Q1. Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?

A)   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.

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

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

Q2. 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)   17.76%; 18.6%.

C)   0.18%; 18.6%.

Q3. 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%.

Q4. 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)   4.49%.

C)   0.00%.

答案和详解如下：

Q1. Consider the following statements about the geometric and arithmetic means as measures of central tendency. Which statement is least accurate?

A)   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.

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

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

Correct answer is A)

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.

Q2. 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)   17.76%; 18.6%.

C)   0.18%; 18.6%.

Correct answer is B)

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%.

Q3. 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%.

Correct answer is A)

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%.

Q4. 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)   4.49%.

C)   0.00%.

Correct answer is B)

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%.

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