Reading 7: Statistical Concepts and Market Returns-LOS e习题 2010, 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 calculates the rate of return that would have to be earned each year to match the actual, cumulative investment performance.

C) 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.

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

C) 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.

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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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A stock had the following returns over the last five years: 15%, 2%, 9%, 44%, 23%. What is the respective geometric mean and arithmetic mean for this stock?

A) 17.76%; 23.0%.

B) 0.18%; 18.6%.

C) 17.76%; 18.6%.

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A stock had the following returns over the last five years: 15%, 2%, 9%, 44%, 23%. What is the respective geometric mean and arithmetic mean for this stock?

A) 17.76%; 23.0%.

B) 0.18%; 18.6%.

C) 17.76%; 18.6%.

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Geometric mean = [(1.15)(1.02)(1.09)(1.44)(1.23)]^1/5 ? 1 = 1.17760 = 17.76%.

Arithmetic mean = (15 + 2 + 9 + 44 + 23) / 5 = 18.6%.

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Trina Romel, mutual fund manager, is taking over a poor-performing fund from a colleague. Romel wants to calculate the return on the portfolio. Over the last five years, the fund’s annual percentage returns were: 25, 15, 12, -8, and –14. Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund’s geometric return:

       Geometric Return    Geometric compared to Arithmetic

A) 4.96%   greater than

B) 12.86%   greater than

C) 4.96%   less than

bmaggie

Trina Romel, mutual fund manager, is taking over a poor-performing fund from a colleague. Romel wants to calculate the return on the portfolio. Over the last five years, the fund’s annual percentage returns were: 25, 15, 12, -8, and –14. Determine if the geometric return of the fund will be less than or greater than the arithmetic return and calculate the fund’s geometric return:

       Geometric Return    Geometric compared to Arithmetic

A) 4.96%   greater than

B) 12.86%   greater than

C) 4.96%   less than

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The geometric return is calculated as follows:

[(1 + 0.25)(1 + 0.15)(1 + 0.12)(1 - 0.08)(1 – 0.14)]^1/5 – 1,

or [1.25 × 1.15 × 1.12 × 0.92 × 0.86]^0.2 – 1 = 0.4960, or 4.96%.

The geometric return will always be less than or equal to the arithmetic return. In this case the arithmetic return was 6%.

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An investor has a $12,000 portfolio consisting of $7,000 in stock A with an expected return of 20% and $5,000 in stock B with an expected return of 10%. What is the investor’s expected return on the portfolio?

A) 15.8%.

B) 12.2%.

C) 15.0%.

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An investor has a $12,000 portfolio consisting of $7,000 in stock A with an expected return of 20% and $5,000 in stock B with an expected return of 10%. What is the investor’s expected return on the portfolio?

A) 15.8%.

B) 12.2%.

C) 15.0%.

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Find the weighted mean where the weights equal the proportion of $12,000. (7,000 / 12,000)(0.20) + (5,000 / 12,000)(0.10) = 15.8%.

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Michael Philizaire is studying for the Level I CFA examination. During his review of measures of central tendency, he decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, -5, -5. The geometric return is closest to:

A) 11.60%.

B) 0.00%.

C) 4.49%.

bmaggie

Michael Philizaire is studying for the Level I CFA examination. During his review of measures of central tendency, he decides to calculate the geometric average of the appreciation/deprecation of his home over the last five years. Using comparable sales and market data he obtains from a local real estate appraiser, Philizaire calculates the year-to-year percentage change in the value of his home as follows: 20, 15, 0, -5, -5. The geometric return is closest to:

A) 11.60%.

B) 0.00%.

C) 4.49%.

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The geometric return is calculated as follows:

[(1 + 0.20) × (1 + 0.15) × (1 + 0.0) (1 ? 0.05) (1 ? 0.05)]^1/5 – 1,

or [1.20 × 1.15 × 1.0 × 0.95 × 0.95]^0.2 – 1 = 0.449, or 4.49%.