Question 1

Last year, you purchased a stock at a price of $53.60 a share. Over the course of the year, you received $1.50 in dividends and inflation averaged 2.9%. Today, you sold your shares for $55.90 a share. What is your approximate real rate of return on this investment?

Accepted Answer

The real rate of return adjusts the nominal return for the effects of inflation. First, calculate the nominal return: $$ \text{Nominal Return} = \frac{\text{Ending Value} + \text{Dividends} - \text{Beginning Value}}{\text{Beginning Value}} $$ $$ \text{Nominal Return} = \frac{55.90 + 1.50 - 53.60}{53.60} = \frac{3.80}{53.60} \approx 0.0709 \text{ or } 7.09\% $$ Then, adjust for inflation using the formula: $$ \text{Real Rate of Return} = \frac{1 + \text{Nominal Rate}}{1 + \text{Inflation Rate}} - 1 $$ $$ \text{Real Rate of Return} = \frac{1 + 0.0709}{1 + 0.029} - 1 \approx \frac{1.0709}{1.029} - 1 \approx 0.0407 \text{ or } 4.07\% $$ Therefore, the approximate real rate of return is 4.2%, rounding to the nearest tenth.

Question 2

Bianco Corporation has experienced returns of -5%, 20%, 10% and -8% returns over the past four years. Given this information, calculate the company's standard deviation.

Accepted Answer

The standard deviation is calculated by first finding the mean (average) return, then finding the squared differences from the mean for each year, averaging those squared differences, and finally taking the square root of that average. For Bianco Corporation, the mean return is (−5% + 20% + 10% − 8%) / 4 = 4.25%. The squared differences from the mean are (−9.25%)^2, (15.75%)^2, (5.75%)^2, and (−12.25%)^2, which average to 172.5625%. The square root of 172.5625% is approximately 13.12%, indicating the standard deviation of the returns.

Question 3

Eight months ago, you purchased 400 shares of Winston, Inc. stock at a price of $54.90 a share. The company pays quarterly dividends of $.50 a share. Today, you sold all of your shares for $49.30 a share. What is your total percentage return on this investment?

Accepted Answer

The answer of Eight months ago, you purchased 400 shares...

Question 4

A stock had returns of 5%, 16%, - 10%, and 18% over the past four years. What is the geometric average return for this time period?

Accepted Answer

The geometric average return is calculated by multiplying the returns (expressed as decimal numbers), taking the nth root (where n is the number of returns), and subtracting 1. Here, it's ((1.05 * 1.16 * 0.90 * 1.18)^(1/4)) - 1 = 0.066 or 6.6%.

Question 5

The common stock of Petersen and White Importers yielded returns of 42%, -5%, -18%, 9%, and 12% over the past 5 years, respectively. The arithmetic average return for this period of time is _____% while the geometric average return is _____%.

Accepted Answer

The arithmetic average return is calculated by summing the annual returns and then dividing by the number of years. (42 - 5 - 18 + 9 + 12) / 5 = 8%. The geometric average return, which accounts for compounding, is found by multiplying the returns (as 1 + return), taking the nth root (where n is the number of returns), and then subtracting 1. This gives a geometric average return of approximately 6.19%.

Question 6

Destiny Corporation has experienced returns of 20%, -10%, 25% and -5% returns over the past four years. Given this information, calculate the company's geometric average returns.

Accepted Answer

The geometric average return is calculated using the formula: [(1 + R1) * (1 + R2) * ... * (1 + Rn)]^(1/n) - 1, where R1, R2, ..., Rn are the returns for each period. For Destiny Corporation, this calculation is: [(1 + 0.20) * (1 - 0.10) * (1 + 0.25) * (1 - 0.05)]^(1/4) - 1 = (1.20 * 0.90 * 1.25 * 0.95)^(1/4) - 1 ≈ 1.0642 - 1 = 0.0642 or 6.42%.

Question 7

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year.

What is the dividend yield for the investment?

Accepted Answer

The dividend yield is calculated as the annual dividend per share divided by the current stock price. In this case, the annual dividend per share is $4, and the current stock price is $47. Therefore, the dividend yield is $4/$47 = 0.085, or 8.5%.

Question 8

What are the geometric and arithmetic average returns for a stock with annual returns of 5%, 10%, -8%, and 16%?

Accepted Answer

The answer of What are the geometric and arithmetic average...

Question 9

The three probability ranges used with a normal distribution are defined as the _____ ranges.

Accepted Answer

The three probability ranges used with a normal distribution are defined as the 68%, 95%, and 99% ranges, corresponding to one, two, and three standard deviations from the mean, respectively.

Question 10

You purchased a bond on January 1, 2002 for $839.67. The bond has a $1,000 face value, an 8% annual coupon, and can be sold for $822.33 on December 31, 2002. What is your percentage return on investment for the year?

Accepted Answer

The total return on investment includes both the interest received and the capital gain or loss. The bond pays an 8% annual coupon on its $1,000 face value, which equals $80 in interest. The capital loss is the difference between the purchase price ($839.67) and the selling price ($822.33), which is -$17.34. The total return is the sum of the interest received and the capital loss, which is $80 - $17.34 = $62.66. The percentage return on investment is calculated as (total return / purchase price) * 100 = ($62.66 / $839.67) * 100 = 7.5%.

Question 11

Today, you sold 100 shares of Natural, Inc. stock. Your total return on these shares is 10.5%. You purchased the shares one year ago at a price of $25.75 a share. You have received a total of $110 in dividends over the course of the year. What is your capital gains yield on this investment?

Accepted Answer

The capital gains yield can be calculated by finding the difference between the selling price and the purchase price, then dividing by the purchase price. The total return is 10.5%, which includes both the capital gains yield and the dividend yield. The dividend yield is calculated as $110 in dividends divided by the initial investment (100 shares * $25.75/share = $2575), which is 4.27%. Therefore, the capital gains yield is the total return (10.5%) minus the dividend yield (4.27%), resulting in a capital gains yield of 6.23%.

Question 12

An investor purchased a stock for $1.61 per share, held it for one year, and sold it for $3.03 a share. The stock did not pay a dividend. Inflation for that year was 3.2% and Treasury bills returned 3.7%. What is the real rate of return on this investment?

Accepted Answer

The answer of An investor purchased a stock for $1.61...

Question 13

What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%?

Accepted Answer

The answer of What are the arithmetic and geometric average...

Question 14

Treadwell Motors stock returned 11%, 14%, 3%, and 9% over the past 4 years, respectively. The arithmetic average return for this period is _____%.

Accepted Answer

The answer of Treadwell Motors stock returned 11%, 14%, 3%,...

Question 15

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year.

What is the total percentage return for the investment?

Accepted Answer

The total return includes both the capital gain and the dividend income. The capital gain is ($47 - $45) * 100 = $200. The dividend income is $4 * 100 = $400. So, the total return is $200 + $400 = $600. The initial investment was $45 * 100 = $4500. Therefore, the total percentage return is ($600 / $4500) * 100 = 13.3%.

Question 16

A stock had returns of 8%, 11%, -2%, 5%, and 13% over the past 5 years, respectively. What is the geometric average rate of return for this time period?

Accepted Answer

The geometric average rate of return is calculated by finding the product of the returns (expressed as a decimal plus one), taking the nth root (where n is the number of returns), and then subtracting one and converting back to a percentage. For these returns, the calculation is as follows: [(1.08) * (1.11) * (0.98) * (1.05) * (1.13)]^(1/5) - 1 = 0.0687 or 6.87%.

Question 17

What percentage of the population is represented within one standard deviation?

Accepted Answer

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

Question 18

Over the 1970-2005 period, the standard deviation of returns for small stocks has averaged ______________ per year.

Accepted Answer

The standard deviation of returns for small stocks over the 1970-2005 period has averaged 22.58% per year, indicating a higher level of volatility compared to other asset classes.

Question 19

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year.

What is the capital gains yield for the investment?

Accepted Answer

The capital gains yield is calculated as the percentage increase in the stock price, which is the difference between the selling price and the purchase price divided by the purchase price. Here, it is (($47 - $45) / $45) * 100 = 4.4%.

Question 20

Over the 1957-2005 period, the standard deviation of returns for Canadian common stocks has averaged _________ per year.

Accepted Answer

The standard deviation of returns for Canadian common stocks over the 1957-2005 period has averaged 16.17% per year. This measure indicates the volatility or risk associated with investing in these stocks during that timeframe.

Quiz 12: Lessons From Capital Market History

Last year, you purchased a stock at a price of $53.60 a share. Over the course of the year, you received $1.50 in dividends and inflation averaged 2.9%. Today, you sold your shares for $55.90 a share. What is your approximate real rate of return on this investment?

Bianco Corporation has experienced returns of -5%, 20%, 10% and -8% returns over the past four years. Given this information, calculate the company's standard deviation.

Eight months ago, you purchased 400 shares of Winston, Inc. stock at a price of $54.90 a share. The company pays quarterly dividends of $.50 a share. Today, you sold all of your shares for $49.30 a share. What is your total percentage return on this investment?

A stock had returns of 5%, 16%, - 10%, and 18% over the past four years. What is the geometric average return for this time period?

The common stock of Petersen and White Importers yielded returns of 42%, -5%, -18%, 9%, and 12% over the past 5 years, respectively. The arithmetic average return for this period of time is _% while the geometric average return is _%.

Destiny Corporation has experienced returns of 20%, -10%, 25% and -5% returns over the past four years. Given this information, calculate the company's geometric average returns.

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year. What is the dividend yield for the investment?

What are the geometric and arithmetic average returns for a stock with annual returns of 5%, 10%, -8%, and 16%?

The three probability ranges used with a normal distribution are defined as the _____ ranges.

You purchased a bond on January 1, 2002 for $839.67. The bond has a $1,000 face value, an 8% annual coupon, and can be sold for $822.33 on December 31, 2002. What is your percentage return on investment for the year?

Today, you sold 100 shares of Natural, Inc. stock. Your total return on these shares is 10.5%. You purchased the shares one year ago at a price of $25.75 a share. You have received a total of $110 in dividends over the course of the year. What is your capital gains yield on this investment?

An investor purchased a stock for $1.61 per share, held it for one year, and sold it for $3.03 a share. The stock did not pay a dividend. Inflation for that year was 3.2% and Treasury bills returned 3.7%. What is the real rate of return on this investment?

What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%?

Treadwell Motors stock returned 11%, 14%, 3%, and 9% over the past 4 years, respectively. The arithmetic average return for this period is _____%.

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year. What is the total percentage return for the investment?

A stock had returns of 8%, 11%, -2%, 5%, and 13% over the past 5 years, respectively. What is the geometric average rate of return for this time period?

What percentage of the population is represented within one standard deviation?

Over the 1970-2005 period, the standard deviation of returns for small stocks has averaged ______________ per year.

You purchase 100 shares of stock at a price of $45 per share. One year later, the shares are selling for $47 per share. In addition, a dividend of $4 per share is paid at the end of each year. What is the capital gains yield for the investment?

Over the 1957-2005 period, the standard deviation of returns for Canadian common stocks has averaged _________ per year.