FRM一级模拟题(2)
FRM一级模考
FRM一级模拟题1 . Which of the following statements regarding the lease rate in commodity futures contracts is incorrect?I The lease rate is the return required by the lender in exchange for lending a commodity.II Assuming it is positive, as the lease rate increases, the futures price for a commodity increases.III In a cash-and-carry arbitrage, the lease rate is earned whether or not the underlying commodity is actually loaned.IV Lease rates are similar to dividends paid lo the lender of a share of common stock.V If the lease rate is less than the risk-free rate, the forward market is said to be in contango.A . II and IIIB . III and VC . I, III, and VD . II and IVAnswer: AThe lease rate is the amount that a lender requires as compensation for Jending a commodity. In determining the price of a commodity futures contract, the lease rate, 81, is subtracted from the risk-free rate, r, as follows:Assuming a positive lease rate, the lease rate effectively reduces the futures price, all else constant.This also assumes that there is an active market for lending the commodity underlying the futures contract. The lease rate can only be earned by actually lending the underlying commodity.2 . .Consider the factors that affect the price of futures contracts on various commodities. Which of the following statements does not accurately describe the relationship between a commodity's futures price and its underlying factors?A. Gold futures have an implicit lease rate which, because it is not actually paid by commodity borrowers, creates incentive to' hold physical rather than synthetic gold as ideal strategy to gain gold exposure.B. Natural gas is produced relatively consistently but has seasonal demand, causing the futures price to rise steadily in the fall months, since natural gas is too expensive to store.C. The cost of storing corn, which has relatively constant demand, causes the futures price to rise until the next harvest at which point the price falls.D. Relatively constant worldwide demand for oil and its ability to be cheaply transported keep oil prices relatively stable in the absence of short-run supply and demand.Answer: AGold futures have an implicit lease rate, because it is not actually paid by commodity borrowers, which creates incentive to hold physical rather than synthetic gold as ideal strategy to gain gold exposure.Gold can be loaned out to financial intermediaries and other investors willing to pay the lease rate (the price for borrowing the gold) to the lender. Thus, holding physical gold requires the investor to forgo earning the lease rate while also incurring storage costs. Therefore, the ideal gold exposure strategy is generally to hold synthetic gold.3 . The S&P 500 index is trading at l,025. The S&P 500 pays an expected dividend yield of l .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: A4 . Which of the following statements describing the role of a convenience yield in pricing 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, an d IV onlyD. I and II onlyAnswer: BThe convenience yield suggests there is a benefit, or convenience, to owning the spot asset. This generally means the spot price of the underlying asset will be above the futures price (normal backwardation). The convenience yield serves to reduce the cost of carry in the futures pricing relationship. .5 . Consider a 6-month futures contract on the S&P 500, and suppose the current value of the index is1330. Suppose the dividend yield is l.5% annually for the stocks underlying the index, and that the continuously compounded risk-free interest rate is 5.5% annually. What is the cost of carry for this futures contract?A. 4.0%B. -4.0%C. 2.0%D. -2.0%。
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一级模考
FRM一级模拟题1. Given the following 1-year transition matrix, what is the probability that a Baa rated firm will default over a 2-year period?a. 5.00%.b. 9.75%.c. 14.50%.d. 20.00%.解析：bAt the end of year 1 there is a 5% chance of default and an 80% chance that the firm will maintain a Baa rating. In year 2, there is a 5% chance of default if the firm was rated Baa after 1 year (80% x 5% = 4%). There is a 0% chance of default if the firm was rated Aaa after 1 year (10% x 0% = 0%). Also, there is a 15% chance of default if the firm was rated Caa after 1 year (5% x 15% =0.75%). The probability of default is 5% from year 1 plus 4.75% chance of default from year 2(i.e., 4% + 0% + 0.75%) for a total probability of default over a 2-year period of 9.75%.2 . Isabelle Burns, FRM, is an investment advisor for a firm whose client base is composed of high net worth individuals. In her personal portfolio, Burns has an investment in Torex, a company that has developed software to speed up internet browsing. Burns has thoroughly researched Torex and believes the company is financially strong yet currently significantly undervalued. According to the GARP Code of Conduct, Burns may:a. not recommend Torex as long as she has a personal investment in the stock.b. not recommend Torex to a client unless her employer gives written consent to do so.c. recommend Torex to a client, but she must disclose her investment in Torex to the client.d. recommend Torex to a client without disclosure as long as it is a suitable investment for the client.解析：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.3. Donaldson Capital Management, a regional money management firm, manages nearly $400 million allocated among three investment managers. All portfolios have the same objective, which is to produce superior risk-adjusted returns (by beating the market) for their clients. You have beenfollowing information based on the last ten years of returns.During the same time period the annual rate of return on the marker portfolio was 13% with a standard deviation of 19%. In order to assess the portfolio performance of the above managers, you should use:a. the Treynor measure of performance.b. the Sharpe measure of performance.c. the Jensen measure of performance.d. none of the above.解析：bThe Trcynor 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.4. Which of the following statements about the central limit theorem is least likely correct?a. The variance of the distribution of sample means is s2 / n.b. The central limit theorem has limited usefulness for skewed distributions.c. The mean of the population and the mean of all possible sample means are equal.d. When the sample size n is large, the sampling distribution of the sample means is approximately normal.解析：bThe central limit theorem holds for any distribution as long as the sample size is large (i.e., n > 30).5. Bank regulators are examining the loan portfolio of a large, diversified lender. The regulatorsfollowing is most likely the area that the regulator will want to focus on?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 increase 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 larger than expected.d. Unexpected loss, since the bank will need to set aside additional capital for the unlikely event that default losses are larger than expected.解析：dUnexpected 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.。
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一级模拟题1 . What is the lower pricing bound for a European call option with a strike price of 80 and one year until expiration? The price of the underlying asset is 90, and the. 1-year interest rate is 5% per annum. Assume continuous compounding of interest.A. 14.61B. 13.90C. 10.00D. 5.90Answer: BThe lower bound is the difference between the stock price and the present value of the strike price2 . The price of an American call stock option is equal to an otherwise equivalent European call stock option at time t when:I The stock pays continuous dividends from t to option expiration T. .. II The interest rates follow a mean-reverting process between t and T. .III The stock pays no dividends from t to option expiration T.IV Interest rates are non-stochastic between t and T.A. II and IVB. III onlyC. I and III .D. None of the above; an American option is always worth more than a European option. Answer: BThe only economic reason to exercise early is if the stock pays a dividend, and the full effect of the dividend payment is not expressed in a change in 'the stock price. If the stock does not pay a dividend, the price of an American option should be equal to the price of a European option. If the position pays a continuous dividend, the stock price will be adjusted for the value of the dividend3 . The current price for shares of ABC Co. is $100 and they pay no dividends. Interest rates are 6.00% per (annual 30/360), i.e. a completely flat yield curve. What is the approximate price of a perpetual call option with a strike price of 100 0n I share of ABC, if the call will be automatically exercised only when ABC reaches $150?A. $18B. $25C. $33D. $50Answer: CWith a flat yield curve and a rate of 6%, it will take 7 years for the FV of $100 to teach $150. The present value of $50 received in 7 years at 6 percent is $33.3. You can relate this without the use of the interest rate:4 . Which statement is false about the value of an option?A. At expiration, its premium equals intrinsic value.B. Before expiration, its premium is the sum of time and intrinsic value.C. It is determined by an option-pricing model.D. Intrinsic value is the difference between the market price and the strike price. Answer: CA case can be made for answer C based upon semantics; it can be argued that models don't determine values. The value of an option is the market price at which it trades.5 . A six-month call option sells for $30, with a strike price of $120. lf the stock price is $100 per share and the risk-free interest rate is 5%, what is the price of a 6-month put option with a strike price of $120?A. $39.20B. $44.53 .C. $46.28D. $47.04Answer: D。
FRM一级模考
FRM一级模拟题1 . A hedger calculates the covariance between the spot and the futures prices to be 0.05, the spot standard deviation to be 0.3, and the futures standard deviation to be 0.2. What is the optimal hedge ratio for this position?a. 0.075.b. 0.033.c. 0.250.d. 1.250.2. For an option-free bond, what are the effects of the convexity adjustment on the magnitude (absolute value) of the approximate bond price change in response to an increase in yield and in response to a decrease in yield, respectively?Decrease in yield Increase in yielda. Increase in magnitude Decrease in magnitudeb. Increase in magnitude Increase in magnitudec. Decrease in magnitude Decrease in magnituded. Decrease in magnitude Increase in magnitude3. Which of the following statements about the univariate, multivariate, and standard normal distributions is least likely correct?a. A univariate distribution describes a single random variable.b. A multivariate distribution specifies the probabilities for a group of related random variables.c. The standard normal random variable, denoted Z, has mean equal to 1 and variance equal to 1.d. The need to specify correlations is a distinguishing feature of the multivariate normal distribution in contrast to the univariate normal distribution.4. Which of the following statements regarding hypothesis testing are false?I. A Type I error is rejecting the null hypothesis when it is true.II. Reject the null hypothesis if p-value < significance level.III. The critical z-value for a one-tailed test of significance at the 0.05 level will be either +1.96 or -1.96.IV. The test statistic for hypotheses concerning equality of variances is computed asa. I and II.b. I and III.c. II and III.d. III and IV.5. Which of the following statements incorrectly describe(s) the Taylor Series approximation?I. The first and second derivatives of a function for the relationship between a financial derivative and its underlying asset estimate the delta and rate of change of delta, respectively.II. The Taylor Series provides good approximation estimates of price changes in callable bonds or mortgage-backed securities.III. The Taylor Series provides a good approximation for changes in a well-behaved quadratic function.a. I and II.b. II only.c. III only.d. II and III.。
FRM一级模考
FRM一级模拟题1 . Research and model projections indicate that a specific event is likely to move the CHF against the USD. While the direction of the move is highly uncertain, it is highly likely that magnitude of the move will be significant. Based on this information, which of the following strategies would provide the largest economic benefit?A. Long a call option on USD/CHF and long a put option on USD/CHF with the same strike price and expiration date.B. Long a call option on USD/CHF and short a put option on USD/CHF with the same strike price and expiration date.C. Short a call option on USD/CHF and short a put option on USD/CHF with the same strike price and expiration date.D. Short a call option on USD/CHF and long a put option on USD/CHF with the same strike price and expiration date.Answer: AWhile the direction of the move is highly uncertain, it is highly likely that magnitude of the move will be significant; we can see that we should take a trend trading. So, we buy a call option and buy a put-option, this strategy calls straggle.2 . Which of the following strategies creates a calendar spread?A. Buy a call option with a certain strike price and buy a longer maturity call option with the same strike price.B . Sell a call option with a certain strike price and buy a longer maturity call option with the same strike price.C . Buy a call option with a certain strike price and sell a longer maturity call option with the same strike price.D . Sell a call option with a certain strike price and sell a longer maturity call option with the same strike price.Answer: BDefinition of calendar spread3 . Your bank is an active player in the commodity market. The view of the economist of the bank is that inflation is expected to rise moderately in the near term and market volatility is expected to remain low. The traders are advised to undertake deals on the metals exchange to align your book to conform with the expectations of the economist of the bank. As risk manager, you are asked to monitor the positions of the traders to make sure that they have the exposures to inflation and market volatility sought by the bank. Which trader has taken an appropriate position among the traders you are monitoring?A. Trader A bought a call and a put, both with 90 days to expiration and with strike price equal to the existing spot level.B. Trader B bought a put option with a down-and-in knock in feature.C. Trader C bought a call option at the existing spot levels and sold a call at a higher strike price, both with 90 days to expiration.' D. Trader D sold a call option and bought a put at the existing levels, both with 90 days to expiration.Answer: CInflation is expected to rise moderately in the near term and market volatility is expected to remain low, stock price will increase moderately, so, choose bull spread.4 . Your bank is using the Black-Scholes model for valuation and pricing of exchange rate options with implied volatility of the at-the money options imputed from the market quotes. However, the research staff is now suggesting that exchange rate markets are exhibiting a volatility smile and theexisting valuations are incorrect. As a risk manager, you will be more concerned in which of the following situations?A. When the portfolio mainly consists of at-the-money long calls and puts.B. When the portfolio mainly consists of short put positions in deep out-of money options.C. When the portfolio mainly consists of short positions in at-the-money calls and puts.D. When the portfolio mainly consists of long call positions in deep out-of-money options. Answer: BWhen exchange rate markets exhibit a volatility smile, option at the money has smallest volatility. So A and C is incorrect. Generally speaking, long call option suffer limited loss when underlying asset drops, but short put suffer a huge loss. So, risk manager will be more concerned with short put position. D is correct.。
FRM一级模考
FRM一级模拟题1. The test statistic for an F-test of the equality of two sample variances is the:A. product of the two sample variancesB. ratio of the two sample standard deviationsC. product of the two sample standard deviationsD. ratio of the two sample variancesAnswer: DThe test statistic for an F-test of the equality of two sample variances is the ratio of the two sample variances,2. You have collected monthly returns for a mutual fund and want to 'test the null hypothesis that the standard deviation exceeds the advertised standard deviation of3.5%. The most appropriate test statistic is based on a:A. F-testB. t-testC. z-testD. chi-square testAnswer: DThe chi-square test is used to test hypotheses about a single population variance.3. lf the sample size is greater than 30 and population variance is unknown, the appropriate test for the sample mean is the:A. t-testB. z-testC. p-test or F-testD. t-test or z-testAnswer: DThe central limit theorem makes it appropriate to use the z-test with an unknown variance if the sample size is large enough (n > 30), regardless of the distribution of the population. Since thet-distribution and the z-distribution converge as sample size increases, either test is appropriate, although the t-test is a more conservative estimate. .Hypothesis Test4. What is the appropriate alternative hypothesis to test the statistical significance of the intercept term in the following regression?Answer: AIn this regression, al is the intercept term. To test the statistical significance means to test the Null hypothesis that al is equal to zero versus the alternative that not equal to zero.5. An analyst wants to test whether the variance of return from pharmaceutical stocks is different from that of the overall market. For this purpose, he obtains the following data from a sample of 21 pharmaceutical stocks and a sample of 41 stocks that are representative of the market. Mean return from pharmaceutical stocks = 8%, Standard deviation of return from pharmaceutical stocks = 9.2%, Mean return from market stocks = 12%, Standard deviation of return from market stocks = 13%. Based on this information and a 0.05 significance level:A. there is suffrcient evidence for a difference between the variance of pharmaceutical stocks and the variance of the market stocksB. there is insufficient evidence for a difference between the variance of pharmaceutical stocks and the variance of the market stocksC. there is sufflcient evidence that there is no difference between the variance of pharmaceutical stocks and the variance of the market stocksD. there is insufficient evidence that there is no difference between the variance of pharmaceutical stocks and the variance of the market stocksAnswer: B。
FRM一级模考
FRM一级模拟题1 . Which of the foIIOWJng are characteristics of a normal distribution?I Skewness equals to zeroII Mean less than medianIII Kurtosis greater than zeroIV Continuous and unboundedA. I and IVB. II and IIIC. I, II and IllD. I, Ill and IVAnswer: DThe characteristics of a norma] distribution are:Jt is a continuous distribution.Jt is bell shaped.Jt is symmetrical about the mean.Jt peaks at the mean expected value.It extends theoretically from negative infinity to positive infinity (the probability asymptotically approaches zero at plus and minus infinity).It has a skewness of zero (i.e. it is symmetric).It has a kurtosis (the level of peakedness) of three.Below three the distribution is platykurtic.2 .Given two variables X and Y that are lognormally distributed, what is the distribution of X x Y?A. Normal 'B. LognormalC. ExponentialD. None of the aboveAnswer: BIf X and Y are lognormally distributed, log(X) and.log(Y) will be normally distributed, which means that log(X) + log(Y) = log(XY) is also normally distributed, implying that XY must be lognormally distributed.3 .Which of the following statements conceming probability distributions is/are CORRECT?The mean of a uniform distribution is (a + b)/2.II The variance of a standard normal distribution is l.III Risk analysts would not be able to assume a distribution is normal which kurtosis is equal to 3.IV For acontinuous uniform distribution with upper bound 8 and lower bound l, the probability of X = 3 is approximately 33%.A . I, III, and IV onlyB . I, II and III onlyC . I and II onlyAnswer: CThe mean of a uniform distribution is (a + b)/2. A standard normal distribution has a mean of 0 and a variance of l. For a continuous uniform distribution, the probability of a variable being equal to a specific vajue is zero. One of the properties of a standard normal distribution is that kurtosis is equal t0 3.4 .Which one of the following statements about the normal distribution is NOT accurate?A. Kurtosis equals 3B. Skewness equals 1C. The entire distribution can be characterized by two moments, mean and varianceD. The normal density function has the following expression:Answer: BThe skewness of the normal distribution is 0, not l.The kurtosis of the normal distribution is 3, the normal distribution can be completely described by its mean and variance, and the density function of the normal distribution is' as shown.5 .Which of the following statements is the most accurate about the relationship between a normal distribution and a Student's t-distribution that have tlhe same mean and standard deviation?A. They thave tlhe same skewness and the same kurtosisB. Tlhe Student's t-distribution has larger skewness and larger kurtosisC. The kurtosis of a Student's t-distribution converges to that of tlhe normal distribution as tlhe number of degrees of freedom increasesD. Tlhe normal distribution is a good approximation for tlhe Student's t-distribution when the number of degrees of freedom is small。
FRM一级模考
FRM一级模拟题1 . Which of the following best describes the relationship between leverage, margin calls, position size, and liquidity as presented in the Long-Term Capital Management case?a. Leverage allows a firm to establish large positions than can generate large margin calls and force, liquidations that can exacerbate declining market prices.b. Leverage can help offset the risk of being unable to meet large margin calls generated from large positions, thereby increasing a firm's liquidity.c. Margin calls create leverage that can force a firm to assume illiquid positions even in small trades.d. Margin calls decrease the liquidity of a position unless the firm uses leverage to decrease the size of a hedge.2. For the past four years, the returns on a portfolio were 6%, 9%, 4%, and 12%. The corresponding returns of the benchmark were 7%, 10%, 4%, and 10%. The minimum acceptable return is 7% and the mean squared deviation from the minimum return is 2.5. The portfolio's Sortino ratio is:a. 0.4743.b. 0.2143.c. 0.5303.d. 0.6700.3. A portfolio manager manages a $10 million portfolio that has a beta of 1.0 relative to the S&P 500. The S&P 500 futures are trading at 1,100 and the multiplier is 250. He would like to hedge exposure to market risk over the next few months. Suppose that at the maturity of the futures contract, the market index is trading at 1,090 and the portfolio has experienced a 1% decline in value. Evaluate the following statements:I. The appropriate hedge for the portfolio is a long position in 36 contracts.II. The net impact of the market decline on the appropriately hedged portfolio is a gain of $10,000.a. Only statement I is correct.b. Only statement II is correct.c. Both statements are correct.d. Neither statement is correct.4. Given the following 1-year transition matrix, what is the probability that an Aaa rated firm will default over a 2-year period?a. 0.00%.b. 0.50%.c. 0.65%.d. 0.23%.5. A manager forecasts a bond portfolio return of 10% and estimates a standard deviation of annual returns of 4%. Assuming a normal returns distribution and that the manager is correct:a. the 90% confidence interval will be from 3.20% to 17.2%.b. there is a 95% probability that the portfolio return will be between 2.16% and 17.84%.c. the 1% confidence interval will be from -0.32% to 20.32%.d. there is a 32% probability that the portfolio return will be between 6% and 14%.。
frm一级模考试题第二套答案_程黄维
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 . In perfect capital markets, the only exception to the idea that firm hedging activities do not increase firm value is when:A .Diversifiable risk is decreased.B .Systematic risk is decreased.C .There are no exceptions.D .Risk premiums are very high.Answer: CIn perfect capital markets, there is no exception to the rule that hedging will NOT increase firm value. Assuming perfect markets, shareholders can hedge at the same cost as the firm. They will not pay the firm to do something that they can do on their own account at the same price.2 . A portfolio manager wishes to leverage her equity position using index futures to a beta of l.5. She currently has a well-diversified $250 million equity portfolio with a beta correlated to the market. The current value of the S&P futures index is 1,200 (multiplier of 250). How many contracts are necessary to adjust the beta of this portfolio?A. Short 417 contractsB. Short l,250 contractsC. Long 417 contracts .D: Long l,250 contractsAnswer: CTo increase the beta of the portfolio from the market beta (1.0) t0 1.5, the portfolio managershould take a long position:3 .The capital asset pricing model (CAPM) is based on several limiting assumptions that the arbitrage pricing theory (APT) attempts to alleviate.Which of the following statements is correct regarding the CAPM? The CAPM:A.Does not assume that the expected excess returns for the market are known.B.Assumes that the market portfolio should be the one with the highest Sharpe ratio of all possible portfolios.C.Does not assume that investors have access to the same information.D. Assumes that investors' expectations reading risk and return are not identical but normally distributed. '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 samefor risk and return are identical.4 .All of the following are assumptionof the Capital Asset Pricing Model EXCEPTA .Each investor seeks to maximize the expected utility of wealth at the end ofthat investor's horizon.B . Investors can borrow and lend at the same risk-free rate.C. Investors have the same expectations concerning returns.D. The time horizons of investors are normally distributed.Answer: DThe 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.5. Which of the following statements regarding the valuation applications of the CAPM is least likely correct?A. According to the CAPM, only systematic risk is rewarded with higher expected returns.B. In a frictionless market, financial transactions to reduce a firm's systematic risk will not increase firm value.C .Operational changes to reduce a firm's systematic risk may increase firmvalue.D. The value of a firm's equity is equal to the present value of its expected netincome, where the appropriate discount rate is the expected rate of returnfrom the CAPM.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).Factor Models and APT。
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.。
FRM一级模考
FRM一级模拟题1 . Which of the following is not a characteristic of self-insurance as a means to hedge against catastrophic and operational losses?a. External insurance offers protection against a broader range of operational risks than self-insurance.b. Using captive insurers has tax benefits associated with self-insurance.c. Exercising risk prevention and control is a form of self-insurance.d. Establishing a contingent line of credit that becomes available in the event of a large operational loss is one method of self-insurance.2. To equitize the cash portion of assets under management, a portfolio manager enters into a longg futures position on the S&P 500 index with a multiplier of 250. The cash position is $5,000,000, which at the current futures value of 1,000 requires the manager to be long 20 contracts. If the current initial margin is $12,500 per contract, and the current maintenance margin is $10,000 per contract, the variation margin the portfolio manager needs to advance if the futures contract value falls to 985 at the end of the first day of the position is closest to:a. $15,000.b. $30,000.c. $300,000.d. $75,000.3. Assume that the current 1-year forward exchange rate is 1.200 USD per EUR. An Amcrican bank pays a 2.4% annual interest ratc on a 1-year deposit and a4.0% annual interest rate on a 3-year USD deposit. A European bank pays a 1.5% annual interest rate for a 1-year deposit and a 2.0% annual interest rare for a 3-year EUR deposit. The forward exchange rate in USD per EUR for exchange three years from today is closest to:a. 1.224.b. 1.249.c. 1.261.d. 1.296.4.WEB, an investment-banking firm, is the principal underwriter for MTEX's upcoming debenture issue. Lynn Black, FRM, is an analyst with WEB, and she learned from an employee in MTEX's programming department that a serious problem was recently discovered in the software program of its major new product line. In fact, the problem is so bad that many customers have canceled their orders with MTEX. Black checked the debenture's prospectus and found no mention of this development. The red herring prospectus has already been distributed. According to the GARP Code of Conduct, Black's best course of action is to:a. inform her immediate supervisor at WEB of her discovery.b. keep quiet because this is material nonpublic inside information.c. notify potential investors of the omission on a fair and equitable basis.d. report her discovery to the Division of Corporation Finance of the Securities and Exchange Commission.5. Which of the following theories often used to explain the term structure of interest rates is based on the idea that most investors prefer short-term liquid deposits, all else equal?a. Liquidity preference theory.b. Supply-demand theory.c. Market segmentation theory.d. Unbiased expectations theory.。
FRM一级模考
FRM一级模拟题1 . .Y our firm's fixed-income portfolio has interest-only bonds(10), callable corporate bonds, inverse floaters, noncallable corporate bonds. Y our boss wants to know which of the following securities can lose value as yields decline.A. Callable corporate onlyB. Inverse floater onlyC. IO and callable corporate bondD. IO and noncallable corporate bondAnswer: CIO has a negative Duration as the yield decline, the price of the IO will also decline.Callable corporate bond has a negative duration when the bond price is close to the strike price of the call option embedded with the bond. And the price will decrease when the yield decline.If Callable Bond is called before it reaches to the theoretical values, it will lose its potential value.2 . A convertible bond trader has purchased a long-dated convertible bond with a call provision. Assuming there is a 50% chance that this bond will be converted into stock, which combination of stock price and interest rate level would constitute the worst case scenario?A. Decreasing rates and decreasing stock pricesB. Decreasing rates and increasing stock pricesC. Increasing rates and decreasing stock pricesD. Increasing rates and increasing stock pricesAnswer: CThe value of a call increases with the maturity of the call and the volatility of the underlying asset value (which here also increases with the maturity of the swap contract). So A and D are wrong. In contrast, the value of the right to receive an asset at K decreases as K increases.3 . What is the main reason why convertible bonds are generally issued with a call?A. To make their analysis less easy for investorsB. To protect against unwanted takeover bidsC. To reduce durationD. To force conversion if in-the-moneyAnswer: DConvertible bonds are usually issued with a call option to force the holder to convert the bond into shares if the stock price rises and the conversion feature becomes valuable.4 . Issuers generally issue convertible bonds with a call to:A. Manage their durationB. Make their valuation easierC. Force conversion if in-the-moneyD. Protect against corporate predatorsAnswer: CIssuer generally issue convertible bonds with a call to limit the downside if the share price rises sharply and force their conversion.5 . Consider 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 unchangedAnswer: A.The convertible bond implicitly gives bondholders a call option on the underlying stock. The delta of 'this option will vary between 0 (when the option is extremely out of the money) and l (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 underlying stock.。
FRM一级模考
专注国际财经教育FRM一级模拟题1 . Consider a portfolio consisting of a long 5-year right to pay fixed swaption and a short 5 year right to receive fixed swaption, with the same strike rate, the same maturity and underlying swap rate, and identical rate basis for the payments. Which of the following instruments can be best used to hedge the interest rate risk in this portfolio?A. Eurodollar FuturesB. Interest rate swapsC. Treasury bondsD. Interest rate capsAnswer: BThe portfolio can be hedged using interest rate swaps paying floating and receiving fixedBeta Hedging2 . Consider an equity portfolio with market value of USD l00M and a beta of l.5 with 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 t0 0.8?A. Long 600 S&P 500 futures contractsB. Short 600 S&P 500 futures contractsC. Long 280 S&P 500 futures contracts ~D. Short 280 S&P 500 futures contractsAnswer: DTo reduce the beta of a portfolio, one needs to lower the position's exposure to the market. Thus, one needs to short futures contracts. The number of futures contracts, N, is:。
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。
FRM一级模考
FRM一级模拟题1. Roger Smith, FRM, has been invited to join a group of analysts in touring the riverboats of River Casino Corp. For the tour, River Casino has arranged chartered flights from casino to casino since commercial flight schedules are invenient and not practical for the group's time schedule. River Casino has also arranged to pay the hotel bill for the three nights of the tour. The trip is purely business. According to the GARP Code of Conduct, Smith:a. may accept the arrangements as they are.b. may accept the flight but must pay his own hotel bill.c. must offer to pay for his share of the airfare and his own hotel bill.d. must decline to accept the trip because the arrangements are inappropriate.2. SCU stock is currently priced at $106 per share, and the risk-free interest rate is3.25%. Assuming that SCU does not pay any dividends, what is the lower bound of an American put option on SCU that expires in three months and has an exercise price of $110?a. $0.b. $0.48.c. $3.11.d. $4.00.3. Which of the following hedged positions would be subject to basis risk?I. A jet-fuel wholesaler expects the price of jet fuel to fall in one year. The wholesaler therefore establishes a short position in a 1-year crude oil contract to offset price declines.II. A jewelry maker is expecting to make large monthly purchases of gold in each of the next nine months, but is afraid the price will rise. The company enters into a long strip hedge using gold futures.III. A drilling company will have one million barrels of crude oil available for sale in August on the east coast. It is currently February so the company has taken a short 6-month crude oil futures position on one million barrels for east coast delivery.IV. A grain company must deliver one million bushels of corn in six, nine, and twelve months. The company enters into a short stack hedge using 3-month futures contracts on corn.V. Hedging Spanish natural gas futures for delivery in Louisiana.a. I, II, and IV.b. II, IV, and V.c. I, IV, and V.d. I, III, and V.4. Which of the following may be disadvantages of using implied volatility to predict the future volatility?I. The implied volatility model assumes that asset returns follow a continuous time lognormal diffusion process.II. Options with the same underlying assets may be trading at different "vol" terms.III. Irnplied volatility is less than actual volatility on average.IV. Data is limited to a few assets and markets.a. II only.b. I, II, and IV only.c. III and IV only.d. I, II, III, and IV.5. Firmwide hedging can make managerial stock ownership a more effective device to induce managers to maximize firm value by:a. eliminating sources of fluctuation in market value that are not under management control.b. reducing information asymmetry.c. reducing systematic risk.d. insuring the present value of expected costs of financial distress are equal to the costs of the hedging strategy employed.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
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。