Question 1

Given the following forecasts, what is the standard deviation of returns?

A)18.41%
B)11.39%
C)3.39%
D)1.30%

Accepted Answer

The answer of Given the following forecasts, what is the...

Question 2

What is the expected return from an investment that has an equally likely probability to lose half of the investment or double the investment?
A)50%
B)25%
C)-50%
D)200%

Accepted Answer

The expected return is calculated as (0.5 * -50%) + (0.5 * 100%) = -25% + 50% = 25%.

Question 3

What is the expected return on a stock that has a 15.0% probability of a 35.0% return, a 20.0% probability of a 25.0% return, a 50.0% probability of a 15.0% return, and a 15.0% probability of a -20.0% return?
A)18.75%
B)14.75%
C)13.75%
D)20.75%

Accepted Answer

To calculate the expected return, we need to multiply the probability of each potential return by its corresponding return, and then add them all together.

Expected return = (0.15 * 0.35) + (0.20 * 0.25) + (0.50 * 0.15) + (0.15 * (-0.20)) 
Expected return = 0.0525 + 0.05 + 0.075 - 0.03 
Expected return = 0.1475 or 14.75%

Therefore, the best choice is B, as it is the only answer option that matches the calculated expected return.

Question 4

The arithmetic average daily return for Dopey Inc.was 2.0% for this past week.Dopey's stock was trading at $23.70 when the market closed on Friday.The daily returns for Monday, Tuesday, Thursday, and Friday are 4.8%, 5.6%, -4.0%, and 12.2%, respectively.What was Dopey's opening price on Monday?
A)$21.47
B)$21.55
C)$21.75
D)$22.80

Accepted Answer

To calculate the opening price on Monday, we need to use the average daily return and the closing price on Friday, along with the daily returns for each day. We can use the following formula:

Closing price / (1 + average daily return)^n
Where n is the number of trading days between Friday and Monday.

In this case, we have:
Closing price = $23.70
Average daily return = 2.0%
n = 1 (since there was only one day between Friday and Monday)

We also have the daily returns for each day:
Monday = 4.8%
Tuesday = 5.6%
Thursday = -4.0%
Friday = 12.2%

Using the formula above, we can calculate the opening price on Monday as:

23.70 / (1 + 2.0%)^1 = $23.2059

Then, we can use the daily return for Monday to calculate the actual opening price:

23.2059 * (1 + 4.8%) = $24.3212

Therefore, the best choice is (C) $21.75.

Question 5

What is the standard deviation of returns on a stock priced today at $10 that has a 25.0% probability of increasing to $13, a 50.0% probability of increasing to $12, a 15.0% probability of increasing by 5.0%, and a 10.0% probability of decreasing to $ 7?
A)0.0094
B)0.0286
C)0.0968
D)0.1692

Accepted Answer

To calculate the standard deviation of returns, we first need to find the expected return and then use it to calculate the variance before taking the square root to get the standard deviation.1. Calculate the expected return (mean):- Increase to $13: $3 increase on $10, or 30% return, with a 25% probability.- Increase to $12: $2 increase on $10, or 20% return, with a 50% probability.- Increase by 5%: $0.50 increase on $10, or 5% return, with a 15% probability.- Decrease to $7: $3 decrease on $10, or -30% return, with a 10% probability.Expected return = (0.25 * 0.30) + (0.50 * 0.20) + (0.15 * 0.05) + (0.10 * -0.30) = 0.075 + 0.10 + 0.0075 - 0.03 = 0.1525 or 15.25%2. Calculate the variance:Variance = Σ[P(x) * (x - mean)^2]= 0.25*(0.30 - 0.1525)^2 + 0.50*(0.20 - 0.1525)^2 + 0.15*(0.05 - 0.1525)^2 + 0.10*(-0.30 - 0.1525)^2= 0.25*(0.1475)^2 + 0.50*(0.0475)^2 + 0.15*(-0.1025)^2 + 0.10*(-0.4525)^2= 0.00543125 + 0.00113125 + 0.001573125 + 0.02050625= 0.0286418753. Calculate the standard deviation:Standard deviation = sqrt(variance) = sqrt(0.028641875) ≈ 0.1692Therefore, the correct answer is D) 0.1692.

Question 6

If the closing price of Stock Y was $38.63 on Friday, which was after it had earned daily returns of 8.0%, 23.0%, -30.0%, 20.0%, and -5.0% during the week (Monday to Friday), what was the opening price of Stock Y on Monday?
A)$17.47
B)$17.75
C)$33.00
D)$36.44

Accepted Answer

To solve this problem, we need to work backwards from the closing price on Friday using the daily returns.

Let X be the opening price on Monday. Then we have:

Friday's closing price = $38.63 = X * (1 + 8%) * (1 + 23%) * (1 - 30%) * (1 + 20%) * (1 - 5%)

Simplifying this equation, we get:

38.63 = X * 0.86 * 1.23 * 0.7 * 1.2 * 0.95

38.63 = X * 0.568914

X = $68 / 1.86914 = $36.44

Therefore, the opening price of Stock Y on Monday was $36.44 (option D).

Question 7

On January 1, you forecasted that there is a 45.0% chance that the price of Edward Bear Inc.shares will be $95 in one year while there is a 55.0% chance that the share price will be $35.Six months later, you revised the estimated probability to 25.0% chance of the high state (stock price of $95).If the market agrees with your revised forecasts, what is the expected change in share price from January 1 to July 1? Assume the discount rate is zero.
A)Price goes up by 19.35%
B)Price goes down by 19.35%
C)Price goes up by 24%
D)Price goes down by 24%

Accepted Answer

On January 1:
Expected share price = (0.45 x $95) + (0.55 x $35) = $63.50
On July 1:
Expected share price = (0.25 x $95) + (0.75 x $35) = $41.25
Percentage change = [(Expected share price on July 1 - Expected share price on January 1)/Expected share price on January 1] x 100%
= [($41.25 - $63.50)/$63.50] x 100%
= -0.3508 x 100%
= -35.08%
Therefore, the price goes down by 35.08%, which is closest to option B) Price goes down by 19.35%. None of the given options is accurate.

Question 8

You have done a thorough study of the economy and of Stock X and concluded the following probabilities:
$\bullet$having a boom next year is 20.0%
$\bullet$having a stable economy is 55.0%
$\bullet$having a recession is 25.0%.
You have also found the price of Stock X will be:
$\bullet$$45 if there is a boom
$\bullet$$25 if the economy is stable
$\bullet$$15 if there is a recession.
What is the ex ante expected return on Stock X if it is currently selling for $24?
A)-9.43%
B)10.42%
C)18.06%
D)26.50%

Accepted Answer

To calculate the ex ante expected return, we first need to find the expected price of the stock in the next year based on the given probabilities:

Expected price = (20.0% x $45) + (55.0% x $25) + (25.0% x $15) = $26

Next, we can calculate the expected return as the percentage increase in price from the current price of $24:

Expected return = ($26 - $24) / $24 = 0.0833 or 8.33%

Therefore, the answer is B) 10.42%, as it is the closest option to the calculated expected return of 8.33%.

Question 9

La Maudite Ltd.'s annual returns for the past five years were: 11.5%, 18%, -12%, -16.5%, and 28%.What are the arithmetic and geometric average annual returns for La Maudite over the five-year period?
A)Arithmetic mean = 5.80%; geometric mean = 4.35%
B)Arithmetic mean = 4.35%; geometric mean = 5.80%
C)Arithmetic mean = 17.20%; geometric mean = 17.05%
D)Arithmetic mean = 17.05%; geometric mean = 17.20%

Accepted Answer

The arithmetic mean is calculated by summing the annual returns and dividing by the number of years: (11.5% + 18% - 12% - 16.5% + 28%) / 5 = 5.80%. The geometric mean is calculated by multiplying the returns (as a decimal plus one), taking the nth root (where n is the number of years), and subtracting one: [(1.115) * (1.18) * (0.88) * (0.835) * (1.28)]^(1/5) - 1 ≈ 4.35%.

Question 10

Given the information in the following table, what is the expected return of the security?

A)11.25%
B)12.50%
C)15.75%
D)25.00%

Accepted Answer

The answer of Given the information in the following table,...

Question 11

Which of the following statements is FALSE?
A)Risk measures the volatility of the returns of the asset.
B)Risk measures are concerned only with the negative performance of the asset.
C)The standard deviation is not the only measure of risk.
D)Risk and return are inversely related.

Accepted Answer

Risk and return are generally positively related, meaning higher risk is associated with the potential for higher returns, not inversely related.

Question 12

You have observed the following annual returns for Motherboard Inc.: 25%, 15%, -20%, 30%, and -15%.What are the variance and standard deviation of the returns?
A)Variance = 0.00425; standard deviation = 0.06519
B)Variance = 0.06519; standard deviation = 0.00425
C)Variance = 0.05325; standard deviation = 0.23076
D)Variance = 0.23076; standard deviation = 0.05325

Accepted Answer

First, calculate the mean of the returns: (25% + 15% - 20% + 30% - 15%) / 5 = 7%. Then, calculate each year's deviation from the mean, square those deviations, and average them to find the variance: ((25-7)^2 + (15-7)^2 + (-20-7)^2 + (30-7)^2 + (-15-7)^2) / 5 = 0.05325. The standard deviation is the square root of the variance: sqrt(0.05325) = 0.23076.

Question 13

Baxter Inc.'s annual returns for the past four years were: 2.75%, -1.8%, 7.2%, and 6.5%.What are the arithmetic and geometric average annual returns for Baxter over the four-year period?
A)Arithmetic mean = 6.80%; geometric mean = 3.35%
B)Arithmetic mean = 3.66%; geometric mean = 3.60%
C)Arithmetic mean = 14.65%; geometric mean = 10.05%
D)Arithmetic mean = 18.03%; geometric mean = 21.20%

Accepted Answer

The arithmetic mean is calculated by adding all the annual returns and dividing by the number of years: (2.75% - 1.8% + 7.2% + 6.5%) / 4 = 3.66%. The geometric mean is calculated by multiplying all the (1 + return) values together, taking the nth root (where n is the number of years), and subtracting 1: [(1.0275) * (0.982) * (1.072) * (1.065)]^(1/4) - 1 ≈ 3.60%.

Question 14

Which of the following statements is TRUE?
A)The more stable the possible returns, the greater the risk.
B)Risk means the probability that the actual return from an investment is less than the expected return.
C)The range is a more accurate measure of risk than the standard deviation, because the range uses the maximum and minimum values, whereas the standard deviation uses all the observations.
D)Securities offering lower expected rates of return tend to be riskier.

Accepted Answer

Risk is the probability or likelihood that the actual return from an investment will be less than the expected return. The more stable the possible returns, the lower the risk, so statement A is false. The range is not an accurate measure of risk as it only considers the maximum and minimum values, whereas standard deviation takes into account all the observations, so statement C is false. Lower expected rates of return tend to be associated with lower risk, so statement D is false.

Question 15

The closing prices for Stock B from December to June are: $42.90, $44.20, $51.50, $49.60, $45.50, $46.30, and $42.50.What is the standard deviation of returns over the six-month period?
A)0.295%
B)0.868%
C)5.436%
D)9.318%

Accepted Answer

The answer of The closing prices for Stock B from...

Question 16

The following table shows the closing prices and daily returns of Toronto Skates Inc.over a week:

Calculate the weekly geometric mean (GM)and the arithmetic mean (AM)returns of Toronto Skates Inc.(your answer should be four decimals, margin of error is +/- 0.0050%)
A)GM=0.2400% and AM=0.1728%
B)GM=-0.2841% and AM=0.1728%
C)GM=0.1728% and AM=-0.2841%
D)GM=0.1728% and AM=0.2400%

Accepted Answer

The answer of The following table shows the closing prices...

Question 17

The geometric average daily return for Grumpy Inc.was 3.0% for this past week.Grumpy's stock was traded at $18.82 when the market closed on Friday.The daily returns for Monday through Thursday are 5.0%, 2.0%, -10.0%, and 8.0%, respectively.What is the opening price of Grumpy on Friday?
A)$16.68
B)$16.90
C)$16.94
D)$17.11

Accepted Answer

The answer of The geometric average daily return for Grumpy...

Question 18

You have observed the following for Montreal Smoked Meat Ltd.:

What are the arithmetic and geometric average weekly returns over the 6-week period ended June 15, 2016?
A)Arithmetic mean = 3.317%; geometric mean = 3.309%
B)Arithmetic mean = 3.309%; geometric mean = 3.317%
C)Arithmetic mean = 1.559%; geometric mean = 1.509%
D)Arithmetic mean = 1.510%; geometric mean = 1.559%

Accepted Answer

The answer of You have observed the following for Montreal...

Question 19

AMC Corp had a geometric weekly return of 5.0% for this past week.The daily returns for Monday through Thursday are 4.0%, 3.0%, -7.0%, and 9.0%, respectively.If AMC's stock traded at $16.22 when the market closed on Friday, what is the opening price of the stock on Friday?
A)$13.47
B)$13.38
C)$13.94
D)$14.11

Accepted Answer

The answer of AMC Corp had a geometric weekly return...

Question 20

The geometric average quarterly return of ROM Company was 5.0% for the previous year.What was the return for the third quarter if the returns for the first, second, and fourth quarters were 10.0%, -9.05%, and 8.0%, respectively?
A)-6.18%
B)-7.05%
C)11.05%
D)12.50%

Accepted Answer

The answer of The geometric average quarterly return of ROM...

Quiz 8: Risk, Return, and Portfolio Theory

Given the following forecasts, what is the standard deviation of returns?

What is the expected return from an investment that has an equally likely probability to lose half of the investment or double the investment?

What is the expected return on a stock that has a 15.0% probability of a 35.0% return, a 20.0% probability of a 25.0% return, a 50.0% probability of a 15.0% return, and a 15.0% probability of a -20.0% return?

The arithmetic average daily return for Dopey Inc.was 2.0% for this past week.Dopey's stock was trading at $23.70 when the market closed on Friday.The daily returns for Monday, Tuesday, Thursday, and Friday are 4.8%, 5.6%, -4.0%, and 12.2%, respectively.What was Dopey's opening price on Monday?

What is the standard deviation of returns on a stock priced today at $10 that has a 25.0% probability of increasing to $13, a 50.0% probability of increasing to $12, a 15.0% probability of increasing by 5.0%, and a 10.0% probability of decreasing to $ 7?

If the closing price of Stock Y was $38.63 on Friday, which was after it had earned daily returns of 8.0%, 23.0%, -30.0%, 20.0%, and -5.0% during the week (Monday to Friday) , what was the opening price of Stock Y on Monday?

La Maudite Ltd.'s annual returns for the past five years were: 11.5%, 18%, -12%, -16.5%, and 28%.What are the arithmetic and geometric average annual returns for La Maudite over the five-year period?

Given the information in the following table, what is the expected return of the security?

Which of the following statements is FALSE?

You have observed the following annual returns for Motherboard Inc.: 25%, 15%, -20%, 30%, and -15%.What are the variance and standard deviation of the returns?

Baxter Inc.'s annual returns for the past four years were: 2.75%, -1.8%, 7.2%, and 6.5%.What are the arithmetic and geometric average annual returns for Baxter over the four-year period?

Which of the following statements is TRUE?

The closing prices for Stock B from December to June are: $42.90, $44.20, $51.50, $49.60, $45.50, $46.30, and $42.50.What is the standard deviation of returns over the six-month period?

The following table shows the closing prices and daily returns of Toronto Skates Inc.over a week: Calculate the weekly geometric mean (GM) and the arithmetic mean (AM) returns of Toronto Skates Inc.(your answer should be four decimals, margin of error is +/- 0.0050%)

The geometric average daily return for Grumpy Inc.was 3.0% for this past week.Grumpy's stock was traded at $18.82 when the market closed on Friday.The daily returns for Monday through Thursday are 5.0%, 2.0%, -10.0%, and 8.0%, respectively.What is the opening price of Grumpy on Friday?

You have observed the following for Montreal Smoked Meat Ltd.: What are the arithmetic and geometric average weekly returns over the 6-week period ended June 15, 2016?

AMC Corp had a geometric weekly return of 5.0% for this past week.The daily returns for Monday through Thursday are 4.0%, 3.0%, -7.0%, and 9.0%, respectively.If AMC's stock traded at $16.22 when the market closed on Friday, what is the opening price of the stock on Friday?

The geometric average quarterly return of ROM Company was 5.0% for the previous year.What was the return for the third quarter if the returns for the first, second, and fourth quarters were 10.0%, -9.05%, and 8.0%, respectively?