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07FRM真题答案3

07FRM真题答案3
07FRM真题答案3

94.The joint probability distribution of random variables X and Y is given by f (x, y)=k*x*y for

x=1,2,3, y=1,2,3, and k is a positive constant. What is the probability that X+Y will exceed 5?

a.1/9

b.1/4

c.1/36

d.Cannot be determined

95.Which of the following is not an approach for detecting style drift of hedge funds?

a.Performance attribution

b.Peer group comparison

c.Cash flow analysis

https://www.wendangku.net/doc/666750335.html,munication with fund manager

96.To hedge against future, unanticipated, and significant increases in borrowing rates, which of

the following alternatives offers the greatest flexibility for the borrower?

a.Interest rate collar

b.Fixed for floating swap

c.Call swaption

d.Interest rate floor

97.Assume the true distribution of returns is leptokurtotic. If we assume normality when we

calculate the V aR, then which of the following statements is true:

a.The 95% V aR is overstated.

b.The 95% V aR is understated.

c.The 95% V aR is appropriate.

d.We cannot state the relationship between the true V aR and the calculated V aR.

The next three questions use the following data:

98. A portfolio consists of two bonds. The credit-V aR is defined as the maximum loss due to

defaults at a confidence level of 98% over a one-year horizon. The probability of joint default of the two bonds is 1.27%, and the default correlation is 30%.

Bond V alue one year forward One year cumulative default probability Recovery rate B1=USD 1,000,000 3% 60%

B2=USD 600,000 5% 40%

What is the expected credit loss of the portfolio?

https://www.wendangku.net/doc/666750335.html,D 0

https://www.wendangku.net/doc/666750335.html,D 9,652

https://www.wendangku.net/doc/666750335.html,D 20,348

https://www.wendangku.net/doc/666750335.html,D 30,000

98.What is your best estimate of the credit-V aR for this portfolio of bonds based on the

distribution of losses due to defaults?

https://www.wendangku.net/doc/666750335.html,D 570,000

https://www.wendangku.net/doc/666750335.html,D 400,000

https://www.wendangku.net/doc/666750335.html,D 360,000

https://www.wendangku.net/doc/666750335.html,D 370,000

99.In the previous question, you estimated a V aR that corresponds to the V aR obtained from

CreditRisk+. Suppose that instead you wanted to estimate the V aR using the CreditMetrics approach. If you were given all additional data listed below, which data would you not need to estimate the CreditMetrics-Style credit-V aR?

a.V olatility of firm value for each issuer

b.Transition matrix for downgrades and upgrades in addition to default probabilities

c.Tern structure of credit spreads and interest rates

d.Promised coupon payments and maturity

101. Given the information provided in the table below, what is the risk budget, at the 99% confidence level of the following CHF million equally weighted investment portfolio?

Asset Expected Return V olatility Correlation

Stocks Bonds Stocks 24.00% 18% 1 0.1

Bonds 15.00% 6% 0.1 1

a. CHF 20.97 million

b. CHF 13.98 million

c. CHF 27.96 million

d. CHF 22.77 million

102. The Chief Risk Officer (CRO) of an exporting firm is attempting to estimate the firm’s one-year cash flow at risk. Which of the following issues describes an approach that is irrelevant to the task to the CRO?

a. Because cash flow at risk is generally estimated over a quarter or over a year, it is

necessary to forecast the future values of risk factors.

b. To the extent that the firm’s income from exports is best approximated by a real option

because the firm does not have to export when the price of the foreign currency is

unexpectedly low, the CRO can use option analysis and does not have to worry about

forecasting exchange rates.

c. A parametric approach can be used if exposures to foreign exchange risk factors are

linear, if there are no other risk factors, and if exchange rate changes are normally

distributed.

d. Using a Monte Carlo approach will help the CRO if the firm’s foreign currency income

is a nonlinear function of exchange rates.

103. A single stock has a price of USD 10 and a current daily volatility of 2%. Using the delta-normal method, the V aR at the 95% confidence level of a long at-the-money call on this stock over a one-day holding period is approximately

https://www.wendangku.net/doc/666750335.html,D 1.645

https://www.wendangku.net/doc/666750335.html,D 0.16

https://www.wendangku.net/doc/666750335.html,D 0.33

https://www.wendangku.net/doc/666750335.html,D 0.23

104. Y our bank is using the internal models approach to estimate its general market risk charge.

The multiplication factor ‘k’, set by the regulator, is 3 and banks are allowed to use the square root rule to scale daily V aR. The previous day’s one-day V aR estimate is EUR 3 million, and the average of the daily V aR over the last 60 days is EUR 2 million. Given the above information, what will be the market risk charge for your bank?

a.EUR 9.49 million

b.EUR 28.46 million

c.EUR 6.32 million

d.EUR 18.97 million

105. A portfolio manager has a bond position worth USD 100 million. The position has a modified duration of eight years and a convexity of 150 years. Assume that the term structure is flat.

By how much does the value of the position change if interest rates increase by 25 basis points?

https://www.wendangku.net/doc/666750335.html,D -2,046,875

https://www.wendangku.net/doc/666750335.html,D -2,187,500

https://www.wendangku.net/doc/666750335.html,D -1,953,125

https://www.wendangku.net/doc/666750335.html,D -1,906,250

106. Suppose you are holding 100 Wheelbarrow Company shares with a current price of USD 50.

The daily historical mean and volatility of the return of the stock is 1% and 2%, respectively.

The bid-ask spread of the stock varies over time. The daily historical mean and volatility of the spread is 0.5% and 1%, respectively. Calculate the daily liquidity-adjusted V aR (LV aR) at 99% confidence level (both the return and spread of the stock are normally distributed):

https://www.wendangku.net/doc/666750335.html,D 254

https://www.wendangku.net/doc/666750335.html,D 229

https://www.wendangku.net/doc/666750335.html,D 325

https://www.wendangku.net/doc/666750335.html,D 275

107. Consider the following potential operational risks. Due to a rogue trader, we estimate that over one-year period there is a 10% chance we could lose anywhere between EUR 0 and EUR 100 million (equal probability for all points within that range and 0 probability of any losses outside that range). Due to model risk, we estimate that over a one-year period there is

a 20% chance that we will lose EUR 25 million normally distributed with a standard

deviation of EUR 5 million. Which of the following statements is true?

a.The expected loss from a rogue trader is less than the expected loss from model risk.

b.The expected loss from a rogue trader is greater than the expected loss from model risk.

c.The maximum unexpected loss from a rogue trader at the 95% confidence level is less

than the maximum unexpected loss at the 95% confidence level from model risk.

d.The maximum unexpected loss at the 95% level from a rogue trader is greater than the

maximum unexpected loss at the 95% level from model risk.

108. The risk-free rate is 5% per year and a corporate bond yields 6% per year. Assuming a recovery rate of 75% on the corporate bond, what is the approximate market implied one-year probability of default of the corporate bond?

a. 1.33%

b. 4.00%

c.8.00%

d. 1.60%

109. A mutual fund investing in common stocks has adopted a liquidity risk measure limiting each of its holdings to a maximum of 30% of its 30-day average value traded. If the fund size is USD 3 billion, what is the maximum weight that the fund can hold in a stock with a 30-day average value traded of USD 2.4 million?

a.24.00%

b.0.08%

c.0.024%

d.80.0%

110. Bank A makes a USD 10 million five-year loan and wants to offset the credit exposure to the obligor. A five-year credit default swap (CDS) with the loan as the reference asset trades on the market at a swap premium of 50 basis points paid quarterly. In order to hedge its credit exposure, Bank A

a.sells the five-year CDS and receives a quarterly payment of USD 50,000.

b.buys the five-year CDS and makes a quarterly payment of USD 12,500.

c.buys the five-year CDS and receives a quarterly payment of USD 12,500.

d.sells the five-year CDS and makes a quarterly payment of USD 50,000.

111. Y ou don’t have access to KMV’s data. Y our boss wants you to estimate the probability of default of a credit. To do so, you use the Merton model because the credit you are considering has no systematic risk. In Merton’s model, the distance to default and expected default frequency are:

a.negatively and linearly related.

b.positively and linearly related.

c.negatively and nonlinearly relate

d.

d.positively and nonlinearly related.

112. An investor is investigating three hedge funds as potential investments. Hedge fund A is an equity market neutral fund, B is a global macro fund with emphasis on equity markets, and C is a convertible arbitrage fund. Which answer correctly specifies the funds with the highest exposure to a worldwide, value-weighted equity index and to a credit default swaps index?

Highest Equity Index Exposure Highest Credit Default Swap Index Exposure

a. A C

b. B C

c. B A

d. A B

113. Y our 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.

114. It has been found that the correlations across indices increase during adverse market events

(e.g., severe volatility, market crash). Y ou are assessing the risks of a long-only global equity

portfolio and are asked to describe for your boss the implications adverse market events might have in a V aR context. Which of the following statements is correct about the impact on future estimates of V aR for a long-only global equity portfolio?

a.Following the onset of adverse market events, future V aR estimates will increase if V aR

is estimated using the historical method compared to what would have happened had there been no adverse events.

b.The effect of increased correlation on future V aR estimates cannot be estimated because,

by definition, a crisis is a unique event with no comparable period.

c.The performance of future V aR estimates will remain unaffected since by definition a

crisis has a probability that is much lower than the probability level typically used to estimate V aR.

d.Following the onset of adverse market events, future V aR estimates will decrease if V aR

is estimated using a GARCH (1,1) model compared to what would have happened had there no adverse events.

115. Y ou 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%.

Fund V olatility Performance

Global Asset Management I 24.5% 12.5%

International Momentum II 27.3% 13.6%

Which of the two funds had a higher relative risk-adjusted performance (RAP) last year, and what is the RAP?

a.International Momentum II, 5.42%

b.International Momentum II, 1.18%

c.Global Asset Management I, 4.85%

d.Global Asset Management I, 6.16%

116. Suppose that A and B are random variables, each follows a standard normal distribution, and the covariance between A and B is 0.35. What is the variance of (3A+2B)?

a.14.47

b.17.20

c.9.20

d.15.10

117. The surplus of a pension fund is most important for

a. a defined benefit fund.

b. a defined contribution fund.

c. a sponsoring company with strong financial status that operates in different industries.

d. a young work forc

e.

118. Which of the following statements about liquidity risk elasticity (LRE) is incorrect?

a.LRE is primarily useful for examining marginal changes in funding costs on a net

asset/liability position

b.In calculating the sensitivity of a firm’s net assets to a change in its funding liquidity

premium, LRE assumes a parallel shift in funding costs across all maturities.

c.The LRE is only reliable for small changes in interest costs.

d.The LRE is a cash flow liquidity risk measure, not a present value liquidity risk measur

e.

119. Y our 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 the existing 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.

120. What does a hypothesis test at the 5% significance level mean?

a.P (not reject H0 | H0 is true)=0.05

b.P (not reject H0 | H0 is false)=0.05

c.P (reject H0 | H0 is true)=0.05

d.P (reject H0 | H0 is false)=0.05

121. Bank A has exposure to USD 100 million of debt issued by Company R. Bank A enters into a credit default swap transaction with Bank B to hedge its debt exposure to Company R. Bank

B would fully compensate Bank A if Company R defaults in exchange for premium. Assume

that the defaults of Bank A, Bank B, and Company R are independent and that their default probabilities are 0.3%, 0.5%, and 3.6%, respectively. What is the probability that Bank A will suffer a credit loss in its exposure to Company R?

a. 4.1%

b. 3.6%

c.0.0108%

d.0.0180%

122. A fund manager recently received a report on the performance of his portfolio over the last year. According to the report, the portfolio return is 9.3%, with a standard deviation of 13.5%, and beta of 0.83. The risk-free rate is 3.2%, the semi-standard deviation of portfolio is 8.4%, and the tracking error of the portfolio to the benchmark index is 2.8%. What is the difference between the value of the fund’s Sortino ratio (computed relative to the risk-free rate) and its Sharpe ratio?

a. 1.727

b.0.274

c.-0.378

d.0.653

123. Y our company is expecting a major export order from a London-based client. The receivables under the contract are to be billed in GBP, while your reporting currency is USD. Since the order is a large sum, your company does not want to bear the exchange risk and wishes to hedge it using derivatives. To minimize the cost of hedging, which of the following is the most suitable contract?

a.A chooser option for GBP/USD pair

b.A cross-currency swap where you pay fixed in USD and receive floating in GBP

c.A barrier put option to sell GBP against USD

d.An Asian call option on GBP against USD

124. A bond trader has bought a position in Treasury bonds with a 4% annual coupon rate on February 15, 2015. The DV01 of the position is USD 80,000. The trader decides to hedge his interest rate risk with the 4.5% coupon rate Treasury bonds maturing on May 15, 2017, which has a DV01 of 0.076 per USD 100 face value. To implement this hedge, approximately what face amount of the 4.5% Treasury bonds maturing on May 15, 2017, should the trader sell?

https://www.wendangku.net/doc/666750335.html,D 10,500,000

https://www.wendangku.net/doc/666750335.html,D 80,000

https://www.wendangku.net/doc/666750335.html,D 105,000,000

https://www.wendangku.net/doc/666750335.html,D 80,000,000

125. The bank you work for has a RAROC model. The RAROC model, computed for each specific activity, measures the ratio of the expected yearly net income to the yearly V aR risk estimate. Y ou are asked to estimate the RAROC of its USD 500 million loan business. The average interest rate is 10%. All loans have the same probability of default of 2% with a loss given default of 50%. Operating costs are USD 10 million. The funding cost of the business is USD 30 million. RAROC is estimated using a credit-V aR for loan businesses. In this case, the appropriate credit-V aR for the loans is 7.5%. The economic capital is invested and earns 6%. The RAROC is:

a.19.33%

b.46.00%

c.32.67%

d.13.33%

126. A firm is going to buy 10,000 barrels of West Texas Intermediate Crude Oil. It plans to hedge the purchase using the Brent Crude Oil futures contracts. The correlation between the spot and futures prices is 0.72. The volatility of the spot price is 0.35% per year. The volatility of the Brent Crude Oil futures price is 0.27 per year. What is the hedge ratio for the firm?

a.0.9333

b.0.5554

c.0.8198

d. 1.2099

127. An investor sells a June 2008 call of ABC Limited with a strike price of USD 45 for USD 3

and buys a June 2008 call of ABC Limited with a strike price of USD 40 for USD 5. What is the name of this strategy and the maximum profit and loss the investor could incur?

a. Bear Spread, Maximum Loss USD 2, Maximum Profit USD 3

b. Bull Spread, Maximum Loss Unlimited, Maximum Profit USD 3

c. Bear Spread, Maximum Loss USD 2, Maximum Profit Unlimited

d. Bull Spread, Maximum Loss USD 2, Maximum Profit USD 3

128. 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:

()()t y t drift vol e t =*?+*,and e (t) is distributed ~ N (0,1)

Where drift and vol are known parameters and ?t 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 until you get the full desired path.

b. 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.

129. What type of operational risk caused substantial losses to Barings Bank?

a.Inability to reconcile a new settlement system

b.Unauthorized trading

c.Political turmoil

d.Massive technology failure

130. Which one of the following statements does not apply to the Basel II Advanced Measurement Approach (AMA) for operational risk?

a.In contrast to the credit risk Internal Ratings Based Approaches, banks using the AMA

may estimate the correlation between different types of operational risks if their models satisfy regulatory requirements.

b.In contrast to credit risk regulatory capital for corporate loans, banks using the AMA

may have to set aside capital for both expected and unexpected operational risk losses.

c.Reporting of operational risk exposure to senior management is a necessary condition for

a bank’s ability to use the AMA.

d.To evaluate exposure to high-severity operational risk events, banks using the AMA may

use either scenario analysis of expert opinion or V aR model estimates based on internal data using extreme value theory.

131. The current value of the S&P 500 index is 1457, and each S&P futures contract is for delivery of 250 times the index. A long-only equity portfolio with market value of USD 300,100,000 has beta of 1.1. To reduce the portfolio beta to 0.75, how many S&P futures contract should you sell?

a.288 contracts

b.618 contracts

c.906 contracts

d.574 contracts

132. A bank assigns capital to its traders using component-V aR, which is based on the trading portfolio’s V aR estimated at the 99% confidence level. The market value of the bank’s trading portfolio is HKD 1 billion with a daily volatility of 2%. Of this portfolio, 1% is invested in a trading book with a beta of 0.6 relative to the trading portfolio. The closest estimate of the capital assigned to this trading book is

a.HKD 279,600

b.HKD 167,760

c.HKD 1,977,070

d.HKD 197,400

133. On January 1, 2006, a pension fund has assets of EUR 100 billion and is fully invested in the equity market. It has EUR 85 billion in liabilities. During 2006, the equity market declined by 15%, and yields increased by 1.2%. If the modified duration of the liabilities is 12.5, what is the pension fund’s surplus on December 31, 2006?

a.EUR 15.00 billion

b.EUR 12.93 billion

c.EUR 12.75 billion

d.EUR 12.57 billion

134. Considering options generally (i.e., not only plain vanilla calls and puts), which of the following statements about vega is correct?

a.A deep in-the-money up and out call option has a negative vega.

b.An option holder can never be vega negative.

c.A deep out-of-money digital option has a negative vega.

d.A deep out-of-money up and out call option has a negative vega.

135. Which of the following underlying macroeconomic conditions would leave an emerging market most vulnerable to the contagion effects of a currency crisis?

https://www.wendangku.net/doc/666750335.html,rge current account surplus, low foreign exchange reserves, nonconvertible currency

https://www.wendangku.net/doc/666750335.html,rge current account deficit, low foreign exchange reserves, fully convertible currency

c.Small current account deficit, high foreign exchange reserves, nonconvertible currency

https://www.wendangku.net/doc/666750335.html,rge current account surplus, low foreign exchange reserves, fully convertible currency

136. A three-year, credit-linked note (CLN) with underlying Company Z has a LIBOR+60 bps semi-annual coupon. The face value of the CLN is USD 100. LIBOR is 5% for all maturities.

The current three-year credit default swap spread for Company Z is 90 bps. The fair value of the CLN is closest to

https://www.wendangku.net/doc/666750335.html,D 100.00

https://www.wendangku.net/doc/666750335.html,D 111.05

https://www.wendangku.net/doc/666750335.html,D 101.65

https://www.wendangku.net/doc/666750335.html,D 99.19

137. A fund manager currently has a delta-neutral portfolio with a gamma of –11,000. He is interested in reducing the portfolio gamma to provide protection against large movements in prices. A particular traded call option has a delta of 0.87 and gamma of 3.5. To make the portfolio gamma neutral, how many call options must be bought or sold?

a.Buy 3,143 call options

b.Sell 3,143 call options

c.Buy 2,734 call options

d.Sell 2,734 call options

138. The severity distribution of operational losses usually has the following shape:

a.Symmetrical with short tails

b.Long tailed to the right

c.Uniform

d.Symmetrical with long tails

139. The risk of the occurrence of a significant difference between the mark-to-model value of a complex and/or illiquid instrument and the price at which the same instrument is revealed to have traded in the market is referred to as

a.liquidity risk

b.dynamic risk

c.model risk

d.mark-to-market risk

140. In a collateralized debt obligation (CDO), the Special Purpose V ehicle (SPV) is typically

a.A-rated.

b.AAA-rated.

c.not rate

d.

d.BBB-rated.

2020数学三真题答案

2020年全国硕士研究生入学统一考试 数学(三)试题及解析 一、选择题:1~8小题,每小题4分,共32分.下列每题给出的四个选项中,只有一个选项是符合题目要求的. (1)设()lim x a f x a b x a →-=- ,则sin ()sin lim ( )x a f x a x a →-= - (A).sin b a (B).cos b a (C).sin ()b f a (D).cos ()b f a 【答案】B 【解析】 x x sin ()sin sin ()sin ()lim lim cos ()cos () ()x a a a f x a f x a f x a f x b b f a x a f x a x a =→→---=?=?=--- 设()f x u =,则()()sin ()sin sin sin lim =lim cos cos ()()u f a x a u f a f x a u a u f a f x a u a =→→--==-- 则 x sin ()sin sin ()sin ()sin ()sin ()lim lim lim lim ()()=cos x a a x a x a f x a f x a f x a f x a f x a x a f x a x a f x a x a b a →→→→-----=?=?----- (2)函数11 ln 1()(1)(2) x x e x f x e x -+=--,则第二类间断点个数为() (A).1 (B).2 (C).3 (D).4 【答案】C 【解析】本题考查的是第一类间断点与第二类间断点的定义,判断间断点及类型的一般步骤为:

2018年国家公务员考试行测真题及答案解析(省级)

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