Part 1 Full Length Interactive Mock Exam 1

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?

a) Bankers Trust (BT) proposed an overly complex swap to their clients (P&G and Gibson Greetings) but the swaps experienced colossal losses; the clients sued BT, who never recovered from the ensuing reputational damage
b) Orange County's treasurer (Robert Citron) borrowed through the repo market to purchase inverse floating-rate notes–positions that Citron later said he did not understand–but the combination of excessive leverage and embedded interest-rate risk generated losses that ultimately forced Orange County to file for bankruptcy
c) Sachsen Landesbank set up off-balance-sheet vehicles (guaranteed by Sachsen) that held highly-rated U.S. mortgage-backed securities; the operation was highly profitable, but the 2007-08 subprime crisis wiped out Sachsen's capital
d) If the purpose of the position is designated as hedging (rather than speculation) and if the hedge consists only of some combination(s) of forwards, swaps and/or options–which are the primary building blocks–then the firm can avoid problems suffered by the financial engineering case studies because the firm avoids undue sophistication

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)?

a) The mixture (V) has a greater probability of a negative outcome; i.e., Pr(V<0) > Pr(W<0)
b) The convolution (W) has a greater probability of a negative outcome; i.e., Pr(W<0) > Pr(V<0)
c) They have the same probability of realizing a negative outcome; i.e., Pr(W<0) = Pr(V<0)
d) It cannot be answered because it depends on correlation in the case of (W)

Question 3 of 100

3. Question

Consider a one-year 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 risk-free 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 Black-Scholes-Merton called the Margrabe variation.

Using the Margrabe under these assumptions, the price of this BTC-for-ETH exchange option is $723.11. Further, each of the following statements, ceteris paribus, is true EXCEPT which is false?

a) A higher riskfree rate has no impact on this exchange option's value
b) A higher correlation ρ(BTC, ETH) implies a lower exchange option value
c) An increase in Ethereum's (ETH) spot price will increase the exchange option's value
d) An increase in the Bitcoin (BTC) spot price implies an increase in the exchange option's value

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)?

a) $434,000 and $568,000
b) $651,000 and $852,00
c) $3.6 and $4.7 million
d) $5.9 and $7.7 million

Question 5 of 100

5. Question

According to GARP, each of the following was a causal factor in the 2007-2009 global financial crisis (GFC) EXCEPT which is not a causal factor?

a) Low interest rates
b) The originate-to-distribute (OTD) business model and securitization, especially CDOs
c) An unexpected spike in prepayments due to an acceleration in repeat refinancing
d) Dubious lending practices and risky mortgage loan products (e.g., NINJA) and loan features (e.g., teaser rates)

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*(1-p) = 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)?

a) 2.2750%
b) 8.3500%
c) 11.090%
d) 14.6667%

Question 7 of 100

7. Question

The risk-free rate is 3.0% and the stock price of Discovery Communications (ticker: DISCK) is $20.00. Peter purchases a straddle with six-month European at-the-money 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)?

a) DISCK must move up by at least $2.05
b) DISCK must move down by at least $1.67
c) DISCK must move up or down by at least $3.80
d) DISCK must move up or down by at least $5.75

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)?

a) $2.250 million
b) $3.360 million
c) $5.490 million
d) $7.810 million

Question 9 of 100

9. Question

Which of the following is TRUE about the SWIFT (Society for Worldwide Interbank Financial Telecommunication) case study?

a) The 2015-16 cyber-attack (aka, hack) demonstrated that the SWIFT network was unreliable, and it was subsequently phased out
b) The 2015-16 cyber-attack (aka, hack) successfully exploited vulnerabilities to achieve the theft of about USD 81.0 million
c) The 2015-16 cyber-attack (aka, hack) was an unsuccessful attempt to steal money, and it demonstrated the SWIFT network is essentially impervious to attacks
d) The 2015-16 cyber-attack (aka, hack) was a fictitious news account but the negative press nonetheless shook confidence sufficiently in the network that transactions ground to a halt for several weeks

Question 10 of 100

10. Question

A credit portfolio contains some number of independent credit-sensitive 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)?

a) Less than 0.01%
b) 10.0%
c) 20.0%
d) 33.3%

Question 11 of 100

11. Question

Consider a European call option on a non-dividend-paying 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?

a) Double the riskfree rate (from 3.0%) to 6.0%
b) Increase the stock price by $5.00 (from $100.00) to $105.00
c) Increase volatility by 10.0% (from 20.0%) to 30.0%
d) Double the time to expiration (from six months) to T = 1.0 year

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?

a) Expected losses (EL) can be viewed as payments to an insurance pool, does not itself constitute risk, and is reimbursed through adequate loan pricing
b) Unexpected losses (UL) is the standard deviation of credit losses around the expected loss average
c) Unexpected loss contribution (ULC) is the first partial derivative of the portfolio's unexpected loss (portfolio UL) with respect to the position's weight, w(i)
d) Economic capital (EC) for credit risk is the difference between the expected outcome and the unexpected, negative outcome at a certain confidence level

Question 13 of 100

13. Question

Barbara is a certified FRM who previously generated income statement and profit projections over a five-year 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?

a) She can comply by simply selecting the most probable future outcome; the Code has generally nothing to say about this technical task
b) She can comply but she should qualify her findings to avoid overstating the accuracy of her projections; for example, she can plot a future distribution
c) She should work hard to generate the most precise estimate possible; for example, "sales will go down by 10.85%" is more useful than "sales will go down by 10%"
d) She should avoid the temptation to offer any revised future estimates in the face of several "unknown unknowns" because some future values cannot be estimated with sufficient accuracy

Question 14 of 100

14. Question

Consider the probability mass function (pmf) below. For example, Pr(X = -1.0) = 20.0%.

Random Variables

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?

a) Zero
b) 2.50
c) 3.60
d) 4.40

Question 15 of 100

15. Question

A stock with a volatility of 31.0% is currently trading at $47.00 while the risk-free 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?

a) Stock to stay inside the interval {$35.00 to $55.00}; i.e., both above $35.00 and below $55.00
b) Stock to stay inside the interval {$37.00 to $57.00}; i.e., both above $37.00 and below $57.00
c) Stock to fall outside the interval {$35.00 to $55.00}; i.e., either below $35.00 or above $55.00
d) Stock to fall outside the interval {$40.00 to $54.00}; i.e., either below $40.00 or above $54.00

Question 16 of 100

16. Question

Consider the following one-year migration (aka, transition) matrix:

ratings

When is the soonest that an obligation rated AAA (the highest rating) can default?

a) During the first year (i.e., by the end of the first year) with a margin probability of 2.0%
b) During the second year (i.e., between the end of the first and second year) with a joint probability of 0.1879% (or 0.001879 or 1.879e-3)
c) During the third year (i.e., between the end of the second and third year) with an unconditional probability of 0.00540% (or 0.0000540 or 5.40e-5)
d) During the fourth year (i.e., between the end of the third and fourth year) with a conditional probability of 2.00%

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?

a) S&Ls engaged in a practice called "riding the yield curve" but this was one of the central bank's monetary policy tools and was not meant to be performed by private banks
b) The Fed's restrictive monetary policy led to a dramatic increase in short-term interest rates which wiped out bank's interest rate spread due to their asset-liability mismatch
c) The Fed's expansionary monetary policy led to a dramatic decrease in short-term interest rates which wiped out bank's interest rate spread due to their asset-liability mismatch
d) New regulations introduced in the early 1980s hindered the ability of the savings and loan (S&L) industry to lend and/offer new loan products that could help it grow out of its problems

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?

a) 6.67
b) 8.00
c) 8.25
d) 9.33

Question 19 of 100

19. Question

Suppose that the 6-month, 12-month, 18-month, and 24-month overnight indexed swap (OIS) zero rates with continuous compounding are 2.00%, 2.40%, 3.00%, and 3.60%, respectively. Suppose further that the six-month 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).

swap rate

Finally and importantly, assume the two-year 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 risk-free rate for discounting purposes.

Which is nearest to an estimate for the forward LIBOR rate for the 18- to 24-month period, F(1.5, 2.0)?

a) 3.880%
b) 4.503%
c) 5.747%
d) 6.950%

Question 20 of 100

20. Question

In regard to through-the-cycle (TTC) versus at-the-point (aka, point in time, PIT) approaches to credit ratings, each of the following statements is true EXCEPT which is false?

a) Agency (i.e., external) credit ratings tend to be through-the-cycle (TTC)
b) Through-the-cycle (TTC) is conditional, while at-the-point (PIT) is unconditional
c) Credit spreads are at-the-point (PIT) and PIT measures incorporate more information
d) During crisis periods, PIT approaches imply higher expected and unexpected loss (EL & UL) such that PIT tends to be pro-cyclical

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 double-digit 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 price-conscious (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 buy-and-hold investor who purchased high-conviction 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?

a) A = Home bias, B = Mental accounting, C = Ostrich effect, D = Herding, E = Groupthink, F = Framing
b) A = Loss aversion, B = Framing, C = Ostrich effect, D = Mental accounting, E = Anchoring, F = Feedback effects
c) A = Groupthink, B = Herding, C = Home bias, D = Framing, E = Loss aversion, F = Ostrich effect
d) A = Mental accounting, B = Home bias, C = Loss aversion, D = Groupthink, E = Feedback effects, F = Herding

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%.

probability

Which of the following is TRUE about, respectively, the unconditional and conditional relationship between events A and B?

a) A and B are unconditionally dependent but conditionally (on event C) independent
b) A and B are unconditionally dependent and also conditionally (on event C) dependent
c) A and B are unconditionally independent but conditionally (on event C) dependent
d) A and B are unconditionally independent and also conditionally (on event C) independent

Question 23 of 100

23. Question

Below are given three-month 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 then-prevailing three-month LIBOR.

Eurodollar futures contract

Which is nearest to the implied 393-day zero rate expressed per annum with continuous compounding?

a) 3.601%
b) 4.380%
c) 5.538%
d) 6.026%

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 highest-rated 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?

a) A-1 or P-1
b) AA or Aa
c) B or B
d) BBB or Baa

Question 25 of 100

25. Question

GARP explains that “perhaps the biggest argument for ERM is that an enterprise-level 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?

a) Identify hidden and/or dangerous concentrations including (for example) geographical, industry, product, or among suppliers
b) Vertical vision recognizes potential threats to the whole enterprise ideally in their early stages to reduce the leverage effect of time
c) Portfolio thinking permits the business units to specify a more accurate distribution that incorporates the allocation of corporate overhead
d) Thinking beyond silos acknowledges diversification among risk types and better understanding of how interactions might worsen enterprise threats

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 “bot-views.” It uploads the same data file from yesterday to both applications. The first application detects 200 bot-views and the second application detects 300 bot-views. Among these, only 40 bot-views were detected by both applications. All bot-views are equally likely to be located, but clearly both applications only identify a minority of the bot-views (otherwise there would be a much higher number of identified bot-views common to both applications). Further, the identification of a bot-view by one application is independent of its identification by the other application. How many malicious bot-views did the web page experience on this day?

a) 300
b) 460
c) 540
d) 1,500

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.

US Treasury Bond

If the future contract’s settlement price is $99.00, then which bond is the cheapest to deliver (CTD)?

a) Bond #1
b) Bond #2
c) Bond #3
d) Bond #4

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:

sovereign default

Which of the four countries is most likely to default?

a) Country A is the most likely to default because debt above 100% is highly predictive of default and overwhelms the other indicators
b) Country B is the most likely to default because it is the only country with three (out of four) negative indicators
c) Country C is the most likely to default because it has an autocratic government
d) It is unclear: each has two negative (and two positive) indicators; further, quantification of this scorecard is an insufficient predictor

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

a) BCBS 239 offers the advantage of a uniform blueprint for a compliant IT infrastructure
b) Every systematically important financial institution (SIFI) complied with the original timeline
c) Compliance with BCBS 239 is a subjective exercise and the standards for each bank are bespoke
d) While praised for its theory, critics say BCBS 239 forgets to address risk management data and models

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%?

standard deviation

a) About 1.0%
b) About 5.0%
c) About 11.3%
d) About 20.0%

Question 31 of 100

31. Question

The six-month 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)

a) There is no arbitrage because the futures contract is fairly priced
b) Borrow dollars and invest USD for six months at 1.0%; and enter into (long) futures contract to buy pesos
c) Borrow dollars, convert immediately to pesos and invest in MXN for six months at 7.0%; and enter into (short) futures contract to sell pesos
d) Borrow pesos, convert immediately to dollars and invest in USD for six months at 1.0%; and enter into (long) futures contract to buy pesos

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/explore-our-products/international-country-risk-guide/

a) Taiwan is very low risk
b) This score is irrelevant for investment purposes
c) This score can be neither normalized nor standardized
d) This score cannot be used to rank Taiwan against other countries

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?

a) 5.00%
b) 7.50%
c) 10.00%
d) Not enough information

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:

correlation

Which is nearest to the correlation coefficient between portfolio returns, R(i), and the benchmark returns, R(b)?

a) 0.4937
b) 0.5150
c) 0.6237
d) We cannot know without the adjusted R^2

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 six-month (0.5 years) corn forward contract?

a) Zero
b) + 4.08%
c) + 8.33%
d) Not enough information (need risk-free rate and exact spot price)

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 2-year key rate, KR01(2-year) is equal to $0.030 per 100 face amount and has a daily volatility, σ(bps), of 12.0 basis points
The 5-year key rate, KR01(5-year) 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 non-parallel 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)?

a) $159,500
b) $170,100
c) $182,700
d) $219,300

Question 37 of 100

37. Question

During a 36-month period during which the risk-free 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?

a) If the investor is diversified (or the portfolio represents only a fraction of the investor's entire wealth), the Treynor (TPI) is a good measure and Peter's TPI is better than Betty's
b) If the investor is not diversified (or the portfolio represents the investor's entire wealth), the Sharpe (SPI) is a good measure and Betty's SPI is better than Peter's
c) Betty's portfolio already lies on the efficient frontier such that we do not expect her to sustain further improvement in the reward-to-variability ratio
d) If Betty's and Peter's portfolio belong to different peer groups, Jensen's alpha is a good measure for ranking them and Betty's (Jensen's) alpha is better than Peter's

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?

a) 24,700
b) 26,100
c) 27,900
d) 30,500

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 over-valued. 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?

a) $39,500
b) $45,000
c) $47,000
d) $51,500

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 multi-factor 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, on-the-run 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 multi-factor risk metrics: key-rate exposures, partial ’01s, and forward-bucket ’01s. For which of the four objectives is key-rate exposures best suited?

a) I. only
b) III. only
c) I. and IV. only
d) I., II., III. and IV.; i.e., all four

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)?

a) E(R) = 0.040 + 0.511 × σ(P)
b) E(R) = 0.137 + 0.511 × σ(P)
c) E(R) = 0.040 + 0.375 × β(P,M)
d) E(R) = 0.077 + 0.511 × β(P,M)

Question 42 of 100

42. Question

Consider the following quadratic trend model:

Which of the following functions correctly characterizes this trend?

a) Tr = 10 + 0.3*TIME + 0.3*TIME^2
b) Tr = 10 + 30*TIME – 0.3*TIME^2
c) Tr = 10 – 0.4*TIME – 0.4*TIME^2
d) Tr = 10 – 30*TIME + 0.5*TIME^2

Question 43 of 100

43. Question

A 30-year zero-coupon 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 35-basis point increase (“shock up”) in the yield without fully re-pricing 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?

a) To reduce the estimated bond price drop by $0.1230 so that the total estimated drop is only $2.2199
b) To reduce the estimated bond price decrease by $0.2460 so that the total estimated drop is only $2.0969
c) To increase the estimated bond price decrease by $0.1674 so that the total estimated drop is $2.5102
d) To increase the estimated bond price decrease by $0.5690 so that the total estimated drop is $2.9118

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.

barbells and bullets

However, upon further inspection, Robin considers an alternative to the above-mentioned bullet investment in the 10-year 2 3/8s. Specifically, the alternative is a “barbell” investment in the shorter maturity 5-year 2 1/2s and the longer maturity 30-year 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?

a) 50.4 years^2
b) 78.4 years^2
c) 136.7 years^2
d) 305.9 years^2

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 mortgage-backed 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?

a) Securitization offers at least some diversification of credit risk
b) Securitization transfers a substantial amount of risk, including but not limited to credit risk, from the originator's balance sheet to investors
c) The 2007-2009 global financial crisis (GFC) discredited the principles of securitization as evidenced by the subsequent evaporation of asset-backed securities (ABS)
d) Securitization enables originate-to-distribute (OTD) but the 2007-2009 crisis witnessed poor securitization risk management that allowed too much systemic concentration of risk

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:

historical volatility

Although the actual average historical return is non-zero (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)

a) 5.0% per annum
b) 15.0%
c) 25.0%
d) 35.0%

Question 47 of 100

47. Question

A very risky two-year bond with a face value of $100.00 pays a semi-annual 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 semi-annual 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.

duration

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!)?

a) 1.77 years
b) 1.85 years
c) 1.93 years
d) 2.00 years

Question 48 of 100

48. Question

A speculative (aka, junk) bond has 15.0 years to maturity and pays a semi-annual 6 1/8 coupon; i.e., its coupon rate is 6.125% payable semi-annually. 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?

a) 12.4 years^2
b) 98.0 years^2
c) 124.3 years^2
d) Cannot answer because face value is not given

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?

a) Firms should choose and either adopt tier 1 or tier 2 limits but not both simultaneously
b) Tier 1 (tier one) limit exceedances must be cleared or corrected immediately, while tier 2 (tier two) exceedances are less urgent and can be cleared within a few days or a week.
c) Tier 2 (tier two) limits are specific and often include an overall limit by asset class, an overall stress-test limit, and a maximum drawdown limit
d) Tier 1 (tier one) limits are more generalized and relate to areas of business activity as well as aggregated exposures categorized by credit rating, industry, maturity, and region

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?

a) She wants to forecast forward volatility
b) She wants to incorporate the concept of mean reversion into the model
c) She wants the weights assigned to the historical returns to decline exponentially
d) In terms of best fit, her GARCH(1,1) alpha parameter is 0.92 and beta parameter is 0.13

Question 51 of 100

51. Question

Consider the following steeply upward-sloping spot rate (aka, zero rate) curve where the per annum zero rates are given with continuous compounding (CC):

bond pricing

Which of the following is nearest to the implied six-month forward rate beginning in 1.5 years, F(1.5, 2.0), but where the six-month forward rate is expressed per annum with semi-annual compounding?

a) 3.78%
b) 4.80%
c) 5.90%
d) 6.50%

Question 52 of 100

52. Question

Consider a 9-year bond with a semi-annual 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)?

a) -0.0121
b) 0.0121
c) 0.0747
d) 1.1200

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 enterprise-wide 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.

a) The firm's risk manager(s) is a well-compensated member of the executive staff with compelling career opportunities
b) At least one-third of executive compensation plans consist of stock options, or in the case of private firms, phantom stock options
c) The board has quantified the firm's agency costs and can show that agency costs are within a quantifiable confidence interval, or at least below an upper numeric bound
d) The board's audit committee reports to the board's risk management committee and every member of the board is also a member of the board's risk management committee

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, anti-derivative) of the pdf. Each of the following is true about these probability functions EXCEPT which is false?

a) The limits of a cumulative distribution function (CDF) must be zero and one; i.e., F(-∞) = 0 and F(+∞) = 1.0
b) For both discrete and random variables, the cumulative distribution function (CDF) is necessarily an increasing function
c) In the case of a continuous random variable, we cannot talk about the probability of a specific value occurring; e.g., Pr[R = +3.00%] is meaningless
d) Bayes Theorem can only be applied to discrete random variables, such that continuous random variables must be transformed into their discrete equivalents

Question 55 of 100

55. Question

Richard plans to invest $10,000.00 today in a zero-coupon 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?

a) Zero
b) $39.80
c) $215.75
d) $425.10

Question 56 of 100

56. Question

Assume that the following upward-sloping zero rate (aka, spot rate) curve prevails:

coupon effect

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?

a) Given this spot rate curve, the two-year par rate (aka, par yield) must be less than 3.4%
b) Given this spot rate curve, a zero-coupon bond with a two-year maturity must have a yield (yield to maturity) of 3.4%
c) Given this spot rate curve, a coupon-bearing bond with a two-year maturity must have a yield (yield to maturity) that is less than 3.4%
d) Given this spot rate curve, the yields (yields to maturity) of all bonds with two-year maturities must be identical due to the Law of One Price

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?

a) Derivatives represent a decision to transfer (or mitigate) the risk(s) when the firm neither wants to retain nor avoid the risk
b) Because hedging can only mute the volatility of accrual-based earnings, hedging cannot increase (or even alter) the firm's cash flows and therefore cannot influence agency risks
c) A large conglomerate (i.e., a firm with multiple business units operating in different industries/sectors) is more likely to create natural hedges than a small, focused firm
d) Airlines can cross-hedge the cost of jet fuel with futures contracts on (crude or heating) oil, but if the commodity's price drops rapidly, unhedged airlines are likely to outperform their hedged competitors

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, Range-bound, or Bull):

joint probability

About this joint probability matrix, each of the following statements is correct EXCEPT which is false?

a) The unconditional probability of a Bear Market is 19.0%
b) The probability of a Bull Market conditional on Up Inflation is about 58.8%
c) The probability of a Down Inflation conditional on a Bear Market is about 21.4%
d) The joint probability of Up Inflation and Range-bound Market is 8.0%

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 cross-hedge, 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 cross-hedge, 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?

a) 14.0
b) 22.0
c) 31.0
d) 40.0

Question 60 of 100

60. Question

Exactly one year ago, Sally purchased a $100.00 face value bond that pays a semi-annual 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?

a) 5.57%
b) 5.78%
c) 6.00%
d) 6.22%

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?

a) For an activity to increase shareholder value, its RAROC should be higher than the cost of equity capital
b) Four applications of RAROC include business comparison, investment analysis, pricing strategies, and risk management cost/benefit analysis
c) Advantages of RAROC include (i) it has one universal regulatory definition (without credible variants), such that benchmarking against peers is easy; and (ii) it is easy to implement in practice
d) If RAROC's denominator is economic capital, which is typical, then its numerator should be an after-tax risk-adjusted expected return where the risk-adjusted refers to an adjustment for expected losses

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}:

Mean and standard deviation

We are informed that (X) and (Y) are independent. What is the expected value of the product of X and Y, E(X*Y)?

a) 15.0
b) 21.0
c) 30.5
d) 35.0

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

a) If the basis unexpectedly weakens, the company's net cost will be less than $290,000; i.e., the company will be better off than it planned
b) If the basis unexpectedly strengthens, the company's net cost will be more than $290,000; i.e., the company will be worse off than it planned
c) If the basis converges to zero as expected, the company's net cost will be $290,000 regardless of whether the spot price increases or decreases
d) If the forward curve unexpectedly shifts to backwardation (aka, inverted forward curve), the company's net cost will be less than $290,000; i.e., the company will be better off than it planned

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 non-dividend-paying 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?

a) A loss of few dollars less than $8.00; i.e., 100 * [$5.88 * ($3.00/$90.00) * 0.410] minus (-) gamma adjustment
b) A loss of few dollars more than $8.00; i.e., 100 * [$5.88 * ($3.00/$90.00) * 0.410] plus (+) gamma adjustment
c) A loss of few dollars less than $123.00; i.e., 100 * ($3.00 * 0.410) minus (-) gamma adjustment
d) A loss of few dollars more than $123.00; i.e., 100 * ($3.00 * 0.410) plus (+) gamma adjustment

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?

a) Effective risk management should reduce a credit portfolio's expected loss (EL) to approximately zero
b) Expected loss is a product of (i) the probability of the risk event occurring; (ii) the severity of the loss if the risk event occurs, and (iii) the expected recovery rate
c) While expected loss (EL) is a function of default correlation, unexpected loss (UL) is NOT influenced by portfolio granularity
d) Although banks theoretically do not need to set aside provisions when loan products are accurately priced, in realistic practice, banks should provision for expected losses

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*(1-p) > 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)?

a) 13 defaults
b) 18 defaults
c) 21 defaults
d) 24 defaults

Question 67 of 100

67. Question

Which statement is TRUE about the shape of the commodities forward curve?

a) In a normal market (aka, contango), the basis is positive
b) In an inverted market (aka, backwardation) the basis is negative
c) An inverted market (aka, backwardation) might be explained by negative interest rates but does not necessarily imply negative rates
d) In a contango (aka, normal) market with a static forward curve, the price of a futures contract will INCREASE as time to maturity approaches zero

Question 68 of 100

68. Question

Sally owns a non-dividend-paying stock that is currently trading at $60.00. As a hedge, she buys an out-of-the-money three-month 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 Black-Scholes-Merton 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/082718-t4-815-1-zlookup.jpg).

a) $1.55
b) $2.63
c) $3.89
d) $4.40

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:

risk typology

Which of the following is most likely TRUE about their typology?

a) This typology is incorrect because it does not comport with any of the typologies approved by regulators, including Basel
b) If the typology is good then any and all newly identified risks should be slotted into an existing risk type within the typology
c) Although not illustrated directly here, many of the risk types interact with one another so that risk might flow or cascade from one type to another
d) It is incorrect to locate Liquidity risk as a top-level risk (i.e., alongside Credit and Market risk) because it should be a sub-risk to operational risk

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?

a) If she uses the normal distribution to approximate the binomial, then six observed exceptions return a test statistic of about 4.40
b) If she observed zero exceptions, at any realistic confidence level she will not be able to dismiss a 99.0% confident VaR model as bad; i.e., she cannot reject null hypothesis that 99.0% VaR model is good
c) If she observed three exceptions, at any realistic confidence level she will not be able to dismiss a 99.0% confident VaR model as bad; i.e., she cannot reject null hypothesis that 99.0% VaR model is good
d) Because the binomial distribution (implied by the backtest) is non-negative, a one-sided test is appropriate; if she prefers a two-sided test, then she should instead employ the negative binomial distribution

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.

Futures contracts

Which of the following statements about this scenario is TRUE?

a) The investor has excess margin on two of the days
b) The margin calls are triggered only when the investor closes out contracts
c) The simulation is missing margin calls on days one (1), two (2) and five (5)
d) The investor's holding period return is a loss of about 1.67% which is equal to -1,000 ÷ 60,000

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?

a) -$20.00
b) Zero
c) $480.00
d) $4,960.00

Question 73 of 100

73. Question

In a single-factor economy, each of the following portfolios (A, B, and C) is well-diversified:

Fama-French three factor model

You discover there is NOT an arbitrage strategy among these three portfolios. In this case, what should be the expected return of Portfolio (C)?

a) 13.3%
b) 16.3%
c) 18.5%
d) 21.0%

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.

Bayes' Theorem

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)?

a) 20.0%
b) 37.5%
c) 50.0%
d) 80.0%

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 six-month 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)?

a) There is no arbitrage opportunity
b) Cash and carry: Buy the commodity at the current spot price and short the futures contract for a future profit of about $0.250
c) Cash and carry: Buy the commodity at the current spot price and short the futures contract for a future profit of about $1.390
d) Reverse cash and carry: Sell short the commodity at the current spot price and buy the futures contract for a future profit of about $0.140

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)

a) Stress testing is a non-statistical risk measure that may employ scenario analysis as one approach
b) An acceptable proxy for stress testing is to generate value at risk (VaR) with a series of progressively increasing confidence levels; e.g., 99.0%, 99.50%, 99.75%, 99.90%, and 99.99%
c) While backtesting validates model parameter(s) using a large number of actual, historical observations; stress testing on the other hand uses a small number of extreme movements in market variables
d) Unlike value at risk (VaR) which indicates neither the magnitude nor shape of extreme losses beyond the VaR threshold, stress testing DOES attempt to characterize the magnitude/shape of the extreme loss tail

Question 77 of 100

77. Question

Suppose that there are two independent economic factors, F1 and F2 . The risk-free rate is 1.0%, and all stocks have independent firm-specific components with a standard deviation of 25%. The following are well-diversified 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%:

Multifactor Models

Which is the correct return-beta relationship in this economy?

a) E[R(P)] = 1.0% – β(F1)*6.0% – β(F2)*4.0%
b) E[R(P)] = 1.0% – β(F1)*5.0% + β(F2)*2.0%
c) E[R(P)] = 1.0% + β(F1)*9.0% + β(F2)*3.0%
d) E[R(P)] = 1.0% + β(F1)*12.0% + β(F2)*8.0%

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?

a) Yes, because the test statistic of 3.33 is greater than the critical value of 1.690
b) Yes, because the test statistic of 10.0 is greater than the critical value of 2.030
c) No, because the test statistic of 10.0 is less than the critical value of 12.706
d) Because the population distribution and variance are both unknown, we do not have a reliable test statistic for the sample mean

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)

a) 1.40%
b) 3.60%
c) 5.00%
d) 7.50%

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 two-day volatility given by 1.40%*SQRT(2) = 1.980%. However, if the lag-1 autocorrelation of returns is significantly positive at 0.60, then which is NEAREST to the corresponding scaled two-day volatility?

a) 1.64%
b) 1.98%
c) 2.33%
d) 2.50%

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; mean-variance framework) and the capital asset pricing model (CAPM), each of the above portfolios is valid and plausible EXCEPT which is not possible?

a) Portfolio A
b) Portfolio B
c) Portfolio C
d) Portfolio D

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:

Covariance and correlation

If Y = 3*X + 5, then what is the variance of Y, σ^2(Y)?

a) 1.29
b) 5.51
c) 11.61
d) 16.61

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% semi-annual coupon bond that matures on July 10th, 2025. The bond has a semi-annual yield of 8.0%; i.e., 8.0% per annum with semi-annual 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?

a) $121.60
b) $124.91
c) $127.13
d) $135.57

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 zero-coupon bond with 5.0 years to maturity, plus
50% invested in a zero-coupon 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 basis-point 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% one-month value at risk (relative VaR: worst expected loss relative to expected future value)?

a) 95,000
b) 105,750
c) 129,900
d) 178,400

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?

a) 0.095
b) 0.200
c) 0.330
d) 0.475

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.

Gaussian Copula

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?

a) 0.25%
b) 0.71%
c) 1.36%
d) 1.82%

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)

a) 9.0%
b) 18.0%
c) 36.0%
d) 72.0%

Question 88 of 100

88. Question

Consider a six-month at-the-money (ATM) European call option on a non-dividend-paying stock with a current price of $80.00. Peter the Risk Analyst has employed a two-step (i.e., three months per step) binomial model to price the option, as displayed below:

Two-step binomial models

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 risk-free rate is 4.0%. Which of the following is nearest to the risk-neutral probability of the stock price going up in a single step?

a) 45.61%
b) 46.44%
c) 48.70%
d) 52.52%

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 decision-makers 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)

a) Accuracy
b) Comprehensiveness
c) Clarity and usefulness
d) Manual workarounds

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 Black-Scholes-Merton 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 fat-tailed in practice.” How can Peter overcome this objection and include a fat-tailed assumption in his model?

a) He could assume the errors follow a GARCH process
b) He could assume the errors are drawn from a fat-tailed distribution; e.g., student's t
c) Either he could either assume errors follow a GARCH process or that errors are drawn from a fat-tailed distribution
d) Monte Carlo simulation cannot overcome this objection, this is a disadvantage of Monte Carlo simulation in comparison to bootstrapping

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:

Basic bank functions

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)

a) None
b) About $1.50 million
c) About $3.97 million
d) About $14.46 million

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 in-the-money 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?

a) -3,500
b) +7,200 (unchanged)
c) +8,400
d) +11,900

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?

a) 5.100%
b) 7.900%
c) 8.880%.
d) 9.540%

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?

a) 360
b) 3,600
c) 10,000
d) 36,000

Question 95 of 100

95. Question

Below are a summary balance sheet and income statement for Deposits and Loans Corporation (DLC):

Major risks faced by banks

Each of the following statements is true EXCEPT which is false?

a) Before-tax return on equity (ROE) is 12.0%
b) Leverage is 19.0 or 20.0 (depending on our definition of leverage)
c) If loan losses jump to 6.0% of assets next year, and nothing else changes, this will completely wipe out the equity shareholders
d) If during 2016 DLC had borrowed $10 million (specifically +$10.0 to subordinated long-term debt) in order to buy back shares (i.e., -$10.0 equity), and its income statement were unaffected, then its ROE would triple (3x) due to this increase in leverage

Question 96 of 100

96. Question

Trader Joe (who is unrelated to the awesome grocery store!) takes a long position in 100 out-of-the-money (OTM) put option contracts when the non-dividend-paying 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 risk-free 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 re-pricing of the position?

a) $18,280
b) $25,950
c) $29,135
d) $33,640

Question 97 of 100

97. Question

Which of the following is TRUE about the bank’s audit function?

a) Internal audit is necessary because it is virtually impossible to rate (i.e., assign ratings to) the risk management function
b) The firm's operational risk management should report directly to the internal audit function (who will, therefore, oversee risk management)
c) Internal auditors are responsible for reviewing monitoring procedures, tracking the progress of risk management system upgrades, and affirming the efficacy of vetting processes
d) The assistance of internal audit should not be required to the risk governance function: a properly designed risk governance function should be able to ascertain compliance alone

Question 98 of 100

98. Question

Consider the following discrete probability distribution of asset returns:

Skew, kurtosis, coskew and cokurtosis

As shown, this asset’s expected return is +2.55%. Which is nearest to this variable’s skew; aka, standardized third central moment?

a) -2.25
b) -0.96
c) +0.33
d) +1.06

Question 99 of 100

99. Question

Below is an extract from a mortality table (ages 30 to 34 for males and females):

Life insurance

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?

a) There is no surplus premium; i.e., zero
b) $5,336.00
c) $5,885.00
d) $5,919.00

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 semi-annual coupon at a rate of 4.0% per annum and offers a yield of 5.0% per annum (with semi-annual 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 zero-coupon bond with 30.0 years to maturity that offers a yield (aka, yield to maturity) of 8.0% per annum with semi-annual compound frequency

In terms of their current theoretical prices, which bonds are, respectively, the cheapest and most expensive (among the four)?

a) Bond A is the cheapest and Bond D is the most expensive
b) Bond B is the cheapest and Bond C is the most expensive
c) Bond C is the cheapest and Bond A is the most expensive
d) Bond D is the cheapest and Bond B is the most expensive