may be described as bonds, pass-through securities, or collateralized debt obligations (CDOs)*

This is most likely the definition of:

A) Collateralization

B) Securitization

C) Syndication

D) Debt Assignment

E) Debt Mortality

F) None of the above

**ANSWER**

**Securitization** is the financial practice of pooling various types of contractual debt such as residential mortgages, commercial mortgages, auto loans or credit card debt obligations (or other non-debt assets which generate receivables) and selling their related cash flows to third party investors as securities, which may be described as bonds, pass-through securities, or collateralized debt obligations (CDOs). The Global Association of Risk Professionals will be keen on such FRM concepts, given their recent spotlight in the global financial markets.

**Thus, the correct answer is B.**

**Question 030**

Consider your knowledge of Credit Risk and the various models that have been developed over the years to assess such risk, and then determine which of the following is/are most likely correct:

i) The KMV model is based on the structural approach to calculate EDF. It is best when applied to publicly traded companies. This model also assumes that the company is made up of debt and equity.

ii) In the CreditRisk+ Model each obligor has only two possible end-of-period states, default and non-default. In the event of default, the lender suffers a loss of fixed size; this is the lender’s exposure to the obligor.

iii) The CreditMetrics approach not only captures defaults, but migrations across non-default grades as well. Given a set of forward credit spreads for each grade, CreditMetrics can estimate a distribution over the change in mark-to-market value attributable to portfolio credit risk.

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- The KMV model is based on the structural approach to calculate EDF (credit risk is driven by the firm value process). It is best when applied to publicly traded companies, where the value of equity is determined by the stock market. In the KMV Model, having a complex financial structure is welcomed. This model also assumes that the company is made up of debt and equity.
- The CreditRisk+ Model was originally been developed by Credit Suisse Financial Products (CSFP) and is a model of default risk. Each obligor has only two possible end-of-period states, default and non-default. In the event of default, the lender suffers a loss of fixed size; this is the lender’s exposure to the obligor.
- CreditMetrics captures not only defaults, but migrations across non-default grades as well. Given a set of forward credit spreads for each grade, CreditMetrics can estimate a distribution over the change in mark-to-market value attributable to portfolio credit risk.

**Thus, the correct answer is G.**

**Question 031**

Determine which of the following is/are correct with respect to Loss Severity Distributions. Loss Severity Distributions:

i) Are bounded by +1

ii) Are Asymmetrical, having long tails to the left

iii) Should include large losses

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

Loss Severity Distributions:

- Are bounded by
**zero ( 0 )** - Are Asymmetrical, having long tails
**to the right** - Should include large losses

**Thus, the correct answer is C.**

**Question 032**

Determine which of the following is/are considered to be true:

i) Market Risk Models typically depend on Historical Data

ii) Operational Risk VaR Models typically depend on Scenario Analysis

iii) Back-testing is considered to be a useful form of validation for Market Risk Models

iv) Market Risk Models and Operational Risk Models differ with respect to the time horizon used in calculating Value at Risk

A) i and ii only

B) i and iii only

C) i, ii and iii only

D) i, ii and iv only

E) i, iii and iv only

F) ii, iii and iv only

G) i, ii, iii and iv

H) None of the above

**ANSWER**

The following are considered to be true:

- Market Risk Models typically depend on Historical Data
- Operational Risk VaR Models typically depend on Scenario Analysis
- Back-testing is considered to be a useful form of validation for Market Risk Models
- Market Risk Models and Operational Risk Models differ with respect to the time horizon used in calculating Value at Risk

**Thus, the correct answer is G.**

**Question 033**

With regards to the Basel II Non‐Advanced Methodology, determine which of the following is most likely correct:

A) The Standardized Approach will incorporate information from the last 1 year of Gross Income to derive a bank’s Operational Risk Capital charge

B) The Standardized Approach will incorporate information from the last 2 years of Gross Income to derive a bank’s Operational Risk Capital charge

C) The Standardized Approach will incorporate information from the last 3 years of Gross Income to derive a bank’s Operational Risk Capital charge

D) The Standardized Approach will incorporate information from the last 4 years of Gross Income to derive a bank’s Operational Risk Capital charge

E) The Standardized Approach will incorporate information from the last 5 years of Gross Income to derive a bank’s Operational Risk Capital charge

F) The Standardized Approach will incorporate information from the last 6 years of Gross Income to derive a bank’s Operational Risk Capital charge

G) None of the above

**ANSWER**

The following is considered to be correct:

The Standardized Approach will incorporate information from the last 3 years of Gross Income to derive a bank’s Operational Risk Capital charge

**Thus, the correct answer is C.**

**Question 034**

Determine which of the following is/are most likely correct:

i) Eurodollar Rates are the consideration for Uncollateralized Deposits

ii) The Fed Funds Rate is the consideration for Collateralized Loans

iii) Having an increase in the TED Spread will cause the cost of bank borrowing to go down

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- Eurodollar Rates are the consideration for Uncollateralized Deposits
- The Fed Funds Rate is the consideration for Collateralized Loans
- Having an increase in the TED Spread will cause the cost of bank borrowing
**to go up**

**Thus, the correct answer is D.**

**Question 035**

Determine the correct risk definition pairings below:

i) Rollover Risk is a measure of the difference between the interest income generated by financial institutions and the amount of interest paid out to their lenders, relative to the amount of their interest-earning assets

ii) Matched Funding refers to the matching of assets and liabilities with the same duration

iii) Interest Margin Risk is a risk associated with the refinancing of debt. This is commonly faced by countries and companies when their debt is about to mature and needs to be rolled over into new debt

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

**Net Interest Margin**( NIM ) is a measure of the difference between the interest income generated by financial institutions and the amount of interest paid out to their lenders, relative to the amount of their interest-earning assets- Matched Funding refers to the matching of assets and liabilities with the same duration
**Rollover Risk**is a risk associated with the refinancing of debt. Rollover Risk is commonly faced by countries and companies when their debt is about to mature and needs to be rolled over into new debt

**Thus, the correct answer is B.**

**Question 036**

Assumptions of the Capital Assets Pricing Model ( CAPM ) will include which of the following:

i) There are no taxes

ii) There are no transaction costs

iii) Investors have homogenous expectations with respect to expected returns

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

Assumptions of the Capital Assets Pricing Model ( CAPM ) will include:

- There are no taxes
- There are no transaction costs
- Investors have homogenous expectations with respect to expected returns
- Investors can borrow and lend at the risk free rate
- Investors can short sell any stock

**Thus, the correct answer is G.**

**Question 037**

You are being asked to consider a hedge fund that is long US$459 million in a given set of equities and short US$258 in another set of stocks. Assuming that the risk free rate of interest is 1.09%, the fund’s equity is US$222 and the fund’s beta is approximately 0.59, determine this entity’s Gross Leverage and Net Leverage.

A) Gross Leverage = 3.23 Net Leverage = 0.91

B) Gross Leverage = 4.25 Net Leverage = 23

C) Gross Leverage = 2.89 Net Leverage = 87

D) Gross Leverage = 1.69 Net Leverage = 25

E) Gross Leverage = 3.87 Net Leverage = 68

F) Gross Leverage = 4.59 Net Leverage = 88

G) None of the above

**ANSWER**

Ignoring the useless data, we have the following;

The Gross Leverage will be given: ( 459 + 258 ) / 222 = **3.23**

The Net Leverage will be given: ( 459 – 258 ) / 222 = **0.91**

**Thus, the correct answer is A.**

**Question 038**

Determine which of the following is/are most likely correct:

i) Gamma measures the rate at which delta changes when the underlying stock moves $1

ii) Gamma is lowest for short-term, at-the-money options

iii) Gamma can only be positive

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- Gamma measures the rate at which delta changes when the underlying stock moves $1
- Gamma is
**highest for short-term, at-the-money options** - Gamma
**can be either positive or negative**

**Thus, the correct answer is A.**

**Question 039**

You are being asked to consider your knowledge of Portfolio Construction Techniques in Risk Management. Determine which of the following is/are most likely correct:

i) Quadratic Programming will explicitly consider only two elements: Alpha and Transaction Costs

ii) An advantage of Quadratic Programming is that it can include all the constraints and limitations one finds in a linear program. This should be the best of all worlds

iii) A disadvantage of Quadratic Programming is that it requires a great many more inputs than the other portfolio construction techniques

A) i only

B) ii only

C) iii only

D) i and ii only

E) i and iii only

F) ii and iii only

G) i, ii and iii

H) None of the above

**ANSWER**

The following are considered to be correct:

- Quadratic Programming will
**explicitly consider three ( 3 ) elements: Alpha, Risk and Transaction Costs** - An advantage of Quadratic Programming is that it can include all the constraints and limitations one finds in a linear program. This should be the best of all worlds
- A disadvantage of Quadratic Programming is that it requires a great many more inputs than the other portfolio construction techniques

**Thus, the correct answer is F.**

**Question 040**

You are told that the investment manager of a large fund has experienced returns coming in below the benchmark S&P 500 index only a few times over the past 10 years. What is the best risk measure that you could employ to determine the manager’s performance?

A) The Sharpe Ratio

B) The Jensen Alpha

C) The Information Ratio

D) The Sortino Ratio

E) The Systematic Risk

F) The Unsystematic Risk

**ANSWER**

In this example, we are essentially trying to determine the downside performance of the fund manager and the Sortino Ratio would be the best option as it measures the downside risk of returns. Given the relatively good performance over the years, using several of the other measures will produce results that are unfairly high and in favour with the manager. Please know the definitions for these various ratios in your FRM test – they are typically an easy source of points to score in the exam

**Thus, the correct answer is D.**

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