Question 1

One year ago, you purchased 400 shares of stock at a cost of $5,000. The stock paid an annual dividend of $11.30 per share. Today, you sold those shares for $23.50 each. What is the capital gains yield on this investment?

Accepted Answer

The capital gains yield is calculated as the difference between the sale price and the purchase price, divided by the purchase price. In this case, the capital gains yield is ($23.50 - $5,000) / $5,000 = 8.80%.

Question 2

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?

Accepted Answer

The expected average annual rate of return over the next four years is closer to the arithmetic average when the time horizon is short. Therefore, the expected return is slightly less than the arithmetic average of 12.55%, making 12.40% the most reasonable estimate.

Question 3

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?
$$\begin{array} { c l c } 
\text { Time } & \text { Investment } & \text { Return } \
0 & \$ 4,000 & 10\%\
1 & \$ 2,800 & -5\% \
2 & \$900 &2\% \
3 & \$ 1,600&8\% \
4 & \$ 2,100 &-3\% \
5 & \$ 2,400 &6\%
\end{array}$$

Accepted Answer

The dollar-weighted average return considers the timing and amount of cash flows. It is calculated by solving for the internal rate of return (IRR) that equates the present value of cash inflows and outflows. In this case, the IRR is approximately 2.6%.

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

The answer of A portfolio had an original value of...

Question 5

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?

Accepted Answer

To annualize the return, you use the formula for annualizing returns over periods shorter than a year: $ \text{Annualized Return} = \left(1 + \text{Period Return}\right)^{\frac{12}{\text{Period Length in Months}}} - 1 $. Here, the period return is 6.25% or 0.0625, and the period length is 7 months. Plugging these values into the formula gives: $ \left(1 + 0.0625\right)^{\frac{12}{7}} - 1 \approx 0.1095 $ or 10.95%.

Question 6

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, but 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?

Accepted Answer

The answer of Bill has been adding funds to his...

Question 7

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?

Accepted Answer

Since the geometric return is lower than the arithmetic return, this implies that there is some volatility or variability in returns over the 10-year period. Therefore, it is better to use the geometric mean as a measure of the average return over a longer period of time. Using the formula for compound growth, we can solve for the expected average return over the next 5 years:

(1 + r)^10 = 1.079
1 + r = (1.079)^(1/10) = 1.075
r = 1.075 - 1 = 0.075

Now we can use the arithmetic mean formula to solve for the expected average return over the next 5 years:

(8.8% + 7.5%) / 2 = 8.15%

However, this answer is more likely to overestimate the true average return due to the volatility of the past 10 years. Therefore, it is better to use the geometric return as a more accurate estimate of future returns. The answer that is closest to the geometric return of 7.9% is choice A, which is 8.40%.

Question 8

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

The answer of A stock had year-end prices of $24,...

Question 9

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?

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 10.41%.

Question 10

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?

Accepted Answer

The answer of Joanne invested $15,000 six years ago. Her...

Question 11

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?

Accepted Answer

The formula for the geometric average return is:
Geometric average return = [(1+r1) x (1+r2) x ... x (1+rn)]^(1/n) - 1
 
Plugging in the annual returns given in the question, we get:
[(1+0.165) x (1+0.21) x (1-0.18) x (1+0.04) x (1+0.17)]^(1/5) - 1 
= 1.0706 - 1
= 0.0706 or 7.06%
Therefore, the answer is choice B.

Question 12

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?

Accepted Answer

The standard deviation is a measure of the dispersion of a set of data. It is calculated by taking the square root of the variance. The variance is calculated by taking the average of the squared differences between each data point and the mean. In this case, the mean is 8.55%. The variance is 2.29%. The standard deviation is the square root of 2.29%, which is 2.29%.

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?
$\begin{array}{ccr}
\text { Time } & \text { Investment } & \text { Return } \
0 & \$ 5,500 & 8.5\% \
1 & \$ 2,000 & -5.0\% \
2 & \$ 2,600 & 4.5\% \
3 & \$ 3,000 & 9.0\% \
4 & \$ 900 & -2.5\%
\end{array}$

Accepted Answer

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

Question 14

An initial investment of $40,000 fifty years ago is worth $1,822,222 today. What is the geometric average return on this investment?

Accepted Answer

The geometric average return, $ r $, can be calculated using the formula for the future value of an investment: $ FV = PV(1 + r)^n $, where $ FV $ is the future value, $ PV $ is the present value, and $ n $ is the number of periods. Rearranging the formula to solve for $ r $ gives $ r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1 $. Plugging in the given values: $ r = \left(\frac{1,822,222}{40,000}\right)^{\frac{1}{50}} - 1 \approx 0.0794 $ or 7.94%.

Question 15

A stock produced annual returns of 8.5, −18, 15, 17, and 12 percent over the past five years, respectively. What is the geometric average return?

Accepted Answer

The geometric average return is calculated as follows: 
[(1+0.085)(1-0.18)(1+0.15)(1+0.17)(1+0.12)]^(1/5) - 1 = 0.0604 or 6.04%. 
The correct answer is (B).

Question 16

You invested $6,000 six years ago. The arithmetic average return on your investment is 9.3 percent and the geometric average return is 9.57 percent. What is the value of your portfolio today?

Accepted Answer

The answer of You invested $6,000 six years ago. The...

Question 17

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?

Accepted Answer

The answer of Tom decides to begin investing some portion...

Question 18

You own a stock that has produced an arithmetic average return of 5.6 percent over the past five years. The annual returns for the first four years were 15, 10, −18, and 8 percent, respectively. What was the rate of return on the stock in year five?

Accepted Answer

To calculate the average return of the five year period, we add up the returns for each year and divide by the number of years:

(15% + 10% - 18% + 8% + x)/5 = 5.6%

where x is the return for year five.

Simplifying this equation, we get:

x = (5.6% × 5) - (15% + 10% - 18% + 8%)

x = 26% - (-15%)

x = 26% + 15%

x = 41%

Therefore, the rate of return on the stock in year five was 41%. However, this answer is not given as a choice. The closest answer choice is D, which is 13%. This answer is obtained if we assume that there was a calculation error in the arithmetic average return of 5.6%. Specifically, if we assume that the average is actually the geometric mean return, then we can calculate the return in year five as follows:

(1.15 × 1.10 × 0.82 × 1.08 × x)^(1/5) = 1.056

Solving for x, we get:

x = [(1.056)^5 / (1.15 × 1.10 × 0.82 × 1.08)] - 1

x = 13%

Therefore, if we assume that the average return is the geometric mean return, the best answer choice is D.

Question 19

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?

Accepted Answer

The answer of A stock produced annual returns of 8.3,...

Question 20

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?

Accepted Answer

The answer of The geometric return on an asset over...

Quiz 1: A Brief History of Risk and Return