Part 1 Full Length Interactive Mock Exam 1
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Question 1 of 100
1. Question
Case studies that feature financial engineering by way of complex derivatives include Bankers Trust, the Orange County case, and Sachsen Landesbank. In regard to these financial engineering cases, each of the following statements is true EXCEPT which is false?
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Question 2 of 100
2. Question
Let’s assume two normal variables: X ~ N(0, 3.0^2) and Y ~ N(4.0, 9.0^2). Let V be a mixture distribution where X has a component weight of 80% and Y has a component weight of 20%. Let W = 0.80*X + 0.20*Y with the assumption that X and Y are independent; that is, this W is the sum of independent, random variables.
Which is more likely (the mixture or the convolution) to realize a negative outcome; that is, is Pr(V<0) > Pr(W<0), or on the other hand, is Pr(W<0) > Pr(V<0)?
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Question 3 of 100
3. Question
Consider a oneyear exchange option to give up 14.0 units of Ethereum (aka, ether or ETH) for one unit of Bitcoin (BTC). The current price of Bitcoin is $4,200.00 BTC and the current price of one unit of ether is $300.00 ETH. The riskfree interest rate is 2.0% per annum with continuous compounding. The per annum volatility of Bitcoin is 50.0% and the volatility of Ethereum is 38.0%. Their correlation, ρ(BTC, ETH) = 0.540. We can price an exchange option with a simple variation on the BlackScholesMerton called the Margrabe variation.
Using the Margrabe under these assumptions, the price of this BTCforETH exchange option is $723.11. Further, each of the following statements, ceteris paribus, is true EXCEPT which is false?
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Question 4 of 100
4. Question
Consider a credit portfolio that contains three positions. The exposure (EAD) of each position is $10.0 million. Further, our model assumes the shape of the loss distribution (aka, the credit risk of each exposure) is identical for each exposure, although their means vary as follows:
 Exposure #1 has a default probability of 2.0% and unexpected loss (UL) of $597,000
 Exposure #2 has a default probability of 4.0% and unexpected loss (UL) of $840,000
 Exposure #3 has a default probability of 6.0% and unexpected loss (UL) of $1,023,500
The pairwise default correlation is 0.40 among each exposure pair, such that the portfolio’s unexpected loss is $1,920,250. In regard to Exposure #1, its risk contribution is given by $597,000 * [$597,000 + ($840,000 * 0.40) + ($1,023,500 * 0.40)] / $1,920,250 = $417,348. Because the capital multiplier, CM, is set at 5.50 to reflect a specified confidence level, the economic capital for Exposure #1, EC(#1) = $417,348 * 5.50 = $2,295,415, or about $2.30 million.
Which of the following is NEAREST, respectively, to the required economic capital for the second and third exposures, EC(#2) and EC(#3)?
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Question 5 of 100
5. Question
According to GARP, each of the following was a causal factor in the 20072009 global financial crisis (GFC) EXCEPT which is not a causal factor?
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Question 6 of 100
6. Question
A hedge fund’s big data algorithm can predict the market’s direction on five out of eight days (62.5%). Each day’s prediction is either a success (e.g., market goes up and algo predicts up) or a failure (e.g., market goes down but algo predicts up). If we dubiously assume the predictions are independent, the binomial distribution fits a series of daily predictions over, say, a week or a month. Over two months, the probability of each day’s predication being successful, p, equals 5/8 or 62.5% and the number of days, n, equals 60.
We observe that n*p = 60*62.5% = 37.5 and n*(1p) = 60*37.5% = 22.5, and both of these values (i.e., 37.5 and 22.5) are greater than 10; this satisfies a conventional test that says we can use the normal to approximate the binomial. For example, if p were only 1.0%, then n*p = 6, but 6 is less than 10, and such a binomial is deemed to be too skewed to be approximated by the normal distribution. But ours passes the test so we will approximate with the normal distribution.
If we do rely on the normal distribution to approximate this binomial where p = 5/8 and n = 60, what is the probability that the algo makes a correct prediction on only half the days or worse; i.e., where X is the number of successful predictions and we approximate with the normal distribution, what is the Pr(X <= 30)?
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Question 7 of 100
7. Question
The riskfree rate is 3.0% and the stock price of Discovery Communications (ticker: DISCK) is $20.00. Peter purchases a straddle with sixmonth European atthemoney options; i.e…, S = K = $20.00. If the price of a call option is $2.05, then how much will the stock price need to move in order for him to at least achieve breakeven profit (reminder that profit = final payoff +/ initial premium)?
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Question 8 of 100
8. Question
A credit portfolio contains an adjusted exposure of $30.0 million with a default probability of 4.0%. In regard to loss given default (LGD), the Portfolio Manager estimates an (LGD) of 40.0% with a standard deviation, σ(LGD), of 40.0%. What is the position’s unexpected loss (UL)?
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Question 9 of 100
9. Question
Which of the following is TRUE about the SWIFT (Society for Worldwide Interbank Financial Telecommunication) case study?
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Question 10 of 100
10. Question
A credit portfolio contains some number of independent creditsensitive assets with identical default probabilities; as the defaults are i.i.d., we can use the binomial distribution to characterize the number of defaults. We are told the expected number of defaults is 4.0 with a variance of 3.80. Which is nearest to the probability of exactly four defaults; Pr(X = 4  binomial with mean of 4.0 and variance of 3.80)?
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Question 11 of 100
11. Question
Consider a European call option on a nondividendpaying stock that has a current price, c = $6.37, if we make the following assumptions:
 S(0) = K = $100.00 and this option has a delta, N(d1) = 0.570
 Volatility, σ = 20.0% and this option has vega = 27.8
 Riskfree rate, Rf = 3.0%
 Time to expiration, T = 0.5 years or six months
Each of the following changes will INCREASE the value of this option, but which factor change will produce the SMALLEST change to the option’s value?
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Question 12 of 100
12. Question
Consider a credit portfolio that includes many loans. In order to derive economic capital (EC) for credit risk, we need to quantify four measures: expected losses (EL), unexpected losses, unexpected loss contribution (ULC), and economic capital (EC). In regard to these four measures, each of the following definitions or descriptions is true EXCEPT which is inaccurate?
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Question 13 of 100
13. Question
Barbara is a certified FRM who previously generated income statement and profit projections over a fiveyear horizon in response to her client’s request. Subsequent to the coronavirus outbreak, her client asks Barbara to generate revised financial projections (income statement and balance sheet) and provide the best single point estimate of future revenue, profit, and equity. Barbara utilizes Monte Carlo simulation. Although her client has asked for a single point estimate of these future financial metrics, Barbara perceives that the virus (and the consequential responses) render economic predictions extremely difficult and necessarily laced with great uncertainty. Which of the following is probably her BEST approach to the problem?
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Question 14 of 100
14. Question
Consider the probability mass function (pmf) below. For example, Pr(X = 1.0) = 20.0%.
As we can see, this distribution is symmetrical, so we know that its skewness is zero without performing any calculations. We are told the variance is 1.20 (although we can calculate the variance). What is this distribution’s kurtosis?
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Question 15 of 100
15. Question
A stock with a volatility of 31.0% is currently trading at $47.00 while the riskfree rate is 3.0%. An investor purchases a European straddle with a strike price of $45.00: a straddle is a call and a put on the same stock with identical strike prices and expiration dates. The straddle expires in nine months (0.75 years). The price of the put is $3.50. Among the following choices, which best summarizes the final stock price required (in nine months, at expiration) in order for the trader to realize at least a positive net PROFIT on this trade?
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Question 16 of 100
16. Question
Consider the following oneyear migration (aka, transition) matrix:
When is the soonest that an obligation rated AAA (the highest rating) can default?
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Question 17 of 100
17. Question
Arguably the U.S. savings and loan (S&L) crisis in the 1980s had multiple causes, but among the following which is the BEST summary explanation of the S&L crisis?
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Question 18 of 100
18. Question
A discrete random variable is characterized by the probability mass function (pmf) as given by f(x) = x*a, and its domain is the set of integers {6, 7, 8., 9, and 10}. What is the variable’s expected value?
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Question 19 of 100
19. Question
Suppose that the 6month, 12month, 18month, and 24month overnight indexed swap (OIS) zero rates with continuous compounding are 2.00%, 2.40%, 3.00%, and 3.60%, respectively. Suppose further that the sixmonth LIBOR rate is 2.60% with semiannual compounding. The forward LIBOR rate for the period between 6 and 12 months is 3.00% with semiannual compounding. The forward LIBOR rate for the period between 12 and 18 months is 3.60% with semiannual compounding. (Please Note: this question is inspired by Hull’s Example 7.2 in 10th Edition).
Finally and importantly, assume the twoyear swap rate is 4.00%. Conditional on the realization of the LIBOR forward rates, the future cash flow in six months is, therefore (2.60% – 4.00%)/2 *$100.0 = $0.70 and its present value is about $0.70*exp(0.020*0.50) = $0.693; that is, we are using the OIS zero rates as the riskfree rate for discounting purposes.
Which is nearest to an estimate for the forward LIBOR rate for the 18 to 24month period, F(1.5, 2.0)?
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Question 20 of 100
20. Question
In regard to throughthecycle (TTC) versus atthepoint (aka, point in time, PIT) approaches to credit ratings, each of the following statements is true EXCEPT which is false?
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Question 21 of 100
21. Question
Alice, Bert, Chris, Don, Eva, and Fred are individual investors. Each of them exhibits a particular behavioral bias.
 Alice (A) invested in the stock Cloudera (CLDR) and bad news (aka, new information) renders her original thesis obsolete but she is reluctant to sell today because an exit implies the realization of a 30.0% loss on the position and she much prefers to sell after her position experiences a doubledigit gain
 Bert (B) can buy a new smartphone for $79.00 but he cannot resist a sale and prefers to pay $100.00 because it represents a 50.0% discount from the retail (MSRP) price
 Chris (C) attends an investment conference but he avoids the seminar focusing on recession risks because he is overweight homebuilders and he worries the topic will make him anxious with worry
 Don (D), who enjoys food shopping, tends to be priceconscious (e.g., he seeks bargains) when he pays cash at Sprouts or Trader Joes, but when he uses his Amazon credit card at Whole Foods he doesn’t worry about the cost because he doesn’t look at the statement for several days or weeks
 Eva (E) purchased Facebook (FB) at $160.00 because his firm’s price target was $200.00, and he decides to ignore new information until the price reaches this level
 Fred (F) was previously a patient buyandhold investor who purchased highconviction stocks and only checked his portfolio once a week, but last year he signed up for a subscription to Seeking Alpha and since that time his buy/sell transactions have quintupled because he’s reading news about his portfolio holdings every day
Which of the following correctly matches the individual investor to his or her behavioral bias?
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Question 22 of 100
22. Question
The probability graph below illustrates event A (the yellow rectangle) and event B (the blue rectangle). The unconditional probability of event A is 50.0% and the unconditional probability of event B is 44.0%; i.e., Pr(A) = 50.0% and Pr(B) = 44.0%. Their overlap is graphed by the green rectangle such that Pr(A ∩ B) = 27.0%. The orange rectangle conditions on the event C. For example, conditional on event C, there is a 50.0% probability that event A occurs, Pr(A  C) = 50.0%.
Which of the following is TRUE about, respectively, the unconditional and conditional relationship between events A and B?
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Question 23 of 100
23. Question
Below are given threemonth Eurodollar Futures quotes for contracts with maturities of, respectively, 300, 393, and 486 days; for example, 94.50 is the Eurodollar Futures quote for a contract that matures in 300 days and settlement will be based on the thenprevailing threemonth LIBOR.
Which is nearest to the implied 393day zero rate expressed per annum with continuous compounding?
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Question 24 of 100
24. Question
Quotecan Corporation has issued a bond with the following features, characteristics and/or qualities: Quotecan’s interest coverage ratio (i.e., earnings before interest and taxes, EBIT, divided by interest expense) is within reasonable limits such that, at least in the near term, investors have adequate protection and should expect their interest and principal payments on the bond. On the one hand, the bond is better than junk. On the other hand, the bond carries more credit risk than bonds issued by the highestrated corporations like, for example, Microsoft (MSFT), Apple (AAPL), Exxon Mobil (XOM), Johnson & Johnson (JNJ), Walmart (WMT). To be more specific, Quotecan’s capacity to repay may be impaired if adverse economic conditions materialize, or if circumstances suddenly change. While these obligations are not speculative in their entirety, they do contain just a few speculative elements which may render the protective elements unreliable over a longer time horizon.
Based on these facts, which credit rating is most likely assigned to Quotecan’s bond offering?
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Question 25 of 100
25. Question
GARP explains that “perhaps the biggest argument for ERM is that an enterpriselevel perspective is the best way to prioritize risks and optimize risk management.” Each of the following is one of the four key reasons that enterprise risk might demand the practice of (or, the art and science of) enterprise risk management, ERM, EXCEPT which is NOT one of the four key reasons?
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Question 26 of 100
26. Question
Yesterday a web page hosted by Acme received tens of thousands of page views, but some were views by malicious bots. Acme utilizes two software applications to detect these malicious “botviews.” It uploads the same data file from yesterday to both applications. The first application detects 200 botviews and the second application detects 300 botviews. Among these, only 40 botviews were detected by both applications. All botviews are equally likely to be located, but clearly both applications only identify a minority of the botviews (otherwise there would be a much higher number of identified botviews common to both applications). Further, the identification of a botview by one application is independent of its identification by the other application. How many malicious botviews did the web page experience on this day?
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Question 27 of 100
27. Question
The counterparty with the short position in a Treasury bond futures contract has decided to deliver and is trying to decide between the four bonds displayed below; e.g. the quoted price of bond #4 is $129.41 and its conversion factor (CF) is 1.290.
If the future contract’s settlement price is $99.00, then which bond is the cheapest to deliver (CTD)?
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Question 28 of 100
28. Question
Rebecca is evaluating four different countries in an attempt to determine their respective default risk. She evaluates the countries in four categories: degree of indebtedness as measured by debt as a percentage of gross domestic product; social service/pension commitments as estimated by the average age of the population; nature of the economy (e.g., diverse versus concentrated in oil as a natural resource), and monetary policy. The four countries are summarized in the exhibit below:
Which of the four countries is most likely to default?
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Question 29 of 100
29. Question
GARP explains that the Basel Committee on Banking Supervision’s standard number 239 (aka, BCBS 239) “was a major driver in the rise of the chief data officer (CDO) function. The CDO is typically responsible for standardizing a firm’s approach to data management.”[1] In addition, which of the following statements is also TRUE about the Basel Committee on Banking Supervision’s standard number 239 (aka, BCBS 239)?
[1] 2020 FRM Part I: Foundations of Risk Management, 10th Edition. Pearson Learning Solutions, 10/2019
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Question 30 of 100
30. Question
The promoter of a new cryptocurrency claims that its monthly price volatility is 25.0%, or more specifically, is not greater than 25.0%. The monthly returns for the most recent 36 months are displayed below; the sample volatility is observed to be 32.0%. Which is nearest to the probability that the promoter’s claim is correct, and the true price volatility of the cryptocurrency is less than or equal to 25.0%?
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Question 31 of 100
31. Question
The sixmonth interest rates in Mexico and the United States are 7.0% and 1.0% per annum, respectively, with continuous compounding. The spot price of the Mexican peso is MXN/USD $0.05650, that is, about 17.70 pesos per one US dollar. If the futures price for a contract deliverable in six months is $0.0610 (i.e., about 16.39 pesos per one US dollar), then which of the following best exploits the arbitrage opportunity (this question is inspired by Hull’s EOC Problem 5.14)[1]?
[1] John C. Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014)
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Question 32 of 100
32. Question
Political Risk Services (The PRS Group) provides numerical measures of country risk for more than a hundred countries. Its International Country Risk Guide (ICRG) rating “comprises 22 variables in three subcategories of risk: political, financial, and economic. A separate index is created for each of the subcategories. The Political Risk index is based on 100 points, Financial Risk on 50 points, and Economic Risk on 50 points. The total points from the three indices are divided by two to produce the weights for inclusion in the composite country risk score.”[1]
As of July 2018, according to Damodaran, Taiwan’s composite (ICRG) score was 85. Which of the following is TRUE?
[1] https://www.prsgroup.com/exploreourproducts/internationalcountryriskguide/
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Question 33 of 100
33. Question
Consider the following three portfolios where we know the expected excess returns of Portfolios A and B; i.e., E[ER(A)] = 6.0% and E[ER(B)] = 8.4% and these in excess of the riskfree rate. For Portfolios A and B, we also know the factor betas: β(A,1) = 0.40, β(A,2) = 1.20, β(B,1) = 0.80, β(A,1) = 1.50. The unknowns are the two risk premiums on the two factors, F(1) and F(2):
 Portfolio A: E[ER(A)] = β(A,1)*F(1) + β(A,2)*F(2) = 0.40*F(1) + 1.20*F(2) = 6.0%
 Portfolio B: E[ER(B)] = β(B,1)*F(1) + β(B,2)*F(2) = 0.80*F(1) + 1.50*F(2) = 8.4%
 Portfolio C has the following betas: β(C,1) = 1.30 and β(C,2) = 0.90
If Portfolio C has betas as given by β(C,1) = 1.30 and β(C,2) = 0.90, what is the expected excess return of Portfolio C?
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Question 34 of 100
34. Question
In order to evaluate the potential of a linear relationship between portfolio returns and a benchmark index, your colleague Richard conducted a univariate regression analysis. He regressed the benchmark index returns, B(i), as the dependent (aka, response) variable against portfolio returns, R(i), as the independent (aka, explanatory) variable. Here is his summary output:
Which is nearest to the correlation coefficient between portfolio returns, R(i), and the benchmark returns, R(b)?
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Question 35 of 100
35. Question
Assume we can express the storage cost of corn as a constant proportion of the spot price. If the storage costs suddenly increased from 9.0% per annum (e.g., $0.36 per bushel when the spot price of corn is $4.00 per bushel) to 17.0% per annum (e.g., $0.68 per bushel when the spot price of corn is 4.00 per bushel), which is nearest to the predicted PERCENTAGE INCREASE in the price of a sixmonth (0.5 years) corn forward contract?
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Question 36 of 100
36. Question
A bond portfolio with a face value of $7.0 million is exposed to the following two key rates:
 The 2year key rate, KR01(2year) is equal to $0.030 per 100 face amount and has a daily volatility, σ(bps), of 12.0 basis points
 The 5year key rate, KR01(5year) is equal to $0.090 per 100 face amount and has a daily volatility, σ(bps), of 25.0 basis points
As the curve experiences significant nonparallel shifts, the correlation between the key rates is only 0.440. Which of the following is nearest to the daily volatility of the portfolio (in dollars)?
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Question 37 of 100
37. Question
During a 36month period during which the riskfree rate was 2.0%, consider a comparison between the market portfolio and two fund managers, Betty and Peter:
 The market portfolio’s excess return was +6.0% (its gross return was +8.0%) with a volatility of 24.0% per annum
 Peter’s portfolio’s excess return was +7.0% (his gross return was + 9.0%) with a volatility of 36.0% per annum and beta, β(P,M) = 0.750
 Betty’s portfolio’s excess return was +11.0% (her gross return was + 13.0%) with a volatility of 44.0% per annum and beta, β(B,M) = 1.650
If the capital asset pricing model (CAPM) is valid, then each of the following statements is true EXCEPT which is false?
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Question 38 of 100
38. Question
Based on a regression analysis, the following model was produced to predict housing starts (given in thousands) within a certain geographical region; e.g., one of the larger U.S. states. The time series model contains both a trend and a seasonal component and is given by the following:
The trend component is reflected in the variable, TIME(t), where (t) is the month. Seasonality is reflected by the intercept (20.10) plus the three seasonal dummy variables (D2, D3, and D4) in order to capture quarterly seasonality. Winter includes December, January, and February. Spring includes March, April, and May and is indicated by dummy D(2t). Summer includes June, July, and August and is indicated by dummy D(3t). Finally, fall includes September, October, and November and is indicated by D(4t).
The model starts in November 2016; for example, y(T+1) refers to December 2016 and y(T+2) refers to January 2017. What does the model predict for October 2018?
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Question 39 of 100
39. Question
In April 2017, Portfolio Manager Jeff believed that the shares of Chorizo Fast Casual Restaurants Incorporated (“Chorizo Inc”), trading at $380.00 per share, were overvalued. He instructed his broker to short 1,000 shares. In May, Chorizo Inc paid a dividend of $6.00 per share. In July, due to a food contamination incident, the shares plummeted to $$333.00, when Jeff closed out his position. The total borrowing fee was $1,500.00. What was Jeff’s net profit?
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Question 40 of 100
40. Question
Peter is a Financial Analyst whose boss asked him to develop a model, or if necessary a set of models, that are multifactor risk models for the firm’s fixed income and derivative investment portfolios. Specifically, there are four objectives as follows:
I. To measure and hedge the risk of bond portfolios in terms of the relatively small number of liquid bonds available, in particular, ontherun government bonds
II. To measure and hedge the risk of a portfolio of swaps in terms of the highly liquid money market and swap instruments, which are more numerous
III. To measure the risk of mixed portfolios not terms of other securities but instead to model direct changes to the shape of the term structure
IV. To measure portfolio volatility by assuming a term structure of volatility but doing so without an excessive “curse of dimensionality;” i.e., avoiding too many correlation pairs
For these four objectives, Peter has three basic multifactor risk metrics: keyrate exposures, partial ’01s, and forwardbucket ’01s. For which of the four objectives is keyrate exposures best suited?
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Question 41 of 100
41. Question
The plot below illustrates an actual portfolio possibilities curve (PPC, dashed line). Two prominent portfolios (minimum variance and market portfolio) are also plotted.
The green point is the minimum variance portfolio, MVP, which has an expected return of 7.70% and standard deviation, σ, of 10.0%. The red triangle is the Market Portfolio that has an expected return of 11.0% and standard deviation, σ, of 13.7%. If the riskfree rate is 4.0%, what is the formula for the capital market line (CML)?
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Question 42 of 100
42. Question
Consider the following quadratic trend model:
Which of the following functions correctly characterizes this trend?
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Question 43 of 100
43. Question
A 30year zerocoupon bond with a face value of $100.00 has a yield of 5.0% per annum with continuous compounding. Peter the analyst wants to estimate the impact of a 35basis point increase (“shock up”) in the yield without fully repricing the bond. Using duration, he estimates the bond price will drop by 10.50% or $2.34287. This was easy to compute as the bond has a duration of 30.0 years and 30.0 * 0.00350 = 10.50%. However, this calculation forgets to include a convexity term. Which is nearest to the additional impact of the convexity term only?
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Question 44 of 100
44. Question
On May 28, 2019, Robin the Portfolio Manager considers the purchase of $100.0 million face amount of the U.S. Treasury 2 3/8s (2.375%) due November 15, 2028, at a cost of $90,250,000. She refers to this as her “bullet” investment. After an analysis of the interest rate environment, she is comfortable with the pricing of the bond at a yield of 3.60% and with its duration of 8.32 years.
However, upon further inspection, Robin considers an alternative to the abovementioned bullet investment in the 10year 2 3/8s. Specifically, the alternative is a “barbell” investment in the shorter maturity 5year 2 1/2s and the longer maturity 30year 4 5/8s. The barbell would be constructed to have the same COST and DURATION as the bullet investment. Which of the following is nearest to the convexity of the alternative barbell portfolio?
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Question 45 of 100
45. Question
Securitization is a trend that is over fifty years old: The Housing and Urban Development Act of 1968 gave birth to Ginnie Mae (https://www.ginniemae.gov/) in an effort to promote homeownership by way of guaranteeing residential mortgagebacked securities (MBS). As GARP explains (see Figure 4.2 of Chapter 4) there have been several milestones along the way. Each of the following statements about securitization is true EXCEPT which is false?
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Question 46 of 100
46. Question
Consider the following series of closing stock prices over the ten most recent trading day (this is similar to Hull’s Table 10.3)[1] along with daily log returns, squared returns and summary statistics:
Although the actual average historical return is nonzero (i.e., 0.001511), for purposes of estimating volatility we will assume that the expected daily mean return is zero. For the purpose of scaling the daily volatility to annual volatility, we will further assume i.i.d. returns and 250 trading days per year. Which is nearest to the simple (i.e., historical unweighted), unbiased per annum volatility estimate?
[1] John C. Hull, Options, Futures, and Other Derivatives, 10th Edition (New York: Pearson Prentice Hall, 2017)
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Question 47 of 100
47. Question
A very risky twoyear bond with a face value of $100.00 pays a semiannual coupon of 18.0% and has a yield (yield to maturity) of 15.0% with continuous compounding. Its price is therefore $104.032 as shown below. Please note that we could infer the price by translating the continuous rate into its semiannual equivalent which is given by 2*[exp(0.150/2)1] = 15.577% and then using the calculator: N = 4, I/Y = 15.577/2 = 7.7885%, PMT = 9, FV = 100 and CPT PV –> $104.032. The final column displays the weight of each cash flow’s present value as a proportion of the bond’s price.
Which is nearest to the bond’s duration (please note that because the yield is continuously compounded, this is the special case where Macaulay duration is equal to modified duration, so we don’t really need to specify which!)?
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Question 48 of 100
48. Question
A speculative (aka, junk) bond has 15.0 years to maturity and pays a semiannual 6 1/8 coupon; i.e., its coupon rate is 6.125% payable semiannually. Its yield is 11.00%. If we assume a reasonable shock value (i.e., less than 100 basis points), which of the following is nearest to the bond’s effective convexity?
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Question 49 of 100
49. Question
In regard to limits policies, GARP explains that “optimal risk governance requires the ability to link risk appetite and limits to specific business practices. Accordingly, appropriate limits need to be developed for each business as well as for the specific risks associated with the business (as well as for the entire portfolio of the enterprise).” Most institutions set two types of limits, tier 1 (one) and tier 2 (two) limits. About these limits, which of the following is TRUE?
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Question 50 of 100
50. Question
For the purpose of updating volatility for an asset return series, your colleague Anita is trying to choose between an EWMA and a GARCH(1,1) volatility model. Among the following reasons, which is the BEST reason to prefer the EWMA over the GARCH(1,1) model?
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Question 51 of 100
51. Question
Consider the following steeply upwardsloping spot rate (aka, zero rate) curve where the per annum zero rates are given with continuous compounding (CC):
Which of the following is nearest to the implied sixmonth forward rate beginning in 1.5 years, F(1.5, 2.0), but where the sixmonth forward rate is expressed per annum with semiannual compounding?
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Question 52 of 100
52. Question
Consider a 9year bond with a semiannual 10.0% coupon that has a current price of $119.780 and a yield of 7.000%. If the yield drops to 6.850%, the bond’s price increases to $120.900. If this is the case, then which of the following is nearest to the bond’s dollar value of ’01 (DV01)?
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Question 53 of 100
53. Question
GARP explains that “risk management must be implemented across the entire enterprise under a set of unified policies and methodologies. (This is called enterprise risk management …). The infrastructure of risk management, which includes both physical resources and clearly defined operational processes, must be up to the task of an enterprisewide scope.”[1] However, it is a difficult and daunting task to evaluate the fitness of a firm or bank’s risk management system. Among the following features, indicators, or characteristics, which is MOST LIKELY to signify that the firm is serious about its risk management process?
[1] 2020 FRM Part I: Foundations of Risk Management, 10th Edition. Pearson Learning Solutions, 10/2019.
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Question 54 of 100
54. Question
Let f(x) represent a probability function (which is called a probability mass function, p.m.f., for discrete random variables and a probability density function, p.d.f., for continuous variables) and let F(x) represent the corresponding cumulative distribution function (CDF); in the case of the continuous variable, F(X) is the integral (aka, antiderivative) of the pdf. Each of the following is true about these probability functions EXCEPT which is false?
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Question 55 of 100
55. Question
Richard plans to invest $10,000.00 today in a zerocoupon bond with a promised return of 7.0% per annum. This return is possible because he will not be repaid until the bond matures in ten (10) years. He calculates the future principal repayment, but his calculation assumes the rate is an equivalent annual interest rate; aka, effective annual rate. His advisor informs him that the actual rate is 7.0% per annum with monthly compounding. Compared to his original future value, how many dollars greater is Richard’s revised future principal repayment?
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Question 56 of 100
56. Question
Assume that the following upwardsloping zero rate (aka, spot rate) curve prevails:
Tuckman introduces the concept of a coupon effect in Chapter 3. Each of the following statements relates to this coupon effect and is necessarily true EXCEPT which statement is false?
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Question 57 of 100
57. Question
To hedge risk, the firm’s toolbox includes derivatives such as swaps, futures, forwards, and options. About the use of derivatives to hedge, each of the following is true EXCEPT which is inaccurate?
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Question 58 of 100
58. Question
The following joint probability matrix captures the relationship between Inflation (which can be either Down, Steady or Up) and the Market (which can be either Bear, Rangebound, or Bull):
About this joint probability matrix, each of the following statements is correct EXCEPT which is false?
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Question 59 of 100
59. Question
Viaflex Airlines expects to purchase 2.0 million gallons of jet fuel in two months and decides to use heating oil futures for hedging (each heating oil contract traded by the CME Group is on 42,000 gallons of heating oil). Their corporate treasury department decides to base the hedge on the last 15 months of price changes. The standard deviation of the change, ΔS, in jet fuel prices per gallon was $0.0210 and the standard deviation of the change, ΔF, in the futures price for the contract on heating oil was $0.0280. As this will be a crosshedge, the correlation between the price changes is 0.880. Below are displayed the price changes and the resulting OLS regression line; for example, the coefficient of determination equals 0.7747 which is the square of the correlation coefficient.
Please note that although heating oil futures contracts will be used for this crosshedge, Viaflex will NOT be “tailing the hedge;” i.e., the hedge will be based on the intended quantity of gallons purchased. Which of the following is nearest to the optimal number of contracts that should be used to hedge?
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Question 60 of 100
60. Question
Exactly one year ago, Sally purchased a $100.00 face value bond that pays a semiannual coupon with a coupon rate of 9.0% per annum. When she purchased the bond, it had a maturity of 10.0 years and its yield to maturity (YTM; aka, yield) was 6.00%. If the bond’s price today happens to be unchanged from one year ago (when she purchased the bond), which of the following is nearest to the bond’s yield (yield to maturity) today?
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Question 61 of 100
61. Question
One of the risk management building blocks is the need to balance risk and reward. Specifically, GARP says, “Economic capital provides the firm with a conceptually satisfying way to balance risk and reward. For each activity, firms can compare the revenue and profit they are making from an activity to the amount of economic capital required to support that activity.” Each of the following statements is true about RAROC EXCEPT which is inaccurate?
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Question 62 of 100
62. Question
The following probability matrix contains the joint probabilities for random variables X = {2, 7, or 12} and Y = {1, 3, or 5}:
We are informed that (X) and (Y) are independent. What is the expected value of the product of X and Y, E(X*Y)?
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Question 63 of 100
63. Question
It is currently March and a company plans to purchase copper in December. The spot price of copper is $2.80 in March while the December futures contract price is $2.90; i.e., the forward curve is “in contango” with a $0.10 basis. A company employs a long hedge on the assumption that the futures price will converge to the spot price in December, when the contract matures. The company’s future “net cost” will include the cost to purchase copper at the future prevailing spot price plus (or minus) the gain (or loss) on the futures position. The company anticipates the spot/futures price will be $3.00 in December. The company goes long four contracts, each for 25,000 pounds of copper.[1]
Under these assumptions, each of the following statements is true EXCEPT which is false?
[1] http://www.cmegroup.com/trading/metals/base/copper_contract_specifications.html
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Question 64 of 100
64. Question
As a market maker, Toughgreen Financial has written (aka, taken a short position in) a single contract for 100 call options on a nondividendpaying stock whose volatility is 36.0% per annum when the riskless rate is 3.0%. Their strike price is $100.00 but the options are underwater because the current stock price is $90.00. The option term is six months. At the current stock price, each option has a value of $5.88 and each option’s percentage delta, Δ = +0.410. From Toughgreen’s perspective, if the stock price increases by +$3.00 to $93.00, which is nearest to the impact on the position’s value?
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Question 65 of 100
65. Question
According to GARP, one of the building blocks in risk management is a proper understanding of the difference between expected loss, unexpected loss, and extreme risk; aka, tail risk. In regard to this building block, which of the following statements is TRUE?
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Question 66 of 100
66. Question
Peter is analyzing a granular portfolio that consists of 300 independent and identically distributed (i.i.d.) obligors where each obligor has a default probability of 5.0%. The default pattern of this portfolio is characterized by a binomial distribution. Because he does not have time to compute the binomial, he will use a normal deviate of 2.33 to approximate a 99.0% value at risk (VaR) that employs µ + σ*2.33 to estimate the worst expected number of defaults with 99.0% confidence. This approximation is justified under one rule of thumb that requires n*(1p) > 10 and n*p >10, which is barely true in this case, as 300*5% = 15.0. Which of the following is Peter’s estimate of 99.0% VaR (please note this is technically an absolute VaR as we including the mean, we are not looking for an unexpected loss)?
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Question 67 of 100
67. Question
Which statement is TRUE about the shape of the commodities forward curve?
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Question 68 of 100
68. Question
Sally owns a nondividendpaying stock that is currently trading at $60.00. As a hedge, she buys an outofthemoney threemonth European put option on the stock with a fixed strike price of $57.00, which is a 5.0% discount to the current stock price. The stock’s volatility is 36.0% per annum. The riskfree rate is 4.0%. According to the BlackScholesMerton model, what is the value of the put? (here is a Z lookup table snippet that you can use http://www.bionicturtle.com/images/2018/forum/082718t48151zlookup.jpg).
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Question 69 of 100
69. Question
Galaxy Financial is a large bank whose risk department developed the following risk typology after surveying key stakeholders within the bank:
Which of the following is most likely TRUE about their typology?
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Question 70 of 100
70. Question
Sally the Risk Analyst conducted a backtest of her firm’s 99.0% confident value at risk (VaR) model. Her sample window included 120 trading days. In regard to her VaR backtest over 120 days, each of the following statements is true EXCEPT which is false?
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Question 71 of 100
71. Question
The table below itemizes an investor’s long position gold futures contracts. On the first day, the investor buys ten (10) contracts when the futures price is $1,200.00. Because the initial margin is $6,000 per contact, the investor must deposit a total of $60,000 in the margin account. The maintenance margin is $4,000 per contract. Over the subsequent eight days, the futures price fluctuates as shown.
Which of the following statements about this scenario is TRUE?
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Question 72 of 100
72. Question
A credit portfolio contains five identical bonds. Each bond has a face value of $1,000 and default probability of 80 basis points (0.80%). The bonds are completely independent: their pairwise default correlations are zero. If any bond defaults, we will assume it has a 50.0% recovery rate. With respect to any of the individual bonds, consider the following definitions:
 The worst expected loss with 99.0% confidence is zero, because the default probability is less than the 1.0% significance level. In this way, the relative VaR is zero.
 The unexpected loss is given by (loss quantile) – EL; in this case, 0 – (0.0080 * $1,000 * 0.50) = $4.00. In this way, the 99.0% credit value at risk (CVaR) is $4.00.
The estimation of the portfolio CVaR illustrates VaR’s lack of subadditivity. Which of the following is nearest to the portfolio’s 99.0% CVaR?
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Question 73 of 100
73. Question
In a singlefactor economy, each of the following portfolios (A, B, and C) is welldiversified:
You discover there is NOT an arbitrage strategy among these three portfolios. In this case, what should be the expected return of Portfolio (C)?
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Question 74 of 100
74. Question
Your firm employs a 95.0% value at risk (VaR) model and monitors its performance by comparing the actual daily profit and loss (P&L) to the VaR level. If the actual loss exceeds the VaR, this is called an “exception.” There is an unconditional (aka, prior) 80.0% probability that your firm’s VaR model is good; in this case of an accurate model, an exception will occur with 5.0% (conditional) probability. However, if the VaR model is bad (inaccurate), then the conditional probability of an exception is 10.0%. These assumptions are illustrated below.
Exceptions occur independently (i.i.d.). If we observe two (2) exceptions in a row, what is the posterior probability that the model is actually bad (bonus: what is the probability of observing an exception tomorrow)?
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Question 75 of 100
75. Question
The spot price of commodity, S(0), is currently $30.00. For a futures contract on the same commodity, the theoretical futures price assumes the cost of carry (COC) model where this commodity has no storage, income or convenience such that theoretically F(0) = S(0)*exp(r*T) under continuous compounding, or under an assumption of annual compound frequency, F(0)=S(0)*(1+r)^T. The riskfree rate, r, is 1.0% with continuous compounding. If the observed sixmonth forward price on the commodity, F(0, 0.5), is $30.40 then which of the following is the correct arbitrage trade (i.e., trade that exploits the arbitrage opportunity)?
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Question 76 of 100
76. Question
In the wake of the global financial crisis (GFC), stress testing has received prominent media attention. Siddique and Hasan explain that “stress testing has many approaches. For example, at many institutions, finance and treasury have had ownership of the budgeting process. Hence, centralized stress testing could be housed in such a central function. Other institutions have taken a more decentralized approach, wherein the central function has only acted as an aggregator. Effective stress testing does not need a given organisational form or approach. However, a given organisational form will require certain aspects to ensure effectiveness. For example, in a decentralized approach towards stress testing, consistency across the organisation becomes important, and the institution will need to find ways of ensuring that consistency.”[1]
Each of the following statements is true about stress testing EXCEPT which is false?
[1] Siddique and Hasan, Stress Testing: Approaches, Methods, and Applications (London: Risk Books, 2013)
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Question 77 of 100
77. Question
Suppose that there are two independent economic factors, F1 and F2 . The riskfree rate is 1.0%, and all stocks have independent firmspecific components with a standard deviation of 25%. The following are welldiversified portfolios; e.g., Portfolio (A) has a beta sensitivity to factor the first factor, β(F1), of 1.20 and an expected return of 13.0%:
Which is the correct returnbeta relationship in this economy?
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Question 78 of 100
78. Question
Henry’s firm is contemplating a switch from spreadsheets to data analytics software primarily because his firm’s risk managers believe that the spreadsheets are responsible for too many errors. Certain members of the finance staff function, however, disagree; the hypothesis of these “Excel sympathizers” is that the firm’s current spreadsheets contain no more than one bug per sheet. To test their hypothesis, a sample of 36 sheets is carefully analyzed. The sample mean is 1.50 bugs per sheet with a (sample) standard deviation of 0.90. If the desired confidence level is 95.0%, should Henry reject the null hypothesis that the true error rate is not greater than 1.0 bug per sheet?
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Question 79 of 100
79. Question
A fund of funds divides its money equally between four hedge funds who earn –3.0%, +1.0%, +11.0%, and +21.0% before fees in a particular year. The fund of funds charges “1% plus 10%” and the hedge funds charge “1% plus 20%” (due to competitive pressures this is reduced from “2% plus 20%”). The hedge funds’ incentive fees are calculated on the return after management fees. The fund of funds incentive fee is calculated on the net (after management and incentive fees) average return of the hedge funds in which it invests and after its own management fee has been subtracted. Which is nearest to the return to investors in the fund of funds? (note this is a variation on Hull’s EOC Question 4.17)[1]
[1] John C. Hull, Risk Management and Financial Institutions, 5th ed (Hoboken, New Jersey: John Wiley & Sons, 2018)
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Question 80 of 100
80. Question
The daily standard deviation of a risky asset is 1.40%. If daily returns are independent, then of course we can use the square root rule (SRR) to scale into a twoday volatility given by 1.40%*SQRT(2) = 1.980%. However, if the lag1 autocorrelation of returns is significantly positive at 0.60, then which is NEAREST to the corresponding scaled twoday volatility?
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Question 81 of 100
81. Question
Assume the riskfree rate is 3.0% while the market portfolio has a return of 13.0% (i.e., excess return is 10.0%) with volatility of 15.0%. Further, the following four portfolios are observed:
 Portfolio (A) has an expected return of 11.0% with volatility of 8.0%
 Portfolio (B) has an expected return of 7.0% with volatility of 20.0% and its correlation to the market is 0.30
 Portfolio (C) has a beta with respect to the market β(C, M) = 1.50 and its realized return of +20.0% implies an alpha of +2.0%
 Portfolio (D) has a beta with respect to the market β(C, M) = 0.40 and its realized return of +9.0% implies an alpha of +2.0%
Under the conditions of modern portfolio theory (MPT; meanvariance framework) and the capital asset pricing model (CAPM), each of the above portfolios is valid and plausible EXCEPT which is not possible?
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Question 82 of 100
82. Question
A discrete random variable can assume a value of {1, 2, 3, 4 or 5} with the following probabilities, where the sum of f(x)*X and f(x)*X^2 is also shown:
If Y = 3*X + 5, then what is the variance of Y, σ^2(Y)?
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Question 83 of 100
83. Question
Suppose it is April 20, 2018 and we want to infer the quoted price of a government bond that accrues interest on an actual/actual basis. The bond under consideration is a 12.0% semiannual coupon bond that matures on July 10th, 2025. The bond has a semiannual yield of 8.0%; i.e., 8.0% per annum with semiannual compounding. Because coupons are paid semiannually on government bonds (and the final coupon is at maturity), the most recent coupon date is January 10, 2018, and the next coupon date is July 10, 2018. The (actual) number of days between January 10, 2018, and April 20, 2018, is 100; and the (actual) number of days between January 10, 2018, and July 10, 2018, is 181. What is nearest to the bond’s quoted price?
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Question 84 of 100
84. Question
A fund manager’s $1.0 million bond portfolio contains the following two long bond positions:
 50% invested in a zerocoupon bond with 5.0 years to maturity, plus
 50% invested in a zerocoupon bond with 8.0 years to maturity
For these risky bonds, the yield curve is flat at 8.0% per annum with annual compounding. However, with respect to yield changes at their respective maturities, the correlation between these two bonds is imperfectly at ρ = 0.70. The monthly yield volatility is 100 basis points; i.e., the annual basispoint volatility is 1.0% * sqrt(12) = 3.46%. Yield changes are assumed to be normally distributed. Which of the following is nearest to the bond portfolio’s 99.0% onemonth value at risk (relative VaR: worst expected loss relative to expected future value)?
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Question 85 of 100
85. Question
A portfolio with a volatility of 30.0% has a Treynor measure of 0.080. The portfolio has a correlation of 0.50 with the market index which itself has a volatility of 20.0%. What is the portfolio’s Sharpe measure?
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Question 86 of 100
86. 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 87 of 100
87. Question
Suppose the following assumptions for a certain defined benefit pension plan:
 Employees work for 35.0 years earning wages that increase with inflation.
 They retire with a pension equal to 70.0% of their final salary.
 This pension also increases with inflation. The pension is received for 18.0 years.
 The pension fund’s income is invested in bonds that earn the inflation rate.
Which of the following is nearest to an estimate of the percentage of an employee’s salary that must be contributed to the pension plan if it is to remain solvent? Hint: Do all calculations in real rather than nominal dollars. (Please note this is based on Hull’s EOC Question 3.15)[1]
[1] John C. Hull, Risk Management and Financial Institutions, 5th edition (Hoboken, New Jersey: John Wiley & Sons, 2018)
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Question 88 of 100
88. Question
Consider a sixmonth atthemoney (ATM) European call option on a nondividendpaying stock with a current price of $80.00. Peter the Risk Analyst has employed a twostep (i.e., three months per step) binomial model to price the option, as displayed below:
Peter’s model matches the up and down movements to his estimate of the stock’s prospective volatility, which he assumes is 34.0% per annum. The riskfree rate is 4.0%. Which of the following is nearest to the riskneutral probability of the stock price going up in a single step?
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Question 89 of 100
89. Question
About risk reporting practices, the Committee says “[51.] Accurate, complete and timely data is a foundation for effective risk management. However, data alone does not guarantee that the board and senior management will receive appropriate information to make effective decisions about risk. To manage risk effectively, the right information needs to be presented to the right people at the right time. Risk reports based on risk data should be accurate, clear and complete. They should contain the correct content and be presented to the appropriate decisionmakers in a time that allows for an appropriate response. To effectively achieve their objectives, risk reports should comply with the following principles. Compliance with these principles should not be at the expense of each other …”[1]
Each of the following is a risk reporting principle EXCEPT which is not a risk reporting principle?
[1] “Principles for Effective Data Aggregation and Risk Reporting,” (Basel Committee on Banking Supervision Publication, January 2013)
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Question 90 of 100
90. Question
Peter used a simple Monte Carlo simulation to estimate the price of an Asian option. In his first step, he specified a geometric Brownian motion (GBM) which is the same process used in the BlackScholesMerton model. His boss Sally observes, “This is nice work Peter, but the drawback to this approach is that you’ve assumed underlying returns are normally distributed. Yet we know that returns are fattailed in practice.” How can Peter overcome this objection and include a fattailed assumption in his model?
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Question 91 of 100
91. Question
Regulators estimate that Deposits and Loans Corporation (DLC) will report a profit that is normally distributed with a mean of $1.30 million and a standard deviation of $3.0 million. Below is displayed the summary Balance Sheet for DLC:
How much equity capital IN ADDITION to DLC’s current equity position should regulators require for there to be a 99.9% chance of the capital not being wiped out by losses? (this is a variation on Hull’s EOC Question 2.15)[1]
[1] John C. Hull, Risk Management and Financial Institutions, 5th edition (Hoboken, New Jersey: John Wiley & Sons, 2018)
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Question 92 of 100
92. Question
After Barbara wrote (i.e., sold) 100 put option contracts, the trade’s position delta was +7,200. The put options were inthemoney as the stock price was $70.00 while the options’ strike price was $100.00. Each contract was for 100 put options. The percentage gamma of each put option was +0.0120. If the stock price subsequently, immediately decreased by $10.00 to $60.00, which is nearest to an estimate of the trade’s new position delta?
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Question 93 of 100
93. Question
The riskfree rate is 3.0% and the market portfolio’s expected return is 10.0% (put another way, the market’s excess expected return is 7.0%). Consider two portfolios:
 Portfolio A has a high volatility, σ(A) = 50.0% per annum, but its correlation to the market portfolio is only, ρ(A, M) = 0.30
 Portfolio B has a moderate volatility, σ(B) = 30.0% per annum, and its correlation to the market portfolio is, ρ(B, M) = 0.70
If both portfolios lie on the security market line (SML), and if Portfolio A has an expected return, ER(A) = 7.20%, then what is the expected return of Portfolio B?
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Question 94 of 100
94. Question
Paul is a researcher who is using Monte Carlo simulation in order to determine what effect heteroscedasticity has upon the size and power of a test for autocorrelation. If the variance of the estimate, var(x), of his quantity of interest is 36.0 and he requires a standard error of the estimate, S(x), to be no greater than 0.10, how many replications does his simulation require?
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Question 95 of 100
95. Question
Below are a summary balance sheet and income statement for Deposits and Loans Corporation (DLC):
Each of the following statements is true EXCEPT which is false?
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Question 96 of 100
96. Question
Trader Joe (who is unrelated to the awesome grocery store!) takes a long position in 100 outofthemoney (OTM) put option contracts when the nondividendpaying stock price is $88.00 and its volatility is 28.0%; each contract is for 100 options. The strike price is $80.00, and the option term is six months. The riskfree rate is 5.0%. The value of each option is $4.38, and the position’s value is $43,800.00. With respect to these puts, the immediate percentage delta, Δ = 0.2550 and gamma, Γ = 0.0130. If the stock price jumps by +$7.00 to $95.00, which is nearest to the position’s value as approximated by delta and gamma; i.e., without a full repricing of the position?
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Question 97 of 100
97. Question
Which of the following is TRUE about the bank’s audit function?
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Question 98 of 100
98. Question
Consider the following discrete probability distribution of asset returns:
As shown, this asset’s expected return is +2.55%. Which is nearest to this variable’s skew; aka, standardized third central moment?
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Question 99 of 100
99. Question
Below is an extract from a mortality table (ages 30 to 34 for males and females):
Suppose a woman aged 30 years old buys a $1.0 million whole life insurance policy and she pays an annual premium of $6,000. What is approximately the surplus premium in the first year of the policy?
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Question 100 of 100
100. Question
Analyst Patricia is analyzing the following four bonds:
 Bond A is a $100.00 face value bond with 7.0 years to maturity that pays a monthly coupon at a rate of 6.0% per annum and offers a yield of 5.0% per annum (with monthly compound frequency)
 Bond B is a $100.00 face value bond with 10.0 years to maturity that pays a semiannual coupon at a rate of 4.0% per annum and offers a yield of 5.0% per annum (with semiannual compound frequency)
 Bond C is a $100.00 face value bond with 10.0 years to maturity that pays an annual coupon at a rate of 7.0% per annum and offers a yield of 6.0% per annum (with annual compound frequency)
 Bond D is a $1,000.00 face value zerocoupon bond with 30.0 years to maturity that offers a yield (aka, yield to maturity) of 8.0% per annum with semiannual compound frequency
In terms of their current theoretical prices, which bonds are, respectively, the cheapest and most expensive (among the four)?
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