Quant. Methods (1)
Suppose that 5 percent of the stocks meeting your stock-selection criteria are in the telecommunications (telecom) industry. Also, dividend-paying telecom stocks are 1 percent of the total number of stocks meeting your selection criteria. What is the probability that a stock is dividend paying, given that it is a telecom stock that has met your stock selection criteria?
0.2
A bank quotes a stated annual interest rate of 4.00%. If that rate is equal to an effective annual rate of 4.08%, then the bank is compounding interest: daily. quarterly. semiannually.
A
A firm will select two of four vice presidents to be added to the investment committee. How many different groups of two are possible? 6 12 24
A
A portfolio manager would like to calculate the compound rate of return on an investment. Which of the following mean returns will he most likely use? Geometric Harmonic Arithmetic
A
A portfolio provides the following returns over a five-year period. Year 1 2 3 4 5 Return 10% −25% 8% 5% 7% The compound rate of return of the portfolio across the five-year period is closest to: 0.02%. 1.00%. −9.31%
A
For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to: 555. 563. 576.
A
If the probability that Zolaf Company sales exceed last year's sales is 0.167, the odds for exceeding sales are closest to: 1 to 5. 1 to 6. 5 to 1.
A
Which of the following most accurately describes a distribution that is more peaked than normal? Leptokurtic Mesokurtic Platykurtic
A
A bank offers an effective annual rate (EAR) of 12%. Assuming quarterly compounding, the stated annual interest rate is closest to: 11.66%. 12.55%. 11.49%.
A bank offers an effective annual rate (EAR) of 12%. Assuming quarterly compounding, the stated annual interest rate is closest to: 11.66%. 12.55%. 11.49%.
Given a portfolio of five stocks, how many unique covariance terms, excluding variances, are required to calculate the portfolio return variance? 10 20 25
A is correct. A covariance matrix for five stocks has 5 × 5 = 25 entries. Subtracting the 5 diagonal variance terms results in 20 off-diagonal entries. Because a covariance matrix is symmetrical, only 10 entries are unique (20/2 = 10).
A graphical depiction of a continuous distribution shows the left tail to be longer than the right tail. The distribution is best described as having: negative skewness. leptokurtosis. positive skewness.
A is correct. A negatively skewed distribution appears as if the left tail has been pulled away from the mean. The average magnitude of negative deviations from the mean is larger than the average magnitude of positive deviations.
Which of the following groups best illustrates a population? The 500 companies in the S&P 500 Index The NYSE-listed stocks in the Dow Jones Industrial Average The Lehman Aggregate Bond Index as a representation of the US bond market
A is correct. A population is defined as all members of a specified group. The S&P 500 Index consists of 500 companies, so this group is the population of companies in the index.
In descriptive statistics, an example of a parameter is the: median of a population. mean of a sample of observations. standard deviation of a sample of observations.
A is correct. Any descriptive measure of a population characteristic is referred to as a parameter.
Equity return distributions are best described as being: leptokurtic. platykurtic. mesokurtic.
A is correct. Most equity return distributions are best described as being leptokurtic (i.e., more peaked than normal).
Published ratings on stocks ranging from 1 (strong sell) to 5 (strong buy) are examples of which measurement scale? Ordinal Interval Nominal
A is correct. Ordinal scales sort data into categories that are ordered with respect to some characteristic and may involve numbers to identify categories but do not assure that the differences between scale values are equal. The buy rating scale indicates that a stock ranked 5 is expected to perform better than a stock ranked 4, but it tells us nothing about the performance difference between stocks ranked 4 and 5 compared with the performance difference between stocks ranked 1 and 2, and so on.
Two portfolios have unimodal return distributions. Portfolio 1 has a skewness of 0.77, and Portfolio 2 has a skewness of -1.11. Q. Which of the following is correct? For Portfolio 1, the median is less than the mean. For Portfolio 1, the mode is greater than the mean. For Portfolio 2, the mean is greater than the median.
A is correct. Portfolio 1 is positively skewed, so the mean is greater than the median, which is greater than the mode.
From an approved list of 25 funds, a portfolio manager wants to rank 4 mutual funds from most recommended to least recommended. Which formula is most appropriate to calculate the number of possible ways the funds could be ranked? Permutation formula Multinomial formula Combination formula
A is correct. The permutation formula is used to choose r objects from a total of n objects when order matters. Because the portfolio manager is trying to rank the four funds from most recommended to least recommended, the order of the funds matters; therefore, the permutation formula is most appropriate.
A manager invests €5,000 annually in a security for four years at the prices shown in the following table. Purchase Price of Security (€) Year 1 62.00 Year 2 76.00 Year 3 84.00 Year 4 90.00 Q. The average price paid for the security is closest to: €76.48. €77.26. €78.00.
A. Harmonic mean
The least accurate statement about measures of dispersion for a distribution is that the: range provides no information about the shape of the data distribution. arithmetic average of the deviations around the mean will be equal to one. mean absolute deviation will be either less than or equal to the standard deviation.
B is correct. The arithmetic sum of the deviations around the mean will always equal zero, not one.
A distribution with excess kurtosis less than zero is termed: mesokurtic. platykurtic. leptokurtic.
B
A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock's present value is closest to: $31. $126. $133.
B
An individual wants to be able to spend €80,000 per year for an anticipated 25 years in retirement. To fund this retirement account, he will make annual deposits of €6,608 at the end of each of his working years. He can earn 6% compounded annually on all investments. The minimum number of deposits that are needed to reach his retirement goal is closest to: 51. 40. 28.
B
Common stock prices are approximately lognormally distributed. Therefore, it is most likely that conventional (discrete) common stock prices are: leptokurtic. skewed to the right. skewed to the left.
B
The variance of returns of Asset A is 625. The variance of returns of Asset B is 1,225. The covariance of returns between Asset A and Asset B is 600. The correlation of returns between Asset A and Asset B is closest to: 0.29. 0.69. 0.47.
B
Which of the following sequences best represents the relative sizes of the mean, median, and mode for a positively skewed unimodal distribution? mode ≤ median ≤ mean mode < median < mean mean < median < mode
B
The stated (quoted) annual interest rate on an automobile loan is 10%. The effective annual rate (EAR) of the loan is 10.47%. The frequency of compounding per year for the loan is closest to: quarterly. monthly. weekly.
B is correct
A consumer purchases an automobile using a loan. The amount borrowed is €30,000, and the terms of the loan call for the loan to be repaid over five years using equal monthly payments with an annual nominal interest rate of 8% and monthly compounding. The monthly payment is closest to: €626.14. €608.29. €700.00.
B is correct.
For a positively skewed unimodal distribution, which of the following measures is most accurately described as the largest? Median Mean Mode
B is correct. For a positively skewed unimodal distribution, the mode is less than the median, which is less than the mean.
The height of a bar in a histogram represents the matching data interval's: relative frequency. absolute frequency. cumulative frequency.
B is correct. In a histogram, the height of each bar represents the absolute frequency of its associated data interval.
Investors should be most attracted to return distributions that are: negatively skewed. positively skewed. normal.
B is correct. Investors should be attracted by a positive skew (distribution skewed to the right) because the mean return falls above the median. Relative to the mean return, positive skew amounts to a limited, though frequent, downside compared with a somewhat unlimited, but less frequent, upside.
For a distribution of 2,000 observations with finite variance, sample mean of 10.0%, and standard deviation of 4.0%, what is the minimum number of observations that will lie within 8.0% around the mean according to Chebyshev's Inequality? 720 1,500 1,680
B is correct. Observations within 8% of the sample mean will cover an interval of 8/4 or two standard deviations. Chebyshev's Inequality says the proportion of the observations P within k standard deviations of the arithmetic mean is at least 1 − 1/k2 for all k > 1. So, solving for k = 2: P = 1 - ¼ = 75%. Given 2,000 observations, this implies at least 1,500 will lie within 8.0% of the mean.
Which of the following groups best illustrates a sample? The set of all estimates for Exxon Mobil's EPS for next financial year The FTSE Eurotop 100 as a representation of the European stock market UK shares traded on Wednesday of last week that also closed above £120/share on the London Stock Exchange
B is correct. The FTSE Eurotop 100 represents a sample of all European stocks. It is a subset of the population of all European stocks.
When analyzing investment returns, which of the following statements is correct? The geometric mean will exceed the arithmetic mean for a series with non-zero variance. The geometric mean measures an investment's compound rate of growth over multiple periods. The arithmetic mean accurately estimates an investment's terminal value over multiple periods.
B is correct. The geometric mean compounds the periodic returns of every period, giving the investor a more accurate measure of the terminal value of an investment.
The arithmetic and geometric mean are calculated for the same data. If there is variability in the data, compared with the arithmetic mean, the geometric mean will most likely be: greater. smaller. equal.
B is correct. The geometric mean is always less than or equal to the arithmetic mean. The only time the two means will be equal is when there is no variability in the observations.
A group of fund analysts have to select the first, second, and third best fund manager of the year for 2012 based on their subjective judgment. If 10 fund managers are candidates for the three awards, the number of ways in which each analyst can make his ranking is closest to: 30. 720. 120.
B is correct. This problem is a counting one in which order does matter. For this reason, use the permutation formula
A return distribution with frequent small gains and a few extreme losses is most likely to be called: leptokurtic. positively skewed. negatively skewed.
C is correct. A return distribution with negative skew has frequent small gains and a few extreme losses.
Over the past 240 months, an investor's portfolio had a mean monthly return of 0.79%, with a standard deviation of monthly returns of 1.16%. According to Chebyshev's inequality, the minimum number of the 240 monthly returns that fall into the range of −0.95% to 2.53% is closest to: 80. 107. 133.
C is correct. According to Chebyshev's inequality, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 - 1/k2 for all k > 1.
A fund manager would like to estimate the probability of a daily loss higher than 5% on the fund he manages. He decides to use a method that uses the relative frequency of occurrence based on historical data. The resulting probability is best described as a(n): subjective probability. a priori probability. empirical probability.
C is correct. An empirical probability is a probability estimated from data as a relative frequency of occurrence.
The probability of Event A is 40%. The probability of Event B is 60%. The joint probability of AB is 40%. The probability (P) that A or B occurs, or both occur, is closest to: 40%. 84%. 60%.
C is correct. P(A or B) = P(A) + P(B) − P(AB) = 0.40 + 0.60 − 0.40 = 0.60 or 60%.
A manager will select 20 bonds out of his universe of 100 bonds to construct a portfolio. Which formula provides the number of possible portfolios? Permutation formula Multinomial formula Combination formula
C is correct. The combination formula provides the number of ways that r objects can be chosen from a total of n objects, when the order in which the r objects are listed does not matter. The order of the bonds within the portfolio does not matter.
The covariance of returns is positive when the returns on two assets tend to: have the same expected values. be above their expected value at different times. be on the same side of their expected value at the same time.
C is correct. The covariance of returns is positive when the returns on both assets tend to be on the same side (above or below) their expected values at the same time, indicating an average positive relationship between returns.
The nominal risk-free rate is best described as the sum of the real risk-free rate and a premium for: maturity. liquidity. expected inflation.
C is correct. The sum of the real risk-free interest rate and the inflation premium is the nominal risk-free rate.
Which of the following best describes how an analyst would estimate the expected value of a firm under the scenarios of bankruptcy and survivorship? The analyst would use: the addition rule. conditional expected values. the total probability rule for expected value.
C is correct. The total probability rule for expected value is used to estimate an expected value based on mutually exclusive and exhaustive scenarios.
A financial contract offers to pay €1,200 per month for five years with the first payment made immediately. Assuming an annual discount rate of 6.5%, compounded monthly the present value of the contract is closest to: €63,731. €61,330. €61,663.
C is correct. Using a financial calculator: N = 60; the discount rate (I/Y) = (6.5%/12) = 0.54166667; PMT = €1,200; Future value = €0; Mode = Begin; Calculate present value (PV): PV = €61,662.62.
