1、注册金融分析师一级-8 及答案解析(总分：75.00，做题时间：90 分钟)一、B单项选择题/B(总题数：3，分数：75.00)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? A. 0.58% B. 1.14% C. 2. 28%（分数：2.50）A.B.C.(2).What percentage of mutual fund invest
2、ors have incomes greater than $42000? A. 15.87% B. 24.76% C. 84.13%（分数：2.50）A.B.C.根据下表所示的数据解答问题： B投资组合的预期回报率和标准差/B投资组合 A B CE(Rp) 16% 7% 15% p 33% 12% 28%（分数：40.00）(1).Given a threshold level of return of 5%, use the Roys safety-first criterion to choose the optimal portfolio. A. portfolio A B. port
3、folio B C. portfolio C（分数：2.50）A.B.C.(2).Given a threshold level of return of 5%, use the Roys safety-first criterion to choose the optimal portfolio. A. portfolio A B. portfolio B C. portfolio C（分数：2.50）A.B.C.(3).For a lognormal distribution, the: A. mean equals the median. B. probability of a nega
4、tive outcome is zero. C. probability of a positive outcome 50%.（分数：2.50）A.B.C.(4).If a stocks initial price is $10 and its year-end price is $14, then its continuous compounded annual rate of return is: A. 19.6% B. 28.7% C. 33.6%（分数：2.50）A.B.C.(5).Using hypothesized parameter values and a random num
5、ber generator to study the behavior of certain asset returns is part of: A. Monte Carlo simulation. B. historical simulation. C. standardizing a random variable.（分数：2.50）A.B.C.(6).Sample error is defined as: A. an error that occurs when a sample of less than 30 elements is drawn. B. an error that oc
6、cur 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.（分数：2.50）A.B.C.(7).According to the central limit theorem, a sampling distribution of the sample mean will be approximately norm
7、al only if: A. the sample size is large. B. the underlying distribution is normally distributed. C. the variance of the underlying distribution is known.（分数：2.50）A.B.C.(8).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 th
8、is population, the standard error of the sample mean is closest to: A. 0.05 B. 0.12 C. 0.39（分数：2.50）A.B.C.(9).Which of the following is least likely to be a desirable property of an estimate? A. unbiasedness B. reliability C. consistency（分数：2.50）A.B.C.(10).Which of the following is least likely a pr
9、operty of t-distribution? A. As the degrees of freedom get larger, the variance approaches zero. B. It is defined by a single parameter, the degrees 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.（分数：2.50）A.B.C.(11)
10、.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? A. sample size B. reliability factor C. degrees of freedom（分数：2.50）A.B.C.(12).A random sample of 64 supermarket customer spent an average of $43. Assu
11、ming the distribution is normal and the population standard deviation is $15, the 90% confidence interval for the population mean is closest to: A. 41.085 to 44.915 B. 40.218 to 45.782 C. 39.916 to 46.084（分数：2.50）A.B.C.(13).Tuross Online, Inc., sells books by mail. A sample of 16 recent orders showe
12、d 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 population mean is closest to. A. 31.2699 to 38.7301 B. 33.7352 to 36.2648 C. 34.2318 to 35.7682（分数：2.50）A.B.C
13、.(14).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? A. The z-statistic at with n degrees of freedom. B. The t-statistic at /2 with n degrees of freedom. C. The t-stat
14、istic at /2 with n-1 degrees of freedom.（分数：2.50）A.B.C.(15).The acceptable test statistic for constructing confidence intervals for the population mean of a normally distributed when the variance is unknown and the sample size is large (n30) is the: A. z-statistic. B. t-statistic. C. z-statistic or
15、t-statistic, hut t-statistic is more preferred.（分数：2.50）A.B.C.(16).An analyst who uses historical data that was not publicly available at the time period being studied will have a sample with: A. look-ahead bias. B. time-period bias. C. sample selection bias.（分数：2.50）A.B.C.某投资者认为某地区房屋的平均价格高于 350000美
16、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：30.00）(1).The appropriate alternative hypothesis is: A. H : $350000. B. H : $350000. C. H : $350000.（分数：2.50）A.B.C.(2).The value of the calculated test statistic is: A. z=0.8. B. z=1.6. C. z=3.2.（分数：2.50）A.
17、B.C.(3).At a 3% level of significance, the investor should: A. reject the null hypothesis. B. fail to reject the null hypothesis. C. neither reject nor fail to reject the null hypothesis.（分数：2.50）A.B.C.(4).If the significance level of a test is 0.1 and the probability of a Type error is 0.4, what is
18、 the power of the test? A. 0.04 B. 0.5 C. 0.6（分数：2.50）A.B.C.(5).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 H0: =$26 versus H 0: $26. At a 5% level of significance, the null hypothesis: A
19、. should be rejected. B. can not be rejected. C. can not be tested using this sample information provided.（分数：2.50）A.B.C.(6).Consider the hypotheses structured for sample A and sample B as H0: A= B versus Ha: A B, At a 10% level of significance, the null hypothesis: A. should be rejected. B. can not
20、 be rejected. C. can not be tested using this sample information provided.（分数：2.50）A.B.C.(7).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
21、 standard 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? A. The population and sample variances are significantly different. B.
22、 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.（分数：2.50）A.B.C.(8).Which of the following statements is least likely to be an advantage of technical analysis? A. It tells the analyst when to bu
23、y. B. It tells the analyst why investors are buying. C. It incorporates psychological as well as economic reasons for price changes.（分数：2.50）A.B.C.(9).When the relative over-the-counter (OTC) to NYSE volume ratio is decreasing, contrary-opinion technicians would do which of the following? A. Hold. B
24、. Be bearish and sell. C. Be bullish and buy.（分数：2.50）A.B.C.(10).If the confidence index (CI) increases (and the implied yield spread narrows), investors are doing which of the following? A. Selling quality bonds. B. Buying quality bonds. C. Selling common stocks.（分数：2.50）A.B.C.(11).When debit balan
25、ces (i.e. margin debit) in brokerage accounts decrease: 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.（分数：2.50）A.B.C.(12).If the relative strength ratio increa
26、ses, which of the following statements is correct? A. The market 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 percent
27、age increase.（分数：2.50）A.B.C.注册金融分析师一级-8 答案解析(总分：75.00，做题时间：90 分钟)一、B单项选择题/B(总题数：3，分数：75.00)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? A. 0.58% B. 1.14% C. 2. 28%（分数：2.50）A.B.C. 解析：解析 * F(-2)
28、=PX-2=1-F(2)=1-0.9772=0.0228 即基金投资者的收入低于 21000美元的百分比为 2.28%。(2).What percentage of mutual fund investors have incomes greater than $42000? A. 15.87% B. 24.76% C. 84.13%（分数：2.50）A. B.C.解析：解析 * F(1)=PX1=0.8413 PX1=1-0.8413=0.1587 即基金投资者的收入高于 42000美元的百分比为 15.87%。根据下表所示的数据解答问题： B投资组合的预期回报率和标准差/B投资组合 A B
29、 CE(Rp) 16% 7% 15% p 33% 12% 28%（分数：40.00）(1).Given a threshold level of return of 5%, use the Roys safety-first criterion to choose the optimal portfolio. A. portfolio A B. portfolio B C. portfolio C（分数：2.50）A. B.C.解析：解析 * * 显然，投资组合 A的 SFR比率最大，从而根据罗伊安全优先标准，该投资组合为最佳投资组合。(2).Given a threshold level o
30、f return of 5%, use the Roys safety-first criterion to choose the optimal portfolio. A. portfolio A B. portfolio B C. portfolio C（分数：2.50）A.B.C. 解析：解析 * 显然，投资组合 C的 SFR比率最大，从而根据罗伊安全优先标准，该投资组合为最佳投资组合。(3).For a lognormal distribution, the: A. mean equals the median. B. probability of a negative outcome
31、 is zero. C. probability of a positive outcome 50%.（分数：2.50）A.B. C.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。 *(4).If a stocks initial price is $10 and its year-end price is $14, then its continuous compounded annual rate of retur
32、n is: A. 19.6% B. 28.7% C. 33.6%（分数：2.50）A.B.C. 解析：解析 基于连续复利的年回报*(5).Using hypothesized parameter values and a random number generator to study the behavior of certain asset returns is part of: A. Monte Carlo simulation. B. historical simulation. C. standardizing a random variable.（分数：2.50）A. B.C.解析
33、：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(6).Sample error is defined as: A. an error that occurs when a s
34、ample 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.（分数：2.50）A.B.C. 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
35、的抽样误差等于样本平均值减去总体平均值。因此，本题的正确选项为 C。(7).According to the central limit theorem, a sampling distribution of the sample mean will be approximately normal only if: A. the sample size is large. B. the underlying distribution is normally distributed. C. the variance of the underlying distribution is known.
36、（分数：2.50）A. B.C.解析：解析 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。(8).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: A. 0.05 B. 0.12 C. 0
37、.39（分数：2.50）A.B.C. 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*(9).Which of the following is least likely to be a desirable property of an estimate? A. unbiasedness B. reliability C. consistency（分数：2.50）A.B. C.解析：解析 估计值的选择标准包括以下三个方面： (1)无偏性(unbiasedness
38、)。具有无偏性的统计量是指统计量的期望值等于你想要估计的参数值。例如，样本平均值*的期望值等于总体平均值 ，从而样本平均值是总体平均值的一个无偏估计值。 (2)有效性(efficiency)。如果与其他具有无偏性的统计量相比，某个无偏统计量的样本分布具有最小的方差，则该统计量不仅具有无偏性，而且还具有有效性。例如，样本平均值不仅是总体平均值的一个无偏估计，且是总体平均值的一个有效估计。 (3)一致性(consistency)。具有一致性的统计量是指参数估计的准确性随着样本空间的增加而提高。这是因为，随着样本空间的增加，样本平均值的标准误差随之减少，从而样本分布更加集中于总体平均值附近。 因此，
39、本题中的选项 B(可靠性)最不可能属于估计值的选择标准。(10).Which of the following is least likely a property of t-distribution? A. As the degrees of freedom get larger, the variance approaches zero. B. It is defined by a single parameter, the degrees of freedom, which is equal to n-1. C. It has more probability in the tails
40、and less at the peak than a standard normal distribution.（分数：2.50）A. B.C.解析：解析 如下图所示，随着自由度(样本空间 n)的增大，t 分布的图形无限趋近于正态分布，从而其方差逐渐趋近于正态分布的方差，而非逐渐趋于零。 *(11).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?
41、 A. sample size B. reliability factor C. degrees of freedom（分数：2.50）A.B. C.解析：解析 可靠因子的增长将使总体平均值的置信区间相应扩大，而样本空间和自由度的增长则使总体平均值的置信区间相应缩小。因此，本题的正确选项为 B。(12).A random sample of 64 supermarket customer spent an average of $43. Assuming the distribution is normal and the population standard deviation is $1
42、5, the 90% confidence interval for the population mean is closest to: A. 41.085 to 44.915 B. 40.218 to 45.782 C. 39.916 to 46.084（分数：2.50）A.B.C. 解析：解析 由于总体方差已知且样本空间足够大(n30)，因而该总体平均值的置信区间应采用以下构建方式：*式中，*表示总体平均值(样本平均值)的点估计值，z /2 表示可靠因子，*表示样本平均值的标准误差(其中 表示总体的标准差，n 表示样本空间)。z/2 =z0.05=1.645，从而置信区间为：*因此，总体
43、平均值的 90%的置信区间最接近于 39.91646.084。(13).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 th
44、e population mean is closest to. A. 31.2699 to 38.7301 B. 33.7352 to 36.2648 C. 34.2318 to 35.7682（分数：2.50）A. B.C.解析：解析 由于总体方差未知且样本空间较小(n30)，因而该总体平均值的置信区间应采用以下构建方式：*式中，*表示总体平均值的点估计值，t /2 表示 t分布的可靠因子，*表示样本平均值的标准误差(其中 s表示样本的标准差，n 表示样本空间)。本题的样本空间为 16，从而其自由度 df=16-1=15。通过查询 t分布函数表可知，t 15，0.025 =2.1315。可
45、以确定置信区间为：*因此，总体平均值的 95%的置信区间最接近于 31.269938.7301。(14).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? A. The z-statistic at with n degrees of freedom. B. The t-statistic
46、 at /2 with n degrees of freedom. C. The t-statistic at /2 with n-1 degrees of freedom.（分数：2.50）A.B.C. 解析：解析 当总体服从正态分布，且方差未知时，应当使用在 /2 处、自由度为 n-1的 z统计量来构建总体平均值的置信区间。 还需要指出的是，尽管在样本空间足够大(n30)的情况下，也可以使用 z统计量。但考虑到本题并未明确指出样本空间的大小，而无论样本空间的大小如何，均可以使用 t统计量来构建总体平均值的置信区间，从而可知 t统计量为最理想的检验统计量。因此，本题的正确选项为 C。(15)
47、.The acceptable test statistic for constructing confidence intervals for the population mean of a normally distributed when the variance is unknown and the sample size is large (n30) is the: A. z-statistic. B. t-statistic. C. z-statistic or t-statistic, hut t-statistic is more preferred.（分数：2.50）A.B
48、.C. 解析：解析 根据中心极限定理，随着样本空间的增加，样本平均值分布将趋近于正态分布。对于样本分布为非正态分布，且总体方差未知的情况，则只要样本空间 n足够大(n30)，就可以通过查询 t分布函数表来构建置信区间。当然，对于上述情况，也可以使用标准正态分布的 z分布函数表。但是，使用 t值将使所得到的置信区间更为保守，即置信区间的区间范围更大，因此在多数情况下建议使用 t值。因此，本题的正确选项为 C。(16).An analyst who uses historical data that was not publicly available at the time period being studied will have a sample with: A. look-ahead bias. B. time-period bias. C. sample selection bias.（分数：2.50）A. B.C.解析：解
