Question 1

A stock has an average return of 19.2 percent and a standard deviation of 10.7 percent.In any one given year,you have a 95 percent chance that you will not lose more than _____ percent nor earn more than ____ percent if you invest in this security.

Accepted Answer

95 percent probability range = 0.192 ± (2 × 0.107) = -2.2 percent to 40.6 percent

Question 2

A stock has produced returns of 11 percent,18 percent,-6 percent,-13 percent,and 21 percent for the past five years,respectively.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.11 + 0.18 - 0.06 - 0.13 + 0.21)/5 = 0.062σ² = [(0.11 - 0.062)² + (0.18 - 0.062)² + (-0.06 - 0.062)² + (-0.13 - 00.062)² + (0.21 - 0.062)²]/(5 - 1) = 0.02247σ = √0.02247 = 14.99 percent

Question 3

Over the past six years,a stock had annual returns of 14 percent,-3 percent,8 percent,21 percent,-16 percent,and 4 percent,respectively.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.14 - 0.03 + 0.08 + 0.21 - 0.16 + 0.04)/6 = 0.046667σ² = [(0.14 - 0.046667)² + (-0.03 - 0.046667)² + (0.08 - 0.046667)² + (0.21 - 00.046667)² +(-0.16 - 0.046667)² + (0.04 - 0.046667)²]/(6 - 1) = 0.017027σ = √0.017027 = 13.05 percent

Question 4

A security produced returns of 13 percent,18 percent,9 percent,23 percent,and -17 percent over the past five years,respectively.Based on these five years,what is the probability that this stock will earn more than 24.76 percent in any one given year?

Accepted Answer

Average return = (0.13 + 0.18 + 0.09 + 0.23 - 0.17)/5 = 0.092σ² = [(0.13 - 0.092)² + (0.18 - 0.092)² + (0.09 - 0.092)² + (0.23 - 00.092)² + (-0.17 - 00.092)²]/(5 - 1) = 0.024220σ = √0.024220 = 0.155628Upper end of 68 percent probability range = 0.092 + 0.155628 = 24.76 percentProbability of earning more than 24.76 percent = (1 - 0.68)/2 = 16 percent

Question 5

Over the past four years,large-company stocks and U.S.Treasury bills have produced the returns stated below.During this period,inflation averaged 2.8 percent.Given this information,the average real rate of return on large-company stocks was ___ percent as compared to _____ percent for Treasury bills.

Accepted Answer

Large-company stocks:Average nominal return = (0.15 + 0.07 + 0.04 + 0.18)/4 = 0.11Average real rate: r = (1.11/1.028) - 1 = 7.98 percentU.S. Treasury bills:Average nominal return = (0.06 + 0.03 + 0.02 + 0.04)/4 = 0.0375Average real rate: r = (1.0375/1.028) - 1 = 0.92 percent

Question 6

You purchased 1,500 shares of KFC stock five years ago and have earned annual returns of 7.1 percent,11.2 percent,5.25 percent,-4.7 percent,and 11.8 percent,respectively.What is your arithmetic average return?

Accepted Answer

Arithmetic average = (0.071 + 0.112 + 0.0525 - 0.047 + 0.118)/5 = 6.13 percent

Question 7

Over the past four years,a stock produced returns of 15 percent,6 percent,11 percent,and 22 percent,respectively.Based on these four years,what range of returns would you expect to see 95 percent of the time?

Accepted Answer

Average return = (0.15 + 0.06 + 0.11 + 0.22)/4 = 0.135σ² = [(0.15 - 0.135)² + (0.06 - 0.135)² + (0.11 - 0.135)² + (0.22 - 00.135)²]/(4 - 1) = 0.004567σ = √0.004567 = 0.067577 95 percent probability range = 0.0.135 ± (2 × 0.067577)Range of returns = -0.02 percent to 27.02 percent

Question 8

A stock produced returns of 16 percent,9 percent,and 21 percent over three of the past four years,respectively.The arithmetic average for the past four years is 10 percent.What is the standard deviation of the stock's returns for the four-year period?

Accepted Answer

Average return = 0.10 = (0.16 + 0.09 + 0.21 + x)/4x = -0.06σ² = [(0.16 - 0.10)² + (0.09 - 0.10)² + (0.21 - 0.10)² + (-0.06 - 0.10)²]/(4 - 1) = 0.0138σ = √0.0138 = 11.75 percent

Question 9

A security produced returns of 12 percent,-11 percent,-2 percent,15 percent,and 9 percent over the past five years,respectively.Based on these five years,what is the probability that an investor in this stock will lose more than 17.06 percent in any one given year?

Accepted Answer

Average return = (0.12 - 0.11 - 0.02 + 0.15 + 0.09)/5 = 0.046σ² = [(0.12 - 0.046)² + (-0.11 - 0.046)² + (-0.02 - 0.046)² + (0.15 - 0.046)² + (0.09 - 0.046)²]/(5 - 1) = 0.01173σ = √0.01173 = 0.108305Lower end of 95 percent probability range = 0.046 - (2 × 0.108305) = -17.06 percentProbability of losing more than 17.06 percent = (1 - 0.95)/2 = 2.5 percent

Question 10

Home Grown Tomatoes stock returned 28.7 percent,2.6 percent,13.1 percent,12.2,and 11.8 percent over the past five years,respectively.What is the arithmetic average return for this period?

Accepted Answer

Arithmetic average = (0.287 + 0.026 + 0.131 + 0.122 + 0.118)/5 = 13.68 percent

Question 11

A stock produced returns of 19 percent,27 percent,and -38 percent over three of the past four years,respectively.The arithmetic average for the past four years is 7 percent.What is the standard deviation of the stock's returns for the four-year period?

Accepted Answer

Average return = 0.07 = (0.19 + 0.27 - 0.38 + x)/4x = 0.20σ² = [(0.19 - 0.07)² + (0.27 - 0.07)² + (-0.38 - 0.07)² + (0.20 - 0.07)²]/(4 - 1) = 0.091267σ = √0.091267 = 30.21 percent

Question 12

Your portfolio has provided you with returns of 8.6 percent,14.2 percent,-3.7 percent,and 12.0 percent over the past four years,respectively.What is the geometric average return for this period?

Accepted Answer

Geometric average return = (1.086 × 1.142 × 0.963 × 1.120)^1/4 - 1 = 7.54 percent

Question 13

The common stock of Hillshire Farms has yielded 16.3 percent,7.2 percent,11.8 percent,-3.6 percent,and 9.7 percent over the past five years,respectively.What is the geometric average return?

Accepted Answer

Geometric average return = (1.163 × 1.072 × 1.118 × 0.964 × 1.097)^1/5 - 1 = 8.07 percent

Question 14

A bond has an average return of 6.3 percent and a standard deviation of 3.8 percent.What range of returns would you expect to see 68 percent of the time on this security?

Accepted Answer

68 percent probability range = 0.063 ± 0.038 = 2.5 percent to 10.1 percent

Question 15

Kelly decided to accept the risk and purchased a high growth stock.Her returns for the past five years are 48 percent,39 percent,-56 percent,61 percent,and -24 percent,respectively.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.48 + 0.39 - 0.56 + 0.61 - 0.24)/5 = 0.136σ² = [(0.48 - 0.136)² + (0.39 - 0.136)² + (-0.56 - 0.136)² + (0.61 - 00.136)² + (-0.24 - 0.136)²]/(5 - 1) = 0.258330σ = √0.258330 = 50.83 percent

Question 16

A stock has yielded returns of 6 percent,11 percent,14 percent,and -2 percent over the past four years,respectively.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.06 + 0.11 + 0.14 - 0.02)/4 = 0.0725σ² = [(0.06 - 0.0725)² + (0.11 - 0.0725)² + (0.14 - 0.0725)² + (-0.02 - 00.0725)² ]/(4 - 1) = 0.004892σ = √0.004892 = 6.99 percent

Question 17

Over the last four years,the common stock of Plymouth Shippers has had an arithmetic average return of 9.3 percent.Three of those four years produced returns of 14.1 percent,15.6 percent,and 3.4 percent,respectively.What is the geometric average return for this four-year period?

Accepted Answer

Arithmetic average return = 0.093 = (0.141 + 0.156 + 0.034 + x)/4x = 0.041Geometric average return = [1.141 × 1.156 × 1.034 × 1.041)^1/4 - 1 = 9.16 percent

Question 18

Over the past four years,a stock produced returns of 23 percent,-39 percent,4 percent,and 16 percent,respectively.Based on these four years,what range of returns would you expect to see 99 percent of the time?

Accepted Answer

Average return = (0.23 - 0.39 + 0.04 + 0.16)/4 = 0.01σ² = [(0.23 - 0.01)² + (-0.3 - 0.01)² + (0.04 - 0.01)² + (0.16 - 0.01)²]/(4 - 1) = 0.077267σ = √0.077267 = 0.277969 99 percent probability range = 0.01 ± (3 × 0.277969)Range of returns = -82.39 percent to 84.39 percent

Question 19

Five years ago,you purchased 600 shares of stock.The annual returns have been 7.2 percent,-19.4 percent,3.8 percent,14.2 percent,and 27.9 percent,respectively.What is the variance of these returns?

Accepted Answer

Average return = (0.226 + 0.187 + 0.113 - 0.198 + 0.024)/5 = 0.0704σ² = [(0.226 - 0.0704)² + (0.187 - 0.0704)² + (0.113 - 0.0704)² + (-0.198 - 0.0704)² + (0.024 - 0.0704)²]/(5 - 1) = 0.028453

Question 20

A stock has produced returns of 16.6 percent,3.4 percent,11.7 percent,and -9.2 percent over the past four years,respectively.What is the geometric average return?

Accepted Answer

Geometric average return = (1.166 × 1.034 × 1.117 × 0.908)^1/4 - 1 = 5.16 percent

Quiz 10: Some Lessons From Capital Market History

A stock has an average return of 19.2 percent and a standard deviation of 10.7 percent.In any one given year,you have a 95 percent chance that you will not lose more than _ percent nor earn more than percent if you invest in this security.