Question

A stock produced returns of 14 percent, 17 percent, and −10 percent over three of the past four years, respectively. The arithmetic average for the past four years is 6 percent.

Show you work here (be as detailed and organized as possible):

- What is the missing return (i.e., the return in the fourth year)?

- What is the geometric average return over the four years?

- What is the standard deviation of returns of the stock? Show your work clearly below.

Answer #1

1)

0.06 = (0.14 + 0.17 - 0.1 + Missing return) / 4

0.24 = 0.14 + 0.17 -0.1 + Missing return

**Missing return = 0.03 or 3.00%**

2)

Geometric average = [(1 + R1)(1 + R2)(1 +R3)(1 + R4)]^1/n - 1

Geometric average = [(1 + 0.14)(1 + 0.17)(1 - 0.1)(1 + 0.03)]^1/4 - 1

Geometric average = [1.236433]^1/4 - 1

Geometric average = 1.0545 - 1

**Geometric average = 0.0545 or 5.45%**

3)

Standard deviation = {[(0.14 - 0.06)^2 + (0.17 - 0.06)^2 + (-0.1 - 0.06)^2 + (0.03 - 0.06)^2] / 4 - 1}^1/2

Standard deviation = {[0.0064 + 0.0121 + 0.0256 + 0.0009] / 3}^1/2

Standard deviation {0.015}^1/2

**Standard deviation = 0.1225 or 12.25%**

8.
A stock had returns of 16.11 percent, 23.82 percent, −11.53
percent, and 9.58 percent over four of the past five years. The
arithmetic average return over the five years was 13.16 percent.
What was the stock return for the missing year?
9. A stock had returns of 17.59 percent, −7.11 percent, and
23.81 percent for the past three years. What is the standard
deviation of the returns?

A stock had returns of 16 percent, 12 percent, 19 percent, 17
percent, 18 percent, and -1 percent over the last six years.
What is the arithmetic return for the stock?
What is the geometric return for the stock?

Over the past four years, a stock produced returns of 6
percent, 8 percent, 19 percent, and 2 percent, respectively. Based
on these four years, what range of returns would you expect to see
95 percent of the time?

A stock had returns of 15 percent, 14 percent, 18 percent, 5
percent, 16 percent, and 2 percent over the last six years. What is
the arithmetic return for the stock? What is the geometric return
for the stock?

Q1) A stock earned annual returns of 5%, 10%, -7%, and 16% for
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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?
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A stock produced total returns of 15%, 12%, -20%, and 36% over
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Bond ratings issued by Moody’s specifically account for interest
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(b)
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