注册金融分析师一级-17及答案解析.doc

1、注册金融分析师一级-17 及答案解析(总分：100.00，做题时间：90 分钟)一、单项选择题(总题数：36，分数：100.00)1.Consider a universe of ten bond from which an investor will ultimately purchase seven bond for his portfolio. If the order in which he buys these bonds is ignored, how many potential 5-bond combinations are there?（分数：2.50）A.7B.120C.2

2、8802.根据下表所示的数据解答问题： 离散型随机变量 X 的概率分布 X 1 2 3 4 5 P(X) 0.18 0.16 0.08 0.25 0.33 The cdf of 4, or F(4) is:（分数：2.50）A.0.25B.0.42C.0.673.A random variable with a finite number of equally likely outcomes is best described as a:（分数：2.50）A.binomial distribution.B.discrete uniform distribution.C.continuous u

3、niform distribution.4.A recent study indicated that 70% of all college students have a notebook PC. The probability that exactly three college students will have a notebook PC in a random selection of four is approximately:（分数：2.50）A.0.10B.0.41C.0.705.Assume that 45% of candidates who sit for CFA ex

4、amination pass it the first time in China. Of a random sample of 30 candidates in China who are sitting for the exam for the first time, what is the expected number of candidates that will pass?（分数：2.50）A.12.45B.14.00C.15.366.A continuous uniform distribution has the parameters a = 2 and b = 10. The

5、 F(7) is:（分数：2.50）A.0.375B.0.500C.0.6257.Approximately 90% of all observations for a normally distributed random variable fall in the interval:（分数：2.50）A.E(x)1.65B.E(x)1.96C.E(x)2.588.An analyst determined that approximately 99 percent of the observations of daily sales for a company were within the

6、 interval from $230000 to $480000 and that daily sales for the company were normally distributed. The standard deviation of daily sales for the company was closest to:（分数：2.50）A.$35682B.$43785C.$484509.For a standard normal distribution, F(0) is:（分数：2.50）A.0.0B.0.5C.1.010.For the standard normal dis

7、tribution, P0X1.88 is:（分数：2.50）A.0.47B.0.49C.0.97一项针对基金投资者的研究表明，投资者的年人均收入服从平均值为 35000 美元、标准差为 7000 美元的正态分布。试根据上述条件解答问题：（分数：5.00）(1).What percentage of mutual fund investors have incomes less than $21000?（分数：2.50）A.0.58%B.1.14%C.2. 28%(2).What percentage of mutual fund investors have incomes greater

8、than $42000?（分数：2.50）A.15.87%B.24.76%C.84.13%根据下表所示的数据解答问题： 投资组合的预期回报率和标准差 投资组合 A B C E(R p ) 16% 7% 15% p 33% 12% 28% （分数：5.00）(1).Given a threshold level of return of 5%, use the Roy“s safety-first criterion to choose the optimal portfolio.（分数：2.50）A.portfolio AB.portfolio BC.portfolio C(2).Given

9、a threshold level of return of 5%, use the Roy“s safety-first criterion to choose the optimal portfolio.（分数：2.50）A.portfolio AB.portfolio BC.portfolio C11.For a lognormal distribution, the:（分数：2.50）A.mean equals the median.B.probability of a negative outcome is zero.C.probability of a positive outco

10、me 50%.12.If a stock“s initial price is $10 and its year-end price is $14, then its continuous compounded annual rate of return is:（分数：2.50）A.19.6%B.28.7%C.33.6%13.Using hypothesized parameter values and a random number generator to study the behavior of certain asset returns is part of:（分数：2.50）A.M

11、onte Carlo simulation.B.historical simulation.C.standardizing a random variable.14.Sample error is defined as:（分数：2.50）A.an error that occurs when a sample of less than 30 elements is drawn.B.an error that occur during collection, recording, and tabulation of data.C.the difference between the value

12、of a sample statistic and the value of the corresponding population parameter.15.According to the central limit theorem, a sampling distribution of the sample mean will be approximately normal only if:（分数：2.50）A.the sample size is large.B.the underlying distribution is normally distributed.C.the var

13、iance of the underlying distribution is known.16.Assume that a population has a mean of 25 with a standard deviation of 3. If a random sample of 60 observations is drawn from this population, the standard error of the sample mean is closest to:（分数：2.50）A.0.05B.0.12C.0.3917.Which of the following is

14、least likely to be a desirable property of an estimate?（分数：2.50）A.unbiasednessB.reliabilityC.consistency18.Which of the following is least likely a property of t-distribution?（分数：2.50）A.As the degrees of freedom get larger, the variance approaches zero.B.It is defined by a single parameter, the degr

15、ees of freedom, which is equal to n-1.C.It has more probability in the tails and less at the peak than a standard normal distribution.19.An increase in which of the following items is most likely to result in an increase in the width of the confidence interval for the population mean?（分数：2.50）A.samp

16、le sizeB.reliability factorC.degrees of freedom20.A random sample of 64 supermarket customer spent an average of $43. Assuming the distribution is normal and the population standard deviation is $15, the 90% confidence interval for the population mean is closest to:（分数：2.50）A.41.085 to 44.915B.40.21

17、8 to 45.782C.39.916 to 46.08421.Tuross Online, Inc., sells books by mail. A sample of 16 recent orders showed the mean time taken to send out these orders was 35 hours with a sample standard deviation of 7 hours. Assuming the population is normally distributed, the 95% confidence interval for the po

18、pulation mean is closest to.（分数：2.50）A.31.2699 to 38.7301B.33.7352 to 36.2648C.34.2318 to 35.768222.What is the most appropriate test statistic for constructing confidence intervals for the population mean when the population is normally distributed, but the variance is unknown?（分数：2.50）A.The z-stat

19、istic at with n degrees of freedom.B.The t-statistic at /2 with n degrees of freedom.C.The t-statistic at /2 with n-1 degrees of freedom.23.The acceptable test statistic for constructing confidence intervals for the population mean of a normally distributed when the variance is unknown and the sampl

20、e size is large (n30) is the:（分数：2.50）A.z-statistic.B.t-statistic.C.z-statistic or t-statistic, hut t-statistic is more preferred.24.An analyst who uses historical data that was not publicly available at the time period being studied will have a sample with:（分数：2.50）A.look-ahead bias.B.time-period b

21、ias.C.sample selection bias.某投资者认为某地区房屋的平均价格高于 350000 美元。由该地区随机抽取的 64 幢房屋组成的样本的平均价格为 355000 美元。已知总体标准差为 25000 美元，该投资者希望基于 3%的显著水平进行假设检验。试根据上述条件解答问题。（分数：7.50）(1).The appropriate alternative hypothesis is:（分数：2.50）A.H: $350000.B.H: $350000.C.H: $350000.(2).The value of the calculated test statistic is

22、:（分数：2.50）A.z=0.8.B.z=1.6.C.z=3.2.(3).At a 3% level of significance, the investor should:（分数：2.50）A.reject the null hypothesis.B.fail to reject the null hypothesis.C.neither reject nor fail to reject the null hypothesis.25.If the significance level of a test is 0.1 and the probability of a Type erro

23、r is 0.4, what is the power of the test?（分数：2.50）A.0.04B.0.5C.0.626.某样本 A 和样本 B 分别由 36 个观测值和 25 个观测值组成，并均取自服从正态分布的总体。已知样本A 的平均值为 30 美元，标准差为 8 美元；样本 B 的平均值为 34 美元，标准差为 6 美元。试根据上述条件解答问题。 Consider the hypotheses structured for sample A as H 0 : =$26 versus H 0 : $26. At a 5% level of significance, the

24、null hypothesis:（分数：2.50）A.should be rejected.B.can not be rejected.C.can not be tested using this sample information provided.27.Consider the hypotheses structured for sample A and sample B as H 0 : A = B versus H a : A B , At a 10% level of significance, the null hypothesis:（分数：2.50）A.should be re

25、jected.B.can not be rejected.C.can not be tested using this sample information provided.28.A study was conducted to determine whether the standard deviation of monthly maintenance cost of an airplane is $500. A sample of 25 airplanes of same model had a mean monthly maintenance cost of $4300 and a s

26、tandard deviation of $545. Using a 10% level of significance, which of the following is the most appropriate conclusion regarding the difference between the hypothesized value of the population variance and the sample variance?（分数：2.50）A.The population and sample variances are significantly differen

27、t.B.The population and sample variances are not significantly different.C.There are no tests that may be used to test variance differences in small samples.29.Which of the following statements is least likely to be an advantage of technical analysis?（分数：2.50）A.It tells the analyst when to buy.B.It t

28、ells the analyst why investors are buying.C.It incorporates psychological as well as economic reasons for price changes.30.When the relative over-the-counter (OTC) to NYSE volume ratio is decreasing, contrary-opinion technicians would do which of the following?（分数：2.50）A.Hold.B.Be bearish and sell.C

29、.Be bullish and buy.31.If the confidence index (CI) increases (and the implied yield spread narrows), investors are doing which of the following?（分数：2.50）A.Selling quality bonds.B.Buying quality bonds.C.Selling common stocks.32.When debit balances (i.e. margin debit) in brokerage accounts decrease:（

30、分数：2.50）A.smart money technicians interpret this as a bearish sign.B.smart money technicians interpret this as a bullish sign.C.contrary-opinion technicians interpret this as a bullish sign.33.If the relative strength ratio increases, which of the following statements is correct?（分数：2.50）A.The marke

31、t index price increase equals the stock price increase.B.The market index price percentage increase is less than the stock price percentage increase.C.The market index price percentage increase is greater than the stock price percentage increase.注册金融分析师一级-17 答案解析(总分：100.00，做题时间：90 分钟)一、单项选择题(总题数：36，

32、分数：100.00)1.Consider a universe of ten bond from which an investor will ultimately purchase seven bond for his portfolio. If the order in which he buys these bonds is ignored, how many potential 5-bond combinations are there?（分数：2.50）A.7B.120 C.2880解析：解析 由题意可知，本题是一道组合问题。 即有 120 种由 5 种债券组成的潜在组合。 在上面的

33、计算过程中，我们用到了以下重要公式： 2.根据下表所示的数据解答问题： 离散型随机变量 X 的概率分布 X 1 2 3 4 5 P(X) 0.18 0.16 0.08 0.25 0.33 The cdf of 4, or F(4) is:（分数：2.50）A.0.25B.0.42C.0.67 解析：解析 F(4)=PX4 =PX=1+PX=2+PX=3+PX=4 =0.18+0.16+0.08+0.25 =0.67 本题也可以采用以下计算方法： F(4)=PX4=1-PX=5=1-0.33=0.67 这里需要注意的是，根据累积分布函数的定义，累积分布函数应当包含边界值的概率。因此，在本题中，F

34、(4)应当包含 X=4 的概率。相应地，选项 B 的计算结果是错误的。3.A random variable with a finite number of equally likely outcomes is best described as a:（分数：2.50）A.binomial distribution.B.discrete uniform distribution. C.continuous uniform distribution.解析：解析 离散型均匀随机变量(discrete uniform random variable)是指所有可能结果的概率都相等的离散型随机变量，即等

35、可能性的随机变量。从而该种随机变量的离散分布函数 F(x n )=np(x)，其中n 表示分布函数取值的个数。且各种可能结果的概率均为 1/N，其中 N 为所有可能结果的个数。因此，本题的正确选项为 B。4.A recent study indicated that 70% of all college students have a notebook PC. The probability that exactly three college students will have a notebook PC in a random selection of four is approxima

36、tely:（分数：2.50）A.0.10B.0.41 C.0.70解析：解析 由于每名大学生只有两种结果，即拥有一台笔记本电脑或不拥有一台笔记本电脑，因而该项试验属于伯努利试验。n 重伯努利试验服从参数为 n 和 P 的二项式分布。其计算公式为： 在本题中，n=4，x=3，p=0.7，从而有： 5.Assume that 45% of candidates who sit for CFA examination pass it the first time in China. Of a random sample of 30 candidates in China who are sittin

37、g for the exam for the first time, what is the expected number of candidates that will pass?（分数：2.50）A.12.45B.14.00 C.15.36解析：解析 n 重伯努利试验中事件 A 发生次数 x 的期望值 E(X)的计算公式为： E(X)=np 式中，p 为各次独立试验中事件 A 发生的概率。 显然，上述 n 重伯努利试验中的二项式随机变量 X 服从参数为 n 和 p 的二项式分布，即 XB(n，p)。 在本题中，n=30，p=0.45，则通过考试的考生人数的期望值 E(X)=np=300.

38、45=14。6.A continuous uniform distribution has the parameters a = 2 and b = 10. The F(7) is:（分数：2.50）A.0.375B.0.500C.0.625 解析：解析 由于 7 介于 210 之间，因而7.Approximately 90% of all observations for a normally distributed random variable fall in the interval:（分数：2.50）A.E(x)1.65 B.E(x)1.96C.E(x)2.58解析：解析 如图所示，

39、90%的正态分布置信区间为E(x)-1.65，E(x)+1.65。因此，本题的正确选项为 A。 8.An analyst determined that approximately 99 percent of the observations of daily sales for a company were within the interval from $230000 to $480000 and that daily sales for the company were normally distributed. The standard deviation of daily sale

40、s for the company was closest to:（分数：2.50）A.$35682B.$43785C.$48450 解析：解析 由于观测值服从正态分布，从而其平均值位于区间中央，亦即平均值 =(230000+480000)/2=355000 美元。 99%的置信区间为 -2.58， 9.For a standard normal distribution, F(0) is:（分数：2.50）A.0.0B.0.5 C.1.0解析：解析 标准正态分布是指平均值为 0，标准差为 1 的正态分布，如图所示。 10.For the standard normal distributio

41、n, P0X1.88 is:（分数：2.50）A.0.47 B.0.49C.0.97解析：解析 由标准正态分布函数表可知，F(1.88)=0.97。 P0X1.88=F(1.88)-F(0)=0.97-0.5=0.47一项针对基金投资者的研究表明，投资者的年人均收入服从平均值为 35000 美元、标准差为 7000 美元的正态分布。试根据上述条件解答问题：（分数：5.00）(1).What percentage of mutual fund investors have incomes less than $21000?（分数：2.50）A.0.58%B.1.14%C.2. 28% 解析：解析

42、 (2).What percentage of mutual fund investors have incomes greater than $42000?（分数：2.50）A.15.87% B.24.76%C.84.13%解析：解析 根据下表所示的数据解答问题： 投资组合的预期回报率和标准差 投资组合A B C E(R p ) 16% 7% 15% p 33% 12% 28% （分数：5.00）(1).Given a threshold level of return of 5%, use the Roy“s safety-first criterion to choose the opt

43、imal portfolio.（分数：2.50）A.portfolio A B.portfolio BC.portfolio C解析：解析 (2).Given a threshold level of return of 5%, use the Roy“s safety-first criterion to choose the optimal portfolio.（分数：2.50）A.portfolio AB.portfolio BC.portfolio C 解析：解析 11.For a lognormal distribution, the:（分数：2.50）A.mean equals t

44、he median.B.probability of a negative outcome is zero. C.probability of a positive outcome 50%.解析：解析 由下图可知，对数正态分布的图形不具对称性，因而其平均值不等于中位数，选项 A 不正确。由该图我们还可知，对于对数正态分布而言，结果为负的概率为零，结果为正的概率为 100%。因此，选项 B 正确，而选项 C 则不正确。 12.If a stock“s initial price is $10 and its year-end price is $14, then its continuous c

45、ompounded annual rate of return is:（分数：2.50）A.19.6%B.28.7%C.33.6% 解析：解析 基于连续复利的年回报13.Using hypothesized parameter values and a random number generator to study the behavior of certain asset returns is part of:（分数：2.50）A.Monte Carlo simulation. B.historical simulation.C.standardizing a random variabl

46、e.解析：解析 蒙特卡罗模拟法是一项基于影响证券价值的单个或多个风险因素的分析方法，其目的是建立一个证券价值分析的分布模型。对于每一个风险因素，都应当确定该风险因素应遵循的概率分布参数。计算机被用来基于假设的概率分布为每一个风险因素设定随机变量。每一套随机生成的风险因素都被用于对证券价值的价格模型分析。这一过程将被重复很多次，收集到的资产价值分布将被描绘成一幅反映证券预期(平均)价值和证券价值可能偏离其平均值程度的参照图。因此，本题的正确选项为 A。重复很多次，收集到的资产价14.Sample error is defined as:（分数：2.50）A.an error that occur

47、s when a sample of less than 30 elements is drawn.B.an error that occur during collection, recording, and tabulation of data.C.the difference between the value of a sample statistic and the value of the corresponding population parameter. 解析：解析 抽样误差是指样本统计值(如平均值、方差和标准差等)与其对应的总体参数之间的差值。例如，平均值的抽样误差等于样本

48、平均值减去总体平均值。因此，本题的正确选项为 C。15.According to the central limit theorem, a sampling distribution of the sample mean will be approximately normal only if:（分数：2.50）A.the sample size is large. B.the underlying distribution is normally distributed.C.the variance of the underlying distribution is known.解析：解析

49、根据中心极限定理，当样本空间 n 足够大时(n30)，样本平均值的抽样分布趋近于正态分布。因此，本题的正确选项为 A。16.Assume that a population has a mean of 25 with a standard deviation of 3. If a random sample of 60 observations is drawn from this population, the standard error of the sample mean is closest to:（分数：2.50）A.0.05B.0.12C.0.39 解析：解析 样本平均值的标准误差是指样本平均值分布的标准差，其计算公式为： 式中， 表示样本平均值的标准误差， 表示总体的标准差，n 表示样本空间的大小。 样本平均值的标准误差 17.Which of the following is least likely to be a desirable property of an estimate