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s mon stock over the four years? A. % B. % C. % D. % 26 A [()()(.90)()]1/4 1 = % Question ID: 18527 A stock had the following returns over the last five years: 10 percent, 22 percent, 2 percent, 26 percent, 5 percent. What is the geometric mean for this stock? A. B. C. D. B Geometric mean = ()()()()()20 –1 = – 1 = – 1 = x 100 = Question ID: 19382 Given the following annual returns, what are the population and standard deviation, respectively? 1995: 15%, 1996: 2%, 1997: 5%, 1998: 7%, 1999: 0%. A. , B. , C. , D. , 27 A The population variance is found by taking mean of all squared deviations from the mean. [ (153)2 + (23)2 + (53)2 + (73)2 + (03)2 ] / 5 = The population standard deviation is found by taking the square root of the population variance. Question ID: 19700 Assume that the following returns are a sample of annual returns for firms in the clothing industry. Given the following sample of returns, what are the sample variance and standard deviation? Firm 1 Firm 2 Firm 3 Firm 4 Firm 5 15% 2% 5% (7%) 0% A. Variance Standard Deviation B. Variance Standard Deviation C. Variance Standard Deviation D. Variance Standard Deviation D The sample variance is found by taking the sum of all squared deviations from the mean and dividing by (n1). (153)2 + (23)2 + (53)2 + (73)2 + (03)2/(51) = 28 The sample standard deviation is found by taking the square root of the sample variance. √ = Question ID: 19697 An investor has a portfolio with 10 percent cash, 30 percent bonds, and 60 percent stock. If last year’s return on cash was percent, the return on bonds was percent, and the return on stock was 25 percent, what was the return on the investor’s portfolio? A. %. B. %. C. %. D. %. C Find the weighted mean of the returns. ( x ) + ( x ) + ( x ) = % Question ID: 19380 An investor has a $15,000 portfolio consisting of $10,000 in stock A with an expected return of 20 percent and $5,000 in stock B with an expected return of 10 percent. What is the investor’s expected return on the portfolio? A. %. B. %. C. %. D. %. D Find the weighted mean where the weights equal the proportion of $15,000. [(10,000/15,000) *] + [(5,000/15,000 * ) = %. 29 Question ID: 19701 In a skewed distribution, approximately how many observations will fall between two standard deviations from the mean? A. 75%. B. 95%. C. 25%. D. 84%. A Because the distribution is skewed, we must use Chebyshev’s Inequality, which states that the proportion of observations within k standard deviations of the mean is at least 1 – (1/k2). 1 – (1/22) = , or 75%. Note that for a normal distribution, 95% of observations will fall between +/ 2 standard deviations of the mean. Question ID: 19892 The mean monthly return on a sample of small stocks is percent with a standard deviation of percent. What is the coefficient of variation? A. 128%. B. 78%. C. 64%. D. 84%. B The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s/mean. , or 78%. 30 Question ID: 19384 The mean monthly return on (. Treasury bills) Tbills is percent with a standard deviation of percent. What is the coefficient of variation? A. 840%. B. 84%. C. 168%. D. 60%. D The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s/mean, or , or 60%. Question ID: 18544 The mean and standard deviation of returns from Stock A and B are represented below. Arithmetic Mean Standard Deviation Stock A 20% 8% Stock B 15% 5% The coefficient of variation of the two stocks is given by: A. and B. and C. and D. and C CV = Standard Deviation / Mean =(8/20)= and (5/15)= 31 Question ID: 19893 Which of the following statements regarding the Sharpe ratio is TRUE? The Sharpe ratio measures: A. dispersion relative to the mean. B. peakedness of a return distrubtion. C. excess return per unit of risk. D. total return per unit of risk. C The Sharpe ratio measures excess return per unit of risk. Remember that the numerator of the Sharpe ratio is (portfolio return – risk free rate), hence the importance of excess return. Note that dispersion relative to the mean is the definition of the coefficient of variation, and the peakedness of a return distribution is measured by kurtosis. Question ID: 19896 A distribution with a mean that is less than its median: A. is positively skewed. B. is negatively skewed. C. has positive excess kurtosis. D. has negative excess kurtosis. D A distribution with a mean that is less than its median is a negatively skewed distribution. A negatively skewed distribution is characterized by many small gains and a few extreme losses. Note that kurtosis is a measure of the peakedness of a return distribution. 32 Question ID: 19895 If a distribution is positively skewed: A. the mode is greater than the median. B. the mean is greater than the median. C. the median, mean, and mode are equal. D. the mode is greater than the mean. B For a positively skewed distribution, the mode is less than the median, which is less than the mean (the mean is greatest). Remember that investors are attracted to positive skewness because the mean return is greater than the median return. Question ID: 19897 Which of the following statements regarding skewness is FALSE? A. In a skewed distribution, 95% of all values will lie within plus or minus two standard deviations of the mean. B. A positively skewed distribution is cha