Question 1

A stock produced annual returns of 8.3,-21,12,42,and 9 percent over the past five years,respectively.What is the geometric average return?
A) 5.78 percent
B) 6.03 percent
C) 6.34 percent
D) 7.21 percent
E) 8.20 percent

Accepted Answer

Geometric average = [(1 + 0.083)(1 - 0.21)(1 + 0.12)(1 + 0.42)(1 + 0.09)]^{1 / 5} - 1 = 8.20 percent

Question 2

A portfolio had an original value of $7,400 seven years ago.The current value of the portfolio is $11,898.What is the average geometric return on this portfolio?
A) 7.02 percent
B) 7.47 percent
C) 7.59 percent
D) 7.67 percent
E) 7.88 percent

Accepted Answer

$7,400 (1 + R)⁷ = $11,898; R = 7.02 percent

Question 3

The geometric return on a stock over the past 10 years was 7.9 percent.The arithmetic return over the same period was 8.8 percent.What is the best estimate of the average return on this stock over the next 5 years?
A) 8.40 percent
B) 9.05 percent
C) 9.08 percent
D) 9.13 percent
E) 9.47 percent

Accepted Answer

Projected return = {[(5 - 1) / (10 - 1)] × 0.0790} + {[(10 - 5) / (10 - 1)] × 0.0880} = 8.40 percent

Question 4

Downtown Industries common stock had returns of 5.2,10.3,9.3,and 9.5 percent,respectively,over the past four years.What is the standard deviation of these returns?
A) 2.29 percent
B) 2.38 percent
C) 2.41 percent
D) 2.59 percent
E) 2.82 percent

Accepted Answer

Mean = (0.052 + 0.103 + 0.093 + 0.095) / 4 = 0.0858 Var = [(0.052 - 0.0858)² + (0.103 - 0.0858)² + (0.093 - 0.0858)² + (0.095 - 0.0858)²] / (4 - 1) = 0.00052492 Std Dev = √ (0.00052492) = 2.29 percent

Question 5

Blackstone Mines stock returned 10.5,17.2,-9.0,and 14.5 percent over the past four years,respectively.What is the geometric average return?
A) 5.84 percent
B) 6.36 percent
C) 7.78 percent
D) 9.94 percent
E) 10.33 percent

Accepted Answer

Geometric average = [(1 + 0.105)(1 + 0.1723)(1 - 0.090)(1 + 0.145)]^{1 / 4} - 1 = 7.78 percent

Question 6

Jim began his investing program with a $4,000 initial investment.The table below recaps his returns each year as well as the amounts he added to his investment account.What is his dollar-weighted average return?

A) 1.6 percent
B) 2.2 percent
C) 2.6 percent
D) 3.2 percent
E) 3.6 percent

Accepted Answer

Using the Cash Flow worksheet in a financial calculator, the cash flows to be entered are:
CF0 = -4000
CF1 = -2800
CF2 = -900
CF3 = -1600
CF4 = -2100
CF5 = -2400
CF6 = 15246.78 (see calculations below)
Solve for IRR = 2.6 percent
4000 × (1.10) = 4400
(4400 + 2800) × (0.95) = 6840
(6840 + 900) × (1.02) = 7894.80
(7894.80 + 1600) × (1.08) = 10254.38
(10254.38 + 2100) × (0.97) = 11983.75
(11983.75 + 2400) × (1.06) = 15246.78

Question 7

Bill has been adding funds to his investment account each year for the past 3 years.He started with an initial investment of $1,000.After earning a 10 percent return the first year,he added $3,000 to his portfolio.In this year his investments lost 5 percent.Undeterred,Bill added $2,000 the next year and earned a 2 percent return.Last year,discouraged by the recent results,he only added $500 to his portfolio,but in this final year his investments earned 8 percent.What was Bill's dollar-weighted average return for his investments?
A) 1.5 percent
B) 2.0 percent
C) 2.5 percent
D) 3.0 percent
E) 3.5 percent

Accepted Answer

Using the Cash Flow worksheet in a financial calculator, the cash flows to be entered are:
CF0 = -1000
CF1 = -3000
CF2 = -2000
CF3 = -500
CF4 = (((((1000 × 1.1) + 3000) × 0.95) + 2000) × (1.02)) + 500) × 1.08 = $7,033.93
Solve for IRR = 3.0 percent

Question 8

One year ago,you purchased 300 shares of stock at a cost of $6,000.The stock paid an annual dividend of $1.10 per share.Today,you sold those shares for $22.50 each.What is the capital gains yield on this investment?
A) 9.96 percent
B) 10.52 percent
C) 12.50 percent
D) 13.81 percent
E) 14.75 percent

Accepted Answer

[($22.50 × 300) - $6,000)] / $6,000 = 12.50 percent

Question 9

The geometric return on an asset over the past 12 years has been 14.50 percent.The arithmetic return over the same period was 14.96 percent.What is the best estimate of the average return on this asset over the next 5 years?
A) 14.47 percent
B) 14.67 percent
C) 14.79 percent
D) 14.88 percent
E) 14.86 percent

Accepted Answer

Projected return = {[(5 - 1) / (12 - 1)] × 0.1450} + {[(12 - 5) / (12 - 1)] × 0.1496} = 14.79 percent

Question 10

A stock had year end prices of $24,$27,$32,and $26 over the past four years,respectively.What is the geometric average return?
A) 2.02 percent
B) 2.18 percent
C) 2.55 percent
D) 2.70 percent
E) 2.81 percent

Accepted Answer

($26 / $24)^{1 / 3} - 1 = 2.70 percent

Question 11

An initial investment of $41,800 fifty years ago is worth $1,533,913 today.What is the geometric average return on this investment?
A) 7.47 percent
B) 8.02 percent
C) 9.23 percent
D) 10.47 percent
E) 11.08 percent

Accepted Answer

$41,800(1 + R)⁵⁰ = $1,533,913; R = 7.47 percent N = 50; PV = -41800, PMT = 0, FV = 1533913 --- I / y = 7.471%

Question 12

You invested $5,000 eight years ago.The arithmetic average return on your investment is 10.6 percent and the geometric average return is 10.23 percent.What is the value of your portfolio today?
A) $9,092
B) $10,623
C) $10,899
D) $10,947
E) $11,195

Accepted Answer

FV = $5,000 × (1 + 0.1023)⁸ = $10,899

Question 13

John began his investing program with a $5,500 initial investment.The table below recaps his returns each year as well as the amounts he added to his investment account.What is his dollar-weighted average return?

A) 1.5 percent
B) 1.8 percent
C) 2.0 percent
D) 2.2 percent
E) 2.6 percent

Accepted Answer

Using the Cash Flow worksheet in a financial calculator, the cash flows to be entered are:
CF0 = -5500
CF1 = -2000
CF2 = -2600
CF3 = -3000
CF4 = -900
CF5 = 15359.31 (see calculations below)
Solve for IRR = 2.6 percent
5500 × (1.085) = 5967.50
(5967.50 + 2000) × (0.95) = 7569.13
(7569.13 + 2600) × (1.045) = 10626.74
(10626.74 + 3000) × (1.09) = 14853.14
(14853.14 + 900) × (0.975) = 15359.31

Question 14

Joanne invested $15,000 six years ago.Her arithmetic average return on this investment is 8.72 percent,and her geometric average return is 8.50 percent.What is Joanne's portfolio worth today?
A) $23,989
B) $24,472
C) $26,409
D) $26,514
E) $26,766

Accepted Answer

FV = $15,000 × (1 + 0.085)⁶ = $24,472.01

Question 15

Over the past five years,an investment produced annual returns of 16.5,21,-18,4,and 17 percent,respectively.What is the geometric average return?
A) 6.42 percent
B) 7.06 percent
C) 8.00 percent
D) 15.60 percent
E) 16.00 percent

Accepted Answer

Geometric average = [(1 + 0.165)(1 + 0.21)(1 - 0.18)(1 + 0.04)(1 + 0.17)]^{1 / 5} - 1 = 7.06 percent

Question 16

A stock has an average arithmetic return of 10.55 percent and an average geometric return of 10.41 percent based on the annual returns for the last 15 years.What is projected average annual return on this stock for the next 10 years?
A) 10.17 percent
B) 10.21 percent
C) 10.38 percent
D) 10.46 percent
E) 10.79 percent

Accepted Answer

Projected return = {[(10 - 1) / (15 - 1)] × 0.1041} + {[(15 - 10) / (15 - 1)] × 0.1055} = 10.46 percent

Question 17

Eileen just sold a stock and realized a 6.25 percent return for a 7-month holding period.What was her annualized rate of return?
A) 9.98 percent
B) 10.95 percent
C) 12.78 percent
D) 15.29 percent
E) 17.20 percent

Accepted Answer

1 + EAR = (1 + 0.0625)^{12 / 7} - 1 = 10.95 percent

Question 18

Leeanne owns a stock that has an average geometric return of 12.30 percent and an average arithmetic return of 12.55 percent over the past six years.What average annual rate of return should Leeanne expect to earn over the next four years?
A) 12.38 percent
B) 12.40 percent
C) 12.44 percent
D) 12.47 percent
E) 12.51 percent

Accepted Answer

Projected return = {[(4 - 1) / (6 - 1)] × 0.1230} + {[(6 - 4) / (6 - 1)] × 0.1255} = 12.40 percent

Question 19

Tom decides to begin investing some portion of his annual bonus,beginning this year with $6,000.In the first year he earns an 8 percent return and adds $3,000 to his investment.In the second his portfolio loses 4 percent but,sticking to his plan,he adds $1,000 to his portfolio.In this year his portfolio returns 2 percent.What is Tom's dollar-weighted average return on his investments?
A) 0.34 percent
B) 1.20 percent
C) 1.54 percent
D) 2.23 percent
E) 2.58 percent

Accepted Answer

Using the Cash Flow worksheet in a financial calculator, the cash flows to be entered are:
CF0 = -6000
CF1 = -3000
CF2 = -1000
CF3 = ((((6000 × 1.08) + 3000) × 0.96) + 1000) × (1.02) = $10,302.82
Solve for IRR = 1.20 percent

Question 20

Celsius stock had year end prices of $42,$37,$44,and $46 over the past four years,respectively.What is the arithmetic average rate of return?
A) 3.17 percent
B) 3.85 percent
C) 4.28 percent
D) 10.63 percent
E) 11.79 percent

Accepted Answer

Annual returns are: ($37 - $42) / $42 = -0.119048; ($44 - $37) / $37 = 0.189189;
($46 - $44) / $44 = 0.045455
Average = (-0.119048 + 0.189189 + 0.045455) / 3 = 3.85 percent

Quiz 1: A Brief History of Risk and Return

A stock produced annual returns of 8.3,-21,12,42,and 9 percent over the past five years,respectively.What is the geometric average return?

A portfolio had an original value of $7,400 seven years ago.The current value of the portfolio is $11,898.What is the average geometric return on this portfolio?

The geometric return on a stock over the past 10 years was 7.9 percent.The arithmetic return over the same period was 8.8 percent.What is the best estimate of the average return on this stock over the next 5 years?

Downtown Industries common stock had returns of 5.2,10.3,9.3,and 9.5 percent,respectively,over the past four years.What is the standard deviation of these returns?

Blackstone Mines stock returned 10.5,17.2,-9.0,and 14.5 percent over the past four years,respectively.What is the geometric average return?

Jim began his investing program with a $4,000 initial investment.The table below recaps his returns each year as well as the amounts he added to his investment account.What is his dollar-weighted average return?

One year ago,you purchased 300 shares of stock at a cost of $6,000.The stock paid an annual dividend of $1.10 per share.Today,you sold those shares for $22.50 each.What is the capital gains yield on this investment?

The geometric return on an asset over the past 12 years has been 14.50 percent.The arithmetic return over the same period was 14.96 percent.What is the best estimate of the average return on this asset over the next 5 years?

A stock had year end prices of $24,$27,$32,and $26 over the past four years,respectively.What is the geometric average return?

An initial investment of $41,800 fifty years ago is worth $1,533,913 today.What is the geometric average return on this investment?

You invested $5,000 eight years ago.The arithmetic average return on your investment is 10.6 percent and the geometric average return is 10.23 percent.What is the value of your portfolio today?

John began his investing program with a $5,500 initial investment.The table below recaps his returns each year as well as the amounts he added to his investment account.What is his dollar-weighted average return?

Joanne invested $15,000 six years ago.Her arithmetic average return on this investment is 8.72 percent,and her geometric average return is 8.50 percent.What is Joanne's portfolio worth today?

Over the past five years,an investment produced annual returns of 16.5,21,-18,4,and 17 percent,respectively.What is the geometric average return?

A stock has an average arithmetic return of 10.55 percent and an average geometric return of 10.41 percent based on the annual returns for the last 15 years.What is projected average annual return on this stock for the next 10 years?

Eileen just sold a stock and realized a 6.25 percent return for a 7-month holding period.What was her annualized rate of return?

Leeanne owns a stock that has an average geometric return of 12.30 percent and an average arithmetic return of 12.55 percent over the past six years.What average annual rate of return should Leeanne expect to earn over the next four years?

Celsius stock had year end prices of $42,$37,$44,and $46 over the past four years,respectively.What is the arithmetic average rate of return?