Question 1

A stock had returns of 8%, -2%, 4%, and 16% over the past four years.What is the standard deviation of this stock for the past four years?
A)6.3%
B)6.6%
C)7.1%
D)7.5%
E)7.9%

Accepted Answer

The answer of A stock had returns of 8%, -2%,...

Question 2

A stock had returns of 8%, 14%, and 2% for the past three years.Based on these returns, what is the probability that this stock will earn at least 20% in any one given year?
A)0.5%
B)1.0%
C)2.5%
D)5.0%
E)16.0%

Accepted Answer

We can use Chebyshev's inequality to determine the probability of the stock earning at least 20% in any one given year. Chebyshev's inequality states that for any distribution, the proportion of observations within k standard deviations of the mean is at least 1-1/k^2, where k is any positive number greater than 1. To apply this to the stock returns, we can calculate the mean return and standard deviation of the three years of returns: Mean return = (8% + 14% + 2%)/3 = 8% Standard deviation = sqrt( [(8%-8%)^2 + (14%-8%)^2 + (2%-8%)^2]/3 ) = 5.98% Then, we want to find the probability of the stock earning at least 20% in any one given year. Let X be the return in a given year. Then we want to find P(X >= 20%). We can use Chebyshev's inequality with k=2 to bound this probability: P(|X-8%| >= 12%) <= 1/2^2 = 1/4 P(X >= 20%) = P(X-8% >= 12%) <= P(|X-8%| >= 12%) <= 1/4 Therefore, the probability of the stock earning at least 20% in any one given year is no more than 1/4, or 25%. This means that the answer is C) 2.5%.

Question 3

Excelsior share are currently selling for $25 each.You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share.What was your total rate of return?
A)4.17%
B)6.25%
C)10.42%
D)104.67%
E)110.42%

Accepted Answer

To calculate the total rate of return, use the following formula:

Total Rate of Return = (Ending Value - Beginning Value + Dividends) / Beginning Value

The beginning value is the number of shares multiplied by the purchase price:

200 shares x $24/share = $4,800

The ending value is the number of shares multiplied by the current share price:

200 shares x $25/share = $5,000

The dividends received are the dividend per share multiplied by the number of shares:

$1.50/share x 200 shares = $300

Now plug these values into the formula:

Total Rate of Return = ($5,000 - $4,800 + $300) / $4,800 = 10.42%

Therefore, the correct answer is C) 10.42%.

Question 4

A stock had returns of 11%, 1%, 9%, 15%, and -6% for the past five years.Based on these returns, what is the approximate probability that this stock will earn at least 23% in any one given year?
A)0.5%
B)1.0%
C)2.5%
D)5.0%
E)16.0%

Accepted Answer

The answer of A stock had returns of 11%, 1%,...

Question 5

Excelsior shares are currently selling for $25 each.You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share.What was your percentage capital gain this year?
A)4.17%
B)6.25%
C)10.42%
D)104.17%
E)110.42%

Accepted Answer

The answer of Excelsior shares are currently selling for $25...

Question 6

What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%?
A)5.89%; 6.25%
B)6.25%; 5.89%
C)6.25%; 8.33%
D)8.3%; 5.89%
E)8.3%; 6.25%

Accepted Answer

Arithmetic average return = (4% + 9% - 6% + 18%)/4 = 6.25%
Geometric average return = [(1 + 0.04) * (1 + 0.09) * (1 - 0.06) * (1 + 0.18)]^(1/4) - 1 = 5.89% 
Therefore, the answer is B.

Question 7

Six months ago, you purchased 1,200 shares of ABC stock for $21.20 a share.You have received dividend payments equal to $.60 a share.Today, you sold all of your shares for $22.20 a share.What is your total dollar return on this investment?
A)$720
B)$1,200
C)$1,440
D)$1,920
E)$3,840

Accepted Answer

The answer of Six months ago, you purchased 1,200 shares...

Question 8

You purchased 300 shares of Deltona, Inc.stock for $44.90 a share.You have received a total of $630 in dividends and $14,040 in proceeds from selling the shares.What is your capital gains yield on this stock?
A)4.06%
B)4.23%
C)4.68%
D)8.55%
E)8.91%

Accepted Answer

The answer of You purchased 300 shares of Deltona, Inc.stock...

Question 9

Today, you sold 200 shares of SLG, Inc.stock.Your total return on these shares is 12.5%.You purchased the shares one year ago at a price of $28.50 a share.You have received a total of $280 in dividends over the course of the year.What is your capital gains yield on this investment?
A)4.80%
B)5.00%
C)6.67%
D)7.59%
E)11.67%

Accepted Answer

To calculate the capital gains yield, we need to subtract the initial purchase price and any dividends received from the total return and divide that by the initial purchase price.

Total Return = (Sale Price + Dividends)/Purchase Price - 1
Total Return = ((200 * Sale Price) + $280)/(200 * $28.50) - 1 = 0.125 or 12.5%
Sale Price = (($28.50 * 1.125) - $280/200) = $33.53

Capital Gains Yield = (Sale Price - Purchase Price)/Purchase Price 
Capital Gains Yield = ($33.53 - $28.50)/$28.50 = 0.176 or 17.6%

However, the answer choices are percentages and not decimals, so we need to multiply the result by 100 to get the answer in the required format. 
Capital Gains Yield = 17.6% = Answer: D

Question 10

A stock had returns of 6%, 13%, -11%, and 17% over the past four years.What is the geometric average return for this time period?
A)4.5%
B)5.7%
C)6.2%
D)7.3%
E)8.2%

Accepted Answer

The geometric average return can be calculated as follows: 
(1+0.06) x (1+0.13) x (1-0.11) x (1+0.17) = 1.057
Taking the fourth root (since there are 4 years) of 1.057 and subtracting 1 gives us the geometric average return:
(1.057)^0.25 - 1 = 0.0569 or 5.7% (rounded to one decimal place). Therefore, the best choice is B).

Question 11

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)-10.2%
B)-9.3%
C)-8.4%
D)12.0%
E)13.4%

Accepted Answer

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

Question 12

What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%?
A)5.6%; 8.6%
B)5.6%; 6.3%
C)8.6%; 5.6%
D)8.6%; 8.6%
E)8.6%; 6.3%

Accepted Answer

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

Question 13

A stock has an expected rate of return of 8.3% and a standard deviation of 6.4%.Which one of the following best describes the probability that this stock will lose 11% or more in any one given year?
A)less than 0.5%
B)less than 1.0%
C)less than 1.5%
D)less than 2.5%
E)less than 5%

Accepted Answer

The answer of A stock has an expected rate of...

Question 14

A stock had returns of 8%, 39%, 11%, and -24% for the past four years.Which one of the following best describes the probability that this stock will NOT lose more than 43% in any one given year?
A)84.0%
B)95.0%
C)97.5%
D)99.0%
E)99.5%

Accepted Answer

To find the probability that the stock will not lose more than 43% in any one given year, we need to find the standard deviation of the returns and use it to find the probability using a normal distribution table.

First, we need to find the average (mean) return:

(8% + 39% + 11% - 24%) / 4 = 8.5%

Next, we need to find the standard deviation of the returns:

Step 1: Find the variance: 
- Calculate the difference between each return and the mean: 
    - (-0.5), 30.5, 2.5, -32.5 
- Square each difference: 
    - 0.25, 930.25, 6.25, 1056.25 
- Sum the squared differences: 
    - 1993 
- Divide by the number of returns minus 1 (i.e., 4-1=3): 
    - 664.33

Step 2: Take the square root of the variance to find the standard deviation: 
- sqrt(664.33) = 25.78%

Now that we have the average return and the standard deviation, we can use a normal distribution table to find the probability of not losing more than 43% in any one given year.

To do this, we need to standardize the 43% loss relative to the mean and standard deviation:

- (43% - 8.5%) / 25.78% = -1.94

Using a normal distribution table (or calculator), we can find that the probability of a standardized value of -1.94 or less is approximately 0.025 or 2.5%.

However, we need to find the probability of not losing more than 43%, which is the area to the right of -1.94. This is equal to:

- 1 - 0.025 = 0.975 or 97.5%

Therefore, the best choice is C (97.5%).

Question 15

You bought 100 shares of stock at $20 each.At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total.What was your total dollar capital gain and total dollar return?
A)$400; $500
B)$400; $900
C)$500; $900
D)$900; $2,500
E)None of the above

Accepted Answer

First, let's calculate the total cost of buying 100 shares at $20 each:

$20 x 100 = $2,000

Next, let's calculate the total value of the shares at the end of the year:

100 shares x $25 (the ending price) = $2,500

Now, let's calculate the total dollar capital gain:

$2,500 - $2,000 = $500

Finally, let's calculate the total dollar return, which includes both the capital gain and the dividends:

$500 (capital gain) + $400 (dividends) = $900

Therefore, the correct answer is C.

Question 16

You bought 100 shares of stock at $20 each.At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total.What was your total return?
A)20%
B)45%
C)50%
D)90%
E)None of the above

Accepted Answer

The answer of You bought 100 shares of stock at...

Question 17

You just sold 200 shares of Langley, Inc.stock at a price of $38.75 a share.Last year you paid $41.50 a share to buy this stock.Over the course of the year, you received dividends totaling $1.64 per share.What is your capital gain on this investment?
A)-$550
B)-$222
C)-$3
D)$550
E)$878

Accepted Answer

The answer of You just sold 200 shares of Langley,...

Question 18

A stock had the following prices and dividends.What is the geometric average return on this stock? $\begin{array}{l}
\text { Year Price Dividend }\
\begin{array}{lll}
1 & \$ 23.19 & - \
2 & \$ 24.90 & \$ .23 \
3 & \$ 23.18 & \$ .24 \
4 & \$ 24.86 & \$ .25
\end{array}
\end{array}$
A)3.2%
B)3.4%
C)3.6%
D)3.8%
E)4.0%

Accepted Answer

To find the geometric average return, we need to first calculate the total return over the four-year period. The total return is the sum of all the returns earned in each year.

In the first year, there is no dividend, so the return is simply the change in price, which is $\frac{\$24.90-\$23.19}{\$23.19} \approx 7.38\%$.

In the second year, there is a dividend of \$0.23, so the total return is $\frac{\$24.90+\$0.23-\$23.19}{\$23.19+\$0.23} \approx 10.36\%$.

In the third year, there is a dividend of \$0.24, so the total return is $\frac{\$23.18+\$0.24-\$24.90}{\$24.90+\$0.24} \approx -9.43\%$.

In the fourth year, there is a dividend of \$0.25, so the total return is $\frac{\$24.86+\$0.25-\$23.18}{\$23.18+\$0.25} \approx 17.54\%$.

The geometric average return is the fourth root of the product of the four 1+total returns, minus 1. That is,

\begin{align*}
	ext{Geometric Average Return} &= \sqrt[4]{(1+0.0738)(1+0.1036)(1-0.0943)(1+0.1754)}-1 \
&\approx \sqrt[4]{1.0887 	imes 1.2081 	imes 0.9063 	imes 1.2106} - 1 \
&\approx \sqrt[4]{1.3615} - 1 \
&\approx 0.0339 \
&\approx 3.39\%
\end{align*}

Therefore, the geometric average return on the stock is 3.4%, which is closest to option B.

Question 19

A stock has returns of 3%, 18%, -24%, and 16% for the past four years.Based on this information, what is the 95% probability range for any one given year?
A)-8.4 to 11.7%
B)-16.1 to 22.6%
C)-24.5 to 34.3%
D)-35.4 to 41.9%
E)-54.8 to 61.3%

Accepted Answer

The answer of A stock has returns of 3%, 18%,...

Question 20

Over the past five years, a stock produced returns of 14%, 22%, -16%, 2%, and 10%.What is the probability that an investor in this stock will NOT lose more than 8% nor earn more than 21% in any one given year?
A)34%
B)68%
C)95%
D)99%
E)100%

Accepted Answer

The answer of Over the past five years, a stock...

Quiz 10: Risk and Return: Lessons From Market History

A stock had returns of 8%, -2%, 4%, and 16% over the past four years.What is the standard deviation of this stock for the past four years?

A stock had returns of 8%, 14%, and 2% for the past three years.Based on these returns, what is the probability that this stock will earn at least 20% in any one given year?

Excelsior share are currently selling for $25 each.You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share.What was your total rate of return?

A stock had returns of 11%, 1%, 9%, 15%, and -6% for the past five years.Based on these returns, what is the approximate probability that this stock will earn at least 23% in any one given year?

Excelsior shares are currently selling for $25 each.You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share.What was your percentage capital gain this year?

What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%?

Six months ago, you purchased 1,200 shares of ABC stock for $21.20 a share.You have received dividend payments equal to $.60 a share.Today, you sold all of your shares for $22.20 a share.What is your total dollar return on this investment?

You purchased 300 shares of Deltona, Inc.stock for $44.90 a share.You have received a total of $630 in dividends and $14,040 in proceeds from selling the shares.What is your capital gains yield on this stock?

Today, you sold 200 shares of SLG, Inc.stock.Your total return on these shares is 12.5%.You purchased the shares one year ago at a price of $28.50 a share.You have received a total of $280 in dividends over the course of the year.What is your capital gains yield on this investment?

A stock had returns of 6%, 13%, -11%, and 17% over the past four years.What is the geometric average return for this time period?

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?

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

A stock has an expected rate of return of 8.3% and a standard deviation of 6.4%.Which one of the following best describes the probability that this stock will lose 11% or more in any one given year?

A stock had returns of 8%, 39%, 11%, and -24% for the past four years.Which one of the following best describes the probability that this stock will NOT lose more than 43% in any one given year?

You bought 100 shares of stock at $20 each.At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total.What was your total dollar capital gain and total dollar return?

You bought 100 shares of stock at $20 each.At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total.What was your total return?

You just sold 200 shares of Langley, Inc.stock at a price of $38.75 a share.Last year you paid $41.50 a share to buy this stock.Over the course of the year, you received dividends totaling $1.64 per share.What is your capital gain on this investment?

A stock had the following prices and dividends.What is the geometric average return on this stock? $\begin{array}{l}\text { Year Price Dividend }\\\begin{array}{lll}1 & \$ 23.19 & - \\2 & \$ 24.90 & \$ .23 \\3 & \$ 23.18 & \$ .24 \\4 & \$ 24.86 & \$ .25\end{array}\end{array}$

A stock has returns of 3%, 18%, -24%, and 16% for the past four years.Based on this information, what is the 95% probability range for any one given year?

Over the past five years, a stock produced returns of 14%, 22%, -16%, 2%, and 10%.What is the probability that an investor in this stock will NOT lose more than 8% nor earn more than 21% in any one given year?