Modlin 3 Questions

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Study Session 3 Sample Questions Investment Tools: Quantitative Methods

Study Session 3

Sample Questions

Investment Tools Quantitative Methods

1A Sampling and Estimation 1. In stratified random sampling:

A. the population is subdivided into subpopulations based on one or more classification criteria

B. each observation has an equal chance of being selected C. we collect observations at equally spaced intervals of time D. we make the assumption that members of the sample come from

the same population Answer A.

Stratified random sampling

In stratified random sampling the population is subdivided into subpopulations based on one or more classification criteria.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,d

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2. The central limit theorem

A. allows us to compute confidence intervals when the sample size is small

B. allows us to calculate estimates from a sample C. has important implications for how we construct confidence intervals

and test hypotheses D. is used when sample size is less than 30

Answer C.

The central limit theorem The central limit theorem has important implications for how we construct confidence intervals and test hypotheses.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,f

3. An analyst wants to determine how growth managers performed last year.

He assumes that the population cross sectional standard deviation of growth manager return is 8% and the sample size selected is 40. Determine the standard error of the sample mean. Assume the returns are independent across managers.

A. 1.765 B. 1.600 C. 1.265 D. 1.125

Answer A.

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Calculating the standard error of the sample mean

The standard error of the sample mean is 1.265. x = n

= 408 = 1.265

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,g

4. The desirable statistical properties of an estimate are:

I. Unbiasedness II. Efficiency III. Consistency

Which is TRUE? A. I only B. II only C. III only D. I, II, and III

Answer D.

Statistical properties of an estimate The desirable statistical properties of an estimate are:

Unbiasedness

Efficiency Consistency

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Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,h

5. Assume that the equity risk premium is normally distributed with a population mean of 8% and a population standard deviation of 15%. Over the last 3 years, equity returns have averaged 4%. A 95 % confidence interval for a sample of 3-year returns is as follows:

A. between -8.974% and 24.974% B. between 5.987% and 23.876% C. between 9.987% and 18.092% D. between 7.098% and 12.098%

Answer

A.

Determining a confidence interval

A 95 % confidence interval for a sample of 3-year returns is between -8.974% and 24.974%

For returns that are normally distributed, a 95% confidence interval is of the form:

x 1.96

n

Lower limit: 8% - 1.96

315 = -8.974%

Upper limit: 8% + 1.96

315 = 24.974%

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Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,j

6. The bias in the inference you draw as a result of prying into the empirical

results of others to guide your own analysis is known as:

A. Survivorship bias B. Data-snooping bias C. Data-mining bias D. Look-ahead bias

Answer B.

Data-snooping bias The bias in the inference you draw as a result of prying into the empirical results of others to guide your own analysis is known as data-snooping bias.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Sampling and Estimation, LOS 1A,o

B. Hypothesis Testing 1. The hypothesis to be tested is known as:

A. The alternative hypothesis B. The Type I hypothesis C. The null hypothesis D. The Type II hypothesis

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Answer C.

The null hypothesis The hypothesis to be tested is known as the null hypothesis.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Hypothesis Testing, LOS 1B,b

2. The economic decision that we make at the end of the statistical process of the hypothesis test:

A. takes into consideration not only the statistical decision, but also all

economic issues pertinent to the decision B. only takes into consideration the statistical decision C. takes into consideration only the investment decision D. does not require a statistical decision to have been made

Answer A.

The economic decision that we make at the end of the statistical process of the hypothesis test

The economic decision that we make at the end of the statistical process of the hypothesis test takes into consideration not only the statistical decision, but also all economic issues pertinent to the decision. Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Hypothesis Testing, LOS 1B,j

2003 www.modlin.org


3. Consider the following information about a fund. The fund has been in

existence for 3 years. Over this period it has achieved a mean monthly return of 3% with a sample standard deviation of monthly returns of 5%. It was expected to earn a 2.5% mean monthly return over the 3-year period. Which test statistic do we use for conducting a test of the hypotheses?

A. f-test with 35 degrees of freedom B. z-test with 36 degrees of freedom

C. t-test with 35 degrees of freedom D. chi-squared test with 35 degrees of freedom

Answer

C. Identifying the appropriate test statistic

T-test with 35 degrees of freedom is used for conducting a test of the hypothesis.

This is a t-test because the population variance is not known

The degrees of freedom is always n 1 which in this case is 36 1 = 35 months

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Hypothesis Testing, LOS 1B,l

2003 www.modlin.org


4. Consider the following information about a fund. The fund has been in

existence for 3 years. Over this period it has achieved a mean monthly return of 3% with a sample standard deviation of monthly returns of 5%. It was expected to earn a 2.5% mean monthly return over the 3-year period

The rejection point(s) at the 0.10 level of significance is/are: A. reject when t < 1.690 or t > -1.690

B. reject when t > 1.690 or t > -1.690 C. reject when t < 1.690 or t < -1.690 D. reject when t > 1.690 or t < -1.690

Answer

D. Interpreting the results of a hypothesis test The rejection point(s) at the 0.10 level of significance are: reject when t > 1.690 or t < -1.690.

The t-tables need to be used.

In this case we look at p = 0.05 because the significance level given is 0.1 and 35 degrees of freedom (36-1) The value read from the table is 1,690 which determines the rejection point(s)

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Hypothesis Testing, LOS 1B,n

2003 www.modlin.org


5. An analyst compiled the following information relating to EPS forecasts.

The analyst wants to forecast quality. The test used to forecast quality is the zero-mean test, which states that optimal forecasts should have a mean forecasting error of 0.

Number of forecasts

Mean Forecast error

Standard deviation of forecast error

100 0.07 0.2 Using a z-test, at the 0.05 level of significance A. we reject the null B. we accept the null C. we have insufficient information to make a decision D. we have committed a Type I error

Answer A. Interpreting the results of a hypothesis test

Using a z-test, at the 0.05 level of significance we reject the null. Z =

1000.2/00.07 =

0.020.07 = 3.5

Note that the calculation of the z-statistic with unknown variance is the same as the calculation of the t-statistic.

When the significance level is 0.05 the rejection points are Z > 1.96 and Z < -1.96. The computed value of Z of 3.5 is greater than 1.96 and this means we reject the null at the 0.05 level.

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Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Hypothesis Testing, LOS 1B,n

C. Correlation and Regression 1. A scatter plot is:

A. a graph of the mean and standard deviation of observations for two data series

B. a graph that shows the relationship between the observations for two data series in two dimensions

C. a graph of the mean, standard deviation and covariance of observations for two data series

D. a graph that shows the relationship between the observations for two data series in one dimension

Answer B. Scatter plot A scatter plot is a graph that shows the relationship between the observations for two data series in two dimensions. Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Correlation and Regression, LOS 1C,a

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2. Covariance is defined as: A. small numbers of observations at either extreme of a sample

B. the variance of the product of the deviations of two random variables from their respective means

C. the expected value of the product of the deviations of two random variables from their respective means

D. the correlation of two variables divided by the product of their sample standard deviations

Answer

C. Covariance

Covariance is defined as the expected value of the product of the deviations of two random variables from their respective means. Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Correlation and Regression, LOS 1C,b

3. The correlation coefficient is:

A. the variance of two variables divided by the product of their sample standard deviations

B. the expected value of two variables divided by the product of their sample standard deviations

C. the expected value of the product of the deviations of two random variables from their respective means

D. the covariance of two variables divided by the product of their sample standard deviations

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Answer

D. The correlation coefficient

The correlation coefficient is the covariance of two variables divided by the product of their sample standard deviations.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Correlation and Regression, LOS 1C,c

4. In correlation analysis, the correlation coefficient measures:

A. the direction between two variables B. the extent of linear association between two variables C. the expected value of the product of the deviations of two random

variables from their respective means D. the direction and extent of linear association between two variables Answer D. Correlation analysis In correlation analysis, the correlation coefficient measures the direction and extent of linear association between two variables. Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Correlation and Regression, LOS 1C,d

2003 www.modlin.org


5. Outliers are:

A. small numbers of observations at either extreme of a sample B. small numbers that lie off the scatter plot

C. large numbers of observations at either extreme of a sample D. the expected values of the products of the deviations of two random

variables from their respective means Answer A. Outliers Outliers are small numbers of observations at either extreme of a sample.

Reference Quantitative Methods for Investment Analysis, Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkle (AIMR, 2001) Study Session 3 2003, Correlation and Regression, LOS 1C,f

C. 1.265= = = 1.265D.I, II, and IIIA. between -8.974% and 24.974%A.A 95 % confidence interval for a sample of 3-year returns is between-8.974% and 24.974%B. Data-snooping biasC.t-test with 35 degrees of freedomD. reject when t > 1.690 or t < -1.690

A. we reject the null

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