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Question 1 of 21
1. Question
A risk manager is estimating the market risk of a portfolio using both the normal distribution and the lognormal distribution assumptions. The manager gathers the following data on the portfolio:
 Expected return per annum: 12.0%
 Expected volatility per annum: 28.0%
 Current portfolio value: USD 10,000,000
 Trading days: 20 per month and 250 per year
Which is nearest to the difference between the normal VaR and the lognormal VaR at the 95.0% confidence level over a onemonth holding period? (Please note this question is inspired by Question #2 in GARP’s 2017 Practice Exam. Reminder than “normal VaR” refers to the assumption that simple arithmetic returns are normally distributed, while “lognormal VaR” refers to the assumption that log returns–aka continuously compounded returns–are normally distributed.)
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Question 2 of 21
2. Question
A risk measure is coherent if is satisfies four properties: monotonicity, subadditivity, positive homogeneity, translation invariance. Which of the following is a TRUE statement?
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Question 3 of 21
3. Question
Donald the risk manager collects 250 trading days of profit and loss (P/L) and plots the daily outcomes in a histogram. The loss tail of the histogram is plotted below, but it is only the worst thirty (30) losses out of the total 250; i.e.., the body of the histogram is not shown:
Under the simple historical simulation (HS) approach, which is nearest to the 95.0% value at risk (VaR)?
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Question 4 of 21
4. Question
A highly risky asset with a very high expected return exhibits the following characteristics:
 Incredibly high expected return of 26.0% per annum
 But this high expected return comes at the cost of high DAILY volatility of 1.0% per day
 Current portfolio value: USD 10,000,000
 Trading days: 20 per month and 250 per year
We are interested in the absolute value at risk (aVaR) where the worst expected loss is expressed as a positive number. In the case of this asset, for example, the 95.0% confident oneday normal aVaR is given by 26.0%/250 + 1.0%*1.645 = +1.541%. In regard to a 95.0% confident VaR, each of the following statements about this asset is true EXCEPT which is false?
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Question 5 of 21
5. Question
Donald the risk manager collects 300 trading days of profit and loss (P/L) data and plots the daily outcomes in a histogram. The loss tail of the histogram is plotted below, but this histogram only displays the worst 21 losses out of 300 days in the full window. Specifically, in this case, the worst loss among the 300 days was a loss of 14.5%; the second worst loss was 12.8%; and the third worst loss was 12.1%. Consequently, there is no bar plotted at the interval (13%, 14%) which is between 13% and 14%.
Which of the following is MOST LIKELY the 99.0% confident expected shortfall (ES)?
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Question 6 of 21
6. Question
Betty the analyst has collected a dataset and seeks to fit a relatively simple univariate distribution to the data. She hopes the data is approximately normal. To test this hypothesis, she generates a quantilequantile plot (QQ plot) using a standard normal distribution as the reference. This QQ plot is displayed below.
Among the following choices, which distribution is probably the best fit for this data?
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Question 7 of 21
7. Question
You want to estimate the 99.0% expected shortfall (ES) but it is much easier to compute the extreme quantiles of the nonnormal distribution, which are shown below:
Which is nearest to a reasonable estimate of the 99.0% expected shortfall (ES) of this distribution?
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Question 8 of 21
8. Question
What is the primary advantage of a bootstrap historical simulation in comparison to basic (aka, simple) historical simulation?
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Question 9 of 21
9. Question
You have collected 100 days (K = 100) of portfolio returns and sorted them. The worst six returns are displayed below. In addition to the returns, you compared the weights implied by simple historical simulation (i.e., 1/100 = 1.0%, 2/100 = 2.0%, …) to the weights implied by an ageweighted historical simulation (aka, “hybrid” approach) where the lambda, λ, parameter is set to 0.90.
As a technical note, rather than view the worst loss observation (i.e., 5.30%) as the quantile for 1.00% probability (in the simple HS approach) or the 2.29% probability (in the ageweighted HS approach), you are going to view each loss observation as a random variable with a probability mass centered on the observation. In this way, for example, under the simple HS the 99.0% VaR would be 4.75% = average(5.30%, 4.20%) rather than 5.30%.
Which of the following is nearest to the 95.0% confident ageweighted HS?
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Question 10 of 21
10. Question
A portfolio consists of two bonds: the first bond has a fiveyear maturity and pays a 4.0% annual coupon, the second bond matures in one year and pays a 1.0% annual coupon. Both bonds conveniently price at par (aka, their yield is equal to their coupon rate). The portfolio’s (Macaulay) duration is 2.815 years.
Each of the following statements is true EXCEPT which is inaccurate?
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Question 11 of 21
11. Question
703.2. A risk manager is backtesting a company’s oneday 99.0% VaR model over a fouryear horizon at a 90.0% twotailed confidence level. If we assume 250 days in a year, so that that backtest sample size is 1,000 days, what is the maximum number of daily losses exceeding the 1day 99.0% VaR that is acceptable to conclude that the model is calibrated correctly?
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Question 12 of 21
12. Question
Zerphase Financial Corporation is going to conduct a backtest of its 99.0% value at risk (VaR) model. The sample window size is 300 days; i.e., the previous 15 months and each month has 20 trading days. The desired twotailed confidence is 95.0%. About this backtest, each of the following statements is true EXCEPT which is false?
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Question 13 of 21
13. Question
Asset correlations are not only important in financial markets, they often exhibit statistically significant and expected properties. However, there do exist several different measures of correlation. According to Meissner, each of the following statements about financial correlation is true EXCEPT which is not accurate?
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Question 14 of 21
14. Question
The default (Pearson) correlation coefficient between two bonds is 0.50. If their individual default probabilities are, respectively, 5.0% and 7.0%, then which is nearest to their joint default probability?
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Question 15 of 21
15. Question
Peter the analyst has compiled the annual returns for two funds, X(i) and Y(i), over the last five years from 2012 to 2016, inclusive. These returns are shown below. Although the data are cardinal, given the small dataset, Peter wants to compute the rank correlation of returns. He sorts the X(i) returns, from worst to best, and shows the corresponding Y(i) returns. For example, in 2015 the X(2015) return of 1.3% was the 3rdworst (and 3rdbest for that matter!); in the same year, the Y(2015) return of +2.1% was the 4thworst (or 2ndbest) among its own return series. Peter also plotted the pairwise rankings, see chart in lower panel below.
What is the Kendall’s tau, τ, for this dataset?
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Question 16 of 21
16. Question
Assume that the sixmonth and oneyear spot rates are 2.00% and 2.10% with semiannual compounding. Consequently, a sixmonth zerocoupon bond with a face value of $1,000 has a price of $990.10 and a oneyear zerocoupon bond has a price of $979.326. A simple onestep binomial determines the possible evolution of the sixmonth rate: with a realworld probability of 50.0% it will increase 30 basis points to 2.30%, and with a realworld probability of 50.0% it will decrease 30 basis points to 1.70%. Following Tuckman’s (Chapter 7) example, we are interested in the price of a call option on a zerocoupon bond, where the call option has a strike price of $990.00 and matures in six months; and the zerocoupon bond matures in one year. The situation is illustrated below.
In the scenario where the sixmonth rate jumps down, from 2.00% to 1.70% with realworld (aka, true) probability of 50.0%, the zerocoupon bond will have a remaining maturity of six months and its price will therefore increase to $991.57 = $1,000/(1+1.70%/2). The option can be exercised for a gain of $1.57 = max($991.57 – $990.00.0). If the current (T = 0) noarbitrage price of the option is $0.260, then which is nearest the riskneutral probability, p, of an jump to the up state?
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Question 17 of 21
17. Question
A hedge fund manager is evaluating interest rate term structure models and she has the following two criteria.
 First, she wants to model “mean revision” by specifying a longrun value (aka, central tendency, call it theta, Θ) for the shortterm rate
 Second, she believes that assuming independence between the short rate’s basispoint volatility and its level is unrealistic: volatility tends to be higher when the level of rates is higher (e.g., during inflation periods) and, on the other hand, when rate levels are low, volatility is limited by the zero bound4
Among the following choices, which model best fits her criteria?
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Question 18 of 21
18. Question
A hedge fund manager is evaluating interest rate term structure models and she has the following four criteria.
 First, she wants to model “mean revision” by specifying a longrun value (aka, central tendency, call it theta, Θ) for the shortterm rate; this is a related to her preference to avoid a socalled timedependent volatility model and, in particular, those timedependent models that imply a flat term structure.
 Second, she wants to be able to parse the true longrun value (aka, interest rate expectation) from a risk premium
 Third, she wants to keep the model relatively simple by assuming the basispoint volatility of the short rate is both constant and independent of the level of the rate.
 Fourth, she prefers the convenience of assuming the terminal distribution of the shortrate is normally distributed.
Among the following choices, which model best fits her criteria?
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Question 19 of 21
19. Question
Peter the Risk Analyst is conducting the valuation of a bilateral derivatives portfolio. The positions are between his firm, Nordyne Financial (NF), and Counterparty Inc. The counterparties do post collateral (i.e., the positions are collateralized) and the interest is paid on overnight cash collateral balances equal to the effective federal funds rate. With respect to his valuation, each of the following is true EXCEPT which is probably false?
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Question 20 of 21
20. Question
A certain stock price is currently trading at $40.00 while it trades options at various strike prices including $30.00, $35.00, $40.00 (i.e., at the money), $45.00 and $50.00. Below are shown, at each of these strike prices, both the computed (model) prices according to the BlackScholesMerton model and the corresponding traded (observed) price of the option. For example, the call option with a strike price of $35.00 has a BlackScholes option price (assuming the same volatility as the ATM option) of $11.22 but this call option is actually trading at $10.591.
In comparison specifically to the lognormal distribution, which best characterizes the implied distribution of the stock price?
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Question 21 of 21
21. Question
Assume we observe the following implied volatility smile, which may be called a volatility skew or smirk and is somewhat typical of equities:
Which of the following statement about this shape of the volatility smile is TRUE?
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