Question 1

One year ago,Barkley's stock sold for $20 a share.During last year,Barkley's paid $1.40 per share in dividends and saw its stock price increase by five percent for the year.Today,the firm announced that it will pay $1.43 per share in dividends this year.What do you know with certainty about the performance of Barkley's stock for this year?

Accepted Answer

Dividend yield_{Last year} = $1.40/$20 = .07,or 7%Dividend yield_{This year} = $1.43/(1.05 × $20)= .0681,or 6.81%

Question 2

Eight months ago,Isaac purchased 50 shares of stock at a price of $65.90 a share.To date,he has received two quarterly dividends of $1.03 a share each.If he sells his shares at the current price of $52.80 a share,what will be his total percentage return?

Accepted Answer

Total percentage return = ($52.80 - 65.90 + (2 × $1.03))/$65.90 = -16.75%

Question 3

A stock returned 13 percent,18 percent,-16 percent and -1 percent annually for the past four years.Based on this information,what is the 99.74 percent probability range for any one given year?

Accepted Answer

Mean = (.13 + .18 - .16 - .01)/4 = .035Total squared deviation = (.13 - .035)² + (.18 - .035)² + (-.16 - .035)² + (-.01 - .035)² = .0701Standard deviation = √.0701/(4 - 1)= .1529 = 15.29%99.74% probability range = 3.5% ± (3 × 15.29%)= -42.4 to 49.4%

Question 4

A stock has an expected rate of return of 14.2 percent and a standard deviation of 23.4 percent.Which one of the following best describes the probability that this stock will lose more than 1/3 of its value in any one year?

Accepted Answer

Lower bound of 95.44 percent probability range = .142 - (2 × .234)= -.326,or -32.6%Probability = (100% - 95.44%)/2 = 2.28%A loss of 1/3,or 33 percent,would be a tad further out into the tail,so a probability of 2.25 percent would be a good approximation.

Question 5

A stock had annual returns of 8 percent,-2 percent,4 percent,and 20 percent over the past four years.What is the standard deviation of these returns?

Accepted Answer

Mean = (.08 - .02 + .04 + .20)/4 = .075Total squared deviation = (.08 - .075)² + (-.02 - .075)² + (.04 - .075)² + (.20 - .075)² = .0259Standard deviation = √.0259/(4 - 1)= .0929 = 9.29%

Question 6

Today,you sold 200 shares of SLG stock for a total of $10,018.Last year,you purchased the stock for $52.30 a share and received $326 in dividends.What is your total rate of return on this investment?

Accepted Answer

Total return = [$10,018 + 326 - (200 × $52.30)]/(200 × $52.30)= -.0111,or -1.11%

Question 7

A stock had returns of 19 percent,12 percent,-29 percent,35 percent,and 4 percent annually for the past five years.Based on these returns,what is the approximate probability that this stock will earn at least 30 percent in any one given year?

Accepted Answer

Mean = (.19 + .12 - .29 + .35 + .04)/5 = .082Total squared deviation = (.19 - .082)² + (.12 - .082)² + (-.29 - .082)² + (.35 - .082)² + (.04 - .082)² = .22508Standard deviation = √.22508/(5 - 1)= .2372Upper end of the 68.26% probability range = .082 + .2372 = .3192,or 31.92%Probability of earning at least 31.92% = (100% - 68.26%)/2 = 15.87%The probability of earning 30 percent or more will be greater than the probability of earning 31.92 percent or more,so an approximation of 16 percent is reasonable.

Question 8

What are the arithmetic and geometric average returns for a stock with annual returns of 11 percent,14 percent,-2 percent and 6 percent?

Accepted Answer

Arithmetic average = (.11 + .14 - .02 + .06)/4 = .0725,or 7.25%Geometric return = (1.11 × 1.14 × .98 × 1.06)^.25 - 1 = .0708,or 7.08%

Question 9

One year ago,Ceegee purchased 200 shares of stock at a price of $18.97 per share.Over the last year,she received total dividend income of $164.What is the dividend yield?

Accepted Answer

Dividend per share = $164/200 = $.82Dividend yield = $.82/$18.97 = .0432,or 4.32%

Question 10

A stock had returns of 7 percent,15 percent,and -1 percent for the past three years.Based on these returns,what is the probability that this stock will earn at least 15 percent in any one given year?

Accepted Answer

Average return = (.07 + .15 - .01)/3 = .07Total squared deviation = (.07 - .07)² + (.15 - .07)² + (-.01 - .07)² = .0128Standard deviation = √.0128/(3 - 1)= .08Upper end of the 68.26% probability range = .07 + .08 = .15,or 15%Probability of earning at least 15% = (100% - 68.26%)/2 = 15.87%

Question 11

A stock had returns of 14 percent,3 percent,9 percent,and -12 percent annually for the past four years.What is the mean and variance of these returns?

Accepted Answer

Mean = (.14 + .03 + .09 -.12)/4 = .0350,or 3.50%Total squared deviation = (.14 - .035)² + (.03 - .035)² + (.09 - .035)² + (-.12 - .035)² = .0381Variance = .0381/(4 - 1)= .0127

Question 12

What are the arithmetic and geometric average returns for a stock with annual returns of 4 percent,12 percent,-8 percent and 9 percent?

Accepted Answer

Arithmetic average = (.04 + .12 - .08 + .09)/4 = .0425,or 4.25%Geometric return = (1.04 × 1.12 × .92 × 1.09)^.25 - 1 = .0396,or 3.96%

Question 13

Six months ago,you purchased 2,400 shares of stock for $21.10 a share.Today,you sold the shares for $22.20 a share.What is your total dollar return on this investment if you received a dividend of $.40 a share?

Accepted Answer

Total dollar return = ($22.20 - 21.10 + .40)× 2,400 = $3,600

Question 14

A stock had returns of 12 percent,6 percent,14 percent,and -3 percent annually for the past four years.What is the mean and standard deviation of these returns?

Accepted Answer

Mean = (.12 + .06 + .14 - .03)/4 = .0725,or 7.25%Total squared deviation = (.12 - .0725)² + (.06 - .0725)² + (.14 - .0725)² + (-.03 - .0725)² = .017475Standard deviation = √.017475/(4 - 1)= .0763,or 7.63%

Question 15

Winslow stock is currently selling for $48 a share.The stock has a dividend yield of 3.1 percent.How much dividend income will you receive per year if you purchase 600 shares of this stock?

Accepted Answer

Dividend income = $48 × .031 × 600 = $892.80

Question 16

One year ago,you purchased a stock at a price of $28.50 a share.Today,you sold the stock and realized a total return of 20.4 percent.Your capital gain was $5.20 a share.What was your dividend yield on this stock?

Accepted Answer

Capital gains yield = $5.20/$28.50 = .1825,or 18.25%Dividend yield = 20.4% - 18.25% = 2.15%

Question 17

Deltona stock sold for $38.60 a share one year ago and pays an annual dividend of $1.55.What does the stock price need to be today for the annual capital gain to be 7.5 percent?

Accepted Answer

Capital gains yield = .075 = (P _{t + 1} - $38.60)/$38.60P _{t + 1} = $41.50

Question 18

One year ago,Stacey purchased 300 shares of IXC Tek stock at a price of $11.23 per share.The stock pays an annual dividend of $.23 per share.Today,Stacey sold all of her shares for $16.20 per share.What is her total dollar return on this investment?

Accepted Answer

Total dollar return = ($16.20 - 11.23 + .23)× 300 = $1,560

Question 19

You just sold 250 shares of stock for $37.75 a share.One year ago,you purchased the stock for $40.50 a share and have received dividends totaling $2.64 per share.What is your capital gain in dollars?

Accepted Answer

Capital gain = ($37.75 - 40.50)× 250 = -$687.50

Question 20

A stock had returns of 7 percent,12 percent,-10 percent,and 17 percent annually over the past four years.What is the geometric average return for this time period?

Accepted Answer

Geometric average = (1.07 × 1.12 × .90 × 1.17)^.25 - 1 = .0599,or 5.99%

Quiz 10: Risk and Return Lessons From Market History