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Question 1 of 100
1. Question
The classic risk management process affirms the job of a risk manager to include four activities: identifying risks; analyzing and measuring risks; assessing the impact of risk events; and managing risks. This process culminates in the series of decisions as to how to handle identified risks. Which of the following is (TRUE as) a common activity of the risk manager?
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Question 2 of 100
2. Question
Below are a set of innovations over ten steps (from initial t = 0 to t = 10) and the first innovation ε(1) = 0.26. The innovations are random Gaussian white noise, ε(t) ~ N(0, σ^2 = 1).
Consider two time series models. The AR(1) model has an intercept, δ, of 0.70, and an AR parameter, φ, of 0.50. The MA(1) model has a mean, μ, of 0.70, and a weight of 0.50. Which of the following is nearest the value at t = 4; i.e., which are the missing values inside the red rectangle?
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Question 3 of 100
3. Question
Consider the price of an asset that begins and $30.00 and ends, after 20 periods, lower at $8.55. Also highlighted are its maximum ($39.23) and minimum price ($6.79) during this 20period life:
Among the following choices, which lookback option has the HIGHEST payoff if its life matches the 20period interval shown?
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Question 4 of 100
4. Question
Consider a large $20.0 million portfolio of 100 loans. In its general form, the portfolio’s unexpected loss is given by:[1]
However, each loan in this portfolio has approximately the same characteristics and size; i.e., the size of each is about $200,000. For modeling purposes, we can set the pairwise correlation coefficient to be constant ρ(i,j) = 0.160 for all i ≠ j. These assumptions greatly simplify the calculation of the portfolio’s unexpected loss and each loan’s contribution to portfolio risk. In this situation, which of the following statements is TRUE?
[1] Gerhard Schroeck, Risk Management and Value Creation in Financial Institutions, (New York: Wiley, 2002
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Question 5 of 100
5. Question
A big part of a risk manager’s job is to identify her firm’s risk factors. Each of the following statements about risk factors is true EXCEPT which is false?
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Question 6 of 100
6. Question
Below are displayed 15 pairwise (X,Y) trials. The simple regression line based on all 15 observations is given by Y1 = 0.488 + 0.425*X. We consider the possibility that the 12th Trial, given by point (X = 2.50, Y = 3.00) might be an outlier. If this point is removed, then the regression based on the remaining 14 observations is given by Y2 = 0.761 + 0.574*X. These results are displayed, including selected summary statistics.
According to Cook’s distance, is the 12th Trial an outlier?
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Question 7 of 100
7. Question
Assume the current price of a stock is $30.00 and imagine that we can only trade the following four options at two strike prices:
 At a strike price of $28.00, we can employ either a call or a put, where c(K=28.00) = $3.98 and p(K=28.00) = $1.46
 At a strike price of $32.00, we can employ either a call or a put, where c(K=32.00) = $2.05 and p(K=32.00) = $3.46
Each of these prices is approximately accurate for a sixmonth option when the volatility is 31.2% (but these details are not necessary to answer the question). If we want to implement a bull spread, how could we do that?
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Question 8 of 100
8. Question
Finlux International seeks to build an internal rating system for its considerable credit portfolio and assigns the project to a team including Alice, Bob, Chris, and Denise. In order to cast a wide net for ideas, each of the team members builds a miniprototype:
I. Alice (A) developed an internal migration matrix based on a sample taken during a recession such that (related) her probabilities are not Markovian, yet to retrieve 5year cumulative default probabilities she raises the matrix to the fifth power (ie., 5year cumulative matrix = M^5) a calculation that might be valid if her probabilities were Markovian
II. Bob (B), in order to maximize the universe of rated bonds, combines ratings for all of the major agencies across industries, countries, asset classes
III Chris (C) uses a method of polling the salespeople who originate the loans on the theory that these are the people with the best “on the ground” knowledge of credit risk
IV. Denise (D) mixed atthepointintime and throughthecycle ratings because she was unaware of which methodological assumption applied to each sourced datasetWhich of the following accurately matches each team member to the bias that afflicts their approach?
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Question 9 of 100
9. Question
One of the risk management building blocks is enterprise risk management (ERM). Which of the following is TRUE as a feature or implication of ERM?
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Question 10 of 100
10. Question
Sally is a portfolio manager at an investment management firm. She wants to test her primary equity portfolio’s reaction to the factors in the FamaFrench threefactor model. She collected excess returns (i.e., net of the riskfree rate) over the last eight years, so that the sample size, n = 96 months. The response (aka, explained, dependent) variable is the portfolio’s excess return. The three explanatory variables are the market factor (MKT), the size factor (SMB), and the value factor (HML). The size factor captures the excess return of small capitalization stocks (SMB = “small minus big”) and the value factor captures the excess returns of value stocks (HML = “high booktomarket minus low booktomarket”)’. Sally’s regression results are displayed below.
Which of the following descriptions of her portfolio is the most accurate?
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Question 11 of 100
11. Question
Consider an atthemoney (ATM) stock option with a strike price of $50.00 and six months’ time to expiration; i.e., S(0) = K = $50.00 and T = 0.5 years. Now imagine the following four variations (I., II., III. and IV) on this option:
I. It is a European CALL option on a nondividendpaying stock while the riskfree rate is 3.0%
II. It is a European CALL option on a stock that pays 1.60% dividend yield (D = $0.40) while the riskfree rate is 3.0%
III. It is a European PUT option on a stock that pays 1.60% dividend yield (D = $0.40) while the riskfree rate is 3.0%
IV. It is a European PUT option on a stock that pays 1.60% dividend yield (D = $0.40) while the riskfree rate is ZERO!
For the three variations where the stock pays a continuous 1.60% dividend, the equivalent present value (over the life of the option) is given by the lump sum, D = $0.40. For those interested, although it is beyond the scope of this question, this translation is given by the following: the PV of dividend, D = S(0)*[exp(q*T)1]; in this case, D = $50.00*[exp(0.0160*0.5)1] = $0.3980.
Each of the above options has a different minimum value (aka, lower bound). However, among the four, which has the LOWEST minimum value?
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Question 12 of 100
12. Question
As of the twentieth century (i.e., beginning 1900 and afterward), each of the following is TRUE about the consequences of sovereign default EXCEPT which is false?
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Question 13 of 100
13. Question
According to GARP, “a recent trend among corporations is to use a boardapproved risk appetite to guide management and (potentially) to inform investors.” Which of the following statements is TRUE about the firm’s risk appetite?
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Question 14 of 100
14. Question
Shown below is the autocorrelation function (ACF) for a time series object that contains the total quarterly beer production in Australia (in megalitres) from 1956:Q1 to 2010:Q2 (source: https://cran.rproject.org/web/packages/fpp2/index.html).
About this ACF and its implications, each of the following statements is true EXCEPT which statement is false?
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Question 15 of 100
15. Question
A nondividend paying stock is currently trading at a price $35.00 when its volatility is 30.0% and the riskfree rate is 3.0%. Consider a chooser option with a strike price of $30.00 that gives the holder the right to choose (a call or put option) in three months and the chosen option, at that point in time, will have a remaining time to maturity of nine months; i.e., T1 = +0.25 years and T2 = +1.0 years. The price of this chooser is $7.710. Which of the following changes, ceteris paribus, will INCREASE the value of this chooser?
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Question 16 of 100
16. Question
The exhibit below combines Tuckman’s Tables 5.6 and 5.7. The situation starts with the underlying trade: a 5×10 payer swaption struck at 4.044% (which gives the buyer the right to buy a fixed rate of 4.044% on a 10year EUR swap in five years such that the underlying security in this option is a 10year swap). This initial swaption trade is highlighted in light blue below. Additionally, the forwardbucket exposures of four swaps are shown in the upper panel. The lower panel highlights three different hedges (discussed in Tuckman) and their respective implied net positions:
Source: Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011)
About these hedges, which of the following statements is TRUE?
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Question 17 of 100
17. Question
The global financial crisis (GFC) of 2007 to 2009 engendered regulatory responses to corporate risk governance. Below are summarized ten key developments. The first SarbanesOxley (SOX) occurred prior to the GFC but is listed for context. The others are grouped naturally into three responses: Basel III and BCBS, DoddFrank, and the European response.
I. Prior to the GFC, SarbanesOxley (SOX) required that the CEO and CFO affirm the accuracy of financial disclosures.
Basel III and BCBS:
II. Basel III (BIII) was a direct response to the GFC. BIII limited core Tier 1 capital to common equity and retained earnings. BIII also imposed new ratios for shortterm liquidity (i.e., LCR) and longterm liquidity (i.e., NSFR).
III. Basel III designed a macroprudential overlay that included a 3.0% leverage ratio; countercyclical capital buffer (CCCB; aka, CCyB); and total lossabsorbing capital (TLAC) standards applicable to GSIBs.
IV. The Basel III framework was revised again in 2016 with the Fundamental Review of the Trading Book (FRTB; aka, part of Basel IV) which included enhanced disclosure requirements.
V. The Basel Committee on Banking Supervision (BCBS) issued Corporate Governance Principles for Banks which–in addition to identifying the importance of an independent risk management function–defines roles for the board, board risk committees, senior management, CROs and internal auditors
DoddFrank:
VI. The 2010 DoddFrank Act strengthened the regulatory reach of the Fed; ended toobigtoofail (TBTF); launched overhaul of derivatives markets; introduced the Volcker Rule; created the Consumer Financial Protection Bureau (CFPB).
VII. The DoddFrank Act also instituted a new approach to scenario analysis and stress testing that included: a topdown approach with macroeconomic scenarios unfolding over several quarters; a focus on the effects of macroeconomic downturns on a series of risk types, including credit risk, liquidity risk, market risk, and operational risk; an approach that is computationally demanding, because risk drivers are not stationary, as well as realistic, allowing for active management of the portfolios; a stress testing framework that is fully incorporated into a bank’s business, capital, and liquidity planning processes; and an approach that not only looks at each bank in isolation but across all institutions. This allows for the collection of systemic information showing how a major common scenario would affect the largest banks collectively.
The European response:
VIII.For banks in Europe, the Supervisory Review and Evaluation Process (SREP) introduced three new principles to banking supervision: (i) A forwardlooking emphasis on the sustainability of each bank’s business model, including during conditions of stress; (ii) An assessment methodology based on best practices within the banking industry, and (iii) An expectation that every bank will ultimately operate under the same standards.
IX. The two key components of SREP are (i) the internal capital adequacy assessment process (ICAAP) and (ii) the internal liquidity adequacy assessment process (ILAAP). The ICAAP incorporates scenario analysis and stress testing; it outlines how stress testing supports capital planning. The ILAAP incorporates potential losses from asset liquidations and increased funding costs during stressful periods.
X. European banks with assets of EUR 30 billion and above must run European Banking Authority (EBA) stress tests. These stress tests are run at the consolidated banking group level (insurance activities are excluded). Two supervisory macroeconomic scenarios covering a threeyear period are provided by the regulator: a baseline scenario and an adverse scenario
In regard to the above list of regulatory responses to the GFC, which of the following statements is TRUE?
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Question 18 of 100
18. Question
Debra is an analyst at a governmental agency. Her boss asked her to investigate whether the Phillips curve applies during highinflation regimes. To answer the question, Debra collected data from the FRED database at the St. Louis Fed (https://fred.stlouisfed.org/). The Phillips curve describes an inverse relationship between unemployment rates and inflation rates; https://en.wikipedia.org/wiki/Phillips_curve. Debra collected monthly data and she regressed the inflation rate against the unemployment rate (conditional on highinflation regimes simply for narrative purposes). Her independent variable is the unemployment rate (FRED code: UNRATE) and here, the dependent variable is the Inflation rate (CPIAUCSL). The units are percentages not decimals; e.g., the dataset includes the month of January in 1982 when the unemployment rate was 8.90 and the inflation rate was 6.38. Her regression results are presented here.
Debra wants to know if an inverse relationship is observed. Which of the following statements about the regression is TRUE?
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Question 19 of 100
19. Question
[This is tedious and difficult. Inspired by the final LO above and Hull’s[1] EOC Question 6.11] Today it is December 31, 2018. The cheapesttodeliver bond in an August 2019 Treasury bond futures contract is a 9.0% coupon bond, and delivery is expected to be made on August 28, 2019. Coupon payments on the bond are made on April 2 and October 2 each year. In this case, therefore, as of settlement today (December 31, 2018) there were 90 days since the last coupon and there will be 92 days until the next coupon. Delivery will be in 240 days (and subsequent coupon date 35 days after delivery, or 275 days from today). The term structure is flat, and the rate of interest with continuous compounding is 3.0% per annum. The conversion factor for the bond is 1.380. The current quoted bond price (for this bond which is assumed to be the cheapest to deliver) is $115.00. What is the quoted futures price for the contract?
[1] John C. Hull, Options, Futures, and Other Derivatives, 10th Edition (New York: Pearson Prentice Hall, 2017). Example 6.2 from Hull, but spreadsheets handcrafted by David Harper.
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Question 20 of 100
20. Question
Suzanne the Risk Analyst is building an interest rate term structure and she is evaluating various candidate models. Her first candidate is Tuckman’s Model 1[1] (aka, normally distributed rates and no drift) which has the advantage of extreme simplicity and is specified by (Tuckman 9.1)27: dr σ*dw. Her colleague Peter observes this is a singlefactor model: the model’s only factor is the shortterm interest rate. Among the following, which is probably the strongest criticism against this model as a singlefactor model?
[1] Bruce Tuckman’s Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011)
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Question 21 of 100
21. Question
The Acme Investment Trading Company perceives the credit risk of a certain public retailer is mispriced by the market. Acme is considering buying or selling a credit default swap (CDS) for the purpose of speculating on this view with respect to the retailer’s credit profile. In comparison to buying or shorting the retailer’s cash bond, Acme has already identified an advantage to the CDS: it has better liquidity. On the other hand, which of the following is a disadvantage of the CDS?
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Question 22 of 100
22. Question
Mary belies that the average net promoter score (NPS) in financial services, as a population, is at least 50. Her onesided null hypothesis is H0: μ(NPS) ≤ 50 and her alternative hypothesis is HA: μ(NPS) > 50. Among a collected sample of 40 firms, her staff observes a sample average NPS of 53.60 with a standard deviation of 9.0. Her staff informs her that the test statistic is 2.53 and the twosided pvalue is 1.556% per the Excel function T.DIST.2T(2.530, 39) = 0.015563. Their report also includes these 95.0% critical tvalues: T.INV(0.95, 39) = 1.685 and T.INV.2T(0.050, 39) = 2.023; as expected, these values are slightly higher than, respectively, the critical Zvalues of 1.645 and 2.33. Each of the following is true EXCEPT which is false?
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Question 23 of 100
23. Question
It is August and Sally is a fund manager with $50.0 million invested in government bonds who is worried that interest rates are expected to be volatile over the next quarter (note: this question is inspired by Hull’s EOC Problem 6.18). She decides to use the December Treasury bond (“Tbond”) futures contract to hedge the value of the portfolio. The current futures price is 10800 or $108.00. Because each contract is for the delivery of $100,000 face value of bonds, the futures contract price is therefore $108,000.00. Suppose the modified duration of the bond portfolio in three months will be 13.0 years. The cheapesttodeliver (CTD) in the Tbond contract is anticipated to be a bond with 18.0 years to maturity that pays a 5.0% semiannual coupon; at maturity, the duration of this CTD bond is expected to be about 12.0 years.
However, the manager does not want to completely neutralize duration. Rather, she wants to REDUCE the portfolio’s duration by 7.0 years, from 13.0 years to 6.0 years. About how many Tbond futures contracts should she trade to achieve this reduction in duration of the net portfolio?
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Question 24 of 100
24. Question
The exhibit below modifies Tuckman’s Table 4.2[1] and shows the prices on May 28, 2019 for two instruments: 10year U.S. note futures contracts, TYU0, and call options with a strike of 120 on the same futures contracts, TYU0C 120.
What is the effective duration of, respectively, the futures, TYU0, and the options, TYU0C 120?
[1] Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011. Modified table from Tuckman; spreadsheet handcrafted by David Harper.
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Question 25 of 100
25. Question
Consider the market portfolio plus three other portfolios (A, B, C) with the following features while the riskfree rate is 3.0%:
Please note the returns are expected gross returns; e.g., the market’s expected return is 9.0% so that its expected excess return is 6.0%. If we assume the capital asset pricing model (CAPM) is valid then which of the following statements is TRUE?
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Question 26 of 100
26. Question
Below is the probability mass function (pmf) of a binomial random variable where the probability of success over 15 trials is 10.0%; i.e., p = 0.10 and n = 15. What is the interquartile range (IQR) of this probability distribution?
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Question 27 of 100
27. Question
Consider an asset with a current price of $120.00 and volatility of 16.0% while the riskfree rate is 3.0%. A regular (aka, vanilla) but deeply outofthemoney (OTM) oneyear European put option on the stock with a strike price of $100.00 has a price of $0.740; i.e., p(S = $120.00, K = $100.00, σ = 0.160, Rf = 0.030, T = 1.0 year) = $0.740.
Now consider the modification of this regular put option into a gap put option with the addition of a trigger price, denoted K2. In this case, the price of the gap put option is given by p(S = $120.00, K1 = $100.00, K2 = trigger price, σ = 0.160, Rf = 0.030, T = 1.0 year). Each of the following statements about this gap option is true EXCEPT which is false?
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Question 28 of 100
28. Question
As shown in the exhibit below in a format similar to Tuckman’s table 3.2[1], the price of a bond as of 5/28/2019 is $113.335. This bond pays a semiannual 10.0% coupon and has maturity of 1.5 years; that is, it matures on 11/30/2020. Currently, the sixmonth forward rates are 0.60%, 1.00% and 1.50% (see green row).
If we make a scenario assumption of UNCHANGED TERM STRUCTURE, which of the following is nearest to the carry rolldown over the next six months?
[1] Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011. Spreadsheet handcrafted by David Harper.
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Question 29 of 100
29. Question
Let Rm(P) denote the monthly return of the portfolio and Rm(B) denote the monthly return of its benchmark. Over a threeyear measurement period, the following statistics are calculated:
 The average monthly return for, respectively, the portfolio and the benchmark was Rm(P) = 8.50% and Rm(B) = 6.90%; therefore, on average, the portfolio outperformed its benchmark by +1.60%.
 The monthly standard deviation of the difference between the portfolio’s and benchmark’s return, σ[Rm(P) – Rm(B)] = 11.80%
 A regression of the portfolio’s excess return against the benchmark’s excess return produced the sample regression function, ERm(P) = 0.0140 + 1.35 * ERm(B); therefore, the regression intercept (aka, alpha) is 1.40%
 The standard error of the regression (SER), which approximates the volatility of alpha, σ(α), is 11.0%
Although the periodicity is monthly, an information ratio is generally annualized. In regard to annualized information ratios, which of the following statements is accurate?
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Question 30 of 100
30. Question
Below is the joint distribution of analyst ratings (i.e., negative, neutral, or positive) and stock returns (5, zero, or +5 in percentage terms).
We are interested in the conditional distribution of stock returns given a negative analyst rating. For example, the expected stock return conditional on a negative analyst rating is [5.0 * (20.0%/25.0%)] + [0 * (5.0%/25.0%)] + [+5 * (0%/25.0%)]= 4.0. The variance of the stock return conditional on a negative analyst rating is [5.0 – (4.0)]^2 * 80% + [0 – (4.0)]^2 * 20% + [+5.0 – (4.0)]^2 * 0% = 4.0. What is the skew of the stock return conditional on a negative analyst rating?
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Question 31 of 100
31. Question
You are trying to model the theoretical forward price of silver using the cost of carry model. Your model is informed by the following four propositions. Each is correct except which is FALSE?
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Question 32 of 100
32. Question
Let the twoyear term structure of zero rates include the following four spot rates: 1.0% @ 0.5 years, 2.0% @ 1.0, 3.0% @ 1.5, and 4.0% @ 2.0 years. Using these discount rates, the price of a twoyear $100.00 face value bond with 4.0% coupon rate is $100.10 (see blue cell) as shown in the exhibit below, where $100.10 is the sum of four discounted cash flows:
Assume the term structure above (i.e., 1.0% @ 0.5 years, 2.0% @ 1.0, 3.0% @ 1.5, and 4.0% @ 2.0 years) remains valid, but a different bond trades at a price of only $95.12. Which of the following is nearest to this bond’s spread?
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Question 33 of 100
33. Question
Each of the following statements is true about the arbitrage pricing theory (APT) model EXCEPT which is false?
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Question 34 of 100
34. Question
Let X = µ + σ*T be the generalized student’s t distribution where X is a linear transformation of the classic student’s t distribution, as represented by T ~ t(df) or sometimes T ~ t(v). Consequently, X is a generalized random variable denoted by X ~ Gen. t(v)(µ, σ^2). If the generalized student’s t distribution happens to be standardized, then it could be represented as X ~ Gen. t(v)(0, 1). If X is a generalized student’s t distribution with µ = 2.0 and σ = 3.0 with degrees of freedom, v = 8, then each of the following is true EXCEPT which is false?
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Question 35 of 100
35. Question
Consider the following upwardsloping but smooth zero rate curve:
There are various theories that attempt to explain the factors that determine the shape of the zero rate curve. If the above zero curve is observed, each of the following theories is plausible EXCEPT which of the following theories is the LEAST LIKELY to be true, if only because it does not comport with the observed zero curve?
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Question 36 of 100
36. Question
Below is a graph of swap rates (represented by the solid green line) and the corresponding, implied sixmonth forward rates (represented by the dotted orange line). Specifically, the sixmonth, 1.0year, 1.5year, 2.0year and 2.5year swap rates are, respectively, 0.70%, 1.20%, 1.50%, 1.50% and 2.0%. The sixmonth forward rates implied by this swap rate curve are: f(0, 0.5) = s(0.5) = 0.7000%; f(0.5, 1.0) = 1.7043%; f(1.0, 1.5) = 2.1089%; f(1.5, 2.0) = 1.5000%; f(2.0, 2.5) = 4.0674%.
Consider the fixed side of a 2.5year swap which pays the swap rate of 2.0%. Because 2.0% is the 2.5year par rate, the present value of 100 face amount of the fixed side of the 2.5year swap is 100. Consider the price of the swap over the following year, in two sixmonth steps:
 After six months, as the swap ages (toward maturity) from 2.5year to a 2.0year swap (but with the same fixed rate, of course)
 After another six months, as the swap ages from a 2.0year swap to a 1.5year swap
If we assume an unchanged term structure as the swap matures from a 2.5year swap to a 1.5year swap, what happens to the price of the fixed side?
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Question 37 of 100
37. Question
Relative to the other principles, compliance rates have been stronger for the Risk Reporting Practices outlined in BCBS 239. In regard to effective risk reporting, each of the following is true EXCEPT which is false?
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Question 38 of 100
38. Question
Let Z be a random variable that is a linear function of random variables X and Y, where Z = 3*X + 7*Y? If the standard deviation of X and Y, respectively, are σ(X) = 4.0 and σ(Y) = 5.0 and the correlation between X and Y is ρ(X,Y) = 0.50, then what is the standard deviation of Z, σ(Z)?
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Question 39 of 100
39. Question
A threeyear bond $1,000.00 face value bond pays a 10.0% semiannual coupon and has a semiannual (aka, bond equivalent) yield of 14.0%. Its price is therefore $904.67. The chart below also shows cash flows as proportional weights:
We can use modified duration to estimate the price impact of a small change in yield. Which of the following is NEAREST to a durationbased (i.e., linearly approximate) estimate of the bond’s price change given a 26 basis point (0.26%) drop (shock down) to the yield?
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Question 40 of 100
40. Question
Assume the following discount function (note that a discount function is a series of discount factors):
Which of the following is nearest to the implied sixmonth forward rate starting in two years, f(2.0, 2.5)? Assume rates are expressed as per annum with semiannual compounding.
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Question 41 of 100
41. Question
According to GARP, each of the following is one of the top ten benefits of enterprise risk management (ERM) EXCEPT which is NOT a benefit of ERM?
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Question 42 of 100
42. Question
Among a set of filtered stocks, a stock screener assigns stocks to one of three style categories: value, quality, or momentum. At the end of each month, the stock’s performance is compared to the S&P such that it either beats or does not beat the index The prior beliefs (aka, unconditional probabilities) are the following: Pr(Style = Value) = 15.0%, Pr(Style = Quality) = 30.0%, and Pr(Style = Momentum) = 55.0%. The stock screener also knows that a Moment stock is more likely than a Quality stock, and much more likely than a Value stock, to beat the index; specifically, the screener knows the following conditional probabilities:
 Pr(Beat  Value) = 40.0%
 Pr(Beat  Quality) = 60.0%
 Pr(Beat  Momentum ) = 80.0%
If we observe that a stock beats the index, what is the probability it is a momentum stock; i.e.., what is Pr(Momentum  Beat)?
Bonus question: if we observe the stock beats the index two months in a row, what is the probability it is a momentum stock; i.e., what is Pr(Momentum  Two consecutive Beats)?
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Question 43 of 100
43. Question
Consider the steep spot (aka, zero) rate curve illustrated below: 3.0% at 0.5 years, 4.0% at 1.0 year, 4.6% at 1.5 years and 5.0% at 2.0 years. Each of these zero rates is per annum with continuous compounding.
Which of the following is nearest to the theoretical price of a twoyear $100.00 face value bond that pays an 8.0% semiannual coupon (4.0% coupon every six months)?
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Question 44 of 100
44. Question
In regard to Tuckman’s discussion of the components and structure of U.S. Treasury STRIPS, which of the following statements is TRUE?
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Question 45 of 100
45. Question
Scenario analysis is an ascendant tool. After the global financial crisis (GFC), regulators insisted that systemically important banks demonstrate their ability to withstand adverse and severely adverse scenarios. Meanwhile, GARP explains, “Scenario analysis, along with stress and sensitivity testing, have risen to become the preeminent risk identification tools for many enterprise risk management (ERM) programs. This is a result of the weaknesses in probabilistic risk metrics (e.g., VaR) that were revealed by the global financial crisis of 2007–2008.”[1]
Which of the following statements is TRUE about scenario analysis?
[1] 2020 FRM Part I: Foundations of Risk Management, 10th Ed. Pearson Learning Solutions, 10/2019. VitalBook file.
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Question 46 of 100
46. Question
Barbara observes a sample with the following statistics: mean of X and standard deviation of Y. She thinks the true (aka, population) mean is Z. She does NOT know the population’s variance, nor does she even know the population’s distribution, including she cannot assume it is normal. If she wants to conduct a hypothesis test of the observed sample mean, each of the following statements is true EXCEPT which is incorrect?
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Question 47 of 100
47. Question
Sally the portfolio manager oversees a $9.0 million largecap equities portfolio with a beta of 1.30. She has decided the portfolio’s beta is too high and calibrates a new target beta of 0.70. If she employs S&P 500 index futures contracts to reduce the beta when the index futures price is 2,400 (the contract size is $250 * S&P 500 index per the specification), then which is nearest to the trade?
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Question 48 of 100
48. Question
On Monday, a bank’s position (the underlying portfolio) on the dollareuro exchange rate has an initial position delta of 11,300 and a position gamma of 25,000. The exchange rate is EURUSD $0.860; i.e., per the currency priority convention, Euro is the base currency. By the end of the week, on Friday, the exchange rate had jumped by +$0.050 to $0.910. The bank entered two trades:
 On Monday, while the exchange rate is EURUSD $0.860, the bank’s first trade neutralized delta; aka, makes the net position “delta neutral”
 On Friday, after the exchange rate had increased to EURUSD $0.910, the bank’s second trade reestablished the net position’s delta neutrality
Which of the following were the bank’s trades? Please note: this question is inspired by Hull’s EOC Problem 19.22[1].
[1] John C. Hull, Risk Management and Financial Institutions, 4th Ed. (Hoboken, NJ: John Wiley & Sons, 2015).
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Question 49 of 100
49. Question
Three famous financial disasters are Continental Illinois (whose failure in 1984 was the largest bank failure in US history prior to the global financial crisis), Lehman Brothers (who was the fourthlargest U.S. investment bank before filing for bankruptcy in 2008), and Northern Rock (who was a fastgrowing British mortgage bank, who in 2008 was forced into public ownership as an alternative to insolvency). What did Continental Illinois, Lehman Brothers, and Northern Rock have in common?
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Question 50 of 100
50. Question
An analyst at your firm has developed a new trading strategy called AlphaGen. She claims there is a 70.0% probability on any given day that the strategy offers true alpha and will generate a profit. After observing ten (10) days of performance, in fact the strategy was profitable only four days. Assume there are only two possible states of the world: either the analyst is correct and the strategy offers true alpha; or the strategy does not offer true alpha and the profit/loss outcome is equally likely to be a gain or loss on any given day. Your prior assumption was that the two states of the world are equally likely: there is s 50.0% probability the strategy offers true alpha, and a 50% probability it does not. These assumptions are illustrated below; e.g., if the strategy does generate alpha, then P[Profit  Alpha] = 70.0%, but if the strategy does not generate alpha, then P[Profit  No Alpha] = 50.0%.
We can also represent the prior probabilities as follows: P[p = 0.70] = 50.0% and P[p = 0.50] = 50.0%. Additionally, because you are an FRM candidate, you are already able to compute the following binomial probabilities:
 Prob[Exactly 4 profits out of 10 days  True Alpha] = binomial[4 successes, 10 trials, p = 0.70, false = p.m.f.] = 0.70^4*0.30^6*C(10,4) = 3.68%
 Prob[Exactly 4 profits out of 10 days  No Alpha] = binomial[4 successes, 10 trials, p = 0.50, false = p.m.f.] = 0.50^4*0.50^6*C(10,4) = 20.51%.
Given the evidence that the strategy was profitable on four days out of ten, which is nearest to the (posterior) probability that the analyst is correct, and the strategy generates true alpha? (note: this question is inspired by Miller’s EOC question 6.4)[1].
[1] Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ: John Wiley & Sons, 2013)
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Question 51 of 100
51. Question
Barbara is a value investor who bought 1,000 shares of Apple (ticker: AAPL) in 2014 when the share price was $95.00 and she considered them undervalued. In hindsight, her view was correct as the shares currently (as of mid2017) trade at $140.00. She now thinks the shares are slightly overvalued. However, she does not want to sell them unless there is a market crash. This is because she believes the shares are likely to trade in a range and may even gain modestly in the future. However, she also believes there is something like a 10.0% probability of a technology sector crash (a possibility enabled by the low interest rate regime). If the technology sector does crash, she fears the AAPL shares could plummet. If the AAPL shares drop, Barbara does want to sell, however, she does not want to sell in a panic at firesale prices.
Specifically, if the shares were to quickly lose more than 13.0% of their current value, Barbara will be eager to sell them. However, she also wants to ensure that she realizes a minimum holding period return (HPR) of 30.0%; and to this HPR dividends have already contributed 6.0%. Therefore, she only wants to sell if the price appreciation (from her $95.00 cost basis) is at least +24.0%. She justifies this conditional view on a belief that if the shares plunge too far such that she cannot realize her HPR threshold, the market will have overreacted. In this case of an overreaction, she believes it will be better to avoid selling in a panic, and instead, she will be better off to await an eventual recovery. Which of the following orders is most consistent with her strategy?
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Question 52 of 100
52. Question
A market maker takes a short position in 1,000 European call options on copper futures. The options mature in three months, and the futures contract underlying the option matures in four months. The current fourmonth futures price is $3.30 per pound, the exercise price of the options is $3.00, the riskfree interest rate is 4.0% per annum, and the volatility of silver futures prices is 20.0% per annum. Which is nearest to the position delta? (note: this question is inspired by Hull’s EOC Question 19.10)[1]
[1] John C. Hull, Risk Management and Financial Institutions, 4th Ed. (Hoboken, NJ: John Wiley & Sons, 2015).
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Question 53 of 100
53. Question
In early 2012, J.P. Morgan Chase (JPM) lost billions on trades executed by the London Whale, the notorious nickname for Bruno Iksil, who assumed massive exposures (masquerading as hedges) in a large credit derivative portfolio. Which of the following BEST summarizes the root cause of the debacle?
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Question 54 of 100
54. Question
Your colleague Peter is selecting probability distributions in order to perform several Monte Carlo simulations. Each of the following choices appears to be logical or sensible, EXCEPT which choice prima facie appears be a mistake?
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Question 55 of 100
55. Question
PlanetZim Financial Bank just entered a position in a derivatives contract. Which of the following features of the derivative position is MOST likely to indicate the trade is a case of SPECULATION, in contrast to a case of a hedge, arbitrage, or marketmaking?
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Question 56 of 100
56. Question
Mark the Risk Analyst is evaluating an atthemoney (ATM) call option on a nondividendpaying stock when the stock’s price is $30.00; i.e., S(0) = K = $30.00. For this option, he has the table shown below. The table displays option prices generated by the BlackScholesMerton option pricing model according to selected input variations of volatility and maturity. In other words, the table displays different values of c = BSM[S(0) = $30.00, K = $30.00, σ, Rf = 0.030, T].
Mark’s option actually expires in eight months; T = 8/12. Further, he observes that the option’s traded price (aka, observed market price) is $3.00. In this case, which of the following is nearest to the call option’s implied volatility?
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Question 57 of 100
57. Question
The Volkswagen emissions scandal concerned over ten million cars during the years 2009 to 2015. The scandal unfolded with significant financial repercussions and massive reputational damage to the company. GARP writes that “the damage to Volkswagen, the world’s biggest carmaker, was significant … Its reputation, particularly in the important US market, took a severe hit. The reputational effect extended beyond the company itself as German government officials expressed concerns that the value of the imprimatur ‘Made in Germany’ would be diminished because of Volkswagen’s actions.” Which of the following most accurately summarizes the Volkswagen emissions case study?
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Question 58 of 100
58. Question
Portfolio manager Peter manages a large portfolio with 100 component positions. He is interested in analyzing the nontrivial cross moments in the portfolio (trivial crossmoments are the position’s coskew/cokurtosis with itself, which is simply the position’s standard skew or kurtosis, so these are analogous to the diagonal of a covariance matrix which is mere variances. Each of the following statements is true EXCEPT which is inaccurate?
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Question 59 of 100
59. Question
The Investment Committee at your endowment just analyzed the historical performance of its asset allocation to hedge funds, which was 20.0% of the fund. It has determined that net of fees these hedge funds did not outperform the S&P 500 on a riskadjusted basis. Consequently, the Committee wants to reallocate this portion to a fund that tracks the S&P 500 index; and the Committee is comfortable mirroring the index with minimum tracking error. An outside consultant proposes an exchangetraded fund (ETF) such as the “Spider” (ticker SPY), but some members want to compare the ETF to an openended or closedended mutual fund that tracks the S&P 500.
In addition to highlighting the fact that the expense ratios tend to be lower for ETFs than mutual funds, the consultant offers the following arguments in favor of an ETF:
I. In contrast to an openended mutual fund, the advantage of the SPDR ETF can be traded at any time, can be shorted, and does not have to be partially liquidated to accommodate redemptions
II. In contrast to a closedended mutual fund whose price tends to trade at a discount to its fair market value, there is never any appreciable difference between the traded price of the SPDR EFT and its fair market value.
Which of the consultant’s argument(s) is (are) TRUE?
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Question 60 of 100
60. Question
A stock has a current price of $71.00 and follows geometric Brownian motion. It offers an expected return of 14.0% with volatility of 23.0% per annum. Which is nearest to the probability that a deeply outofthemoney (OTM) European call option on the stock with a maturity of one year (T = 1.0 year) and an exercise price of $100.00 will be exercised?
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Question 61 of 100
61. Question
According to GARP, “a wave of uncertainty over the valuation of assetbacked structured products exacerbated the [global financial] crisis” as counterparty risk suddenly became priced expensively by counterparties. Consequently, the valuation of these illiquid assets became problematic due to their inherent opacity (until mid2007 counterparty risk was a factor that effectively had NOT even been priced by the market!). Coincidentally, with these VALUATION and TRANSPARENCY issues, which of the following is TRUE about the ensuing liquidity crunch?
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Question 62 of 100
62. Question
Below are the joint probabilities for a cumulative bivariate normal distribution with a correlation parameter, ρ, of 0.30.
If V(1) and V(2) are each variables characterized by a uniform distribution, which is nearest to the joint probability Pr[V(1) < 0.050, V(2) < 0.050] under a Gaussian copula model?
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Question 63 of 100
63. Question
A defined benefit pension fund is 50.0% invested in equities and 50.0% invested in bonds. If we assume the simplest possible balance sheet, which is MOST LIKELY to be the net effect of a scenario where equities are approximately flat, but interest increase by 100 basis points? Please note this is inspired by Hull’s EOC Question 3.18[1], so it makes simplifying assumptions such as (i) the rate increase is a parallel shift of both short and longterm interest rates, (ii) durations are not managed, and (iii) the fund is not hedged.
[1] Source for Hull’s 3.18: John C. Hull, Risk Management and Financial Institutions, 5th edition (Hoboken, New Jersey: John Wiley & Sons, 2018).
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Question 64 of 100
64. Question
Peter initially values a oneyear European put option on a nondividendpaying (q = 0%) stock with the following assumptions:
 Oneyear put option maturity with twelve steps in the binomial model (one for each month): Δt = 1/12
 The strike price is equal to the stock’s current price of $40.00; i.e., atthemoney
 Volatility of stock, σ = 25.0% per annum
 Riskfree rate is 3.0% per annum with continuous compounding, r = 3.0%
Once he performs the twelvestep valuation, he decides to reprice the same option but with only one difference: he will increase the number of steps in the binomial tree to 50 (one for each week) so that each time step Δt = 1/50. In regard to the switch from twelve steps to 50 steps (i.e., Δt = 1/12 → Δt = 1/50), each of the following statements is true EXCEPT which is false?
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Question 65 of 100
65. Question
Peter is a Risk Analyst (and certified FRM) tasked by his firm to evaluate a half dozen vendors and make a recommendation to purchase one of their risk management software packages. The firm has a specific need, and the Risk Committee of the board has given the list of six vendors to Peter because they are each reputable vendors in the software category. Upon seeing the list, Peter realizes that he is friends with one of the CEOs (among the six vendors) because they both volunteer their time to a local charity and, due to this shared interest, they frequently socialize together.
According to GARP’s Code of Conduct, should Peter take any action with respect to a potential conflict of interest?
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Question 66 of 100
66. Question
The data and plot below show a bivariate normal sample distribution. The first two columns, z(1) and z(2), display random standard normal variables, N(0,1). Because X(1) is a (nonstandard) random normal variable with mean, µ, of 2.0 and standard deviation, σ, of 4.0, it is given by X(1) = 2.0 + 4.0 * z(1). On the other hand, X(2) is correlated with X(1) according to the selected correlation parameter, ρ(X1, X2), of 0.80.
What is the missing third realization (“???”) of X(2)?
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Question 67 of 100
67. Question
Below is an extract (selected rows) from a mortality table:
Which is nearest to the probability of a man aged 80 years old dying in the second year (between ages 81 and 82)?
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Question 68 of 100
68. Question
In the event of certain operational loss, the severity of the loss ranges from three to 18. As luck would have it, the loss distribution is similar to the roll of three dice.
For example, in the event of a loss occurrence, the probability of a loss of either three (the minimum loss) or 18 (the maximum loss) is given by approximately (1/6)^3 = 0.4630%; the probability of a loss of four or 17 is 3/6^3 = 1.389%. Which are nearest, respectively, to the 95.0% value at risk (VaR) and 95.0% expected shortfall (ES) for the severity of this loss?
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Question 69 of 100
69. Question
Gorton says, “The recent crisis is often described as being the worst global crisis since the Great Depression, and the evidence supports this label.”[1] The financial crisis included two main panic periods: August 2007 and September‐October 2008. Gorton’s literature review compares the crisis to the long history of previous and numerous financial crises. This comparison produced two interesting features: on the one hand, the authors found a crucial SIMILARITY to historical predicates but, on the other hand, they found a novel DIFFERENCE from previous crises. Which of the following best summarizes, respectively, the feature common (aka, similarity) to previous crises and the novel difference observed in the recent crisis?
[1] Gary Gorton and Andrew Metrick, 2012. “Getting Up to Speed on the Financial Crisis: A OneWeekendReader’s Guide”, Journal of Economic Literature 50:1, 128—150.
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Question 70 of 100
70. Question
You have assumed a singleindex model and regressed the returns for two stocks, stock (A) and stock (B), against the index in separate univariate regressions. This produced the following two linear functions, such that β(A) is 0.80 and β(B) is 1.40:
Additionally, the volatility of the index, σ(M), is 20.0%, the volatility of stock A, σ(A), is 32.0% and the volatility of stock B, σ(B), is 40.0%. Which of the following is the implied correlation between the two stocks?
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Question 71 of 100
71. Question
You are meeting with your FRM study group when one of the members of the group says they are a bit unclear on the definition of the term “short hedge.” The following conversation ensues:
I. Albert says, “It’s simple, if a company owns an asset but wants to hedge its plan to sell the asset at the future spot price, a short hedge is appropriate”
II. Barbara says, “Yes, Albert that is true, but if the company plans to sell the commodity in the future at a predetermined price, then a long hedge is appropriate!”
III. Chris says, “Barbara is correct because a short hedge is simply a hedge where a short futures position is taken.”
IV. Donald says, “Exactly true, Chris. And that means that a short hedge can also be a crosshedge; i.e., these terms are not mutually exclusive.”
V. Erin says, “And I would like to add that the company does not need to own the asset in order to conduct a short hedge.”
VI. Fred says, “And I would like to add that a short hedge implies negative basis, just as a long hedge implies positive basis.”
Which of the statements is (are) accurate?
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Question 72 of 100
72. Question
Patricia the Portfolio Manager owns an option portfolio that contains both long and short positions in European call and put options. The position gamma of the portfolio is negative, specifically it is 19,500. Recall that position gamma is the product of option quantity and each option’s percentage gamma. For example, a long position in 10,000 call options that each have a percentage (per option) gamma of 0.050 has a position gamma of +500; on the other hand, a short position in the same number of options has a position gamma of 500. Position gamma can be summed across the option portfolio.
Patricia initially estimates her option portfolio’s value at risk (VaR) based on a delta approximation. Her analysis quotes VaR in Loss(+)/Profit() format; aka, L/P units. In this way, losses and VaR are expressed as positive values. However, she realizes that such an estimate omits the portfolio’s negative position gamma, so she recomputes the portfolio’s VaR by using a DELTAGAMMA approximation. How does the revised estimate compare to the first deltaonly estimate?
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Question 73 of 100
73. Question
Suppose that three factors have been identified for the U.S. economy:
 Expected inflation rate (IR) is +2.00%
 Expected 10year Treasury yield (TNOTE) is 2.40%
 Expected growth in productivity (PROD) is +3.00%
A stock with an expected return of 9.0% has the following betas with respect to these factors: β(IR) = +1.50, β(TNOTE) = 1.20 and β(PROD) = 0.70. In turns out that that economy’s actual factor performance is given by the following set of results:
 Actual inflation rate (IR) is + 2.60%
 Actual 10year Treasury yield (TNOTE) is 3.00%
 Actual growth in productivity (PROD) +2.00%
What is the revised estimate of the stock’s expected rate of return (note: this is a variation on Bodie’s Problem 10.1)?[1]
[1] Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments, 10th Edition (New York: McGrawHill, 2013)
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Question 74 of 100
74. Question
You would like to describe an account that begins at TIME(0) = $100.00 and compounds continuously at 9.0% per annum. What is a function that characterizes the value of this account, A(t), over time according to such a continuous and constant growth trend?
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Question 75 of 100
75. Question
The current price of a technology index is 3,000 and its yield, q, is 2.0% per annum with continuous compounding; i.e., about 2.010% per annum with semiannual compounding. The riskfree rate is 3.0% per annum with continuous compounding. The discount rate for the index can be determined by the capital asset pricing model (CAPM) where its beta is 1.80 and the market’s expected return is 9.0%; i.e., the market’s expected excess return is 6.0%. Which is nearest to the index’s expected future spot price in 10 months, E[S(+0.833)]?
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Question 76 of 100
76. Question
Which of the following statements is TRUE about the role of validation in stress testing governance?
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Question 77 of 100
77. Question
Assume a sock’s returns are accurately characterized by the FamaFrench threefactor model. The stock’s own factor betas and the risk model’s risk premiums are given below:
What is the firm’s size/value style characteristics and what is the firm’s required rate of return?
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Question 78 of 100
78. Question
What is the crucial difference between bootstrapping and Monte Carlo simulation?
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Question 79 of 100
79. Question
The price of a 72day Treasury bill is quoted as 7.00. Which is nearest to the continuously compounded return (on an actual/365 basis) that an investor will earn on the Treasury bill for the 72day period? (note: inspired by Hull’s EOC Problem 6.8)[1]
[1] John C. Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014)
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Question 80 of 100
80. Question
Linda Allen[1] introduces the following value at risk (VaR) estimation approaches:
 Historical simulation (HS)
 GARCH (1,1)
 Hybrid
 Multivariate density estimation (MDE)
 Historical standard deviation (STDEV)
 Adaptive volatility (AV)
Consider these six summary descriptions:
I. The simplest parametric approach whose weakness is sensitivity to window length and extreme observations
II. The most convenient and prominent nonparametric approach whose weakness is inefficient use of data
III. An interpretation of the exponentially weighted moving average (EWMA) that gives the risk manger a rule that can used to adapt prior beliefs about volatility in the face of news
IV. A parametric approach that assumes conditional returns are normal but unconditional tails are heavy; and that returns are not correlated but conditional variance is meanreverting
V. An approach that weights past squared returns not by time but instead according to the difference between current and past states of the world
VI. An approach that modifies historical simulation by assigning exponentially declining weights to past data such that recent (distant) returns are assigned more (less) weight
Which sequence below correctly matches the VaR estimation approach with its summary description?
[1] Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach (Oxford: Blackwell Publishing, 2004)
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Question 81 of 100
81. Question
According to Ben Bernanke, among the following trigger/vulnerability pairs, which were the primary TRIGGER and (among) the primary VULNERABILITIES, respectively, that led to the financial crisis?
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Question 82 of 100
82. Question
During a recent workweek, Peter recorded the number of dropped calls to the company’s support line. For the tiny sample of five days (n = 5), the average number of dropped calls was 9.60 per day. Peter used Excel’s VAR.P() to retrieve the variance and the result was 1.840. However, his colleague Mary pointed out that this is a biased estimate of the unknown population variance. What is the unbiased estimate of the variance?
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Question 83 of 100
83. Question
A $100.0 million interest rate swap has a remaining life of 15 months. Under the terms of the swap, sixmonth LIBOR is exchanged for 3.60% per annum (compounded semiannually). Sixmonth LIBOR forward rates for all maturities are 3.00% (with semiannual compounding). Two Three months ago, the sixmonth LIBOR rate was 2.90% (this assumption is shown in purple cell below). OIS rates for all maturities are 2.80% with continuous compounding.
Which is nearest to the current value of the swap to the counterparty who is paying the floating rate? (Inspired by Hull’s EOC Problem 7.2, 10th Edition)[1]
[1] Hull, Options, Futures, and Other Derivatives, 10th Edition (New York: Pearson, 2017).
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Question 84 of 100
84. Question
Rebecca has determined that her equity portfolio’s 25day 95.0% confident absolute value at risk (aVaR) is given by µ*Δt + σ*α*sqrt(Δt) = 12,000 + 208,000 = $196,000. She subsequently decides that she wants to translate this into a 10day 99.0% confident aVaR. If the returns are i.i.d. and normally distributed, which of the following is nearest to the translated VaR?
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Question 85 of 100
85. Question
Among the Basel Committee’s Principles for effective risk data aggregation and risk reporting, Principle 2 is “Data architecture and IT infrastructure: A bank should design, build and maintain data architecture and IT infrastructure which fully supports its risk data aggregation capabilities and risk reporting practices not only in normal times but also during times of stress or crisis, while still meeting the other Principles.”[1] The principle includes paragraph 33, where two terms have been replaced with “[keyword #1]” and “[keyword #2]”:
“A bank should establish integrated data [keyword #1 here] and architecture across the banking group, which includes information on the characteristics of the data–i.e., [keyword#2 inserts here]–as well as use of single identifiers and/or unified naming conventions for data including legal entities, counterparties, customers and accounts.” The first keyword, [keyword #1], refers to the categorization or classifications of data; for example, market risk and credit risk are categories of risk. The second keyword, [keyword #2], refers to information about the data.”[1]
Which terms correctly replace, respectively, [keyword #1] and [keyword #2]?
[1] “Principles for Sound Stress Testing Practices and Supervision” (Basel Committee on Banking Supervision Publication, May 2009)
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Question 86 of 100
86. Question
Peter Parker at Betalab Bank emailed a survey to the bank’s customers. The survey included a question that asked them to rank their customer satisfaction on a scale from one to 10. She received 51 responses, and she considers that a random sample (n = 51). Among this sample, the average satisfaction score (on a scale of one to 10) is 8.50 with a sample standard deviation of 1.90. Betalab’s CEO is MaryJane, FRM, and she hopes that the bank’s average customer satisfaction is at least 9.0. MaryJane holds the FRM designation, so she understands that acceptance of the null is more accurately a failure to reject the null, but she is a practical person. Her null hypothesis is that the population’s average customer satisfaction is at least 9.0 (i.e., H0: μ ≥ 9.0 and H1: μ < 9.0). Peter shares his sample findings with five of his colleagues, and each colleague gives different input, as follows:
I. Albert says the test statistic is (8.5 – 9.0) ÷ [1.90 / SQRT(51)] = 1.88, or 1.88 = 1.88
II. Betty says that if the sample size were doubled, ceteris paribus (i.e., same sample mean and sample standard deviation), the test statistic will increase about +41%
III. Chris says that (for n = 51) Mary should use a onesided test, and with onesided 95.0% confidence (aka, 5.0% significance) she should reject the null
IV. Derek says that (for n = 51) Mary can accept (aka, fail to reject) the CEO’s null hypothesis with 95.0% confidence but only if she artificially switches to a twosided hypothesis (i.e., H0: μ = 9.0 and H1: μ ≠ 9.0). Notice how this insincerely “games” the test: the setup here calls for a onesided test.
V. Erin agrees with Chris and says that Mary should use a onesided test per the CEO’s onesided hypothesis but notes that Peter can accept (aka, fail to reject) the null with onesided 99.0% confidence (aka, 1.0% significance)
Which of the five statements is (are) correct?
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Question 87 of 100
87. Question
As she analyzes a stock, Barbara contemplates a straddle because she wants to express her view that there will be a big change in the stock price, either dramatically up or down, but she is uncertain as to the direction. In this way, she wants an option combination strategy that is “long volatility.” However, the straddle is more expensive than she anticipated. Which of the following will allow her to generally express her “long volatility” view (giving her the potential for a large, or even uncapped, payoff in the event of a dramatic price move) but with a cost that is REDUCED in comparison to the straddle?
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Question 88 of 100
88. Question
Shown below is a bank’s portfolio of wholesale exposures (this is Siddique and Hasan’s Table 2.2):[1]
The bank needs to estimate the sensitivities of this portfolio’s losses to changes in two macro variables: gross domestic product (GDP) growth and unemployment. If the bank conducts a stress test, each of the following is likely–or at least reasonable–to be included in the bank’s stress test assumptions EXCEPT which is the LEAST likely to be an assumption in the stress test?
[1] Akhtar Siddique and Iftekhar Hasan, Stress Testing: Approaches, Methods, and Applications (London: Risk Books, 2013)
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Question 89 of 100
89. Question
“Agency costs” is a term used to describe the costs in a situation where the interests of two parties are not perfectly aligned. In the events leading up to the Global Financial Crisis (CFC; aka, credit crisis), which of the following was a source of agency cost?
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Question 90 of 100
90. Question
Barbara just received a dataset. She runs the dataset through five different regression models, where each regression model employs a different estimator for the slope. The properties of the slope estimators include the following:
 Estimator A is biased but has the smallest variance (3.7)
 Estimator B is linear and biased but has a small variance (4.6)
 Estimator C is linear and unbiased but has a medium variance (9.5)
 Estimator D is nonlinear and biased but is consistent and has a large variance (11.8)
 Estimator E is nonlinear and unbiased but has the largest variance (14.1)
Which of these estimators is BLUE?
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Question 91 of 100
91. Question
Patricia wants to hedge her portfolio of exotic options. The portfolio consists mostly of barrier options. She is comparing a classic deltahedge to a static options replication; the static option replication entails shorting a portfolio that replicates certain boundary conditions. Each of the following is a good argument in favor of a static option replication, for the purpose of hedging her portfolio, EXCEPT which is WEAKEST argument?
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Question 92 of 100
92. Question
Assume we follow Tuckman’s[1] illustration and estimate the key rate exposures (i.e., KR01s and key rate durations) for a zerocoupon bond with 30 years to maturity; e.g., CSTRIP. The key interest rate is a par yield. The analysis selects four key rates: 2year, 5year, 10year, and 30year. Further, as Tuckman explains about the rule for rates between neighbors, “each of the four shapes is called a keyrate shift. Each key rate affects par yields from the term of the previous key rate (or zero) to the term of the next key rate (or the last term). For example, the 10year key rate affects par yields of terms 5 to 30 years only. Furthermore, the impact of each key rate is normalized to be one basis point at its own maturity and then assumed to decline linearly, reaching zero at the terms of the adjacent key rates. For the twoyear shift at terms of less than 2 years and for the 30year shift at terms greater than 30 years, however, the assumed change is constant at one basis point.”[1]
About this key rate exposure technique, each of the following statements is true EXCEPT which is false?
[1] Bruce Tuckman, Fixed Income Securities, 3rd Edition (Hoboken, NJ: John Wiley & Sons, 2011)
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Question 93 of 100
93. Question
Each of the following is true about the reempowered role of the Chief Risk Officer (CRO) EXCEPT which is false?
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Question 94 of 100
94. Question
Over the previous six months, two assets generated the monthly returns displayed below under columns X(i) and Y(i). The third and fourth columns display the squared differencefromaveragereturns that inform the univariate variance; the fifth column shows the associated crossproduct that informs their covariance.
Because this is a very small sample, we want to retrieve unbiased sample moments. What are, respectively, the unbiased sample variances of the two variables and their sample covariance?
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Question 95 of 100
95. Question
The price of a dividendpaying stock is $44.00 while the riskfree rate is 3.0%. Consider a European call option and a European put option with identical strike prices, K = $40.00, and identical times to expiration of nine months, T = 0.75 years. The call has a price of $8.95 and the put has a price of $5.36. What is the present value of the dividends expected during the life of the option?
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Question 96 of 100
96. Question
Consider the following oneyear rating transition (aka, migration) matrix illustrated below:
About this migration matrix, each of the following statements is true EXCEPT which is false?
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Question 97 of 100
97. Question
Crouhy writes that “understanding [the difference between expected loss and unexpected loss] is the key to understanding modern risk management concepts such as economic capital attribution and riskadjusted pricing.”[1]
Which of the following statements is TRUE about unexpected loss (UL)?
[1] Michel Crouhy, Dan Galai, and Robert Mark, The Essentials of Risk Management, 2nd Edition (New York: McGrawHill, 2014)
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Question 98 of 100
98. Question
A stock (X1) has three possible returns: 5%, 0, or +5%. The analyst rating (X2) can be negative (denoted by X2= 1), neutral (X2 = 0), or positive (X2 = +1). The probability matrix is displayed below (inside the square). Six joint probabilities are given, but three are missing; for example, the joint probability of a negative analyst rating and a negative stock return, P(X1 = 5% ∩ X2 = 1) = 14.0%.
The bottom row (outside the square) displays the unconditional (aka, marginal) probabilities for the stock; for example, the unconditional Pr(X1 = 5%) = 20.0%. What is the unconditional (aka, marginal) probability that the analyst rating is positive, Pr(X2 = +1)?
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Question 99 of 100
99. Question
The spot price of wheat is $5.00 per bushel while the riskfree rate is 3.0% per annum with continuous compounding. The cost to store wheat is 12.00% per annum as a proportion of the spot price. The traded (observed) price of a ninemonth wheat futures contract, F(0, 0.75), is $5.430. Among the following choices, which of the following scenarios is the most likely?
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Question 100 of 100
100. Question
Peter works for an ESG fund that evaluates political risk. Among the components of political risk, Peter’s fund assigns the greatest weight to corruption. If corruption is the most important criteria, into which of the following countries is Peter’s firm MOST LIKELY to invest; i.e., which is least corrupt?
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