Reading 7: Statistical Concepts and Market Returns-LOS e 习题 2011, including, interpret, measures, average

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Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns

LOS e: Define, calculate, and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean (including a portfolio return viewed as a weighted mean), geometric mean, harmonic mean, median, and mode.

 

 

Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?

A) The difference between the geometric mean and the arithmetic mean increases with an increase in variability between period-to-period observations.

B) The geometric mean may be used to estimate the average return over a one-period time horizon because it is the average of one-period returns.

C) The geometric mean calculates the rate of return that would have to be earned each year to match the actual, cumulative investment performance.

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The arithmetic mean may be used to estimate the average return over a one-period time horizon because it is the average of one-period returns. Both remaining statements are true.

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Which of the following statements about the median is least accurate? It is:

A) more affected by extreme values than the mean.

B) equal to the 50th percentile.

C) equal to the mode in a normal distribution.

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Median is less influenced by outliers since the median is computed as the “middle” observation. On the other hand, all of the data including outliers are used in computing the mean. Both remaining statements are true regarding the median.

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An investor has a portfolio with 10% cash, 30% bonds, and 60% stock. If last year’s return on cash was 2.0%, the return on bonds was 9.5%, and the return on stock was 25%, what was the return on the investor’s portfolio?

A) 36.50%.

B) 18.05%.

C) 22.30%.

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Find the weighted mean of the returns. (0.10 × 0.02) + (0.30 × 0.095) + (0.60 × 0.25) = 18.05%

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Which of the following statements about a normal distribution is least accurate?

A) A normal distribution has excess kurtosis of three.

B) Approximately 68% of the observations lie within +/- 1 standard deviation of the mean.

C) The mean and variance completely define a normal distribution.

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Even though normal curves have different sizes, they all have identical shape characteristics. The kurtosis for all normal distributions is three; an excess kurtosis of three would indicate a leptokurtic distribution. Both remaining choices are true.

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An investor has the following assets:

• $5,000 in bonds with an expected return of 8%.
• $10,000 in equities with an expected return of 12%.
• $5,000 in real estate with an expected return of 10%.

What is the portfolio's expected return?

A) 10.50%.

B) 10.00%.

C) 11.00%.

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Expected return is the weighted average of the individual expected values. The expected return is: [(5,000) × (10.00) + (5,000) × (8.00) + (10,000) × (12.00)] / 20,000 = 10.50%.

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A portfolio is equally invested in Stock A, with an expected return of 6%, and Stock B, with an expected return of 10%, and a risk-free asset with a return of 5%. The expected return on the portfolio is:

A) 8.0%.

B) 7.4%.

C) 7.0%.

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(0.333)(0.06) + (0.333)(0.10) + 0.333(0.05) = 0.07

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Which of the following statements about the arithmetic mean is least accurate?

A) The arithmetic mean of a frequency distribution is equal to the sum of the class frequency times the midpoint of the frequency class all divided by the number of observations.

B) If the distribution is skewed to the left then the mean will be greater than the median.

C) The arithmetic mean is the only measure of central tendency where the sum of the deviations of each observation from the mean is always zero.

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If the distribution is skewed to the left, then the mean will be less than the median.

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For the last four years, the returns for XYZ Corporation’s stock have been 10.4%, 8.1%, 3.2%, and 15.0%. The equivalent compound annual rate is:

A) 9.1%.

B) 9.2%.

C) 8.9%.

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(1.104 × 1.081 × 1.032 × 1.15)^0.25 ? 1 = 9.1%

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What is the compound annual growth rate for stock A which has annual returns of 5.60%, 22.67%, and -5.23%?

A) 7.08%.

B) 6.00%.

C) 8.72%.

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Compound annual growth rate is the geometric mean. (1.056 × 1.2267 × 0.9477)^1/3 – 1 = 7.08%

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Find the mean, median, and mode, respectively, of the following data:

3, 3, 5, 8, 9, 13, 17

A) 8; 8.28; 3.

B) 3; 8.28; 8.

C) 8.28; 8; 3.

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Mean = (3 + 3 + 5 + 8 + 9 + 13 + 17) / 7 = 8.28; Median = middle of distribution = 8 (middle number); Mode = most frequent = 3.