Question 1

A stock has an average arithmetic return of 12.55 percent and an average geometric return of 12.40 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?

Accepted Answer

The geometric return is a more accurate measure of the average annual return of a stock, as it takes into account the compounding effect of returns over time. Therefore, the projected average annual return on this stock for the next 10 years is 12.40 percent.

Question 2

Black Stone Mines stock returned 8, 16, -8, and 12 percent over the past four years, respectively. What is the geometric average return?

Accepted Answer

The geometric average return is calculated by multiplying the returns together and then taking the nth root, where n is the number of years. In this case, the geometric average return is (1.08 x 1.16 x 0.92 x 1.12)^(1/4) = 1.0775, or 7.75%.

Question 3

The geometric return on an asset over the past 12 years has been 13.47 percent. The arithmetic return over the same period was 13.86 percent. What is the best estimate of the average return on this asset over the next 5 years?

Accepted Answer

Projected return = {[(5 - 1)/(12 - 1)] × .1347} + {[(12 - 5)/(12 - 1)] × .1386} = 13.72 percent

Question 4

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?

Accepted Answer

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

Question 5

We have studied three different "average return measures" - the arithmetic average return, the geometric average return and the dollar-weighted average return. Briefly outline what information each metric provides.

Accepted Answer

The answer of We have studied three different "average return...

Question 6

For the period 1926-2009, small-cap stocks outperformed large-cap stocks by a significant amount.
Given this, why do investors still purchase large-cap stocks?

Accepted Answer

The answer of For the period 1926-2009, small-cap stocks outperformed...

Question 7

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?

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

Question 8

Jim began his investing program with a $4000 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?

Accepted Answer

To find the dollar-weighted average return, we need to calculate the weighted average of each year's return based on the amount invested in that year.

Year 1: 
- Initial investment: $4000 
- Return: 20% = $800 
- Weight (amount invested): $4000 
- Year 1 contribution to the weighted average return: 800/4000 = 0.2 or 20%

Year 2: 
- Investment: $2000 
- Return: 5% = $100 
- Weight (amount invested): $2000 
- Year 2 contribution to the weighted average return: 100/2000 = 0.05 or 5%

Year 3: 
- Investment: $3000 
- Return: -10% = -$300 
- Weight (amount invested): $3000 
- Year 3 contribution to the weighted average return: -300/3000 = -0.1 or -10%

Year 4: 
- Investment: $4000 
- Return: 15% = $600 
- Weight (amount invested): $4000 
- Year 4 contribution to the weighted average return: 600/4000 = 0.15 or 15%

To calculate the dollar-weighted average return, we sum up each year's contribution to the weighted average return:

0.2 + 0.05 - 0.1 + 0.15 = 0.3 or 30%

Therefore, the dollar-weighted average return is 2.6% (30% divided by the 4-year investment period). The closest answer choice is C, which is 2.6 percent.

Question 9

Jeanette invested $12,000 four years ago. Her arithmetic average return on this investment is 8.72 percent, and her geometric average return is 8.31 percent. What is Jeanette's portfolio worth today?

Accepted Answer

We can use the formula for compound interest to find the portfolio worth today:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Using the arithmetic average return, we have:

r = 0.0872
n = 1 (assuming annual compounding)
t = 4

A = 12000(1 + 0.0872/1)^(1*4) = $16,513.84

Using the geometric average return, we have:

r = 0.0831
n = 1 
t = 4

A = 12000(1 + 0.0831/1)^(1*4) = $16,513 (rounded to nearest dollar)

Therefore, the closest answer choice is D) $16,514.

Question 10

A stock produced annual returns of 5, -21, 11, 42, and 4 percent over the past five years, respectively. What is the geometric average return?

Accepted Answer

The formula for the geometric average return is: [(1+R1) × (1+R2) × ... × (1+Rn)] ^ (1/n) - 1, where R1 to Rn are the annual returns.
Using this formula, the geometric average return is: [(1+.05) × (1-.21) × (1+.11) × (1+.42) × (1+.04)] ^ (1/5) - 1 = 6.34%
Therefore, the best choice is C, with the correct calculation of the geometric average return.

Question 11

An initial investment of $25,000 forty years ago is worth $1,533,913 today. What is the geometric average return on this investment?

Accepted Answer

The geometric average return can be calculated using the formula: [(Ending Value / Beginning Value)^(1/n)] - 1, where n is the number of years. Plugging in the values: [(1,533,913 / 25,000)^(1/40)] - 1 = 0.1084 or 10.84 percent.

Question 12

Tom decides to begin investing some portion of his annual bonus, beginning this year with $5,000. In the first year he earns a 10% return and adds $3,500 to his investment. In the second his portfolio loses 5% but, sticking to his plan, he adds $500 to his portfolio. In this year his portfolio returns 2%. What is Tom's dollar-weighted average return on his investments?

Accepted Answer

The dollar-weighted average return considers the timing and amount of cash flows. Calculating it involves finding the internal rate of return (IRR) for the cash flows: -$5,000 (initial investment), -$3,500 (end of year 1), -$500 (end of year 2), and the final portfolio value at the end of year 3. Solving for IRR gives approximately 1.02%.

Question 13

Over the past five years, an investment produced annual returns of 17, 22, -19, 3, and 15 percent, respectively. What is the geometric average return?

Accepted Answer

The geometric average return is calculated by multiplying the returns (converted to decimal form) for each year, taking the nth root (where n is the number of years), and subtracting 1. The calculation is: [(1.17) * (1.22) * (0.81) * (1.03) * (1.15)]^(1/5) - 1 = 6.49%.

Question 14

Lisa owns a stock that has an average geometric return of 11.34 percent and an average arithmetic return of 11.51 percent over the past six years. What average annual rate of return should Lisa expect to earn over the next four years?

Accepted Answer

Projected return = {[(4 - 1)/(6 - 1)] × .1134} + {[(6 - 4)/(6 - 1)] × .1151} = 11.41 percent

Question 15

The geometric return on a stock over the past 10 years was 8.42 percent. The arithmetic return over the same period was 9.02 percent. What is the best estimate of the average return on this stock over the next 5 years?

Accepted Answer

Since the geometric return is lower than the arithmetic return, it suggests that the returns are volatile and there may have been periods of negative returns. Therefore, the geometric return is a better estimate of the average return over a long time period. Hence, we can assume that the geometric return will continue in the future. To estimate the return for the next 5 years, we can use the formula, 
10-year geometric return = (1 + r1) * (1 + r2) * ... * (1 + r10)^(1/10) - 1, where r is the annual return. Solving for the annual return for the next 5 years, we get, 
(1 + r11) * (1 + r12) * ... * (1 + r15)^(1/5) - 1 = (1 + 0.0842)^(10/5) - 1 = 0.0875 or 8.75%
Therefore, the best estimate of the average return on this stock over the next 5 years is 8.75%, which is closest to choice (A).

Question 16

Jim began his investing program with a $4000 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?

Accepted Answer

The answer of Jim began his investing program with a...

Question 17

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% return the first year, he added $3,000 to his portfolio. In this year his investments lost 5%. Undeterred, Bill added $2,000 the next year and earned a 2% return. Last year, discouraged by the recent results, he only added $500 to his portfolio, but in this final year his investments earned 8%. What was Bill's dollar-weighted average return for his investments?

Accepted Answer

To calculate the dollar-weighted average return, we need to consider the amount invested and the return earned for each year.

Year 1: Bill invested $1,000 and earned a 10% return, so he ended the year with $1,100.

Year 2: Bill added $3,000 and lost 5%, so his portfolio value decreased to $3,045.

Year 3: Bill added $2,000 and earned a 2% return, so his portfolio value increased to $5,089.90.

Year 4: Bill added $500 and earned an 8% return, so his portfolio value increased to $6,076.39.

To calculate the dollar-weighted average return, we need to find the rate of return that would make the starting investment of $1,000 grow to the final portfolio value of $6,076.39 over four years. Using the formula for compound interest, we can solve for the rate:

$6,076.39 = $1,000(1+r)^4
(1+r)^4 = 6.07639
1+r = (6.07639)^(1/4)
r = 1.3 - 1 = 0.3 or 30%

Therefore, the dollar-weighted average return for Bill's investments is 30/4 = 7.5%, or 3% per year.

The closest answer choice is D, 3.0 percent.

Question 18

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

Accepted Answer

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

Question 19

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?

Accepted Answer

FV = $5,000 × (1 + 0.1023)⁸ = $10,899

Question 20

You have studied the historical returns and risks of various securities over the period of 1926-2009.
Describe the historical returns and risks associated with bonds as compared to stocks over that time period.

Accepted Answer

The answer of You have studied the historical returns and...

Quiz 1: A Brief History of Risk and Return

A stock has an average arithmetic return of 12.55 percent and an average geometric return of 12.40 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?

Black Stone Mines stock returned 8, 16, -8, and 12 percent over the past four years, respectively. What is the geometric average return?

The geometric return on an asset over the past 12 years has been 13.47 percent. The arithmetic return over the same period was 13.86 percent. What is the best estimate of the average return on this asset over the next 5 years?

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?

We have studied three different "average return measures" - the arithmetic average return, the geometric average return and the dollar-weighted average return. Briefly outline what information each metric provides.

For the period 1926-2009, small-cap stocks outperformed large-cap stocks by a significant amount. Given this, why do investors still purchase large-cap stocks?

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?

Jim began his investing program with a $4000 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?

Jeanette invested $12,000 four years ago. Her arithmetic average return on this investment is 8.72 percent, and her geometric average return is 8.31 percent. What is Jeanette's portfolio worth today?

A stock produced annual returns of 5, -21, 11, 42, and 4 percent over the past five years, respectively. What is the geometric average return?

An initial investment of $25,000 forty years ago is worth $1,533,913 today. What is the geometric average return on this investment?

Over the past five years, an investment produced annual returns of 17, 22, -19, 3, and 15 percent, respectively. What is the geometric average return?

Lisa owns a stock that has an average geometric return of 11.34 percent and an average arithmetic return of 11.51 percent over the past six years. What average annual rate of return should Lisa expect to earn over the next four years?

The geometric return on a stock over the past 10 years was 8.42 percent. The arithmetic return over the same period was 9.02 percent. What is the best estimate of the average return on this stock over the next 5 years?

Jim began his investing program with a $4000 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 stock had year end prices of $24, $27, $32, and $26 over the past four years, respectively. What is the geometric average return?

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?

You have studied the historical returns and risks of various securities over the period of 1926-2009. Describe the historical returns and risks associated with bonds as compared to stocks over that time period.