FRM一级练习题(2)

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frm一级题库 2023

frm一级题库 2023

frm一级题库2023
一、单项选择题
1.在2023年FRM考试中,一级考试的合格分数线是多少?
2. A. 400
3. B. 500
4. C. 600
5. D. 700
6.FRM一级考试中,风险管理基础占比多少?
7. A. 15%
8. B. 25%
9. C. 35%
10. D. 45%
11.FRM一级考试中,数量分析占比多少?
12. A. 10%
13. B. 15%
14. C. 20%
15. D. 25%
16.FRM一级考试中,金融市场与产品占比多少?
17. A. 20%
18. B. 25%
19. C. 30%
20. D. 35%
21.FRM一级考试中,估值与风险建模占比多少?
22. A. 15%
23. B. 20%
24. C. 25%
25. D. 30%
二、多项选择题
1.下列哪些科目是FRM一级考试的重要内容?
2. A. 风险管理基础
3. B. 数量分析
4. C. 公司金融
5. D. 金融市场与产品
6. E. 估值与风险建模
7.在FRM一级考试中,下列哪些知识点是考生需要掌握的?
8. A. 市场风险的管理方法
9. B. 信用风险的计算方式
10. C. 操作风险的识别与评估
11. D. 企业价值的评估方法
12. E. 对冲策略的有效性分析
三、简答题
1.请简述FRM一级考试的主要目的。

2.在FRM一级考试中,考生应具备哪些基本能力?。

FRM一级Financialdisaster

FRM一级Financialdisaster

FRM一级Financialdisaster序号当事人涉案公司涉案金额1—Drysdale&ChaseManhattan bank300million2Joseph Jett Kidder Peabody350million 3Nick Leeson Barings Bank起因1. Drysdale borrowed 300M by exploiting a flaw in the US government bond without collateral2. Drysdale took the wrong position and lost all 300M3. Chase manhattan absorbed all the losses cause inexperienced managers in Chase believed they were just a middleman1. The head of the government bond trading desk at Kidder Peabody, Joseph Jett, reported substantial artificial profits. After the false profits were detected, $350 million in previously reported gains had to be reversed, The loss was not actual.2. The system failed to realize that this profit would disappear once financing costs for the cash bond were taken into account.1. Hidden trading losses at Barings induced Nick Leeson to abandon hedging strategies in favor of speculative strategies. A lack of operational oversight and his dual roles as trader and settlement officer allowed him to conceal his activities and losses.2. Speculative strategies:Selling straddle on the Nikkei 225.Long-long futures on Nikkei 225 in both Tokyo and Singapore3. Dual roles经验教训1. Need for more precise methods for computing the value of collateral.2. Need for better process control.The need for a process that forced areas contemplating new product offerings to receive prior approval from representatives of the principal risk control functions within the firm.1. Always investigate a stream of large unexpected profits thoroughly and make sure you completely understand the source.2. Periodically review models and systems to see if changes in the way they are being used require changes in simplifying assumptions.。

FRM一级练习题(2)答案

FRM一级练习题(2)答案

FRM一级练习题(2)答案1. If the daily, 95% confidence level value at risk (VaR) of a portfolio is correctly estimated to be USD 10,000, one would expect that 95% of the time (19 out of 20), the portfolio will lose l ess than USD 10,000; equivalently, 5% of the time (1 out of 20) the portfolio will lose USD 10,000 or more.(A) Incorrect. Portfolio value will decline by USD 10,000 or more.(B) Incorrect. In 1 out of 20 days, portfolio value will decline by USD 10,000 or more.(C) Incorrect. 1 out of 95 days woul d provide a 98.9% confidence level.(D) Correct.2. In imperfect markets, deadweight costs of financial distress or bankruptcy caused by debt financing cannot be hedged by the firm's sharehol ders in the capital markets. Hence it pays for the firm to hedge its cash flow uncertainty via the use of d erivatives contracts. The present value of its more stable cash fl ows in the presence of hedging is greater than the present value of its uncertain expected cash fl ows in the absence of hedging. Transaction costs for capital markets bearing this risk are sufficiently l ow in forward markets. Answers (A), (C), and (D) are incorrect because they contradict the correct answer, (B).3. According to CAPM, the expected return of the portfolio = 0.045 + 1.5(0.11) = 21%, and the expected return of the market portfolio is the risk premium plus the risk-free rate, or 11% +4.5% = 15.5%. Therefore, portfolio A is expected to outperform the market.From the preceding, (B) and (D) are clearly incorrect. (C) is incorrect since beta greater than 1.0 implies portfolio A is riskier than the market portfolio.4. Jensen's measure of a portfolio = ap = E (Rp) – RF –βx [E (RM) – RF] = 8% – 5% – 0.5 x (10% – 5%) = 0.5%(A) is incorrect. This is βP *σmaP = 0.5 * 0.20 = 10%.(B) is incorrect. This is the Black-Treynor ratio: αP /βP = 0.005 / 0.5 = 1%.(D) is incorrect. This is the Sharpe ratio: (E (Rp) – RF) / smaP = 0.03 / 0.2 = 15%.5. The answer is (B), since statement (B) is incorrect. An oil market move from a state of normal backwardation to contango and margin calls created a major cash crunch for Metallgesellschaft.6. Existing risk models generally fail to capture the distribution of large l osses over extended horizons. Theother statements are correct.7. As we know, cov(X, Y1 + Y2) = cov(X, Y1) + cov(X, Y2). So cov(z, x + y) = cov(z, x) + cov(z, y). That means cov(z, x) + cov(z, y) = 0. So if cov(z, x) = 1,cov(z, y) = –1, (A) and (B) are incorrect; if cov(z, x) = cov(z, y) = 0, (C) is incorrect.8. From the given information, there is a 77% chance that stock X increases and a 61% chance that stock Y increases. Since we have no additional information about the distributions, we know the maximum possible probability that both increases cannot be greater than 61%, since stock Y decreases 39% of the time. Suppose whenever Y increases, X increases as well, which is possibl e because X increases 77% of the time, in which case the probability both increase is 61%. This is the maximum possible probability that both increase.(B) is 0.61 * 0.77 = 0.4697.(C) is the maximum probability that both decrease.(D) is the probability that X increases.9. Use Bayes' Theorem:P (Neutral | Constant) = P (Constant | Neutral) * P (Neutral) / P(Constant) = 0.2 * 0.3 / (0.1 * 0.2 + 0.2 * 0.3 + 0.15 * 0.5) = 0.38710. Age and experience are highly correlated and woul d lead to multicollinearity. In fact, l ow t-statistics but a high R2 do suggest this problem also.Answers (A), (B), and (C) are not likely causes and are therefore incorrect.参与FRM的考生可按照复习计划有效进行,另外高顿网校官网考试辅导高清课程已经开通,还可索取FRM 考试通关宝典,针对性地讲解、训练、答疑、模考,对学习过程进行全程跟踪、分析、指导,可以帮助考生全面提升备考效果。

FRM一级_风险管理基础&定量分析答案(★★)

FRM一级_风险管理基础&定量分析答案(★★)

Answer: D StrategiesⅠandⅡboth suggest risk management to reduce the cost of bankruptcy and financial distress may be value enhancing. 5. The role of risk management does NOT involve performing which of the following tasks? A. Make sure that the firm takes greater than the necessary amount of risk. B. Assess all risks faced by the firm. C. Communicate these risks to risk-taking decision makers. D. Monitor and manage these risks.
Answer: D The CAPM assumes that investors all have the same horizon (as well as expectations). This means that the distribution of the horizons is not normal because normality implies a bell-shaped curve distribution, which would have a positive variance and, hence, dispersion. 10. Markowitz Portfolio Theory is not accurately described as including an assumption that: A. risk is measured by the range of expected returns B. for a given risk level, investor prefer higher returns to lower returns C. investors base all their decisions on expected return and risk D. investors focus on utility maximization

FRM一级模拟题(2)

FRM一级模拟题(2)

FRM一级模拟题(2)1、Which one of the foll owing four trading strategies coul d limit the investor's upside potential while reducing her d ownsid e risk compared to a naked long position in the stock?A. A long position in a put combined with a long position in a stockB. A short position in a put combined with a short position in a stockC.Buying a call option on a stock with a certain strike price and selling a call option on the same stock with ahigher strike price and the same expiration dateD.Buying a call and a put with the same strike price and expiration date2、Which one of the foll owing four statements is correct about the early exercise of American options? (1). It is never optimal to exercise an American call option on a non-divid end-paying stock before the expiration date.(2). It can be optimal to exercise an American put option on a non-dividend-paying stock early.(3). It can be optimal to exercise an American call option on a non-dividend-paying stock early.(4). It is never optimal to exercise an American put option on a non-dividend-paying stock before the expiration date.A. 1 and 2B. 1 and 4C. 2 and 3D. 3 and 43、Mr. Black has been asked by a client to write a large option on the S&P 500 ind ex. The option has an exercise price and maturities that are not availabl e for options traded on exchanges. He therefore has to hedge the position dynamically. Which of the foll owing statements about the risk of his position is not correct?A.By selling short index futures short, he can make his portfolio delta neutral.B.There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to bothsmall and large moves in the S&P 500.C. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he haswritten.D.To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.4、The current price of stock ABC is $42 and the call option with a strike at $44 is trading at $3. Expiration is inone year. The corresponding put is priced at $2. Which of the foll owing trading strategies will result in arbitrage profits? Assume that the annual risk-free rate is 10%, and that there is a risk-free bond paying the risk-free rate that can be shorted costl essly. There are no transaction costs.A.Long position in both the call option and the stock, and short position in the put option and risk-free bondB.Long position in both the call option and the put option, and short position in the stock and risk-free bondC.Long position in both the call option and risk-free bond, and short position in the stock and the put optionD.Long position in both the put option and the risk-free bond, and short position in the stock and the putoption5、The foll owing table gives the prices of two out of three U.S. Treasury notes for settlement on August 30, 2008. All three notes will mature exactly one year later on August 30, 2009.Coupon Price2$98.404?6$101.30Approximately, what woul d the price of the 41/2 U.S. Treasury note?A.$99.20B.$99.40C.$99.80D.$100.206、The observed zero yiel d curve is given by the foll owing data:1-year spot rate = 3.65%2-year spot rate = 3.99%3-year spot rate = 4.11%Using the data for the spot curve, the forward rate on a one-year contract maturing in two years is closest to:A. 3.20%B. 3.79%C. 4.33%D. 4.15%7、The spot price of gold is US200/oz and the price of a one-year gold futures contract is US205/oz. Assuming that the annual risk-free rate remains 5% and there are no arbitrage opportunities, which of the foll owing situations would cause backwardation1. Future value of the net cost for carrying physical gol d per oz increases.2. Future value of the net cost for carrying physical gol d per oz decreases.3. There is a net positive benefit from carrying physical gold.4. There is a net negative cost from carrying physical gold.A. 1 and 4 onlyB. 3 onlyC. 2 and 4D. 1 and 38、The foll owing table gives the cl osing prices and yiel ds of a particular liquid bond over the past few days. Day Price YieldMonday $106.3 4.25%Tuesday $105.8 4.20%Wednesday $106.1 4.23%What is the approximate duration of the bond?A.18.8B.9.4C. 4.7D. 1.99、John Flag, the manager of a USD 150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio's annualized return is 12%, with an annualized return volatility of 25%. In the past two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio woul d suffer a 4-sigma daily event, estimate the change in the value of this portfolio.A.$9.48 millionB.$23.70 millionC.$37.50 millionD.$150 million10、A single stock has a price of $10 and a current daily volatility of 2%. Using the delta-normal approximation, the VaR on a l ong at-the-money call on this stock over a one-day holding period is:A.$0.1645B.$0.329C.$1.645D.$16.45Answer and Explanation:1. Long position in a put combined with long position in a stock could limit only the d ownside risk; (A) is incorrect.Short position in a put combined with short position in a stock coul d limit only the upside risk; (B) is incorrect. Buying a call option on a stock with a certain strike price and selling a call option on the same stock with a higher strike price and the same expiration date could limit both the upside and d ownside risk; (C) is correct. Buying a call and a put with the same strike price and expiration date could limit only the d ownsid e risk; (D) is incorrect.2. There are no advantages to exercising early if the investor plans to keep the stock for the remaining life of the call option, because the early exercise woul d sacrifice the interest that woul d be earned. If the strike price is paid out later on expiration date after the early exercise, the investor may suffer the risk that the stock price will fall bel ow the strike price. As the stock pays no dividend, the early exercise will earn no income from the stock. So it is never optimal to exercise an American call option on a non-divid end-paying stock before the expiration date.At any given time during its life, a put option shoul d always be exercised early if it is sufficiently deep in-the-money. So it can be optimal to exercise an American put option on a non-dividend-paying stock early. As a result, answer (A) is correct.3. The short ind ex futures contract makes the portfolio delta neutral. It does not help with large moves.4. (A) is incorrect as this would not yield arbitrage profit.(B) is incorrect as this woul d not yield arbitrage profit.(C) is correct.The put-call parity relation is: stock + put = pv(strike) + callTherefore, for no arbitrage opportunity the foll owing relation should hold:42 + 2 = (44/1.10) + 3But 44 > 43Therefore, there is an arbitrage opportunity. The arbitrage profit is 49 – 42 = 7 by taking a long position in a call and buying the risk-free bond and going short on the stock and the put.(D) is incorrect as this woul d not yield arbitrage profit.5. 2.875% * X +6.25% * (1 – X) = 4.5%X = 52%The portfolio that has cash fl ows identical to the 41/2 bond consists of 52% of the 27/8 and 48% of the 61/4 bonds. As this portfolio has cash fl ows identical to the 41/2 bond, precluding arbitrage, the price of the portfolio should equal to 52% * 97.4 + 48% * 101.30, or $99.806. (A) is incorrect because the rate cannot be bel ow the spot rates as the zero curve has an upward sl ope.(B) is incorrect because the zero curve is upward-sloping and the rate must be higher than 3.99%.(C) is the correct answer:Rf = [(1 + r2) ^ t2/(1 + r1) ^ t1] – 1Rf = (r2t2 – r1t1)/(t2 – t1)[((1 + 3.99%) ^ 2)/(1 + 3.65%)] – 1 = 4.33%(D) is impossibl e because if we invest for a year at 3.65% and the next year at 4.15%, it is not the same as investing during two years at 3.99%.7. The expected spot price 1 year later is US210/oz. So, if no arbitrage opportunity exists, the future value of the net cost for carrying the physical gol d is US5/oz.If the future value of the net cost for carrying the gold per oz increases and exceeds US10/oz, the spot price one year later will be less than the current spot price. Thus backwardation occurs.Also, if the net benefit for carrying the gol d exists and the future value of such benefit exceeds US5/oz (with holding future value of net cost being constant), backwardation occurs too.Also, if the net negative from carrying the gol d exists and the future value of such benefit exceeds US5/oz (with holding future value of net cost being constant), backwardation d oes not occur.Therefore, both statement 1 and statement 3 are correct.(A) is incorrect because statement 3 is correct too.(B) is incorrect because statement 1 is correct too.(C) is incorrect because statement 2 is incorrect.(D) is correct because both statement 1 and statement 3 are correct.Remark: The tricky part of the question is that the candidate may feel confused since the no-arbitrage future price should be US210/oz (if net cost of storage d oes not exist), rather than the price US205/oz given in the question (where the net cost of storage exists).8. The duration can be approximated from the price changes.(106.3 – 105.8)/106.3/.0005 = 9.4(106.3 – 106.1)/106.3/.0002 = 9.4etc.9. Daily volatility is equal to 0.25 * sqrt (1/250) = 0.0158. A 4-sigma event therefore implies a l oss equal to 4*0.0158*150 = 9,486,832The correct answer is (A).(B) calculates the daily volatility and multiplies the volatility by the value of the portfolio.(C) multiplies the portfolio value by its annual volatility, or divides the portfolio value by 4.(D) attempts the shortcut of reducing the portfolio value by 4 times 25%, which is 100% (i.e., the value of the portfolio).10. This question requires candidates to know the formula for the delta-normal VaR approximation, and also to know that the delta of an at-the-money call is 0.5.The correct answer is (A).(B) uses a delta of 1.(C) confuses the decimal point.(D) uses 2 instead of 2% for the volatility.参与FRM的考生可按照复习计划有效进行,另外高顿网校官网考试辅导高清课程已经开通,还可索取FRM 考试通关宝典,针对性地讲解、训练、答疑、模考,对学习过程进行全程跟踪、分析、指导,可以帮助考生全面提升备考效果。

FRM一级模考

FRM一级模考

FRM一级模拟题1 .If the daily returns of two assets are positively correlated, then:A. the covariance of their daily returns must be positiveB. the covariance of their daily returns must be zeroC. the covariance of their daily returns must be negativeD. nothing can be said about the covariance of their daily returnsAnswer: AIf variables are positively correlated, the covariance between the Variables will also be positive.2 .You are given that X and Y are random variables, and each of which follows a standard normal distribution with Covariance (X, Y) = 0.4. What is the variance of (5X+2Y)?A. 11.0B. 29.0C. 29.4D. 37.0Answer: DSince each variable is standardized, its variance is one. Therefore, Var(5X+2Y) = 25 x Var(X)+4xVar(Y)+2 x 5x2x Cov(X,Y) =25+4+8 = 373 . What is the covariance between populations A and B?If the variance ofA is 12, what is the variance of B?A. 10.00B. 2.89C. 8.33D. 14.40Answer:C5 . Which one of the following statements about the correlation coefficient is FALSE?A. It always ranges from -1 to +1B. A correlation coefficient of zero means that two random variables are independentC. It is a measure of linear relationship between two random variablesD. It can be calculated by scaling the covariance between two random variables Answer:BCorrelation describes the linear relationship between two variables. While we would expect to find a correlation of zero for independent .variables, finding a correlation of zero does not mean that two variables are independent.。

frm考试培训训练FRM一级模拟题

frm考试培训训练FRM一级模拟题

frm考试培训训练FRM一级模拟题高顿FRM考试培训训练FRM一级模拟题:If there are restrictions on short selling and borrowing at the risk-free rate,we would expect to see that:A.all investors hold the same market portfolio as predicted by the CAPM.B.highly risk-averse individuals tend to hold heavily diversified portfolios,while those with less risk aversion tend to concentrate their portfolios.C.less risk-averse individuals tend to hold heavily diversified portfolios,while those with more risk aversion tend to concentrate their portfolios.D.both highly risk-averse individuals and those with less risk aversion tend to concentrate their portfolios.Answer:BRestrictions on short selling or borrowing at the risk-free rate make investors construct portfolios with considerably different compositions.Highly risk-averse individuals tend to hold heavily diversified portfolios,while those with less risk aversion tend to concentrate their portfolios.FRM的一级考试四科目复习方法:风险管理基础(Foundations of Risk Management)考试比重:20%和定量分析(Quantitative Analysis)考试比重:20%我的数学底子并不好,理科废柴生。

2021frm一级考试答案

2021frm一级考试答案

2021frm一级考试答案1. 根据FRM一级考试内容,以下哪项风险不属于市场风险?A. 利率风险B. 汇率风险C. 信用风险D. 操作风险答案:D2. FRM一级考试中,对于风险价值(VaR)的计算,以下哪个说法是正确的?A. VaR是预期损失B. VaR是在一个特定置信水平下的最大可能损失C. VaR是平均损失D. VaR是超过某个阈值的损失答案:B3. 在FRM一级考试中,关于债券收益率曲线的描述,以下哪项是不正确的?A. 收益率曲线可以是向上倾斜的B. 收益率曲线可以是向下倾斜的C. 收益率曲线可以是平坦的D. 收益率曲线是固定不变的答案:D4. 在FRM一级考试中,以下哪项不属于信用风险管理的工具?A. 信用衍生品B. 信用评级C. 资产证券化D. 利率互换答案:D5. 根据FRM一级考试内容,以下哪项是操作风险的主要来源?A. 市场波动B. 法律诉讼C. 欺诈行为D. 自然灾害答案:C6. 在FRM一级考试中,以下哪项是流动性风险管理的关键要素?A. 资产负债管理B. 资本充足率C. 利率风险管理D. 信用评级答案:A7. 根据FRM一级考试内容,以下哪项不是风险管理的主要目标?A. 减少损失B. 增加收益C. 遵守法规D. 保护公司声誉答案:B8. 在FRM一级考试中,以下哪项是压力测试的目的?A. 评估在极端市场条件下的表现B. 预测未来的市场趋势C. 评估日常风险管理的有效性D. 计算风险价值(VaR)答案:A9. 根据FRM一级考试内容,以下哪项是风险限额设置的主要依据?A. 历史数据B. 市场预测C. 管理层的风险偏好D. 竞争对手的风险限额答案:C10. 在FRM一级考试中,以下哪项是风险管理框架的核心组成部分?A. 风险识别B. 风险评估C. 风险监控D. 所有选项答案:D结束语:以上是2021年FRM一级考试的部分答案,希望能够帮助考生更好地复习和准备考试。

frm一级 刷题

frm一级 刷题

frm一级刷题1. 关于风险评估,以下哪项描述是正确的?A. 风险评估是识别、分析和衡量风险的过程。

B. 风险评估仅涉及对历史数据的分析和预测。

C. 风险评估仅考虑财务风险。

D. 风险评估是风险管理的一部分。

2. 下列哪个不是风险管理的基本要素?A. 风险识别B. 风险评估C. 风险监控D. 风险预测3. 关于操作风险,以下哪项描述是正确的?A. 操作风险是由外部因素引起的。

B. 操作风险是可以完全避免的风险。

C. 操作风险通常是由内部程序、人员和系统等因素引起的。

D. 操作风险是指因市场价格波动引起的金融风险。

4. 在实施风险管理策略时,以下哪项是首要步骤?A. 风险评估B. 风险识别C. 风险控制措施制定D. 风险监控和调整5. 下列哪项不是风险管理的基本原则?A. 全面风险管理原则B. 分散化原则C. 经济性原则D. 单一风险管理原则6. 关于内部风险报告,以下哪项描述是正确的?A. 内部风险报告必须使用专业术语。

B. 内部风险报告应该仅包括对过去事件的描述。

C. 内部风险报告应该提供关于未来风险的预测。

D. 内部风险报告应该提供清晰、简洁和易于理解的信息。

7. 关于外部风险管理报告,以下哪项描述是正确的?A. 外部风险管理报告必须包含对未来风险的预测。

B. 外部风险管理报告不需要经过第三方审计。

C. 外部风险管理报告应该提供详细的风险管理策略和措施。

D. 外部风险管理报告不需要包含风险管理流程的描述。

8. 下列哪项不是金融风险的类型?A. 市场风险B. 技术风险C. 社会风险D. 经济风险9. 关于VaR,以下哪项描述是正确的?A. VaR是一种用于测量和监控市场风险的工具。

B. VaR是一种用于测量信用风险的工具。

C. VaR是一种用于测量操作风险的工具。

D. VaR是一种用于测量流动性风险的工具。

FRM 一级每日一练

FRM 一级每日一练

FRM一级习题l. Which of the following scenarios is not an example of financial risk?A. An error by a derivatives trader causes a significant loss.B. A significant market downturn causes a firm's pension plan to experience significantlosses.C. A global recession has led to a decrease in demand for a business's products.D. Interest rates increase causing a company to have to make higher coupon payments on itsfloating-rate debt.Answer: CA macroeconomic change that affects the core business operations is a business risk, not afinancial risk.2. Which of the following statements is most likely correct regarding the function(s) offinancialinstitutions in risk management? Financial institutions.I Create markets and instruments to hedge financial risks.II Provide financial risk management advisory services.III Act as a counterparty by assuming the risk of others.A. I onlyB. I and IIC. I and IIID.I, II, and III.Answer: DFinancial institutions perform all of these functions related to financial risk management.3. Which of the following statements is correct regarding valuation and value at risk (VAR)?A. Valuation and VAR are both concerned with the mean of a return distribution.B. Valuation and VAR are both focused on the tails of a return distribution.C. Valuation looks at the tails of a return distribution, while VAR looks at the mean.Answer: DValution is focused on the mean of the returns distributions, while VAR concentrates on those returns in the lower tail.4. In the presence of bankruptcy costs, the statement that best describes risk managementactivities that reduce how the volatility of a firm's cash flow can benefit shareholders is:A. There are no actions that shareholders can take on their own to avoid costly bankruptcy.B. Bankruptcy threatens the life of the firm.C. Bankruptcy costs are unsystematic.D. Bankruptcy costs are too expensive to hedge otherwise.Answer: AFor a risk management activity to have value, the firm must be able to do something forshareholders that they cannot do themselves. The risk of bankruptcy cannot be hedged by shareholders (as beta risk and output-price risk can), thus, it may be value increasing for the firm to hedge this risk. Note that it is not a question that bankruptcy costs are too expensive to hedge; they are impossible to hedge. Although Choices b and c may be correct, they are less relevant to the situation and are, therefore, not the best answers.5. Risk management activities can increase firm value when:I The firm's claimholders cannot replicate the results of the firm's hedging activity.II There is a sufficient number of claimholders.III The firm's claimholders are sufficiently risk-averse.A. I onlyB. I and :I:I onlyC. II and :III onlyD. I, II, and IIIAnswer: BRisk management activities can increase firm value when the firm's claimholders cannot take actions to replicate the results of hedging activity. Claimholders are willing to pay for the firm to do something they cannot do on their own accounts.。

frm一级模考试题第二套答案_程黄维

frm一级模考试题第二套答案_程黄维

(b)
A 90-day European put option to sell £1 for $1.64 costs 2 cents.
A. Gain; Loss
B. Gain; Gain
C. Loss; Loss
D. Loss; Gain
Answer:B. Solution:交易者买了一个180 天的看涨期权,并且同时持有一个180 天远期合约的空头。那么,如果 ST是期末的汇率,那么这份看涨期权的收益是:
long position in 169,000 yen call option with a stike price of 84.5 yen per dollar.
D. A regular bond, a short position in 169,000 yen call option with a strike price of 169 yen per dollar, a
5. At the end of one day a clearinghouse member is long 100 contracts, and the settlement price is $50,000 per contract. The original margin is $2,000 per contract. On the following day the member becomes responsible for clearing an additional 20 long contracts, entered into at a price of $51,000 per contract. The settlement price at the end of this day is $50,200. How much does the member have to add to its margin account with the exchange clearinghouse? A. $40000 B. $20000 C. $16000 D. $36000

FRM一级_金融市场与产品&估值和风险模型习题及答案(★★)

FRM一级_金融市场与产品&估值和风险模型习题及答案(★★)

Financial Markets and Products & Valuation and Risk Models1.In managing a portfolio of domestic corporate bonds, which of the following risksis least important?A.Interest rate risksB.Concentration risksC.Spread risksD.Foreign exchange risksAnswer: De a stated rate of 9% compounded periodically to answer the following threequestions. Select the choice that is the closest to the correct answer.(1) The semi-annual effective rate is:A.9.00%B.10.25%C.9.20%D.9.31%Answer: C(2) The quarterly effective rate is:A.9.00%B.9.31%C.9.20%D.9.40%Answer: B(3) The continuously compounded rate is:A.9.42%B.9.20%C.9.45%D.9.67%Answer: A3.The following Treasury zero rates are exhibited in the marketplace: 6 months = 1.25% 1 year = 2.35%1.5 years =2.58% 2 years = 2.95%Assuming continuous compounding, the price of a 2-year Treasury bond that paysa 6 percent semiannual coupon is closest to:A.105.20B.103.42C.108.66D.105.90Answer: D4. A two-year zero-coupon bond issued by corporate XYZ is currently rated A. Oneyear from now XYZ is expected to remain at A with 85% probability, upgraded to AA with 5% probability, and downgraded to BBB with 10% probability. The risk free rate is flat at 4%. The credit spreads are flat at 40, 80, and 150 basis points for AA, A, and BBB rated issuers, respectively. All rates are compounded annually.Estimate the expected value of the zero-coupon bond one year from now (for USD 100 face amount). Fixed Income Securities:D 92.59D 95.33D 95.37D 95.42Answer: C5.Assuming the long-term yield on a perpetual note is 5%, compute the dollar valueof a 1 bp. Increase in the yield (DV01) for a perpetual note paying a USD 1,000,000 annual coupon.A.-20,000B.-30,000C.-40,000D.-50,000Answer: C6.Given the following portfolio of bonds:What is the value of the portfolio’s DV01 (Dollar value of 1 basis point)?A.8,019B.8,294C.8,584D.8,813Answer: C7.Assuming other things constant, bonds of equal maturity will still have differentDV01 per USD 100 face value. Their DV01 per USD 100 face value will be in the following sequence of highest value to lowest value:A.Premium bonds, par bonds, zero coupon bondsB.Zero coupon bonds, Premium bonds, par bondsC.Premium bonds, zero coupon bonds, par bondsD.Zero coupon bonds, par bonds, Premium bondsAnswer: A8.Which of the following statements about standard fixed rate government bondswith no optionality is TRUE?I.Higher coupon implies shorter duration.II.Higher yield implies shorter duration.III.Longer maturity implies larger convexity.A.I and II onlyB.II and III onlyC.I and III onlyD.I, II, and IIIAnswer: D9.Which of the following is not a property of bond duration?A.For zero-coupon bonds, Macaulay duration of the bond equals its years tomaturity.B.Duration is usually inversely related to the coupon of a bond.C.Duration is usually higher for higher yields to maturity.D.Duration is higher as the number of years to maturity for a bond selling atpar or above increases.Answer: C10.Estimated price changes using only duration tend to:A.Overestimate the increase in price that occurs with a decrease in yield forlarge changes in yield.B.Underestimate the decrease in price that occurs with a increase in yield forlarge changes in yield.C.Overestimate the increase in price that occurs with a decrease in yield forsmall changes in yield.D.Underestimate the increase in price that occurs with a decrease in yield forlarge changes in yield.Answer: D11.A portfolio consists of two positions: One position is long $100M of a two yearbond priced at 101 with a duration of 1.7; the other position is short $50M of a five year bond priced at 99 with a duration of 4.1. What is the duration of the portfolio?A.0.68B.0.61C.-0.68D.-0.61Answer: D12.A zero-coupon bond with a maturity of 10 years has an annual effective yield of10%. What is the closest value for its modified duration?A.9B.10C.100D.Insufficient InformationAnswer: A13.A portfolio manager uses her valuation model to estimate the value of a bondportfolio at USD 125.482 million.The term structure is ing the same model,she estimates that the value of the portfolio would increase to USD 127.723 million if all the interest rates fell by 30bp and would decrease to USD 122.164 million if all the interest rates rose by ing these estimates,the effective duration of the bond is closest to :A. 8.38B. 16.76C. 7.38D. 14.77Answer: C14.A portfolio manager has a bond position worth USD 100 million. The position hasa modified duration of eight years and a convexity of 150 years. Assume that theterm structure is flat. By how much does the value of the position change if interest rates increase by 25 basis points?D -2,046,875D -2,187,500D -1,953,125D -1,906,250Answer: C15.An investment in a callable bond can be analytically decomposed into a:A.Long position in a non-callable bond and a short position in a put optionB.Short position in a non-callable bond and a long position in a call optionC.Long position in a non-callable bond and a long position in a call optionD.Long position in a non-callable and a short position in a call optionAnswer: D16.A European bank exchanges euros for USD, lends them at the U.S. risk-free rate,and simultaneously enters into a forward contract to sell the loan proceeds for euros at loan maturity. If the net effect of these transactions is to earn the risk-free euro rate, it is an example of:A.ArbitrageB.Spot-forward equalityC.Interest rate parityD.The law of one priceAnswer: C17.At the inception of a six-month forward contract on a stock index, the value of theindex was $1,150, the interest rate was 4.4%, and the continuous dividend was1.8%. Three months later, the value of the index is $1,075. Which of the followingstatement is True? The value of the:A.long position is $82.41.B.long position is $47.56.C.short position is $47.56.D.long position is -$82.41.Answer: D18.Assuming the 92-day and 274 day interest rate is 8% (act/360, money market yield)compute the 182-day forward rate starting in 92 days (act/360, money market yield).A.7.8%B.8.0%C.8.2%D.8.4%Answer: B19.The 1-year US dollar interest rate is 3% and the 1-year Canadian dollar interestrate is 4.5%. The current USD/CAD spot exchange rate is 1.5000. Calculate the 1-year forward rate.A. 1.5225B. 1.5218C. 1.5207D. 1.5199Answer: B20.The price of a three-year zero coupon government bond is 85.16. The price of asimilar four-year bond is 79.81. What is the one-year implied forward rate form year 3 to year 4?A. 5.4%B. 5.5%C. 5.8%D. 6.7%Answer: D21.The clearinghouse in a futures contract performs all but which of the followingroles? The clearing house:A.guarantees traders against default from another party.B.splits each trade and acts as a buyer to futures sellers and as a seller tofutures buyers.C.allows traders to reverse their position without having to contract the otherside of the position.D.guarantees the physical delivery of the underlying asset to the buyer offuture contracts.Answer: D22.A weakening of the basis is a consequence of the:A.Spot price increasing faster than the futures price over time.B.Spot price moving according to hyper-arithmetic Brownian motion.C.Futures price increasing faster than the spot price over time.D.Futures price moving according to hyper-arithmetic Brownian motion. Answer: C23.Which of the following statements best describes marking-to-market of a futurescontract? At the:A.End of the day, the maintenance margin is increased for traders who lost anddecreased for traders who gained.B.Conclusion of each trade, the gains or losses from all previous trades in thefutures contract are tallied.C.Maturity of the futures contract, the gains or losses are tallied to the trader’saccount.D.End of the day, the gains or losses are tallied to the trader’s account. Answer: D24.A trader buys one wheat contract (underlying = 5,000 bushels) at a price of $3.05per bushel. The initial margin on the contract is $4,500 and the maintenance margin is $3,750. At what price will the trader receive a maintenance margin call?A.$2.30B.$2.90C.$3.20D.$3.80Answer: B25.The S&P 500 index is trading at 1,025. The S&P 500 pays an expected dividendyield of 1.2% and the current risk-free rate is 2.75%. The value of a 3-month futures contract on the S&P 500 index is closest to:A.$1,028.98B.$1,108.59C.$984.86D.$1,025.00Answer: A26.The current spot price of gold is $325/oz and the price of 90-day gold futurescontract (nominal amount of 100 oz) is $315. If 90-day Treasury bills are trading at yields of 3.55% - 3.58% and storage and delivery costs are ignored, what is the potential arbitrage profit per contract?A.$1,266B.$1,286C.$1,334D.$1,344Answer: C27.Which of the following statements describing the role of a convenience yield inpricing commodity futures is true? The convenience yield:I.will cause contango in the futures pricing relationship.II.Effectively reduces the cost of carry in the futures pricing relationship.III.Eliminates the potential for arbitrage between the futures and spot price.IV.Accounts for additional costs for storing an asset in the futures pricing relationship.A.I onlyB.II onlyC.II, III, and IV onlyD.I and II onlyAnswer: B28.A firm is going to buy 10,000 barrels of West Texas Intermediate Crude Oil. Itplans to hedge the purchase using the Brent Crude Oil futures contract. The correlation between the spot and futures prices is 0.72. The volatility of the spot price is 0.35 per year. The volatility of the Brent Crude Oil futures price is 0.27 per year. What is the hedge ratio for the firm?A. 0.9333B. 0.5554C. 0.8198D. 1.2099Answer: A29.The hedge ratio is the ratio of derivatives to a spot position (or vice versa thatachieves an objective such as minimizing or eliminating risk. Suppose that the standard deviation of quarterly changes in the price of a commodity is 0.57, the standard deviation of quarterly changes in the price of a futures contract on the commodity is 0.85, and the covariance between the two changes is 0.3876. What is the optimal hedge ratio for a 3.-month contract?A.0.1893B.0.2135C.0.2381D.0.2599Answer: D30.Consider an equity portfolio with market value of USD 100M and a beta of 1.5with respect to the S&P 500 Index. The current S&P 500 index level is 1000 and each futures contract is for delivery of USD 250 times the index level. Which of the following strategy will reduce the beta of the equity portfolio to 0.8?A.Long 600 S&P 500 futures contractsB.Short 600 S&P 500 futures contractsC.Long 280 S&P 500 futures contractsD.Short 280 S&P 500 futures contractsAnswer: D31.Corporates normally use FRAs to:A.Lock-in the cost of borrowing in the futureB.Lock-in the cost of lending in the futureC.Hedge future currency exposuresD.Create future currency exposuresAnswer: A32.An investor has entered into a forward rate agreement(FRA) where she hascontracted to pay a fixed rate of 5 percent on $5,000,000 based on the quarterly rate in three months. If interest rates are compounded quarterly, and the floating rate is 2 percent in three months, what is the payoff at the end of the sixth month?The investor will:A.make a payment of $37,500.B.receive a payment of $37,500.C.make a payment of $75,000.D.receive a payment of $75,000.Answer: A33.Consider the following 6x9 FRA ,Assume the buyer of the FRA agrees to acontract rate of 6.35% on a notional amount of 10 million USD ,Calculate the settlement amount of the seller if the settlement rate is 6.85%. Assume a 30/360 day count basis.A.–12,500B.–12,290C.+12,500D.+12,290Answer: B34.XYZ Corporation plans to issue a 10-year bond 6 months from now. XYZ wouldlike to hedge the risk that interest rates might rise significantly over the next 6 months. In order to effect this, the treasurer is contemplating entering into a swap transaction. Under the swap, she should:A.Pay fixed and receive LIBORB.Pay LIBOR and receive fixedC.Either swap (a or b above) will workD.Neither swap (a or b above) will workAnswer: A35.Consider the following plain vanilla swap. Party A pays a fixed rate 8.29% perannum on a semiannual basis (180/360), and receives from Party B LIBOR+30 basis point. The current six-month LIBOR rate is 7.35% per annum. The notional principal is $25M. What is the net swap payment of Party AA.$20,000B.$40,000C.$80,000D.$110,000Answer: C36.A trader executes a $420 million 5-year pay fixed swap(duration 4.433) with oneclient and a $385 million 10year receive fixed swap(duration 7.581) with another client shortly afterwards. Assuming that the 5-year rate is 4.15 % and 10-year rate is 5.38 % and that all contracts are transacted at par, how can the trader hedge his net delta position?A.Buy 4,227 Eurodollar contractsB.Sell 4,227 Eurodollar contractsC.Buy 7,185 Eurodollar contractsD.Sell 7,185 Eurodollar contractsAnswer: B37.Assume an investor with a short position is about to deliver a bond and has fourbonds to choose from which are listed in the following table. The last settlement price is $95.75 (this is the quoted futures price). Determine which bond is the cheapest-to-deliver.Bond Quoted Bond Price Conversion Factor1 99 1.012 125 1.243 103 1.064 115 1.14A. Bond 1B. Bond 2C. Bond 3D. Bond 4Answer: C38.What is the lower pricing bound for a European call option with a strike price of80 and one year until expiration? The price of the underlying asset is 90, and the1-year interest rate is 5% per annum. Assume continuous compounding of interest.A.14.61B.13.90C.10.00D. 5.90Answer: B39.According to Put-Call parity, buying a call option on a stock is equivalent to:A.Writing a put, buying the stock, and selling short bonds (borrowing).B.Writing a put, selling the stock, and buying bonds (lending).C.Buying a put, selling the stock, and buying bonds (lending).D.Buying a put, buying the stock, and selling short bonds (borrowing). Answer: D40.Jeff is an arbitrage trader, and he wants to calculate the implied dividend yield ona stock while looking at the over-the-counter price of a 5-year put and call (bothEuropean-style) on that same stock. He has the following data:• Initial stock price = USD 85• Strike price = USD 90• Continuous risk-free rate = 5%• Underlying stock volatility = unknown• Call price = USD 10• Put price = USD 15What is the continuous implied dividend yield of that stock?A. 2.48%B. 4.69%C. 5.34%D.7.71%Answer: C41.The current price of a stock is $55. A put option with $50 strike price thatexpires in 3 months is available. If N(d1)=0.8133, N(d2)=0.7779, the underlying stock exhibits an annual standard deviation of 25 percent, and current risk free rates are 3.25 percent, the Black-Scholes value of the put is closet to:A.$0.75B.$1.25C.$1.50D.$5.00Answer: A42.Which of the following is the riskiest form of speculation using options contracts?A.Setting up a spread using call optionsB.Buying put optionsC.Writing naked call optionsD.Writing naked put optionsAnswer: C43.A long position in a put option can be synthetically produced by:A.Long position in the underlying and a short position in a call.B.Short position in the underlying and a long position in a call.C.Long position in the underlying and a long position in a put.D.Short position in the underlying and a short position in a put.Answer: B44.ABEX Corporation common stock is selling for $50.00 per share. Both anAmerican call option and a European call option are available on ABEX common, and each have identical strike prices and expiration dates. Which of the following statements concerning these two options is TRUE?A.Because the American and European options have identical terms and arewritten against the same common stock, they will have identical optionpremiums.B.The greater flexibility allowed in exercising the American option willnormally result in a higher market value relative to an otherwise identicalEuropean option.C.The American option will have a higher option premium, because theAmerican security markets are larger than the European markets.D.The European option will normally have a higher option premium because oftheir relative scarcity compared to American options.Answer: B45.Put option values increase as a result of increases in which of the followingfactors?I.V olatilityII.DividendsIII.Stock PriceIV.Time to expirationA.I, II, and IV onlyB.I, III, and IV onlyC.II and IV onlyD.I and III onlyAnswer: A46.Your firm has no prior derivatives trades with its counterparty Super Bank. Yourboss wants you to evaluate some trades she is considering. in particular, she wants to know which of the following trades will increase your firm’s credit risk exposure to Super Bank:I.Buying a put optionII.Selling a put optionIII.Buying a forward contractIV.Selling a forward contractA.I and II onlyB.II and IV onlyC.III and IV onlyD.I, III, and IV onlyAnswer: D47.Which of the following statements about a floor is true?A.floor is a put option and protects against a fall in interest ratesB.floor is a call option and protects against a fall in interest ratesC.floor is a put option and protects against a rise in interest ratesD.floor is a call option and protects against a rise in interest ratesAnswer: A48.You are given the following information about a call option:• Time to maturity = 2 years• Continuous risk-free rate = 4%• Continuous dividend yield = 1%• N(d1) = 0.64Calculate the delta of this option.A.-0.64B.0.36C.0.63D.0.64Answer: C49.Call and put option values are most sensitive to changes in the volatility of theunderlying when:A.both calls and puts are deep in-the-money.B.both puts and calls are deep out-of-the-money.C.calls are deep out-of-the-money and puts are deep in-the-money.D.both calls and puts are at-the-money.Answer: D50.What is the reason for undertaking a Vega hedging? To minimize the:A.Possibility of counterparty default risk.B.Potential loss as a result of a change in the volatility of the underlying sourceof risk.C.Adverse effect due to the government regulation.D.Potential loss as a result of a large movement in the underlying source ofrisk.Answer: B51.Suppose an existing short option position is delta-neutral, but has a gamma of−600. Also assume that there exists a traded option with a delta of 0.75 and a gamma of 1.50. In order to maintain the position gamma-neutral and delta-neutral, which of the following is the appropriate strategy to implement?A. Buy 400 options and sell 300 shares of the underlying asset.B. Buy 300 options and sell 400 shares of the underlying asset.C. Sell 400 options and buy 300 shares of the underlying asset.D. Sell 300 options and buy 400 shares of the underlying asset.Answer: A52.W hich of the following is not an assumption of the BS options pricing model?A. The price of the underlying moves in a continuous fashionB. The interest rate changes randomly over timeC. The instantaneous variance of the return of the underlying is constantD. Markets are perfect,i.e.short sales are allowed,there are on transaction costs or taxes,andmarkets operate continuously.Answer: B53.If risk is defined as a potential for unexpected loss, which factors contribute to therisk of a short call option position?A.Delta, vega, rhoB.Vega, rhoC.Delta, vega, gamma, rhoD.Delta, vega, gamma, theta, rhoAnswer: C54.If risk is defined as a potential for unexpected loss, which factors contribute to therisk of a long straddle position?A.Delta, vega, rhoB.Vega, rhoC.Delta, vega, gamma, rhoD.Delta, vega, gamma, theta, rhoAnswer: B55.Long a call on a stock and short a call on the same stock with a higher strike priceand same maturity is called:A. A bull spreadB. A bear spreadC. A calendar spreadD. A butterfly spreadAnswer: A56.Consider a bullish spread option strategy of buying one call option with a $30exercise price at a premium of $3 and writing a call option with a $40 exercise price at a premium of $1.50. If the price of the stock increases to $42 at expiration and the option is exercised on the expiration date, the net profit per share at expiration (ignoring transaction costs) will be:A.$8.50B.$9.00C.$9.50D.$12.50Answer: A57.An investor sells a June 2008 call of ABC Limited with a strike price of USD 45for USD 3 and buys a June 2008 call of ABC Limited with a strike price of USD40 for USD 5. What is the name of this strategy and the maximum profit and lossthe investor could incur?A.Bear Spread, Maximum Loss USD 2, Maximum Profit USD 3B.Bull Spread, Maximum Loss Unlimited, Maximum Profit USD 3C.Bear Spread, Maximum Loss USD 2, Maximum Profit UnlimitedD.Bull Spread, Maximum Loss USD 2, Maximum Profit USD 3Answer: D58.Which of the following actions would be most profitable when a trader expects asharp rise in interest rates?A.Sell a payer swaption.B.Buy a payer swaption.C.Sell a receiver swaption.D.Buy a receiver swaption.Answer: B59.Initially, the call option on Big Kahuna Inc. with 90 days to maturity trades atUSD 1.40. The option has a delta of 0.5739. A dealer sells 200 call option contracts, and to delta-hedge the position, the dealer purchases 11,478 shares of the stock at the current market price of USD 100 per share. The following day, the prices of both the stock and the call option increase. Consequently, delta increases to 0.7040. To maintain the delta hedge, the dealer shouldA.sell 2,602 sharesB.sell 1,493 sharesC.purchase 1,493 sharesD.purchase 2,602 sharesAnswer: D60.A risk manager for bank XYZ, Mark is considering writing a 6 month American put optionon a non-dividend paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-atbitrage price of the option, Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The risk-free rate is 12% per annum with continuous compounding.What is the risk-neutral probability of the stock price going up in a single step?A. 34.5%B. 57.6%C. 65.5%D. 80.0%Answer: B61.Given the following 30 ordered simulated percentage returns of an asset, calculatethe VaR and expected shortfall (both expressed in terms of returns) at a 90% confidence level.-16, -14, -10, -7, -7, -5, -4, -4, -4, -3, -1, -1, 0, 0, 0, 1, 2, 2, 4, 6, 7, 8, 9, 11, 12, 12, 14, 18, 21, 23A.VaR (90%) = 10, Expected shortfall = 14B.VaR (90%) = 10, Expected shortfall = 15C.VaR (90%) = 14, Expected shortfall = 15D.VaR (90%) = 18, Expected shortfall = 22Answer: B62.What is the correct interpretation of a $3 million overnight VaR figure with 99%confidence level?A.The institution can be expected to lose at most $3 million in 1 out of next100 days.B.The institution can be expected to lose at least $3 million in 95 out of next100 days.C.The institution can be expected to lose at least $3million in 1 out of next 100days.D.The institution can be expected to lose at most $6 million in 2 out of next100 days.Answer: C63.In the presence of fat tails in the distribution of returns, VaR based on thedelta-normal method would (for a linear portfolio):A.underestimate the true VaRB.be the same as the true VaRC.overestimate the true VaRD.cannot be determined from the information providedAnswer: A64.Value at risk (VaR) measures should be supplemented by portfolio stress testingbecause:A.VaR does not indicate how large the losses will be beyond the specifiedconfidence level.B.stress testing provides a precise maximum loss level.C.VaR measures are correct only 95% of the time.D.stress testing scenarios incorporate reasonably probable events.Answer: A65.Assume we calculate a one-week VaR for a natural gas position by rescaling thedaily VaR using the square-root rule. Let us now assume that we determine the “true” gas price process to be mean reverting and recalculate the VaR. Which of the following statements is true?A.The recalculated VaR will be less than the original VaRB.The recalculated VaR will be equal to the original VaRC.The recalculated VaR will be greater than the original VaRD.There is no necessary relation between the recalculated VaR and the originalVaRAnswer: A66.If a portfolio with a VaR of 200 is combined with a portfolio with a VaR of 500,the VaR of the combination could be:I.Less than 200.II.Less than 500.III.More than 200.IV.More than 500.A.I and IIB.III and IVC.I, II and IVD.II, III and IVAnswer: D67.Consider the following portfolio consisting only of stock Alpha. Stock Alpha has amarket value of $635,000 and an annualized volatility of 28%. Calculate the VaR assuming normally distributed returns with a 99% confidence interval for a 10-day holding period and 252 business days in a year. The daily expected return is assumed to be zero.A.$56,225B.$69,420C.$82,525D.$96,375Answer: C68.Babson Bank is interested in knowing the risk exposure of their assets for variousprobabilities and time horizons. Babson has estimated that the annual variance (based on a 250 day year) of their $638 million asset portfolio is 151.29. If Z1%, Z5%, Z10%, are 2.32, 1.65, and 1.28, respectively, which of the following statements is false? The maximum dollar loss that can be expected to be exceeded:A.5% of the time in any six month period is $64.74 millionB.1% of the time on any given day is $11.51 millionC.10% of the time in any given quarter is $50.22 millionD.1% of the time in any given week is $25.25 millionAnswer: A69.The VaR on a portfolio using a 1-day horizon is USD 100 million. The VaR usinga 10-day horizon is:D 316 million if returns are not independently and identically distributedD 316 million if returns are independently and identically distributedD 100 million since VaR does not depend on any day horizonD 31.6 million irrespective of any other factorsAnswer: B70.If stock returns are independently, identically, normally distribution and the annualvolatility is 30%, then the daily VaR at the 99% confidence level of a stock market portfolio is approximately。

FRM一级模考题(二)

FRM一级模考题(二)

FRM一级模考题(二)1. Based on a sample size of 100 and sample mean of $30, you estimate a 95%confidence interval for the mean weekly soft drink expenditures of students at alocal college. Your estimate of the confidence interval is $26.77 to $33.23. Sinceyou knew the standard deviation beforehand, your confidence interval was basedon a standard deviation closest to:A. 1.65.B. 6.59.C. 11.53.D. 16.48.Solution : DWith a known variance, the 95% confidence interval is constructed asSo you know that Solving for a provides 16.48.2. Consider a 1-year European call option with a strike price of $27.50 that iscurrently valued at $4.10 on a $25 stock. The 1-year risk-free rate is 6%. Whichof the following is closest to the value of the corresponding put option?A. $0.00B. $3.12.C. $5.00.D. $6.60.Solution : CUsing put-call parity: p = c + Xe-rT - So = 4.10 + 27.50e-0.06 - 25 = $5.00.3. A binomial interest-rate tree indicates a 1-year spot rate of 4%, and the price of the bond if rates decline is 95.25 and 93.75 if rates increase. The risk-neutral probability of an interest rate increase is 0.55. You hold a call option on the bond that expires in one year and has an exercise price of93.00. The option value is closest to:A. 1.17B. 0.97C. 1.44D. 1.37Solution : DThe call has payoff of 95.25 -93 = 2.25 if rates decline and payoffof 93.75- 93= 0.75 if rates increase. The expected discounted value of the payoffs is [0.55(0.75)+ 0.45(2.25)]/1.04 = 1.37.4. Cooper Industries is the pay-fixed counterparty in an interest rate swap. Theswap is based on a notional value of $2,000,000 and pays a floating rate basedon the 6-month Hong Kong Interbank Offered Rate (HIBOR). Cooper pays afixed rate of 7% semiannually. A swap payment has just been made. The swaphas a remaining life of 18 months, with pay dates at 6, 12, and 18 months. SpotHIBOR rates are shown in the table below.The value of the swap to Cooper Industries is closest to:A. $0.B. $6,346.C. $17,093.D. $72,486.Solution : CThe fixed payments made by Cooper are (0.07 / 2) x $2,000,000 = $70,000. Thepresent value of the fixed payments == $67,762 + $65,398 + $1,849,747 = $1,982,907The value of the floating rate payments received by Cooper at the payment date is thevalue of the notional principal, or $2,000,000.The value of the swap to Cooper Industries is ($2,000,000 - $1,982,907) =$17,093.5. A stack-and-roll hedge as described in the Metallgesellschaft case is bestdescribed as:A. buying futures contracts of different expirations and allowing them to expirein sequence.B. buying futures contracts of different expirations and closing out the positionshortly before expiration.C. using short-term futures to hedge a long-term risk exposure by replacingthem with longer-term contracts shortly before they expire.D. using short-term futures contracts with a larger notional value than thelong-term risk they are meant to hedge.Solution : CA stack is a bundle of futures contracts with the same expiration. Over time, a firmmay acquire stacks with various expiry dates. To hedge a long-term risk exposure, a firmwould close out each stack as it approaches expiry and enter into a contract with a moredistant delivery, known as a roll. This strategy is called a stack-and-roll hedge and isdesigned to hedge long-term risk exposures with short-term contracts. Using short-termfutures contracts with a larger notional value than the long-term risk they are meant tohedge could result in "over hedging" depending on the hedge ratio.。

FRM一级每日一练

FRM一级每日一练

FRM一级每日一练1、Consid er a convertible bond that is trading at a conversion premium of 20 percent. If the value of the underlying stock rises by 25 percent, the value of the bond will:A.Rise by less than 25%.B.Rise by 25%.C.Rise by more than 25%.D.Remain unchanged.Correct answer: A解析:The convertible bond implicitly gives bondhol d ers a call option on the und erlying stock. The delta of this option will vary between 0 (when the option is extremely out of t e money) and 1 (when the option is extremely in the money). In this case, the bond is trading at a conversion premium of 20% so the delta must be somewhere between zero and one, and hence the price of the convertible bond will rise by less than the price of the und erlying stock.2、If a cash fl ow of $10,000 in two years’ time has a PV of $8,455, the annual percentage rate, assuming continuous compounding is CLOSEST to:A. 8.13%.B. 8.39%.C. 8.75%.D. 8.95%.Correct answer: B解析:Continuously compounded rate = In (FV/PV)/N = In (10000/8455)/ 2 =8.39%.3、The current values of a firm's assets and liabilities are 200 million and 160 million respectively. If the asset values are expected to grow by 40 million and liability values by 30 million within a year and if the annual standard deviation of these values is 50 million, the distance from default in the KMV model woul d be closest to:A. 0.8 standard deviations.B. 1.0 standard deviations.C. 1.2 standard deviations.D. Cannot not be determined.Correct answer: B解析:Distance from d efault = (Expected value of assets - Expected value of liabilities) / Standard deviation = (240 ~ 90)/ 50 = 1.0.4、What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yiel d to maturity of 12.51 percent?A. 12.00%.B. 11.49%.C. 12.51%.D. 12.14%.Correct answer: D解析:The semiannual-pay bond equival ent yield of an annual-pay bond = 2 * [(1 + yield to maturity on the annual-pay bond) 0.5 - 1] = 12.14%.5、You want to test at the 0.05 l evel of significance that the mean price of luxury cars is greater than $80,000. A rand om sampl e of 50 cars has a mean price of $88,000. The population standard deviation is $15,000. What is the alternative hypothesis?A. The population mean is greater than or equal to $80,000.B. The population mean is l ess than $80,000.C. The population mean is not equal to $80,000.D. The population mean is greater than is $80,000.Correct answer: D解析:The alternate hypothesis is the statement which will be accepted if the null hypothesis is proven wrong. Therefore, we make whatever we are trying to test as the alternate hypothesis - in this case that the mean price of luxury cars is greater than $80,000, and the null hypothesis as the opposite ( the mean price of luxury cars is less than or equal to $80, 000). This probl em is a common example of how statisticians establish hypotheses by proving that the opposite (i.e. the null hypothesis) is false.6、Suppose that Gene owns a perpetuity, issued by an insurance company that pays $1,250 at the end of each year. The insurance company now wishes to replace it with a decreasing perpetuity of $1,500 decreasing at 1% p.a. without any change in the payment dates. At what rate of interest (assuming a flat yiel d curve) woul d Genebe indifferent between the choices?A. 4%.B. 5%.C. 6%.D. 9%.Correct answer: B解析:1,250 / r = 1,500 / (r + 1%) or, 1,250 x (r + 1 %) = 1,500 x r or, r = 12.5 / (1, 500 - 1,250) = 5%.7、Which of the foll owing is considered to be the responsibility of the legal risk manager?I. Inad equate d ocumentation of OTC d erivatives transactions.II. The enforceability of netting agreements in bankruptcy.III. Default on interest and principal payments.A.I only.B.II only.C.I and II only.D.I,II, and IIICorrect answer: D解析:Legal risk management is concerned with adequate documentation, public filings, compliance with regulatory entities, and some borrower impositions. The l egal manager is also involved in deciding if default has occurred and, of so, assisting with the enforcement of netting agreements.8、An analyst has constructed the foll owing t-test for a portfolio of financial securities whose returns are normally distributed:Number of securities = 40.HO: Mean return >=18 percent.Significance level = 0.1.What is the rejection point for this test?A. 1.304B. 1.684C. 2.021D. 2.023Correct answer: A解析:This is a one-tailed test with 39 degrees of freed om and significance l evel of 0.1. Looking up the Student's - distribution for DF = 39 and p = 0.1, we get the critical value or 1.304.9、Consid er an A-rated institution that funds itself in the wholesale market at LIBOR + 90bps. Which of the foll owing is the most attractive instrument for this firm to take exposure to an AAA – corporate issuer?A. Credit swap.B. Floating rate note.C. Credit-linked note.D. Fixed coupon bond.Correct answer: A解析:This firm has a fairly high funding cost. Funding itself at 90 bps over LIBOR and leading to AAA names at around LIBOR is a l oss making strategy, which rul es out the notes and the bond, The only way this firm can make money is by selling credit protection via a credit swap that does not require it to make a physical investment,10、Which of the foll owing statements about the Treynor ratio is correct?A. the Teynor ratio consid ers both systematic and unsystematic risk of a portfolio.B. the Teynor ratio is equal to the excess return of a portfolio over the risk - free rate divided by the total risk of the portfolio.C. the Teynor ratio can be used to appraise the performance of well - diversified portfolio.D. the Teynor ratio is derived from portfolio theory since it assesses a portfolio’s excess return relative to its risk.Correct answer: CA is incorrect - Treynor ratio consid ers only systematic risk of a well - diversified portfolio.B is incorrect - Treynor ratio denominator is beta of the portfolio.C is correct - this statement is correctD is correct - Treynor ratio is derived from CAPM and not portfolio theory.参与FRM的考生可按照复习计划有效进行,另外高顿网校官网考试辅导高清课程已经开通,还可索取FRM 考试通关宝典,针对性地讲解、训练、答疑、模考,对学习过程进行全程跟踪、分析、指导,可以帮助考生全面提升备考效果。

V3_150420_FRM一级百题_Part_2_梁震宇

V3_150420_FRM一级百题_Part_2_梁震宇

4.
With regard to futures trading, which of the following statements best describe the principle of substitution? A. The clearinghouse changes the designated currency before settlement. B. The exchange takes on the role of the counterparty. C. The clearinghouse takes on the role of the counterparty. D. The exchange can substitute cash for a given commodity at its discretion.
3.
Client A buy one July wheat contract from Client B. On the same day, client B buy the same wheat
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专业·领先·增值
contract from Client C. Assuming open interest started out at Zero, and no delivered were made, what is the addition to open interest for July wheat contracts? A 0. Answer: B Open interest includes contracts not yet liquidated either by an offsetting futures market transaction or delivery. When Client A buy one contract from Client B, the current open interest is one, assuming neither party started with a position in that contract. When Client B buys the same contract from Client C, Client B closes out their short transaction with an offsetting long transaction. The open interest would not change because Client C would simply take the place of Client B. Client A would still be long one contract, and now Client C would be short one contract. Thus, open interest would be one. B 1. C 2. D 3.

FRM一级模考

FRM一级模考

FRM一级模拟题1 . What are the differences between Forward Rate Agreements (FRAs) and Eurodollar Futures?I FRAs are traded on an exchange while Eurodollar Futures are not.II FRAs have better liquidity than Eurodollar Futures.II FRAs have standard contract sizes while Eurodollar Futures do not.A . I onlyB . I and II onlyC . II and III onlyD . None of the aboveAnswer: DEurodollar futures contracts are highly liquid, exchange traded contracts on short term interest rates with standardized contract sizes and terms. FRAs are traded over-the-counter.2 . Consider the following 6x9 FRA, Assume the buyer of the FRA agrees to a contract rate of 6.35% on a notional amount of 1 0 million USD, Calculate the settlement amount of the seller if the settlement rate is 6.85%. Assume a 30/360 day count basis.A. -12,500B. -12,290C. +12,500D. +12,290Answer: BThe seller of an FRA agrees to receive fixed. Since rates are now higher than the contract rate, this contract must show a loss for the seller. The loss is $10,000,000 X (6.85%- 6.35%) x (90860) = $12,500 when paid in arrears (i.e., in 9 months). On the settlement date (i.e., brought forward by 3 months), the loss is $12,500/(1 + 6. 85% x 0.25) = $12,290.3.Consider the following 3x6 FRA Assume the buyer of the FRA agrees to a contract rate of4.87% on a notional amount of 25 million USD Calculate the upfront settlement amount of the 'buyer if the settlement rate is 4.37%. Assume a 30/360 day count basis.A. -31,250B. -30,912C. +31,250D. +31,912 'Answer: B .The buyer of an FRA agrees to pay fixed. Since rates are now lower than the contract rate, this contract must show a loss for the buyer. The loss is $25,000,000 x (4.87% - 4.37%) x (90/360) = $31250, when paid in arrears (i.e., in 6 months). On the settlement date (i.e., brought forward by 3 months), the loss is $31250/(1 + 4.37% x 0.25) =. $30912.4 . A long position in a FRA 2x5 is equivalent to the following positions in the spot marketA . Borrowing in 2 months to finance a 5-month investment.B . Borrowing in 5 months to finance a 2-month investment. .C . Borrowing half a loan amount at 2 months and the remainder at 5 months.D . Borrowing in 2 months to finance a 3-month investment.Answer: DA 2x 5 FRA is equivalent to a commitment to borrow in 2 months (60 days) to finance a 3-month (90-day) investment. Note: According to GARP 's answer key, the correct answer is "b ", but webelieve that 's a mistake.5 . Corporates normally use FRAs to:A. Lock-in the cost of borrowing in the futureB. Lock-in the cost of lending in the futureC. Hedge future currency exposuresD. Create future currency exposuresAnswer: AUsually, corporates use FRAs to lock-in the cost of borrowing in the future。

frm一级2020年考试答案

frm一级2020年考试答案

frm一级2020年考试答案1. 根据FRM一级2020年的考试内容,以下哪项不是风险管理的核心原则?A. 识别风险B. 评估风险C. 接受风险D. 转移风险答案:C2. 在FRM一级考试中,关于市场风险的描述,以下哪项是错误的?A. 市场风险包括股票和债券价格的波动B. 市场风险可以通过分散化投资来降低C. 市场风险是不可避免的D. 市场风险仅包括利率风险答案:D3. 在FRM一级考试中,关于信用风险的以下说法,哪项是正确的?A. 信用风险仅与企业债券相关B. 信用风险可以通过信用衍生品来对冲C. 信用风险与个人信用无关D. 信用风险是银行面临的最大风险答案:B4. 在FRM一级考试中,关于操作风险的以下说法,哪项是错误的?A. 操作风险包括欺诈行为B. 操作风险可以通过内部控制来降低C. 操作风险与市场风险无关D. 操作风险可以通过购买保险来转移答案:C5. 在FRM一级考试中,关于流动性风险的以下说法,哪项是正确的?A. 流动性风险仅与银行有关B. 流动性风险是指资产无法在不显著影响其价格的情况下迅速出售的风险C. 流动性风险可以通过持有大量现金来消除D. 流动性风险与市场流动性无关答案:B6. 在FRM一级考试中,关于风险价值(VaR)的以下说法,哪项是错误的?A. VaR是一种风险度量工具B. VaR可以预测极端市场条件下的潜在损失C. VaR通常用于市场风险的度量D. VaR不能用于信用风险的度量答案:D7. 在FRM一级考试中,关于压力测试的以下说法,哪项是正确的?A. 压力测试是一种定性风险评估方法B. 压力测试用于评估极端市场条件下的风险暴露C. 压力测试不能提供风险的量化度量D. 压力测试与情景分析无关答案:B8. 在FRM一级考试中,关于资本充足性的以下说法,哪项是错误的?A. 资本充足性是指银行持有足够的资本以吸收潜在损失B. 资本充足性可以通过提高资本比率来增强C. 资本充足性与银行的信用评级无关D. 资本充足性是银行稳健经营的重要指标答案:C结束语:以上是FRM一级2020年考试的部分答案,希望对准备考试的同学有所帮助。

FRM一级模考

FRM一级模考

FRM一级模拟题1 .2 . A risk manager has been requested to provide some indication of accuracy of a Monte Carlo simulation. Using l,000 replications of a normally distributed variable S, the relative error in the one-day 99% VaR is 5%. Under these conditions,A. Using l,000 replications of a long option position on S should create a larger relative error.B. Using I 0,000 replications should create a larger relative error.C. Using another set of l,000 replications will create an exact measure of 5.0% for relative error.D. Using l,000 replications of a short option position on S should create a larger relative error.Answer: DShort option positions have long left tails, which makes it more difficult to estimate a left-tailed quantile precisely. Accuracy with independent draws increases with the square root of K. Thus increasing the number of replications should shrink the standard error, so answer b. is incorrect.3 . In pricing a derivative using the Monte Carlo method, we need to stimulate a reasonable number of paths for the price of the underlying asset. Suppose we use a simple model for the return of the underlying asset:Where drift and vol are known parameters and At is a step size. The generation of each path requires a number of steps. Which of the following describes the correct procedure?A. Generate a random number from a normal distribution N (0, 1), use the cumulative normal function to get e (t), which will be fed into the model to get y(t). Repeat the same procedure untilB. Generate a random number from a normal distribution N (0, 1), use the inverse normal function to get e (t), which will be fed into the model to get y (t). Repeat the same procedure until you get the full desired path.C. Generate a random number from a uniform distribution defined in [0, 1], use the cumulative normal function to get e (t), which will be fed into the model to get y(t). Repeat the same procedure until you get the full desired path.D. Generate a random number from a uniform distribution defined in [0, 1], use the inverse cumulative normal function to get e (t), which will be fed into the model to get y(t). Repeat the same procedure until you get the full desired path.Answer: D4 . One advantage of the Brennan and Schwartz model over the Cox-Ingersoll-Ross model for modeling interest-rate dynamics is that the Brennan and Schwartz model:A . gives attention to the mean reversion of interest rates.B . is a more effective method for dealing with complex, leveraged portfolios.C . gives attention to interest-rate volatility:D . allows interest-rate volatility to decline as rates fall.Answer: BThe Brennan and Schwartz model is more effective when fixed-income portfolios become complex.。

20111110 FRM一级模考题第二套答案

20111110 FRM一级模考题第二套答案

FRM一级模考试题(二)——答案1. Answer: DThe Monte Carlo approach allows for whatever relationships the V AR modeler would like to take into account It is the most flexible method for generating V AR; however, it comes at a cost of requiring substantial computing power, especially when the model used to generate portfolio relationships is complex.2. Answer: ATo obtain the d(1.0) discount factor, first solve for d(0.5), In the equation below, the price for Bond A is equated to its terminal cash flow in six months, which is the principal plus the semiannual coupon of $3.00.101.182 = 103.00×d(0.5)d(0.5) = 0.9823Next use the price and cash flows of Bond B to calculate the d(l .0) discount factor. The cash flow in six months is the semiannual coupon of $6.00 and is discounted by d(0.5). The cash flow in one year is the principal plus the semiannual coupon of $6.00.102.341 = 6.00×d(0.5) + 106.00×d(1.0)102.341 = 6.00×0.9823 + 106.00×d(1.0)d(1.0) = 0.90993. Answer: CStop-loss limits are easy to calculate and can be aggregated across assets. Notional limits are easy to calculate but cannot be aggregated across assets. Exposure limits are difficult to calculate and cannot be aggregated across assets.4. Answer: AAccording to Standards 2.1 and 2.2. GARP Members shall act fairly in all situations and must fully disclose any actual or potential conflict to all affected parties. GARP Members should also make full and fair disclosure of all matters that could reasonably be expected to impair independence and objectivity or interfere with respective duties to their employer, clients, and prospective clients. Harrow should disclose to Dominion conflicts that reasonably could be expected to interfere with his independence and objectivity. Both Harrow’s relationship with the president of Miracle and his ownership of a substantial dollar amount of Wonder’s shares represent a potential conflict requiring prompt disclosure to Dominion.5. Answer: AThe level of significance is the probability of rejecting the null hypothesis when it is true. The null hypothesis will be rejected if the z-statistic is greater than 1.645.6. Answer: CAny security with a rating below BBB by S&P or Baa by Moody’s is a speculative or non-investment grade instrument.A strap is betting on volatility in a bullish market since it pays off more on the upside.8. Answer: ALTCM focused on relative value, credit spreads, and equity volatility. Relative value strategies involve arbitraging price differences among similar securities and profiting when the prices converge. Credit spread strategies are predicated on the notion that risk premiums, or credit spreads, will move in a certain direction. LTCM was forecasting that large credit spreads would revert back to lower historical levels. Equity volatility strategies are based on a similar notion of volatility reverting back to historical levels.9. Answer: D=== The researcher is correct that a Standard deviation400; 40040possible consequence of increasing the sample size is sampling more than one population. In addition, increasing sample size will increase its costs. The need for additional precision must be balanced with cost and the risk of sampling more than one population.10. Answer: CUsage given default is not observable (compared to outstandings and commitments. for example). The most important factor in determining loss given default is the asset’s seniority claim. The quality of the underlying collateral is the second most important factor.11. Answer: DAll three statements are correct.12. Answer: CThis is an example of basis risk, the risk that the price of a hedging instrument and the price of the asset being hedged are not perfectly correlated. Basis risk is one of the subtypes of market risk.13. Answer: CSince you are long the portfolio, the appropriate strategy is to short the futures.N = - (75,000,000×9) / (104,406.25×8) = - 808.14. Rounding up to the nearest whole number means that you should short 809 futures contracts.14. Answer: DThe expected value of the portfolio after two years is: (10)(1 - 0.03)(1 - 0.03) ($1,000,000) = $9,409,000. Therefore, the expected cumulative loss is: $10,000,000 - $9,409,000 = $591,000.15. Answer: BIndemnified bonds will hedge adverse internal firm events, such as a large underwriting loss for an insurance company, so Statement II is incorrect. Catastrophe options are traded on the Chicago Board of Trade so Statement III is incorrect.Statements I and II compare the futures to the loan instead of the financing. A perfect hedge on actively traded securities will usually converge so Statement III is incorrect.Statement IV is irrelevant in this situation.17. Answer: CFields violated the Professional Integrity and Ethical Conduct section of the Code of Conduct by misrepresenting the bonds as being safe and secure when in fact they were investing in risky projects and backed only by the revenue generated from those projects. According to the Code, CARP Members shall not knowingly misrepresent details relating to analysis, recommendations, actions, or other professional activities.18. Answer: AThe daily delta-normal V AR is calculated as [Rp — (z)(σ)](value of portfolio). where Rp is the expected 1-day return on the portfolio, z is the z-value corresponding to the desired level of significance, and σis the standard deviation of 1-day, which is calculated as the annual standard deviation divided by the square root of the number of trading days=−=−15%0.0095;217,350[(0.10/250)(2.33)(0.0095)]10,000,00019. Answer: DInvestors achieve the best combinations of risk and return by holding some combinationof the risk-free asset and the market portfolio of risky assets.20. Answer: DAssuming no default risk, the domestic return is 6.25%. The return on the UK investments, however, is equal to the amount invested today (USD25,000,000) / (USD1.642/GBP) = GBP15,225,335, which turns into GBP15,225,335×1.07 = GBP16,291,108 one year from now. Since the forward contract guarantees the exchange rate in the future, that amount of GBP translates into GBP16,291,108×USD1.5800/GBP = USD25,739,951. This is a dollar return to the bank of USD25,739,951/USD25,000,000 - 1 = 2.96%. Hence, the weighted average return to the bank’s investments is (0.5)(6.25%) + (0.5)(2.96%) = 4.61%.21. Answer: DThe classical linear regression model assumes homoskedasticity, which means that the variance does not vary across the sample and would not depend on the value of the dependent variable.22. Answer: BEconomic capital = EV - P(c), where EV is the expected value of the portfolio and P(c) is the portfolio value at the “c” percent confidence level. Thus, $350 million - $250 million = $100 million.23. Answer: DThe rate at which the V AR increases is determined in part by the mean of the distribution. TheV AR increases when the confidence level increases. If the return distribution has a mean equal to zero, then the V AR rises with the square root of the holding period. If the return distribution has a mean greater than zero, then the V AR rises at a lower rate and will eventually decrease.24. Answer: DN = 2×22; PMT = 40/2; FV = 1,000; I/Y = 5/2; CPT →PV = 867.481 = V 0N = 2×22; PMT = 40/2; FV = 1,000; I/Y = 5.05/2; CPT →PV = 861.484 = V +N = 2×22; PMT = 40/2; FV = 1,000; I/Y = 4.95/2; CPT →PV = 873.534 = V -02202873.534861.4842(867.481)Convexity 258.22()(867.481)(0.0005)V V V V y −++−+−===Δ25. Answer: CAll of the statements are correct except for the one relating to SIMEX. Nick Leeson was eligible to trade on the SIMEX.26. Answer: AThe current value of the contract per ton by the formula:0.04(5/12)$110($105)$6.735rtt t t V S Ke V e −−×=−=−=For a 100-ton contract, the value would be $673.5527. Answer: BThe z-statistic equals:(x – μ)/σwhere x is the value for a randomly selected observation from the population, it is the mean value for the population, and σ is the standard deviation of the population. Therefore, as indicated by the formula, the z-statistic is the number of standard deviations x is from the mean (Ecko is correct).According to the normal distribution, 95% of the observations lie within 196 standard deviations of the mean, which implies that 95% of the z-statistics lie within plus and minus 1.96. Therefore, 5% of the z-statistics lie above plus 1.96 and below minus 1.96 and since the normal distribution is symmetrical, then 2.5% of the z-statistics lie below minus 1.96. As a result, 97.5% (not 95%) of the z-statistics lie above minus 1.96. (Charles is not correct).28. Answer: AMetallgesellschaft implemented a stack-and-roll hedging strategy, which uses short-term futures contracts to hedge long-term risk exposure. The stack-and-roll hedge strategy proved ineffective due to interim funding cash outflows created by margin calls and other factors. No offsetting interim cash inflows were available on their long-term customer contracts, creating a liquidity crisis that was exacerbated by their size of their futures positions in relation to the liquidity of the market. However, many economists believe that such a hedging strategy is fundamentally sound.Income bonds pay at most the specified interest, but they may pay less if the company’s income is not sufficient. Participating bonds pay at least the specified interest rate but may pay more if the company’s profits increase. Zero-coupon bonds pa the face value/principal at maturity but is not a cash payment. It is an implied rate of return earned by the bondholder by purchasing the bond at a discount to face value and receiving the full face value at maturity. The interest paid on floating-rate bonds is generally linked to some widely used reference rate such as LIBOR. Although the amount of interest may decrease with LIBOR, the payment is still technically at the specified interest.30. Answer: A(0.0410.02)(0.25)1,0151,020.34e −=31. Answer: ASwaps have a lower value than loans of the notional amount. Loans have exposure to the repayment of principal, whereas swaps counterparties will have exposure only to the difference between the fixed and floating rates times the notional amounts. Statements II and III are irrelevant in this situation.32. Answer: BThe institution is paying USD and receiving JPY so the value of this swap will equal the current exchange rate times the value of the JPY portion minus the value of the USD portion.-0.0050.0052-0.030.032The JPY portion of this swap=70e 3,570JPY3,604,130,000The USD portion of this swap=5.4e 125.4USD123,340,000e e −×−×+=+=The value to the institution = [JPY3604.13 million / (JPY120/USD)] — USD123.34 million = - USD93.3 million.33. Answer: DSubordinated debenture bonds have a claim that is at the bottom of the list of creditors if the issuer goes into default. They are bonds that are, unsecured and have another unsecured bond with a higher claim above them. This means that the issuer has to offer a higher interest rate on the subordinated debentures.In contrast, convertible debentures give the bondholder the right to convert the bond to common stock and this feature will lower the interest rate paid. The cost to the issuer, however, is the possibility of increased dilution of that stock. Equipment trust certificates (ETCs) are generally considered the most secure type of bond since the underlying assets are actually owned by the trustee and rented to the borrower; the greater security lowers the required rate of interest to be paid. Guaranteed bonds are those issued by one company that are guaranteed by other companies. Similar logic as ETCs regarding the lower rate of interest paid by the issuer but there is no guarantee that the issue is free of default risk since the risk will depend on the ability of the guarantor(s) to satisfy all obligations.Large institutions can potentially profit from STRIP mispricings relative to the underlying bonds. They can do this by either buying Treasuries and stripping them or reconstituting STRIPS. Because of the cost involved with stripping/reconstituting, investors generally pay a premium for zero-coupon bond35. Answer: BVega is an option’s sensitivity to changes in volatility of the underlying stock. Vega is close to zero for deep in- or deep out-of-the-money puts and calls. Rho is an option’s sensitivity to changes in interest rates and tends to be the highest for in-the-money calls and puts. Increases in rates will cause larger increases for in-the-money calls, but larger decreases for in-the-money puts. Given this info, Statement II will work because it is a deep in-the-money call, and Statement III will work because it is a short position in a deep in-the-money put. Statement I will not work because it is an at-the-money call (which would be highly sensitive to vega). and Statement IV will not work because rising rates will have little impact on the position since it is an out-of-the-money put.36. Answer: CBusinessman’s risk refers to bonds with a rating at the bottom rung of the investment- grade category (Baa or EBB) or at the top end of the speculative-grade category (Ba and BBB). Therefore, the A, B, and Caa ratings do not fall into this definition.37. Answer: BThe population variance is known (in this case 100), so the standard error of the sample mean is0.67==38. Answer: B{[p×98.45] + [(1 - p)×96.00]} / [1 + (0.025 /2)] = 97.00p = 0.9 and (1 - p) = 0.139. Answer: ABased on the CAPM, the portfolio should earn: E(R) = 0.05 + 0.7(0.10) = 12%. On a risk-adjusted basis, this portfolio lies on the security market line (SML) and thus is earning the proper risk-adjusted rate of return.40. Answer: CStatements I and IV are correct. The daily delta-normal V AR is calculated as [Rp - (z) (σ)]×(Value of Portfolio), where Rp is the expected 1-day return on the portfolio, z is the z-value corresponding to the desired level of significance, and σis the standard deviation of 1-day.-1,907500 = [0.0004 - (2.05)(0.0095)] 100,000,000The historical simulation V AR for 2% is the 5th lowest return, which is -2.59%; therefore, the correct V AR is:-2,590,000 = (-0.0259)(l00,000,000)41. Answer: CThe bank lent USD5,000,000×1.12 = EUR5,600,000 to its German client. At the end of the year, the client repaid, with interest, 5,600,000×1.06 = EUR5,936,000, which was then worth USD5,936,000/0.84 = USD7,066,667. The bank repaid USD5,000,000×1.045 = USD5,225,000, including interest on its borrowed money, which generated a return of (7,066,667 - 5,225,000)/ 5,000,000 = 36.8% on the loan. Alternate method: (1.12/0.84)(1.06) - 1.045 = 0.368.42. Answer: BTo find the correct price of the futures contract, we use the formula:F 0,T ≥S 0e rT +λ(0,T)F 0,T = 0.325e 0.03×3/12+[0.002+0.002(1.0025)+0.002(1.025)2] = 0.3335Since the actual futures price of 0.3368 is higher than the correct price, there is an arbitrage opportunity that can be exploited by selling the overpriced contract. The investor would want to sell the futures contract, borrow at the risk-free rate, and buy the spot asset. The investor would pay off the loan in three months with the proceeds from delivering the cotton against the futures and would have a risk-free profit.43. Answer: CThe delta of an option that is deep in-the-money is close to 1. The addition of the 2,500 long options to bring about gamma neutrality disturbed the original delta neutral position of the portfolio. Since 2,500 options have been added, (2,500)(l.0) = 2,500 shares of the underlying must be sold to restore delta neutrality to the portfolio. Note that answer A could be correct only if the options were at-the-money where delta is 0.5.44. Answer: DNote that the recovery rate is given as 40% which implies the LGD is 60%. We can calculate adjusted exposure as follows.Adjusted exposure = OS + (COM U - OS) UGD= $2,000,000 + ($8,000,000)×(0.60)= $6,800,0006,800,000$353,338UL AE UL ===45. Answer: BAccording to Chebyshev’s inequality, the proportion of the observations within 3, which is k, standard deviations of the mean is at least 1- (1/k 2) = 1- (1 / 32) = 0.89 or 89%.This holds for any distribution, regardless of the shape.46. Answer: BYasuo Hamanaka, the lead copper trader for Sumitomo, established a dominant long position in futures contracts and simultaneously purchased large quantities of physical copper. As the futurecontracts approached delivery, the party with the short position would find little physical copper available for delivery and would be forced to either pay a large premium for physical copper or unwind their short position at unfavorable prices by taking an offsetting long futures position. Either way, the price of copper and/or copper futures would rise and create handsome profits.47. Answer: AA binomial random variable has an expected value or mean equal to np and variance equal to np ×(1 - p). Mean = 12×(0.4) = 4.8; variance = 12×(0.4)×(l - 0.4) = 2.88.48. Answer: CEuropean options can only be exercised at maturity American call options are more likely to be exercised when dividends are large and expiration is close. American put options are less likely to be exercised when dividends are large.49. Answer: DThis is an out-of-the-money covered call. The stock can go up $2 to the strike price, and then the writer will get $3 for the premium. Thus, the maximum profit is $5..50. Answer: AThe change in asset value would be a decrease of [($500,000,000)(7)(0.005)] = $17,500,000, whereas the change in liability value would be a decrease of [($400,000,000)(5)(0.005)] = $10,000,000. The net effect would be a decline in equity value of $7.5 million.51. Answer: DThe trader buys the underlying stock if the stock price rises above $40 to protect against the call being exercised against them. The trader sells the stock if the price falls below $40. The term “stop-loss” refers to protecting the naked position in the option. This strategy is simplistic in that the trader cannot be sure as to when the stock price will rise above the strike price.52. Answer: DCalculate the price of the February (6-month) and May (9-month) forward prices using the following pricing formula which accounts for storage costs:(RF+λ)T0,T 0(0.080.0891)(0.50)0,0.50(0.080.0891)(0.75)0,0.75storage costs(λ)=0.45/5.05=8.91%forward prices(F )=S e 5.05$5.505.05$5.73F e F e ++====The soybean farmer would only be willing to store half the crop until February if the February futures contract price is at Least $5.50/bushel. Similarly, the soybean farmer would only be willing to store the other half of the crop until May if the May futures contract price is at least $5.73/bushel.53. Answer: B91$10,000[1(0.068)($9,828.11360−=54. Answer: DPeople risk relates to the risk associated with fraud perpetrated by internal employees and/or external individuals. It does not relate to incompetnce and lack of suitable training. Presettlement risk is lower than settlement risk because the former allows for offsetting of payments while the latter requires settlement of the full value of payments. Non-directional risks have non-linear exposures to changes in economic or financial variables which is clearly the case with options.55. Answer: CThe firm owns its own production resources and sells wholesale with long-term contracts at fixed prices, so it does not face commodity price risk in acquiring crude oil. Hence, a commodity swap based on oil will not reduce earnings volatility. The firm has issued floating rate notes, however, so its earnings will be sensitive to changes in interest rates. Entering into the pay-fixed side of an interest-rate swap would reduce this source of earnings volatility.56. Answer: Baverage return on portfolio - risk-free rate Sharp ratio(SR)=standard deviation 13.75-5.35(SR)==0.49716.9average return on portfolio - risk threshold Sortino ratio(SOR)=semi-standard deviation 13.75(SOR)=-5.35=0.61213.72average return on portfolio - average return on benchmark information ratio(IR)=tracking error13.75-12.36(IR)==0.1927.2157. Answer: DThe t-statistics for the intercept and coefficient on are significant as indicated by the associated p-values being less than 0.05: 0.0007 and 0.0004 respectively. Therefore, H 0: B 0 = 0 and H 0: B 2 = 0 can be rejected. The F-statistic on the ANOV A table has a p-value equal to 0.0012; therefore, H 0: B 1= B 2 = 0 can be rejected. The p-value for the coefficient on X 1i is greater than five percent; therefore, H 0: B 1 = 0 cannot be rejected.58. Answer: DAll of the statements are correct. Although the risk of their positions was quite small in theory, the size of their positions resulted in them selling at large discounts. They borrowed at favorable terms in their repurchase agreements, but the firm had high leverage which magnified the degree of their losses.59. Answer: BGARP Members shall make full and fair disclosure of all matters that could reasonably be expected to impair independence and objectivity or interfere with respective duties to their employer, clients, and prospective clients.60. Answer: ABecause the options dealer has sold options, the dealer will have a negative gamma and negative vega exposure. When sold, the options are at-the-money, but over time the options will move in or out of the money. Gamma and vega decline as the options move away from an at-the-money position, so gamma and vega will have less of an impact on the value of the option over time. Hence the correct answer is both I and II.61. Answer: ACorrelation of risk factors is included and is therefore not a problem.62. Answer: D We use Bayes’ Theorem to solve this problem(/)()(/)(/)()(/)()P B A P A P A B P B A P A P B not A P not A ×=×+× Or put another way:prob drop given default prob of default total possible outcomes× Total possible outcomes:(prob drop given default ×prob default) + (prob no drop ×prob no default)0.850.08P(A/B)=0.850.080.920.30××+× P(A/B) = 0.068/0.344 = 0.197663. Answer: DThe Brennan and Schwartz model is more effective when portfolios become complex.64. Answer: B1. Jensen’s alpha = actual return - expected return using CAPM2. CAPM E(R) = risk-free rate + beta ×(return on the market - risk-free rate)**Return on the market - risk-free rate = equity risk premium.Use Jensen’s alpha of 4.75% and the actual return of 14.2%. The expected return fromCAPM must be 14.2% - 4.75% = 9.45%.Use this value in the CAPM to find the beta of the portfolio.expected return = risk-free rate + beta ×equity risk premium9.45% = 4.25% + β×6%, therefore β= approximately 0.8765. Answer: CThe GARCH(1,1) estimate of volatility (standard deviation) will be:variance = 0.000008 + (0. 16)(0.034)2 + (0.78)(0.026)2variance = 0.000008 + 0.00018496 + 0.00052728 variance = 0.0007202466. Answer: ACost of delivery:Bond 1: 98 - (91.50×1.02) = $4.67Bond 2: 122 - (91.50×1.27) = $5.80Bond 3: 105 - (91.50×1.08) = $6.18Bond 4 112 - (91.50×1.15) = $6.78Therefore, Bond 1 is the cheapest to deliver.67. Answer: AA stack hedge is less effective than a strip hedge if the yield curve undergoes any other move than a parallel shift.68. Answer: ACARP Members shall make a distinction between fact and opinion in the presentation of analysis and recommendations. The analyst must inform the clients of the change and tell them it is based upon an opinion and not a fact.69. Answer: AThe net cost (concessionality) of MYRA can be defined as: concessionality = (PV of original loan) - (PV of restructured loan)2$150($300)(0.08)$150($150)(0.08)PV of original loan=$312.641.05 1.05+++= concessionality = $312.64— $300 = $12.64 million70. Answer: CStarr’s supervisor states that “the mean 1-year Treasury bill rate should equal four percent.” Therefore, the null hypothesis is: H 0: mean Treasury bill rate equals 4%; and the alternative hypothesis is H A : mean Treasury bill rate does not equal 4%, which is a two-tailed test. Starr’s supervisor also states that “the mean market risk premium should be positive.” Therefore, the null hypothesis is: H 0: mean market risk premium is less than or equal to zero; and the alternative hypothesis is H A : mean market risk premium is greater than zero, which is a one-tailed test.71. Answer: AThe following formula is used to calculate the V AR for a linear derivative:V AR = ΔV AR fThe delta index formula is a sensitivity factor that reflects the change in value of the derivatives contract for a given change in the value of the underlying. The delta adjustment to the V AR of the underlying asset accounts for the fact that the relative changes in value between the underlying and the derivatives may not be one for one but nevertheless are linear in nature. Note that options are non-linear.72. Answer: DAt the 5% level of significance the critical z-statistic for a two-tailed test is 1.96 (assuming a large sample size).The null hypothesis is H0: x = 10%. The alternative hypothesis is H A: x≠10%. Because the computed z-statistic is greater than the critical z-statistic (2.3 > 1.96), we reject the null hypothesis and we conclude that small cap returns are significantly different than 10%.73. Answer: ATo identify if there is mispricing in the 2-year zero-coupon bond, back out its yield using your financial calculator. Using annual compounding FV = 100; PV = -82.6446, N = 2; CPT I/Y = 10.00%.Because its yield is too low (compared to the spot rate of 10.263%), this implies that its price is too high. So we will short this zero-coupon and buy the 2-year coupon bond. We would also short the 1-year zero-coupon bond because its principal repayment can be covered with the first year coupon on the coupon bond.The following calculations provide the arbitrage profit, assuming $1,000,000 of the coupon bond is bought.The 1-year zero-coupon bond will be shorted in an amount corresponding to the first year coupon on the coupon bond, which is 10%×$1,000,000 = $100,000. We will short the PV of this amount, which using the discount factor of 0.952381 (from the zero-coupon bond’s price) is $95,238.10. The 2-year zero-coupon bond will be shorted in an amount corresponding to the second year coupon and principal on the coupon bond, which is $1,100,000. We will short the PV of this amount, which using the discount factor of 0.826446 (from the zero-coupon bond’s price) is $909,090.60.The total receipt from the short sale is $95,238.10 + $909,090.60 = $1,004,328.70.After buying $1,000,000 of the coupon bond, the arbitrage profit is $4,328.70.You can verify that if the yield on the 2-year zero-coupon bond were 10.263%, its pricewould fall to 82.2508, eliminating the arbitrage profit.74. Answer: CThe usual approach is to specify a hypothesis that the researcher wishes to disprove.75. Answer: C0.0450.25$25(0.9737)$20()(0.9652)$5.25c e−×=−=76. Answer: AThe underlying asset of the CBOT catastrophe option is an index of underwriting losses written ona large pool of insurance policies. It is not a specific insurable event. The CBOT catastrophe option is really a spread option that does not provide payoffs until the underlying index rises above a certain level and caps payoffs above a certain level and therefore has limited upside potential. This spread feature limits its usefulness for hedging small losses.77. Answer: DBull and bear spreads are both constructed with either two calls or two puts with a lower and higher strike price.Bull spread: buy the option with lower strike price, sell the option with higher strike price. Bear spread: buy the option with higher strike price, sell the option with lower strike price.This investor is selling an option with low strike price and buying an option with high strike price so it is a bear spread.The maximum profit is found at a price of 50. The profit consists of:• Profit on the long 65 put is $15.• Loss on the net premium is $2 (i.e., paid - 5, earned +3).• Overall profit = +$13.78. Answer: A6666 ( )101.426/(100 5.7/2) 101.426/102.850.986151- months months months months price discount factor total cash flows principal remaining coupon discount factor discount factor year bond price coupon DF princi =+=+===×+12121212102.6427.50.98615107.595.2458750.8860107.5months months monthsmonths pal coupon DF DF DF +×=×+×==Note: we normally use discount factors to find the present value of future cash flows, In the case of bonds the present value of future cash flows is the price.price (present value) = total cash flows ×discount factor79. Answer: BSince the median is higher than the mean, the distribution is negatively skewed. If the mean were higher than the median the distribution would be positively skewed. Since the excess kurtosis is negative, the distribution is platykurtic or less peaked/flatter than normal distribution. Leptokurtic is defined as a distribution which is more peaked than a normal distribution and would have a positive excess kurtosis.80. Answer: AAnswer B is incorrect since unexpected loss involves only one variable. Loss given default is a complex function not adequately described by a simple binomial distribution. The binomial default process implies that credit migration is not possible.81. Answer: A。

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FRM一级练习题(2)1、If the daily, 95% confid ence l evel value at risk (VaR) of a portfolio is correctly estimated to be USD 10,000, one would expect that:A. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or l ess.B. In 1 out of 95 days, the portfolio value will decline by USD 10,000 or l ess.C. In 1 out of 95 days, the portfolio value will decline by USD 10,000 or more.D. In 1 out of 20 days, the portfolio value will decline by USD 10,000 or more.2、By reducing the risk of financial distress and bankruptcy, a firm's use of derivatives contracts to hedge its cash fl ow uncertainty will:A. Lower its value due to the transaction costs of derivatives trading.B. Enhance its value since investors cannot hedge such risks by themselves.C. Have no impact on its value as investors can costl essly diversify this risk.D. Have no impact as only systematic risks can be hedged with derivatives.3、An analyst at CAPM Research Inc. is projecting a return of 21% on portfolio A. The market risk premium is 11%, the volatility of the market portfolio is 14%, and the risk-free rate is 4.5%. Portfolio A has a beta of 1.5. According to the Capital Asset Pricing Model (CAPM), which of the foll owing statements is true?A. The expected return of portfolio A is greater than the expected return of the market portfolio.B. The expected return of portfolio A is less than the expected return of the market portfolio.C. The expected return of portfolio A has l ower volatility than the market portfolio.D. The expected return of portfolio A is equal to the expected return of the market portfolio.4、Suppose portfolio A has an expected return of 8% and volatility of 20%, and its beta is 0.5. Suppose the market has an expected return of 10% and volatility of 25%. Finally, suppose the risk-free rate is 5%. What is Jensen's alpha for portfolio A?A. 10%B. 1%C. 0.5%D. 15%5、Which of the foll owing statements regarding Metallgesellschaft's failure is incorrect?A. The futures and swap positions Metallgesellschaft entered into introduced significant credit risk for the company.B. An oil market move from a state of contango to normal backwardation and margin calls created a major cash crunch for Metallgesellschaft.C. Metallgesellschaft engaged in a stack-and-roll hedge, and as spot prices began to decrease more than futures prices, roll over losses could not be recovered.D. Because of the size of its position in heating and gasoline oil futures, Metallgesellschaft was exposed to market liquidity risk and had difficulty liquidating its position.6、Which of the foll owing statements is incorrect?A. Existing risk models often rely on historical data and are most precise for short horizons, like days.B. Market crises often involve a dramatic withdrawal of liquidity from the market.C. During crisis periods, firms will often make multipl e losses that exceed daily VaRs, and these losses can be large enough to substantially weaken them.D. When evaluating risks associated with a potential crisis period, existing risk models generally fail to effectively incorporate the risk of a decrease in liquidity but do effectively capture the distribution of large losses over an extended horizon beyond one day.7、If cov(z, x + y) = 0 , which of the foll owing must be true?A. cov(z, x) = 0, cov(z, y) = 0B. cov(z, x) * cov(z, y) = 0C. cov(z, x) ! 0, cov(z, y) ! 0D. None of the above8、Angela Santori buys two stocks, stock X and stock Y. Suppose that the only information she has about the return distributions is that the probability of a stock price decrease in one year for stock X is 23% and for stock Y is 39%. What is the highest possibl e probability that both stock prices increase in one year?A. 61%B. 46.97%C. 23%D. 77%9、John is forecasting a stock's performance in 2010 conditional on the state of the economy of the country in which the firm is based. He divides the economy's performance into three categories of "good," "neutral," and"poor" and the stock's performance into three categories of " increase," "constant," and "d ecrease."He estimates:1、The probability that the state of the economy is good is 20%. If the state of the economy is good, theprobability that the stock price increases is 80% and the probability that the stock price decreases is 10%.2. The probability that the state of the economy is neutral is 30%. If the state of the economy is neutral, theprobability that the stock price increases is 50% and the probability that the stock price decreases is 30%.3. If the state of the economy is poor, the probability that the stock price increases is 15% and theprobability that the stock price decreases 70%.Billy, his supervisor, asks him to estimate the probability that the state of the economy is neutral given that the stock performance is constant. John's best assessment of that probability is closest to:A. 20%B. 15.5%C. 19.6%D. 38.7%10、You built a linear regression model to analyze annual salaries for a developed country. You incorporated two independent variables, age and experience, into your model. Upon reading the regression results, you noticed that the coefficient of "experience" is negative, which appears to be counterintuitive. In addition, you have discovered that the coefficients have l ow t-statistics but the regression mod el has a high R2. What is the most likely cause of these results?A. Incorrect standard errorsB. HeteroskedasticityC. Serial correlationD. Multicollinearity参与FRM的考生可按照复习计划有效进行,另外高顿网校官网考试辅导高清课程已经开通,还可索取FRM 考试通关宝典,针对性地讲解、训练、答疑、模考,对学习过程进行全程跟踪、分析、指导,可以帮助考生全面提升备考效果。

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