V1_20140410 FRM 一级模拟考试(二)_题目

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FRM一级模考

FRM一级模拟题1 . Consider a bullish spread option strategy of buying one call option with a $30 exercise price ata 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: AThe investor would exercise her option to Imp the stock at $30 for a total cost of $30 plus the $3 premium she paid for the option and would have the stock called from her at $40. In addition, she would receive the $1.50 premium the was paid for selling this option. The total profit from the transaction can be calculated as: -$30-$3+$40+$1.5 = $8.502 .A . Butterfly SpreadB. Bull SpreadC. Strap SpreadD. Strip SpreadAnswer: ABuying a call at a low exercise price, buying another at a higher exercise price, and selling calls with exercise prices between the high and low is called a butterfly spread3 . Consider the following bearish option strategy of buying one at-the-money put with a strike price of $43 for $6, selling two puts with a strike price of $37 for $4 each and buying one put with a strike price of $32 for $1. If the stock price plummets to $19 at expiration, calculate the net profit/loss per share of the strategy.. A. -2.00 per shareB. Zero - no profit or lossC. 1.00 per shareD. 2.00 per shareAnswer: DThe easiest thing to do is to find the net profit or loss for each position and then add them together,recognizing whether a position is short or long.For 1 long $43 strike put position (gain) : [l x ($43 - $19)]-$6 = $18For 2 short $37 strike puts position (loss) : [2 x ($37 -$7 9)]-(2 x $4) = $28For 1 long $32 strike put position (gain) : [1 x ($32-$19)]- $1 = $12The sum of these profit/loss numbers is a $2 ( 18-28+12) gain。

FRM一级模考

FRM一级模拟题1 . You are asked by your boss to estimate the exposure of a hedge fund to the S&P 500. Though the find claims to mark to market weekly, it does not do so and marks to market once a month. The fund also does not tell investors that it simply holds anExchange Traded Fund (ETF) that is indexed to the S&P 500. Because of the claimsof the hedge fund, you decide to estimate the market exposure by regressing weeklyreturns of the fund on the weekly return of the S&P 500. Which of the followingcorrectly describes a property of your regression estimates? 'A. The intercept of your regression will be positive, showing that the fund has positive alpha when estimated using an OLS regression.B. The beta will be misestimated because hedge fund exposures are nonlinear.C. The beta of your regression will be one because the fund holds the S&P 500.D. The beta of your regression will be zero because the fund returns are not synchronous with the S&P 500 returns.Answer: DThe weekly returns are not synchronized with those of the S & P. As a result, the estimate of beta from weekly data will be too low. According to mark to market monthly, the fund find that it is not synthesized with S&P 500, so the correlation coefficient of S&P 500 and ETF is not the same to one.2 . Consider two stocks, A and B. Assume their annual returns are jointly normally distributed, the marginal. distribution of each stock has mean 2% and standard deviation l0%, and the correlation is 0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?A.2%B. 2.9%C. 4.7%D. 1.1%Answer: B3 . Consider the following estimated linear regression model:4 .A. -0.90B. +0.90C. +0.81D. -0.50Answer: CR-squared is the square of the correlation coefficient and measures the fraction of the variance of Y that is attributable to X. R2 = (_0.90)2 = 0.815 . lf the correlation coefficient of a linear regression is 0.6, the percentage of variation of the dependent variable that is not explained by the independent variable is CLOSEST to:A.36%B.40%C. 60%D. 64%Answer: D。

FRM一级模考

FRM一级模拟题1 . The current price of a stock is $25. A put option with a $20 strike price that expires in six months is available. N(-d1) = 0.0263 and N(-d2) = 0.0349. If the underlying stock exhibits an annual standard deviation of 25%, and the current continuously compounded risk-free rate is 4.25%, the Black-Scholes-Merton value of the put is closest to:a. $5.00.b. $3.00.c. $1.00.d. $0.03.2. What are the minimum values of an American-style and a European-style 3-month call option with a strike price of $80 on a non-dividend-paying stock trading at $86 if the risk-free rate is 3%?American Europeana. $6.00 $6.00b. $6.00 $5.96c. $6.59 $6.00d. $6.59 $6.593. An analyst is testing the hypothesis that the variance of monthly returns for Index A equals the variance of monthly returns for Index B based on samples of 50 monthly observations. The sample variance of Index A returns is 0.085, whereas the sample variance of Index B returns is 0.084. Assuming the samples are independent and the returns are normally distributed, which of the following represents the most appropriate test statistic?a.b.c.d.4. For a given portfolio, the expected return is 10% with a standard deviation of 15%. The beta of the portfolio is 0.75. The expected return of the market is 11% with a standard deviation of 18%.The risk-free rate is 4%. The portfolio's Treynor measure is:a. 0.060.b. 0.012.c. 0.040.d. 0.080.5. An analyst gathers the following data about the mean month returns of four securities.Which security has the lowest and highest level of relative risk as measured by the coefficient of variation?Lowest Highesta. W Yb. W Zc. X Yd. X Z。

FRM一级模考

专注国际财经教育FRM一级模拟题1 . Bank regulators are examining the loan portfolio of a large, diversified lender. The regulators' main concern is that the bank remains solvent during turbulent economic times. Which of the following is most likely the area on which the regulators will want to focus?A. Expected loss, since each asset can expect, on average, to decline in value from a positive probability of default,B. Expected loss, given the decrease in underwriting standards of new loans.C. Unexpected loss, since the bank will need to set aside additional capital for the unlikely event that recovery rates are smaller than expected. .D. Unexpected loss, since the bank will need to set aside additional capital for the unlikely event that usage given default is smaller than expected.Answer: CUnexpected loss is a measure of the variation in expected loss: As a precaution, thebank needs to set aside sufficient capital in the event that actual losses exceedexpected losses with a reasonable likelihood. For example, smaller recovery rateswould be indicative of larger actual losses.2 . Which of the following is (are) characteristic of self-insurance as a means to hedge against catastrophic and operational losses? 'I Using captive insurers has tax benefits associated with self-insurance.II Exercising risk prevention and control is a form of self-insurance.III Establishing a contingent line of credit that becomes available in the event of a large operational loss is one method of self-insurance.A. I onlyB. II onlyC. II and III onlyD. I, II, and IIIAnswer: DCaptive insurers are off-shore, wholly owned subsidiaries that may deduct for tax purposes the discounted value of all future expected losses stemming front a claim spanning several years. Essential this allows self-insurers to deduct losses before they have even occurred. Incurring costs to manage and control operational risk achieves the same result in principle as self-insurance. A contingent line of credit is a form of self-insurance that provides liquidity in the event of a Joss rather than building up cash reserves in anticipation of a loss.。

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

专注国际财经教育FRM一级模拟题1. An analyst gathered the following information about the return distributions for two portfolios during the same time period:Portfolio Skewness KurtosisA -1. 6 1.9B 0.8 3.2The analyst states that the distribution for Portfolio A is more peaked than a normal distribution and that the distribution for Portfolio B has a long tail on the lef-t side of the distribution, Which of the following is correct?A . The analyst's assessment is correct.B . The analyst's assessment is correct for Portfolio A and incorrect for portfolio B.C . The analyst's assessment is incorrect for Portfolio A but is correct for portfolio BD . The analyst is incorrect in his assessment for both portfolios.Common text for questions 2 and 3:A risk manager for Bank XYZ. Mark, is considering writing a 6-month American put option on a non-dividend-pay- ing stock ABC. The current stock price is USD 50 and the strika price of the option is USD 52. In order to find the no-arbitrage pnce 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 annual risk-free rate is 12% with continuous compounding2 . What is the risk-neutral probability of the stock price going up in a single step?a. 34.5%b. 57. 6Yoc. 65.5Yod. 80. 0%3 . The no-arbitrage price of the option is closest toa. USD 2.00b. USD 2.93c- USD 5.22d. USD 5.86。

FRM一级模考

FRM一级模拟题1 . A trader has put on a long position in a 2-year call on a stock whose strike will be determined by the value of the stock in l year's time. You can expect this position: .A. To have no delta, no gamma, and no vegaB. To have no delta, no gamma, and appreciable vegaC. To have small delta, no gamma, and appreciable vegaD. To have small delta, no gamma, no vegaAnswer: CThe 2-year maturity would result in a small delta, while the fact that the exercise price is not yet set would preclude gamma function. The option would, however, have considerable sensitivity to the volatility of the underlying stock price (vega as the value of the call option would increase or decrease along with the volatility of the underlying shares.2 . A portfolio of stock A and options on stock A is currently delta neutral, but has a positive gamma. Which of the following actions will make the portfolio both delta and gamma neutral?A. Buy call options on stock A and sell stock AB. Sell call options on stock A and sell stock AC. Buy put options on stock A and buy stock AD. Sell put options on stock A and sell stock AAnswer: DTo reduce positive gamma, one needs to sell options. When call options are sold, the delta becomes negative and one needs to buy stock to keep delta neutrality. When put options are sold, the delta becomes positive, and one needs to sell stock to keep delta neutrality.3 . Which position is most risky?A. Gamma-negative, delta-neutralB. Gamma-positive, delta-positiveC. Gamma-negative, delta-positiveD. Gamma-positive, delta-neutralAnswer: CA riskier position is one that is expected to move around a lot in value. A delta neutral position should not change in value as the value of the underlying asset changes. This eliminates Choice A and Choice D Choice C is correct because a gamma-negative position means that delta and the change in the underlying asset move inversely with each other.4 . Which of the following Greeks contributes most to the risk of an option that is close to expiration and deep in the money?A. VegaB. RhoC. GammaD. DeltaAnswer: DDelta measures the change in an option's price as the price of the underlying asset changes. An option that has high intrinsic value and a short time to maturity will have a delta close to one, and a gamma, rho and vega all close to zero.5 . Call and put option values are most sensitive to changes in the volatility of the underlying 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: DVega measures the sensitivity of the option value to changes in volatility. Vega is at a maximum when calls and put options are at-the-money.。

FRM一级模考

FRM一级模拟题1 . Imagine a stack-and-roll hedge of monthly commodity deliveries that you continue for the next five years. Assume the hedge ratio is adjusted to take into effect the mistiming of cash flows but is not adjusted for the basis risk of the 'hedge. In which of the following situations is your calendar basis risk likely to be greatest?A. Stack and roll in the front month in oil futures.B. Stack and roll in the 12-month contract in natural gas futures.C. Stack and roll in the 3-year contract in gold futures.D. All four situations will have the same basis risk.Answer: AExplanation: The oil term structure is highly volatile at the short end, making a front-month stack-and-roll hedge heavily exposed to basis fluctuations. In natural gas, much of the movement occurs at the front end, as well, so the 12-month contract won't move as much. In gold, the term structure rarely moves much at all and won't begin to compare with oil and gas.2 . A calendar spread in the S&P futures contracts (long 100 December contracts and short 100 March contracts) carry which of the following major market risk(s) ?I Equity risk.II Interest rate risk.III Dividend risk.A. I, II, and IIIB. I onlyC. I and III onlyD. II and III onlyAnswer: A3 . Which .of the following trade(s) contain basis risk?I Long l,000 lots Nov 07 ICE Brent Oil contracts and short l,000 lots Nov 07 NYMEX WTI Crude Oil contractsII Long l,000 lots Nov 07 ICE Brent Oil contracts and long 2,000 lots Nov 07ICE Brent Oil at-the-money putIII Long l,000 lots Nov 07 ICE Brent Oil contracts and short l,000 lots Dec 07 ICE Brent Oil contractsIV Long l,000 lots Nov 07 ICE Brent Oil contracts and short l,OOO lots Dec 07 NYMEX WTI Crude Oil contracts .A. II and IV onlyB. I and III onlyC. I, III and IV onlyAnswer: CThere is mainly basis risk for positions that are both long and short either different months or contracts. Position II is long twice the same contract and thus has no basis risk (but a lot of directional risk).4 . Consider an FRA (forward rate agreement) 'with the same maturity and compounding frequency as a Eurodollar futures contract. The FRA has a LIBOR underlying. Which of the following statements are true about the relationship between the forward rate and the futures rate?A. The forward rate is normally higher than the futures rate.B. They have no fixed relationship.C. The forward rate is normally lower than the futures rate.D. They should be exactly the same.Answer: CEquation (8.4) shows that the futures rate exceeds the forward rate.Refer to convexity adjustment.5 . A three-month futures contract on an equity index is currently priced at USD 1,000. The underlying index stocks are valued at USD 990 and pay dividends at a continuously compounded rate of 2% and the current continuously compounded risk-free rate is 4%. The potential arbitrage profit per contract, given this set of data, is closest toA. USD 10.00B. USD 7.50C. USD 5.00D. USD l.50Answer: C。

frm考试题及答案

frm考试题及答案FRM（Financial Risk Manager）考试是由全球风险管理专业人士协会（GARP）提供的金融风险管理领域的专业认证考试。

以下是一份模拟的FRM考试题目及其答案：FRM考试模拟题一、单项选择题1. 在现代投资组合理论中，哪一项是投资组合风险的主要来源？A. 系统性风险B. 非系统性风险C. 利率变动D. 汇率波动答案：A2. 以下哪个不是信用评级机构？A. 标准普尔B. 穆迪C. 惠誉D. 花旗银行答案：D3. 风险价值（VaR）是一种衡量投资组合在一定置信水平下，一定时间内可能遭受的最大损失的方法。

它属于哪种风险管理技术？A. 敏感性分析B. 压力测试C. 极值理论D. 统计风险管理答案：D二、多项选择题4. 以下哪些因素会影响期权的时间价值？A. 期权的执行价格B. 期权到期前的时间长度C. 标的资产的波动性D. 无风险利率答案：B, C, D5. 在进行市场风险管理时，以下哪些措施是有效的？A. 多元化投资B. 风险对冲C. 增加杠杆D. 风险转移答案：A, B, D三、简答题6. 描述一下什么是流动性风险，并给出一个金融机构可能面临的流动性风险的例子。

答案：流动性风险是指金融机构在需要时无法以合理成本迅速出售资产或获得资金的风险。

一个例子是银行在金融危机期间面临大量客户同时提取存款，导致银行流动性枯竭。

四、计算题7. 假设一个投资组合由两种资产组成，资产A和资产B。

资产A的预期收益率为10%，标准差为15%，资产B的预期收益率为8%，标准差为10%。

如果投资组合由60%的资产A和40%的资产B组成，且两种资产的相关系数为0.5，请计算投资组合的预期收益率和标准差。

答案：预期收益率 = 0.6 * 10% + 0.4 * 8% = 9.2%标准差= √(0.6^2 * 15%^2 + 0.4^2 * 10%^2 + 2 * 0.6 * 0.4 * 0.5 * 15% * 10%) = √(10.125% + 4% + 6%) = √20.125% ≈ 14.17%结束语：以上题目仅供参考，实际FRM考试内容和难度可能会有所不同。

frm一级模考试题第二套答案_程黄维

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
max ( ST −1.57, 0) − 0.02
而远期合约的收益是：1.6018 − ST
所以这一策略的总收益是：
max ( ST −1.57, 0) − 0.02 +1.6018 − ST
即：
当ST < 1.57时，1.5818 − ST 当ST > 1.57时，0.0118
这说明收益总是正的。在计算中忽略了货币的时间价值，然而即使将其考虑在内这一策略的收益也是正的。 b ．交易者买了90 天的看跌期权，同时持有90 天的远期合约多头头寸。如果ST ：是期末的汇率，那么这份看跌期权的收益是：

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一级模考

FRM一级模拟题1 . Futures and forward prices would be equal in a world with no arbitrageopportunities if:Interest rates were constant.Interest rates were nonstochastic but time varying.Interest rates were stochastic and nonnegative.I and IIIA .I, and IIIB. I, II, and IIIC. I and IID. I onlyAnswer: CFuture and forward prices would be equal if interest rates were either constant or deterministic because the probability of accruing gains and losses would be about even.2 . To best hedge a 5 year floor on the 3-month LIBOR using 3-month LIBOR Eurodollar futures,a trader would need approximately the following number of different expiry dates of futures contracts?A. 5 t0 6, depending on maturity dates.B. 20 t0 21, depending on maturity dates.C. 1, because the term structure is driven by only one factor.D. 19, depending on maturity dates.Answer: DA total of 19 contracts would be needed o The interest rate on floating rate obligations are established at the beginning of the period Therefore, for a five year obligation using quarterly reset dates, 5 x4 - I or 19 contracts would be needed3 . A 90-day Eurodollar futures contract has a constant PVBP of $25.00 per million The 90-day bank bill futures contract on the Sydney Futures Exchange trades on a discount basis and the Price Value of a Basis Point (PVBP) is different for each yield level. Assuming non-negative yields, the PVBP for the bank bill contract will be:A. Always less than the Eurodollar contractB. Always greater than the Eurodollar contractC. Dependent on the market yieldD. $27.00 per millionAnswer: ASince the 90-day bank bill is priced at a discount, mathematically? the PVBP will always be less than $25 as long as rates are positive.4 . For assets that are strongly positively correlated with interest rates, which one of the following is the best selection?A. Long-dated forward contracts will have higher prices than tong-dated futures contracts.C. Long-dated forward and long-dated futures prices are always the same.D. The convexity effect can be ignored for long-dated futures contracts on that asset. Answer: Bl. When interest rates are assumed constant or deterministic, forward and futures prices must be equal.2.With stochastic interest rates, there may be a small difference, depending on the correlation between the value of the asset and interest rates.If the correlation =0 , futures price must be the same as the forward price.1f the correlation>0,. relative to forward contracts, marking-to-market feature of futures contracts is beneficial to a long futures position. As a result, the futures price must be higher in equilibrium. If the correlation<0, the futures price must be lower than the forward price. '5. The Chicago Board of Trade has reduced the notional coupon of its Treasury futures contracts from 8% t0 6%. Which of the following statements are likely to be true as a result of the change?A. The cheapest to deliver status will become more unstable if yields hover near the 6% range.B. . When yields fall below 6%, higher duration bonds will become cheapest to deliver, while lower duration bonds will become cheapest to deliver when yields range above 6%.C. The 6% coupon would decrease the duration of the contract, making it a more effective hedge for the long end of the yield curve.D. There will be no impact at all by the change.Answer: AI.Assume, that we operate in an environment where yields are flat at 5% and all bonds arepricedat par. Discounting at 6% will create CF factors that are lower than one-the longer the maturityof the bond, the greater the difference The net cost P - F x CF will then be greater for longer-term bonds, This tends to favor short-term bonds for delivery. When the term structure is upward sloping, the opposite occurs, and there is a tendency for long-term bonds to be delivered. SoB. C are wrong2.assuming that 6 percent is closer to the actual yield than 8 percent, net cost P - F x CF will be smaller and the cheapest to deliver identification will be less stable.。

FRM一级模考

FRM一级模拟题1 .A simple linear regression of a stock's returns on an industry index provides thefollowing results:Assume that the sample has eight years of quarterly observations.Which of the following statements regarding the interpretation of the regressionis(are) correct?I. The coefficient of determination is 84.7%.II. The index coefficient is significant at the 99% confidence level.III. The correlation coefficient between the stock's returns and the return on the industry index is0.42.a. I only.b. II only.c.I and II.d.I and III.解析：cThe coefficient of determination, or R2= (ESS/TSS) = (998.56 11,178-93) = 84.70%.For simple linear regression, we can find the correlation coefficient, r, by taking thesquareroot of .0=0.92. We can rest the significance of the industry indexcoefficient by taking R2=847(2.4/0.65)= 3.69 and see that this is above 3. which is significant atthe 99% confidence level.2 .Joe Reilly, FRM, and Claire Meyers, FRM, are discussing the level of eventrisk in their bond portfolio. Reilly says that since their portfolio consists ofinvestment grade bonds, event risk should not be a concern. Meyers says thatsince they have a large number of different issues in their portfolio, and eventrisk is idiosyncratic, the event risk in their portfolio is negligible. Which, ifeither, of these statements is based on correct assumptions?a. Neither statement by Reilly nor Meyers are correct.c. The statement made by Meyers is correct, but not the one made by Reilly.d. Both statements made by Meyers and Reilly are correct.解析：aEven investment grade bonds arc exposed to the risk of the issuer being taken over ormerging with another company. Event risk can increase on a market level if there is atrend toward increasing mergers in the economy.3 .An investment analyst takes a random sample of 100 aggressive equity funds andcalculates the average beta as 1.7. The sample betas have a standard deviation of0.4. Using a 95% confidence interval and a z-statistic, which of the followingstatements about the confidence interval and its interpretation is most likelyaccurate? The analyst can be confident at the 95% level that the interval:a. 1.580 to 1.820 includes the mean of the sample betas.b. 1.622 to 1.803 includes the mean of the sample betas.c. 1.622 to 1.778 includes the mean of the population beta.d. 1.634 to 1.766 includes the mean of the population beta.解析：cGiven that the population variance is unknown and the sample size is larce. the 95% confidence interval for the population mean is:n s z x 2∂± The confidence interval is:1.7 ⎪⎭⎫ ⎝⎛±1004.096.1=1.7+-1.96(0.04)=1.7+-0.0784=1.622 to 1.778An investor has a short position valued at $88,442.60 in a 20-year, 5% coupon, U.S.Treasury bond (T-bond) with a yield to maturity (YTM) of 6%. Assume discounting occurs on a semiannual basis.4 .Which of the following is closest to the dollar value of a basis point (DV01)?a. 0.0851.b. 0.0931,c. 0.1025.d. 0.1061.解析：dFor the 6% bond, N = 20 x 2 = 40; I/Y = 6/2 = 3; PMT = 5/2 = 2.5; FV = 100; CPT →= 2.5; FV = 100; CPT→PV=88.3365. P O-P I =88.4426-88.3365= 0.1061. Note:This explanation used an increase in yield. The DVO1 for a decrease in yield is 0.1063.5 .Using a 30-year, 5% coupon, U.S. T-bond yielding 5% with a DVO1 of 0.1544to hedge the interest rate risk in the 20-year bond, which of the followingactions should the investor take?a. Buy $58,760 of the hedging instrument.b. Buy $68,720 of the hedging instrument.c. Sell $69,880 of the hedging instrument.d. Sell $71,290 of the hedging instrument.解析：bThe hedge ratio is (0.1061 f 0.1544) = 0.6872. Since the investor has a short positionin his bond portfolio, the investor needs to buy $0.6872 of par value of the hedginginstrument for every $1 of par value for the 20-year bond.。

FRM一级模考

专注国际财经教育FRM一级模拟题1 . An Asset/Liability Management analyst at a community bank notices that a right to pay fixed swaption was purchased with a notional amount of 200 million with a strike in three months. The bank has only floating rate funding sources. The transaction most likely was done becausethe: .A. bank is anticipating a new $200M fixed rate loan.B. bank is anticipating a new $200M floating rate loan.C. bank is anticipating that a prepayment of $200M will occur on a flxed loan.D. trading area is speculating.Answer: AThe bank purchased the option in order to be able to convert variable rate funding to fixed rate if it needs to. The possibility of making a fixed rate loan would make this a rational strategy.2 . Consider a 2 int0 3-year Bermudan swaption (i.e., an option to obtain a swap that starts in 2 years and matures in 5 years). Consider the following statements:I A lower bound on the Bermudan price is a 2 int0 3 year European swaption.II An upper bound on the Bermudan price is a cap that starts in 2 years and matures in 5 years.III A lower bound on the Bermudan price is a 2 int0 5 year European optionWhich of the following statements is (are) TRUE?A. I onlyB. II onlyC. I and IID. III onlyAnswer: CSince a Bermudan option can be exercised on a discrete set of dates, it is at least as valuable as a European option, so I is correct. A cap would be exercisable continuously during the period, so it would represent the upper bound of the swap (and hence the option on the swap), so II is correct. III confuses the 2 int0 3 year Burmudan swaption and a 2- int0 5-year European option.3 . Which of the following actions would be most profitable when a trader expects a sharp 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: BA payer swaption gives the holder the right to pay fixed rate and receive floating rate. Selling a receiver swaption would also be a profitable strategy as it would mean receiving a premium but with a sharp rise in interest rates buying a payer swaption should be a better deal.。

FRM一级在线模考题答案

FRM一级模考试题（一）——答案1.Answer: CThe historical simulation method may not recognize changes in volatility and correlations from structural changes.2.Answer: CThe dirty price of the bond is calculated as N = 10; I/Y = 2.5; PMT = 30; FV = 1,000; CPT→PV = 1,043.76. Adjusting the PV for the fact that there are only 90 days until the receipt of the first coupon gives $1,043.76×(l.025)90/180 = $1,056.73. Clean price = dirty price - accrued interest = $1056.73 - $30(90/180) = $1,041.73.3.Answer: BGamma (not theta) represents the expected change in delta for a change in the value of the underlying. In-the-money options are more sensitive to changes in rates (rho is higher) than out-of-the-money options.4.Answer: AAssuming no default risk, the domestic return is 7.35%. The return on the UK investments, however, is equal to the amount invested today, (USD$2,000,000)/(USD1.62GBP)= GBP1,234,568, which turns into GBP1,234,568×1.08 = GBP1,333,333 one year from now. Since the forward contract guarantees the exchange rate in the future, this translates into GBP1,333,333 ×USD1.5200/GBP = USD2,026,666. This is a dollar return to the bank of USD2,026,666/ USD2,000,000-1 = 1.33%. Hence, the weighted average return to the bank’s investments is (0.5)×(7.35%) + (0.5)×(1.33%) = 4.34%. Since the cost of funds for the bank is 5.5%, the net interest margin for the bank is 4.34-5.50 = -1.16%.5.Answer: DAll of the statements are correct except choice d: the value of the firm’s equity should be the present value of its expected free cash flows (not net income).6.Answer: D± So youWith a known variance, the 95% confidence interval is constructed as Xknow that 33.23307.Answer: DA 6% rate compounded annually is approximately equivalent to a 5.8269% rate (rounded to four decimal places) compounded continuously. In (1 + 0.06) = 0.058268908 Using put-call parity:0.0582690 4.1027.5025$5.04rTp c XeS e −−=+−=+−=8.Answer: AV AR measures the expected amount of capital one can expect to lose within a given confidence level over a given period of time. One of the problems with V AR is that it does not provide information about the expected size of the loss beyond the V AR. V AR is often complemented by the expected shortfall, which measures the expected loss conditional on the loss exceeding the V AR. Note that since expected shortfall is based on V AR, changing the confidence level may change both measures. A key difference between the two measures is that V AR is not sub-additive, meaning that the risk of two funds separately may be lower than the risk of a portfolio where the two funds are combined. Violation of the sub-additive assumption is a problem with V AR that does not exist with expected shortfall. 9.Answer: CThe fixed payments made by Cooper are (0.07/2)×$2,000,000 = $70,000. The present value of the fixed payments =0.0650.50.0681.0(0.0751.5)($70,000)($70,000)($70,000$2,000,000)$67,762$65,398$1,849,747$1,982,907e e e −×−×−×+++×=++=The value of the floating rate payments received by Cooper at the payment date is the value of the notional principal, or $2,000,000.The value of the swap to Cooper is ($2,000,000-$1,982,907) = $17,093. 10.Answer: CA stack is a bundle of futures contracts with the same expiration. Over time, a firm may acquire stacks with various expiry dates. To hedge a long-term risk exposure, a firm would close out each stack as it approaches expiry and enter into a contract with a more distant delivery, known as a roll. This strategy is called a stack-and-roll hedge and is designed to hedge long-term risk exposures with short-term contracts. Using short-term futures contracts with a larger notional value than the long-term risk they are meant to hedge could result in over hedging” depending on the hedge ratio. 11.Answer: BThe duration of a portfolio of bonds is the weighted average (using market value weights) of thedurations of the bonds in the portfolio. First let’s find the weights.Bond Price as Percentage of Par Face Value $ Market Value $1 95.5000 2,000,000 1,910,0002 88.6275 3,000,000 2,658,8253 114.8750 5,000,000 5,743,750 Total 10,312,575The weights based on market values are:Weight of bond 1 = 1,910,000 / 10,312,575 = 0.1852Weight of bond 2 = 2,658,825 / 10,312,575 = 0.2578Weight of bond 3 = 5,743,750 / 10,312,575 = 0.5570Bond Weights Duration WeightedDuration1 0.1852 6.95 1.28712 0.2578 9.77 2.51873 0.5570 14.81 8.2492Total 12.055012.Answer: CTo increase the beta of the portfolio from the market beta (1.0) to 1.5, the portfolio manager should take a long position:# of contracts =$250,000,000(1.5 1.0)4171,200250−×=×contracts13.Answer: BThe concessionality of a MYRA is defined as the difference between the present value of the loans before and after the restructuring.14.Answer: BThe formula is JB =2222(3)180(43)1[][0]30[]7.5 64644n KS−−+=+==Note that excess kurtosis is equal to K-3 so excess kurtosis of 1 means that kurtosis is 4.15.Answer: CThe rogue traders for both Daiwa and Barings had dual roles as both the head of trading and the head of the back-office support function. This operational risk oversight allowed them to hide millions in losses from senior management. In the Allied Irish Bank case, John Rusnak did not run the back-office operations. The Drysdale Securities case did not deal with a rogue trader.16.Answer: AThe fact that mean> median> mode is consistent with a distribution that is positively skewed. For all normal distributions, kurtosis = 3. Excess kurtosis = kurtosis-3, which is 0 for a normal distribution. In this case, excess kurtosis = 2, which means kurtosis = 5. This means that the distribution being examined is more peaked than the normal distribution and is said to be leptokurtic. 17.Answer: CA change from a Ba to Baa rating is an example of a credit upgrade. A credit upgrade will decrease the likelihood of default (EDF) reducing expected loss. Note that expected loss is an estimate of average future loss. Actual loss is by definition equal to zero until a credit event occurs. 18.Answer: BThe CAPM assumes that the market portfolio should be the portfolio with the highest Sharpe ratio of all possible portfolios and should include all investable assets. It also assumes that the expected excess returns for the market are assumed to be known in that investors have access to the same information. As well, it assumes that returns are normally distributed and investors’ expectations for risk and return ate identical. 19.Answer: CThe 3-month forward rate is calculated as follows:1()(0.0650.05)0.250,()$19$19.07r T T T F S e e δ−−==×=20.Answer: CThe farmer needs to be short the futures contracts. The two sources of basis risk confronting the farmer will result from the fact that he is using a cattle contract to offset the price movement of his buffalo herd, Cattle prices and buffalo prices may not be perfectly positively correlated. As a result, the correlation between buffalo and cattle prices will have an impact on the basis of the cattle futures contract and spot buffalo meat. The delivery date is a problem in this situation, because the farmer’s hedge horizon is winter, which probably will not commence until December or January. In order to maintain a hedge during this period, the farmer will have to enter into another futures contract, which will introduce an additional source of basis risk. 21.Answer: BA scattergram can help determine whether a relationship is positive or negative. Since the population and sample coefficients are almost always different, the residual will very rarely equal the corresponding population error term.Answer: C0.02(0.25)0.04(0.25)01,1001,08025.26qT rT S e Ke e e −−−−−=−=23.Answer: DPractitioners primarily use structural models, while academics are the primary users of statistical models. There are three types of structural models and one of them includes the need to forecast both factor returns and exposures. Factors in structural models are intuitive and well-known, while factors in statistical models are implied factors derived through a statistical operation. Structural models assume an underlying economic relationship between factors and stock returns. 24Answer: ABecause catastrophe bonds are riskier than straight bonds issued by the same firm, they usually have maturities less than three years and are usually non-investment-grade bonds. They also have potentially useful diversification qualities as their returns, being linked to operational losses, are not highly correlated with market returns. 25.Answer: AFor a risk management activity to have value, the firm must be able to do something for shareholders 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. 26.Answer: BIn this case, U = 1.1, D = 0.9, r = 0.035, and the value of the option is $1 if the stock increases and $0 if the stock decreases. The probability of an up movement, ∏U, can be calculated as0.0353/12(0.9)/(1.10.9)0.5439e ×−−=The value of the call option is therefore (0.0353/12)(0.5439$1)/$0.54e××=27.Answer: CStandards 2.1 and 2.2—Conflicts of Interest. Members and candidates must act fairly in all situations and must fully disclose any actual or potential conflict to all affected parties. Sell-side members and candidates should disclose to their clients any ownership in a security that they are recommending.28.Answer: BThe Treynor measure is most appropriate for comparing well-diversified portfolios. That is the Treynor measure is the best to compare the excess returns per unit of systematic risk earned by portfolio managers, provided all portfolios are well-diversified.All three portfolios managed by Donaldson Capital Management are clearly less diversified than the market portfolio. Standard deviation of returns for each of the three portfolios is higher than the standard deviation of the market portfolio, reflecting a low level of diversification.Jensen’s alpha is the most appropriate measure for comparing portfolios that have the same beta. The Sharpe measure can be applied to all portfolios because it uses total risk and it is more widely used than the other two measures. Also, the Sharpe ratio evaluates the portfolio performance based on realized returns and diversification. A less-diversified portfolio will have higher total risk and vice versa.29.Answer: DThe central limit theorem holds for any distribution (skewed or not) as long as the sample size is large (i.e., n >30). The mean of the population and the mean of the distribution of all sample means are equal. The standard deviation of the mean many observations is less than the standard deviation of a single observation.30.Answer: CUnexpected loss is a measure of the variation in expected loss. As a precaution, the bank needs to set aside sufficient capital in the event that actual losses exceed expected losses with a reasonable likelihood. For example, smaller recovery rates would be indicative of larger actual losses.31.Answer: CGiven that the economy is good, the probability of a poor economy and a bull market is zero. The other statements are true. The P(normal market) = (0.60×0.30) + (0.40×0.30) = 0.30. P(good economy and bear market)= 0.60×0.20 = 0.12. Given that the economy is poor, the probability of a normal or bull market = 0.30 + 0.20 = 0.50.32.Answer: DNone of the statements are correct. The historical approach uses historic data from past crisis events, the prospective scenario conditional approach includes correlations between risk factors, and the factor push method is a prospective approach not a historical approach.33.Answer: BRisk management activities can increase firm value when the firm’s claimholders cannot takeactions 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.34.Answer: CTop-down models rely primarily on aggregate historical data. Therefore, they are relatively simple and do not differentiate between high-frequency low-severity events and low-severity, high-frequency events because both are pooled together in the data. The aggregated nature of the data also limits the amount of data used in these models. A limitation of aggregated data, however, is that top-down models do not have diagnostic capabilities like bottom-up models that dissect processes into individual components.35.Answer: CBuying a call (put) option with a low strike price, buying another call (put) option with a higher strike price, and selling two call (put) options with a strike price halfway between the low and high strike options will generate the butterfly payment pattern. Two other wrong answer choices deal with bull and bear spreads, which can also be replicated with either calls or puts. A bull spread involves purchasing a call (put) option with a low strike price and selling a call (put) option with a higher exercise price. A bear spread is the exact opposite of the bull spread.36.Answer: DCaptive insurers are off-shore, wholly owned subsidiaries that may deduct for tax purposes the discounted value of all future expected losses stemming front a claim spanning several years. Essential this allows self-insurers to deduct losses before they have even occurred. Incurring costs to manage and control operational risk achieves the same result in principle as self-insurance. A contingent line of credit is a form of self-insurance that provides liquidity in the event of a loss rather than building up cash reserves in anticipation of a loss.37.Answer: DThe futures contract ended at 985 on the first day. This represents a decrease in value in the position of (1,000-985)×$250×20 = $75,000. The initial margin placed by the manager was $12,500×20 = $250,000. The maintenance margin for this position requires $10,000×20 = $200,000. Since the value of the position declined $75,000 on the first day, the margin account is now worth $175,000 (below the $200,000 maintenance margin) and will require a variation margin of $75,000 to bring the position back to the initial margin. It is not sufficient just to bring the position back to the maintenance margin.38.Answer: CWe are given that the forward exchange rate in one year is 1.200 and are asked to find the exchange rate in three years. This means we need to apply the 2-year forward rate one year fromtoday.The 2-year forward rate in the United States is:1.04811 4.81%==−=The 2-year forward rite in Europe is:1.022512.25%==−=Finally, we can apply interest rate parity:221.04811.200 1.2611.0225t F =×= 39.Answer: AStandards 3.1 and 3.2 relate to the preservation of confidentiality. The simplest, most conservative, and most effective way to comply with these Standards is to avoid disclosing any information received from a client, except to authorized fellow employees who are also working for the client. If the information concerns illegal activities by MTEX, Black may be obligated to report activities to authorities. 40.Answer: AThe liquidity preference theory suggests that the shape of the term structure is determined by the fact that most investors prefer short-term liquid assets, holding return constant. 41.Answer: AIn general, bond prices will tend to increase with maturity when coupon rates are above relevant forward rates. When short-term rates are below the forward rates utilized by bond prices, the investors who invest in longer-term investments will tend to outperform investors who roll over shorter-term investments. 42.Answer: CThe forward rate can be calculated as [(98.2240/96.7713)-1]×2 = 3%. 43.Answer: BThe price is calculated as $15 (0.992556) + $15 (0.982240) + $1,015 (0.967713) = $1,011.85. 44.Answer: AUnique among swaps, equity swap payments may be floating on both sides (and the payments not known until the end of the settlement period). Similar to options, premiums for swaptions are dependent on the strike rate specified in the swaption. The most common reason for entering into commodity swap agreements is to control the costs of purchasing resources, such as oil and electricity. A negative index return requires the fixed-rate payer to pay the percentage decline in the index. 45.Answer: BThe GARCH (1,1) estimate of volatility will be:220.000005(0.13)(0.03)(0.85)(0.022)0.0005330.0231 2.31%volatility ++====46.Answer: B0.04250.5($200.0349)($250.0263)$0.02582$0.03P e −×=××−×=≈47Answer: DThe minimum value for a European-style call option, c T is given by3/12max[0,/(1)]max[0,8680/(1.03)]$6.59T T F S X R −+=−=An American style call option must be worth at least as much as an otherwise identical European-style call option and has the same minimum value Note that this fact alone limits the possible correct responses to Choices a and d. Since the American style call is in the money and therefore must be worth more than the $6 difference between the strike price and the exercise price, you can eliminate Choice a and select Choice d without calculating the exact minimum value. 48.Answer: AThe appropriate test is an F-test, where the larger sample variance (Index A) is placed in the numerator. 49.Answer: DThe formula for the Treynor measure is ()[p FPE R R β−. Thus, the value for the Treynor measurein this case is (0.10 - 0.04)/0.75 = 0.08 50.Answer: DThe coefficient of variation, CV = standard deviation/arithmetic mean, is a common measure of relative dispersion (risk) CV W = 0.4/0.5 = 0.80, CV X = 0.7/0.9 = 0.78; CV Y = 4.7/l.2 = 3.92 and CV Z = 5.2/1.5=3.47 Because a lower relative risk, Security X has the lowest relative risk and Security Y has the highest relative risk.51.Answer: AThe probability of rescheduling sovereign debt is positively related to the debt-service ratio, the import ratio, the variance of export revenue, and the domestic money supply growth.52.Answer: BAccording to the cash-and-carry Formula, the futures price should be:(0.02750.01)0.25e−=1,010$1,014.43Hence, the futures is overvalued, indicating it should he sold and the index be purchased for a risk-free profit of $1,020 —$1,014.43 = $5.57.53.Answer: DHoffman has violated both Standard 1.2-independence and objectivity, which specially mentions that CARP Members must not offer, solicit, or accept any gift, benefit, compensation, or consideration that could be reasonably expected to compromise their own or another’s independence and objectivity, and Standard 2.2-Conflicts of Interest, which states the Members should 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.54.Answer: DThe variability in the receipt of payments from the floating-rate asset is eliminated, as the floating payment of the floating rate leg of the swap offsets the receipt of the floating rate on the asset. The floating-rate payer is effectively left with a fixed-rate asset.55.Answer: DExpected value = (0.4)(10%) + (0.4)(12.5%) + (0.2)(30%) = 15%Variance = (0.4)(10-15)2 + (0.4)(12.5 -15)2 + (0.2)(30 - 15)2 = 57.5Standard deviation =56.Answer: D,,220.05 1.250.2S FS F F Cov HR Beta σ====57.Answer: AOption-free bonds have positive convexity and the effect of (positive) convexity is to increase the magnitude of the price increase when yields fall and to decrease the magnitude of the price decrease when yields rise. 358.Answer: CThe standard normal random variable, denoted Z, has mean equal to 0 and standard variation (and variance) equal to 1. Also, a multivariate distribution is meaningful only when the behavior of each random variable in the group is in some way dependent upon the behavior of others.59.Answer: DThe critical z-value for a one-tailed test of significance at the 0.01 level will be either +2.33 or -2.33. The test statistic for hypotheses concerning equality of variances is 2122S F S = The statement regarding p-value is true. A Type II error is failing to reject the null hypothesis when it is actually false.60.Answer: BThe Taylor Series does not provide good approximations of price changes when the underlying asset is a callable bond or mortgage-backed security. The Taylor Series approximation only works well for “well-behaved” quadratic functions that can be approximated by a polynomial of order two.61.Answer: DLTCM believed that, although yield differences between risky and riskless fixed-income instruments varied over time, the risk premium (or credit spread) tended to revert (decrease) to average historical levels. This was similar to their equity volatility strategy. Also, their balance sheet leverage was actually in line with other large investments banks (but their true leverage, economic leverage, was not considered).62.Answer: BThe benchmark returns are not important here. The average of the portfolio returns is(6+9+4+12)14=31/4=7.75.0.4743==63.Answer: D Neither statement is correct. The appropriate number of contracts for the hedge is:$10,000,000() 1.0()36 1,100250portfolio portfolio value contracts futures price multiplierβ×=×≈×× However, since the manager is long the portfolio, he will want to take a short position in the 36 contracts.Change in value of portfolio = -0.01($10,000,000) = -$100,000.Change in value of futures position = 36(1,100 — 1,090)(250) = $90,000.Net payoff= -$100,000 + $90,000 = -$10,000 The net impact is a loss of $10,00064.Answer: CAt the end of year 1 there is a 0% chance of default and a 90% chance that the firm will maintain an Aaa rating. In year 2, there is a 0% chance of default if the firm was rated Aaa after 1 year (90%×0% = 0%), There is a 5% chance of default if the firm was rated Baa after 1 year (10%×5% = 0.5%). Also, there is a 15% chance of default if the firm was rated Caa after 1 year (0%× 15% = 0%) The probability of default is 0% from year 1 plus 0.5% chance of default from year 2 for a total probability of default over a 2-year period of 0.5%.65.Answer: AThe beta factors used in the standardized approach for operationa1 risk are as follows: trading and sales 18%, retail banking 12% agency and custody services 15%, asset management: 12%.66.Answer: AAccording to put-call parity:000rT c Xe p S −+=+The left-hand side=$4+$45e -0.06×0.5 = $47.67The right-hand side = $4 + $43 = $47Since the value of the fiduciary call is not equal to the value of the protective put, put-call parity is violated and there is an arbitrage opportunity.Sell overpriced and buy underpriced. That is, sell the fiduciary call and buy the protective put. Therefore, sell the call for $4, sell the Treasury bill for $43.67 (i.e., borrow at therisk-free rate), buy the put for $4 and buy the underlying asset for $43. The arbitrageprofit is $0.67.67.Answer: BThe 5-3-2 spread tells us the amount of profit that can be locked in by buying five barrels of oil and producing three barrels of gasoline and two barrels of heating oil.(61.5×3) + (58.5×2) - (55×5) = $26.50 for 5 barrels; $5.30/barrel68.Answer: CUse interest-rate parity to solve this problem. 1.1565 = Se (0.02-0.04)0.25, so S = 1.1623.69.Answer: AUnsystematic risk is asset-specific and, therefore, a diversifiable risk. The market risk premium is also known as the price of risk and is calculated as the excess of the expected return on the market over the risk-free rate of return. The risk premium of an asset is calculated as beta times the excess of the expected return on the market over the risk-free rate of return.70.Answer: C12[()][()] 6.523.56.520.325.88 3.5i i j j i j ij i j i j R E R R E R Cov Cov r σσσσ−×−========××Σ71.Answer: DMoral hazard refers to the fact that an insured party may engage in risky behavior (or at least behave in a less risk-averse manner) knowing that an insurance policy will insulate the party against the consequences of such behavior. The way that Eggenton can mitigate the moral hazard problem is to include a deductible or co-insurance feature that would force JT Cola to pay a portion of the cost should a claim be made against the policy. If a deductible feature were not included in the policy, JT Cola management would have been free to act in any manner they would choose, including manipulating the global cola market, and Federal Insurance Group would have assumed all of the risk.72.Answer: BWe can calculate the expected loss as follows.EL = AE×EDF×LGDMaximum lossAdjusted exposure = OS + (COM U - OS)×UGD= $8,000,000 + ($12,000,000)×(0.75)= 17,000,000EL = ($17,000,000)×(0.02)×(0.80) = $272,000Minimum lossAdjusted exposure = OS + (COM U - OS)×UGD= $8,000,000 + ($12,000,000)×(0.5)= $14,000,000EL = ($14,000,000)×(0.01)×(0.80) = $112,000Therefore, the difference between maximum and minimum loss is:$272,000 - $112,000 = $160,000.73.Answer: ASince the current position is short gamma, the action that must be taken is to go long the option in the ratio of the current gamma exposure to the gamma of the instrument to be used to create the gamma-neutral position (5,000/2 = 2,500). However, this will change the delta of the portfolio from zero to (2,500×0.7) = 1,750. This means that 1,750 of the underlying stock position will need to be said to maintain both gamma and delta neutrality.74.Answer: BYou have purchased a bull spread. You will exercise the call chat you purchased for a net profit of (34 - 25) - 3 = $6 per share. The call that you sold will not be exercised, so your net profit is the cost of $1 per share. Your total net profit is 6 + 1 = $7 per share.75.Answer: AIf the investor has written 15,000 call options, he must go long delta times the short option position to create a delta-neutral position. or buy $15,000×0.50 = 7,500 shares. Note that the delta of a call option, which is exactly at-the-money, is 0.5.76.Answer: BThe historical simulation V AR for 5% is the fifth lowest return, which is -1.59%; therefore, the correct V AR is: -79,500 = (-0.0159)×(5,000,000).77.Because firms tend to release good news more readily than bad news, downgrades may be more of a surprise, so downgrades affect stock prices more than upgrades when the firm reveals the good news associated with the upgrade prior to its occurrence.The “underrating” and “overrating” is seen more with the use of the through-the-cycle approach. As well, the ratings delivered by more specialized and regional agencies tend to be less homogeneous than those delivered by major players like S&P and Moody’s.78.Answer: BOperational risk economic capital is the difference between the loss at a given confidence level and the expected loss. In this case, $500,000 - $50,000 = $450,000.79.Answer: AThe head of the government bond trading desk at Kidder Peabody, Joseph Jett, misreported trades, which allowed him to report substantial artificial profits. After these errors were detected, $350 million in falsely reported gains had to he reversed.80.Answer: BThe R2 of the regression is calculated as ESS/TSS = (92.648/117.160) = 0.79, which means that the variation in industry returns explains 79% of the variation in the stock return. By taking the square root of R2, we can calculate that the correlation coefficient (r) = 0.889. The t-statistic for the industry return coefficient is 1.91/0.31 = 6.13, which is sufficiently large enough for the coefficient to be significant at the 99% confidence interval. Since we have the regression coefficient and intercept, we know that the regression equation is R stock= l.9X + 2.1. Plugging in a value of 4% for the industry return, we get a stock return of 1.9 (4%) + 2.1 = 9.7%.81.Answer: BFixed-rate coupon = 150,000,000×0.055 = $8,250,000B fixed = 8.25e-0.0575+158.25e-0.0625×2 = $147,440,000B floating = $150,000,000V swap= $150,000,000 - $147,440,000 = $2,560,00082.Answer: BThe rate of sampling error has no relation to the sample size; all things being equal, the likelihood of sampling error will be the same regardless of sample size. According to the central limit theorem, the sample mean for large sample sizes will be distributed normally regardless of the distribution of the underlying population.83.。

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一级模考

FRM⼀级模考FRM⼀级模拟题1 . Which of the following statements about the Sortino ratio are valid?I TheSortino ratio is more appropriate for asymmetrical return distributions.II The Sortino ratio compares the portfolio return to the return of a benchmark portfolio. III TheSortino ratio allows one to evaluate portfolios obtained through an optimization algoritlim that uses variance as a risk metric.IV TheSortino ratio is defined on the same principles as the Sharpe ratio, but theSortino ratio replaces the risk free rate with the minimum acceptable return and the standard deviation of returns with the standard deviation of returns below the minimum acceptable return.A. II and IIIB. I, III and IVC. I andIIID. I and IVAnswer: DA. Incorrect. II - The information ratio, not the Sortino ratio, compares the portfolio return to thereturn of a benchmark portfolio. III - The Sortino ratio allows one to evaluate portfolios obtainedthrough an optimization algorithm that uses semi-variance, not variance, as a risk metric.B. Incorrect. III - The Sortino ratio allows one to evaluate portfolios obtained through anoptimization algorithm that uses semi-variance, not variance, as a risk metric.C. Incorrect. III - The Sortino ratio allows one to evaluate portfolios obtained through an optimization algorithm that uses semi-variance, not variance, as a risk metric.D. Correct. I - Since the Sortino ratio uses the notion of semi-variance, it is more appropriate for asymmetric return distributions than any metric that uses standard deviation (such as the Sharpe ratio). IV - The Sortino ratio is similar to the Sharpe ratio, except the risk free rate is replaced with the minimum acceptable return in the numerator and the standard deviation of the returns is replaced with the standard deviation of the returns below the minimum acceptable return in the denominator. II - The information ratio, not the Sortino ratio, compares the portfolio return to the return of a benchmark portfolio. III - The Sortino ratio allows one to evaluate portfolios obtained through an optimization algorithm that uses semi-variance, not variance, as a risk metric.2. An analyst has compiled thefollowing information on a portfolio:. Sortino Ratio: 0.82. Beta: 1.15. Expected return: 12.2%Standard deviation: ll.g%Risk-free rate : 4.75%What is the semi-standard deviation of the portfolio return?A . 0.4%B . 8.2%C. 14.9%D. 9.08%Answer:DAs a result, the correct answer is D.3 .An analyst gathers the following data about the mean monthly returns of four securities.: Which security has the lowest and highest level of relative risk as measured by the Coefficient of variation?Answer: DThe coefficient of variation, CV = standard deviation/arithmetic mean, is a common measure of relative dispersion (risk) CVW = 0.4/0.5 = 0.80, CVX = 0.7/0.9 = 0.78; CVY = 4.7/1.2 = 3.92 and CVZ = 5.2/1.5=3.47 Because a lower relative risk, Security X has the lowest relative risk and Security Y has the highest relative risk.4. You have been asked to evaluate the performance of two hedge funds: Global Asset Management I and International Momentum II. Both are benchmarked to MSCI EAFE. The volatility of EAFE is 17.5% and the annualized performance is 10.6%. The risk-free rate is 3.5%.Which of the two funds had a higher relative risk-adjusted performance (RAP)last year, and what is the RAP?A. International Momentum 11, 9.97%B. International Momentum II, l .18%C. Global Asset Management l, 9.93%D. Global Asset Management l, 6.16%5 .Suppose the daily returns of a portfolio and a benchmark portfolio it is replicatingare as follows:。

FRM一级模考

FRM一级模拟题1 .Value at risk (V AR) can be viewed as a measure of risk capital, which is the economic capital required to support a financial activity. Economic capital is the amount of capital that should be set aside as a cushion against:a. catastrophic losses.b. expected losses.c. unexpected losses.d. expected and unexpected losses.2. A $1,000 par corporate bond carries a coupon rate of 6%, pays coupons semiannually, and has ten coupon payments remaining to maturity. Market rates are currently 5%. There are 90 days between settlement and the next coupon payment. The dirty and clean prices of the bond, respectively, are closest to:a. $1,043.76, $1,026.73.b. $1,056.73, $1,041.73.c. $1,069.70, $1,056.73.d. $1,043.76, $1,071.73.3. Which of the following statements regarding option "Greeks" is(are) correct?I. Vega measures the sensitivity of option prices to changes in volatility.II. Forward instruments cannot be used to create gamma-neutral positions.III. Rho is a much more important risk factor for equities than for fixed-income derivatives.IV. Theta represents the expected change in delta For a change in the value of the underlying.a. I and III only.b. I and II only.c. IV only.d. I, II, and IV.4. The S&P 500 index is trading at 1,015. The S&P 500 pays an expected continuously compounded dividend yield of 2%, and the continuously compounded risk-free rate is 4.1%. The value of a 3-month futures contract on the S&P 500 is closest to:a. 979.86.b. 997.68.c. 1,020.34.d. 1,350.59.5. Which of the following possible portfolios cannot lie on the efficient frontier:a. Portfolio 1 only.b. Portfolio 3 only.c. Portfolios 1 and 4.d. Portfolios 2 and 3.。