### FRM Part I Practice Questions

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# Free FRM Part 1 Practice Questions

## Question 1

## The Governance of Risk Management

Which of the following least explains why the board of directors needs to maintain independence from executive teams, including the chief financial officer, chief risk officer, and the CEO?

A) Board membership may change without adversely affecting the day-to-day running of the company

B) It gives the board an opportunity to hire qualified teams with specialized skills required within each role

C) Independence helps avoid conflict of interest

D) Independence is a compulsory regulatory requirement in most countries

The correct answer is: C)

Although the independence of the board from company executives has many benefits, it may not be a mandatory requirement in most countries. After the 2007/2009 financial crisis, there has been a global push to separate the board from executive teams in large part due to conflict of interests. In particular, a board member who doubles up as the chief risk officer, for instance, may overlook some risks during the appraisal process, with one eye on higher remuneration especially if the remuneration is directly linked to performance. Alternatively, there’s the danger of the board falling under the spell of a charismatic CEO.

## Question 2

## Learning From Financial Disasters

Metallgesellschaft Refining and Marketing (MGRM), a U.S. subsidiary of the German oil company Metallgesellschaft, lost over $1.5 billion as a result of a poor dynamic hedging strategy. What triggered the loss? The company:

A) They are all cases in which the firm, creditors, or its investors were misled about business positions and size of expected cash flows (misleading reporting cases)

B) They resulted from fiduciary/reputational exposure to positions held by customers (Customer conduct cases)

C) They are cases in which the firm, creditors or its investors had adequate information about positions held but were undone by large market moves (large market moves cases)

D) They all happened in the 1970s and early 1980s

The correct answer is: A)

All the above-mentioned financial disasters had a lot to do with misleading reporting. They all involved misrepresentation of the true state of affairs of the firm, including the nature of positions held and their financial implications. For example, in the case of the Chase Manhattan and Drysdale Securities, Drysdale borrowed more funds ($300m) than its capital ($20m) from Chase and inflated the value of the collateral it had. The borrowed funds were used to take bond positions which eventually declined in value, forcing Drysdale into bankruptcy. The borrowed funds could not be repaid.

## Question 3

## Properties of Options

An investment manager is looking for the price of a 3-month put option to trade on the stock of AWWE, but due to infrequent trading of put options on this specific stock, the price quote for the put option is unavailable. Suppose that the investor has found a price quote of $4.5 for a 3-month call option with an exercise price of $75, and the current price of the stock that is $76.5, then estimate the price of the 3-month put option if the risk-free rate of 8%.

A) $3

B) $2.78

C) $1.52

D) $1.43

The correct answer is: C)

Since both sides of the put-call parity equation are equal, we can rearrange the put-call parity, to find the put price.

c + Xe^{-rT} = S + p

p = c – S + Xe^{-rT}

or

put = call – stock + Xe^{-rT}

Put = $4.5 – $76.5 + $75*e^{-rT} = $1.52

## Question 4

## Arbitrage Pricing Theory and Multifactor Models of Risk and Return

ShipLink, a United States cargo company, considers the return earned on its stock as heavily sensitive to GDP and consumer sentiments. You have been given the following data:

Expected return for Shiplink stock = 10%

GDP factor beta = 2

Expected growth in GDP = 3%

Consumer sentiment factor beta = 2.5

Expected growth in consumer sentiment = 2%

Suppose revised macroeconomic data suggests the GDP will grow by 4% rather than 3% and that consumer sentiments will grow by 3% rather than 2%. Determine the revised return for Shiplink stock, assuming no new information is available regarding the firm-specific return.

A) 0.18

B) 0.25

C) 0.145

D) 0.045

The correct answer is: C)

This is a multifactor model where the revised return, R_{i} will be given by:

R_{i} = E(R_{i}) + β_{S, GDP} F_{GDP} + β_{S, CS} F_{CS} + e_{i}

= 0.10 + 2(0.04 – 0.03)+ 2.5(0.03 – 0.02)

= 0.10 + 0.02 + 0.025

= 0.145 = 14.5%

## Question 5

## Principles for Effective Risk Data Aggregation and Risk Reporting

Vijay Kumar, Sonnet Bank’s Chief Risk Officer, writes in the management discussion and analysis (MD&A) section of bank’s annual report that Sonnet Bank, at all times, devotes its human and financial resources to the improvement of risk data aggregation as it considers data aggregation and reporting a part of the bank’s planning processes. He also writes that the bank has established multiple data models that are used as robust automated reconciliation measures. Kumar’s comments are aligned with one of the key principles of risk data aggregation. Identify that principle.

A) Adaptability

B) Comprehensiveness

C) Distribution

D) Data Architecture and Infrastructure

The correct answer is: D)

The 2nd principle of risk data aggregation (i.e. Data Architecture and Infrastructure) requires that a bank devotes its human and financial resources to risk data aggregation in times of stress. In addition, it requires that risk data aggregation and reporting should be a part of the bank’s planning processes and subject to business impact analysis. Banks should establish integrated data classifications and architecture across the banking group.

## Question 6

## Common Univariate Random Variables

The probability that a patient suffering from typhoid will be treated successfully is 0.8. 40 patients are subjected to treatment. Determine the expected value of the number of patients who are treated successfully.

A) 7

B) 28

C) 8

D) 32

The correct answer is: D)

This question tests the knowledge of the mean of the binomial distribution (n, θ)

The expected number of cured patients = E(X) = nθ = 40 * 0.8 = 32

Note that V(X) = nθ (1 – θ)

## Question 7

## Linear Regression

An analyst obtained the following linear regression relationship between 2 variables, *X *and* Y*:

Y = α + β_{1}X

where α =0.45 and β = 0.8823

He proceeded to construct a 2-sided 95% confidence interval for the slope coefficient (β_{1}) and obtained the following interval:

β=0.8823 ± 0.2147

Suppose the analyst decided to test the hypothesis H_{0}: β_{1} = 1 vs H_{a}: β_{1} ≠ 1 at 5% significance, what would be the inference?

A) Reject H_{0}

B) Do not reject H_{0}

C) The slope coefficient is statistically different than “1”

D) Cannot tell from the information provided

The correct answer is: B)

The 95% 2-sided confidence interval contains value “1”. Therefore, if the analyst were to conduct a 2-sided test at the 5% level, he would end up not rejecting the null hypothesis.

## Question 8

## Stationary Time Series

A Financial Risk Manager Exam candidate suggests that a model based on financial theory is likely to lead to a high degree of out-of-sample forecast accuracy. Which of the following best explains why the candidate is correct?

A) A solid financial background significantly increases the chances of the model working in the out-of-sample period as well as for the sample data used to estimate the model’s parameters

B) A financial background increases the chances of use of authentic input data

C) Financial theory incorporates industry-wide variables

D) Financial theory would be easy to understand and research on

The correct answer is: A)

A model based on a solid financial background is likely to bring about good, realistic forecasts since there are high chances that the model will work in the out-of-sample period as well as for the sample data used to estimate the model’s parameters.

## Question 9

## Stationary Time Series

Distinguish between independent white noise and normal (Gaussian white noise).

A) An independent white noise is a time series that exhibits both serial independence and a lack of serial correlation while a normal white process is a time series that’s serially independent, serially uncorrelated, and is normally distributed

B) A normal white noise is a time series that exhibits both derail independence and a lack of serial correlation while an independent white noise is a time series that’s serially independent, serially uncorrelated, and is normally distributed

C) An independent white noise is a time series with equal mean and variance while a normal white noise is a time series where the mean is not equal to the variance

D) An independent white noise is discrete while a normal white noise is continuous

The correct answer is: A)

In addition to being serially independent and uncorrelated, a normal white noise is normally distributed.

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