Question

Consider the following five monthly returns. The arithmetic average monthly return over this period is 1.40% and the geometric average monthly return over this period is 1.33%. Explain the difference between the arithmetic average return and the geometric average return. Are both numbers useful? If so, explain why?

3% -1% 2% 7% -4%

Choose the correct answer below.

Both numbers are useful. The geometric average return tells you what you would actually make if you held the stock over this period. You can use the arithmetic average return over the period as an estimate of the expected return. If you use this estimate, it is what you would expect to make in the next period.

A. Both numbers are useful. The geometric average return tells you what you would actually make if you held the stock over this period. You can use the arithmetic average return over the period as an estimate of the expected return. If you use this estimate, it is what you would expect to make in the next period.

B.There is no difference between arithmetic and geometric average returns. The two are just different methods to get the same answer.

C.The geometric average return is what you would have actually achieved if you had held the stock, so this is the number you care about. The arithmetic average return is useless.

D.The arithmetic average return is the best estimate of what you would earn in the future, so this is the number you care about. The geometric average return is useless.

Answer #1

Consider the following five monthly returns: 7%, -2%, 5%
11%, -3%
a. Calculate the arithmetic average monthly return over this
period and express your answer as a percentage per month.
b. Calculate the geometric average monthly return over this
period.
c. Calculate the monthly variance over this period.
d. Calculate the monthly standard deviation over this
period.

Over a 50 year period an asset had an arithmetic return of 12.1
percent and geometric return of 10 percent.
Musing Blume’s formula, what is your best estimate of the
future annual returns over 10 years? 15 years? 25 years?

Q1) A stock earned annual returns of 5%, 10%, -7%, and 16% for
the last four years.
a) What is the arithmetic average return for the stock over the
last four years?
b) What is the standard deviation of the returns over the last
four years?
c) What is the geometric average return for the stock over the
last four years?
d) What is the holding period return for the stock over the last
four years?
e) What would have...

1. Calculate the rates of return (holding period returns) for
the following stocks:
Stock
Beginning price: P0
Ending price: P1
Dividend payment: D1
A
21.38
16.06
2.6
B
108.74
118.92
5.25
C
4.25
5.58
0.19
Part 1
What was the rate of return for stock A?
Part 2
What was the rate of return for stock B?
Part 3
What was the rate of return for stock C?
2. You bought Samsung stock for $45 on April 1. The stock...

You have found an asset with an arithmetic average return of
13.60 percent and a geometric average return of 10.44 percent. Your
observation period is 30 years. What is your best estimate of the
return of the asset over the next 5 years? 10 years? 20 years?
(Do not round intermediate calculations. Enter your answers
as a percent rounded to 2 decimal places.)

9. You’ve observed the following returns on Barnett
Corporation’s stock over the past five years: -12 percent, 23
percent, 18 percent, 7 percent, and 13 percent
What was the arithmetic average return on the stock over
this five-year period?
What was the variance of the returns over this period?
The standard deviation?
10. For problem 9, suppose the average inflation rate
over this period was 3.2 percent and the average T-bill rate over
the period was 4.3 percent.
A What...

Over the 10 year period from 2001-2018, the geometric average
return for APPLE was 8.2 % and the arithmetic average return was
9.25 %. Compute average return forecasts for 1, 3, 7, 10, and 20
years into the futures.

Ten annual returns are listed in the following table: -19.5%
16.3% 17.9% -49.3% 43.5% 1.6% -16.7% 46.2% 44.8% -3.4%
a. What is the arithmetic average return over the 10-year
period?
b. What is the geometric average return over the 10-year period?
The geometric average return over the 10-year period is (round to
4 decimal places)
c. If you invested $100 at the beginning, how much would you have
at the end? (round to four decimal places)

The annual returns on the stock of a firm during the last four
years are provided below.
___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
a) Find the holding period return of the stock over the
four-year period.
b) Compute the arithmetic average return of the stock over the
four-year period.
c) Calculate the geometric average return of the...

The annual returns on the stock of a firm during the last four
years are provided below.
___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
a) Find the holding period return of the stock over the
four-year period.
b) Compute the arithmetic average return of the stock over the
four-year period.
c) Calculate the geometric average return of the...

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