Question 1

A stock has an expected rate of return of 13 percent and a standard deviation of 21 percent.Which one of the following best describes the probability that this stock will lose at least half of its value in any one given year?

Accepted Answer

Lower bound of 99 percent range = 0.13 - (3 × 0.21) = -50 percentProbability of losing 50 percent or more in any one year is 0.5 percent.

Question 2

Today,you sold 200 shares of Indian River Produce stock.Your total return on these shares is 6.2 percent.You purchased the shares one year ago at a price of $31.10 a share.You have received a total of $100 in dividends over the course of the year.What is your capital gains yield on this investment?

Accepted Answer

Capital gains yield = .062 - [($100/$200)/$31.10] = 4.59 percent

Question 3

A stock has annual returns of 6 percent,14 percent,-3 percent,and 2 percent for the past four years.The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Accepted Answer

Arithmetic average = (0.06 + 0.14 - 0.03 + 0.02)/4 = 4.75 percentGeometric return = (1.06 × 1.14 × 0.97 × 1.02)^.25 - 1 = 4.57 percent

Question 4

Your friend is the owner of a stock which had returns of 25 percent,-36 percent,1 percent,and 16 percent for the past four years.Your friend thinks the stock may be able to achieve a return of 50 percent or more in a single year.Based on these returns,what is the probability that your friend is correct?

Accepted Answer

Average return = (0.25 - 0.36 + 0.01 + 0.16)/4 = 0.015σ = √[1/(4 - 1)] [(0.25 - 0.015)² + (-0.36 - 0.015)² + (0.01 - 0.015)² + (0.16 - 0.015)²] = 0.2689Upper end of 68 percent range = 0.015 + (1 × 0.2689) = 28.39 percentUpper end of 95 percent range = 0.015 + (2 × 0.2689) = 55.28 percentThe probability of earning at least 50 percent in any one year is greater than 2.5 percent but less than 16 percent.

Question 5

One year ago,you purchased 150 shares of a stock at a price of $54.18 a share.Today,you sold those shares for $40.25 a share.During the past year,you received total dividends of $182 while inflation averaged 4.2 percent.What is your approximate real rate of return on this investment?

Accepted Answer

Nominal return = [$40.25 - $54.18 + ($182/150)]/$54.18 = -0.2420Approximate real return = -0.2420 - 0.042 = -28.40 percent

Question 6

Over the past five years,a stock produced returns of 11 percent,14 percent,4 percent,-9 percent,and 5 percent.What is the probability that an investor in this stock will not lose more than 10 percent in any one given year?

Accepted Answer

Average return = (0.11 + 0.14 + 0.02 - 0.09 + 0.05)/5 = 0.05σ = √[1/(5 - 1)][(0.11 - 0.046)² + (0.14 - 0.046)² + (0.04 - 0.046)² + (-0.09 - 0.046)² + (0.05 - 0.046)²] = 0.0886Lower bound of 68% probability range = 0.05 - (1 × 0.0886) = -3.86 percentLower bound of 95% probability range = 0.05 - (2 × 0.0886) = -12.72 percentThe probability of losing 10 percent or more is greater than 2.5 percent but less than 16 percent. Thus, the probability of NOT losing more than 10 percent is greater than 84 percent but less than 97.5 percent.

Question 7

A stock had returns of 11 percent,-18 percent,-21 percent,20 percent,and 34 percent over the past five years.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.11 - 0.18 - 0.21 + 0.20 + 0.34)/5 = .052;σ = √[1/(5 - 1)] [(0.11 - 0.052)² + (-0.18 - 0.052)² + (-0.21 -0.052)² + (0.05 - 0.052)² + (0.34 - 0.052)²] = 24.01 percent

Question 8

A stock has annual returns of 5 percent,21 percent,-12 percent,7 percent,and -6 percent for the past five years.The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Accepted Answer

Arithmetic average = (0.05 + 0.21- 0.12 + 0.07 - 0.06)/5 = 3.00 percentGeometric return = (1.05 × 1.21 × 0.88 × 1.07 × 0.94)^.20 - 1 = 2.37 percent

Question 9

What is the amount of the risk premium on a U.S.Treasury bill if the risk-free rate is 2.8 percent and the market rate of return is 8.35 percent?

Accepted Answer

There is no excess return, or risk premium, for a risk-free security such as the T-bill.

Question 10

Last year,you purchased 500 shares of Analog Devices,Inc.stock for $11.16 a share.You have received a total of $120 in dividends and $7,190 from selling the shares.What is your capital gains yield on this stock?

Accepted Answer

Capital gains yield = [($7,190/500) - $11.16]/$11.16 = 28.85 percent

Question 11

A stock has returns of 18 percent,15 percent,-21 percent,and 6 percent for the past four years.Based on this information,what is the 95 percent probability range of returns for any one given year?

Accepted Answer

Average return = (0.18 + 0.15 - 0.21 + 0.06)/4 = 0.045σ = [1/3{(.18-.045)^2 (.15-.045)^2 (-.21 -.045)^2 (.06-.045)^2 (.06-.045)^2}]^(1/2 = .17748295% probability range = 0.045 ± (2 × 0.177482) percent = -31.00 to 40.00 percent

Question 12

A stock had returns of 15 percent,8 percent,12 percent,-15 percent,and -4 percent for the past five years.Based on these returns,what is the approximate probability that this stock will return at least 20 percent in any one given year?

Accepted Answer

Average return = (0.15 + 0.08 + 0.12 - 0.15 - 0.04)/5 = 0.032σ = √[1/(5 - 1)] [(0.15 - 0.02)² + (0.08 - 0.02)² + (0.12 - 0.02)² + (-0.15 - 0.02)² + (-0.04 - 0.02)²] = 0.1248Upper end of 68 percent range = 0.032 + 0.1248 = 15.68 percentProbability of earning at least 20 percent in any one year is less than 16 percent but greater than 2.5 percent.

Question 13

A stock had returns of 14 percent,13 percent,-10 percent,and 7 percent for the past four years.Which one of the following best describes the probability that this stock will lose no more than 10 percent in any one year?

Accepted Answer

Average return = (0.14 + 0.13 - 0.10 + 0.07)/4 = 0.06σ = √[1/(4 - 1)][(0.14 - 0.06)² + (0.13 - 0.06)² + (-0.10 - 0.06)² + (0.07 - 0.06)²] = 0.11106Lower bound of 68 percent range = 0.06 - (1 × 0.11106) = -5.11 percentLower bound of 95 percent range = 0.06 - (2 × 0.11106) = -16.21 percentProbability of losing more than 10 percent in any given year is between 2.5 and 16 percent. Thus, the probability of NOT losing more than 10 percent is between 84 and 97.5 percent.

Question 14

One year ago,you purchased 500 shares of Best Wings,Inc.stock at a price of $9.75 a share.The company pays an annual dividend of $0.10 per share.Today,you sold all of your shares for $15.60 a share.What is your total percentage return on this investment?

Accepted Answer

Total percentage return = ($15.60 - $9.75 + $0.10)/$9.75 = 61.03 percent

Question 15

Last year,you purchased a stock at a price of $47.10 a share.Over the course of the year,you received $2.40 per share in dividends while inflation averaged 3.4 percent.Today,you sold your shares for $49.50 a share.What is your approximate real rate of return on this investment?

Accepted Answer

Nominal return = ($49.50 - $47.10 + $2.40)/$47.10 = 10.19 percentApproximate real return = 0.1019 - 0.034 = 6.79 percent

Question 16

The common stock of Air United,Inc.,had annual returns of 15.6 percent,2.4 percent,-11.8 percent,and 32.9 percent over the last four years,respectively.What is the standard deviation of these returns?

Accepted Answer

Average return = (0.156 + 0.024 - 0.118 + 0.329)/4 = 0.09775σ = √[1/(4 - 1)] [(0.156 - 0.09775)² + (0.024 - 0.09775)² + (-0.118 - 0.09775)² + (0.329 - 0.09775)²] = 19.05 percent

Question 17

A stock had returns of 16 percent,4 percent,8 percent,14 percent,-9 percent,and -5 percent over the past six years.What is the geometric average return for this time period?

Accepted Answer

Geometric average = (1.16 × 1.04 × 1.08 × 1.14 × 0.91 × 0.95)^1/6 - 1 = 4.26 percent

Question 18

A stock had the following prices and dividends.What is the geometric average return on this stock?

Accepted Answer

Return for year 2 = ($16.10 - $16.40 + $0.50)/$16.40 = 1.2195 percentReturn for year 3 = ($15.48 - $16.10 + $0.50)/$16.10 = -0.7453 percentReturn for year 4 = ($9.15 - $15.48 + $0.75)/$15.48 = -36.0465 percentGeometric return = (1.012195 × 0.9925472 × 0.639535)^1/3 - 1 = -13.71 percent

Question 19

Four months ago,you purchased 1,500 shares of Lakeside Bank stock for $11.20 a share.You have received dividend payments equal to $0.25 a share.Today,you sold all of your shares for $8.60 a share.What is your total dollar return on this investment?

Accepted Answer

Total dollar return = ($8.60 - $11.20 + $0.25) × 1,500 = -$3,525

Question 20

A stock had annual returns of 3.6 percent,-8.7 percent,5.6 percent,and 12.5 percent over the past four years.Which one of the following best describes the probability that this stock will produce a return of 22 percent or more in a single year?

Accepted Answer

Average return = (0.036 - 0.087 + 0.056 + 0.125)/4 = 0.0325∑ = √[1/(4 - 1)] [(0.036 - 0.0325)² + (-0.087 - 0.0325)² + (0.056 - 0.0325)² + (0.125 - 0.0325)²] = 0.0883Upper end of 95 percent range = 0.0325 + (2 × 0.0883) = 20.91 percentUpper end of 99 percent range = 0.0325 + (3 × 0.0883) = 29.75 percentA return of 22 percent or more in a single year has between a 1 percent and a 2.5 percent probability of occurring in any one year.

Quiz 12: Some Lessons From Capital Market History