Question 1

Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%.If the returns are normally distributed,the approximate probability of receiving a return greater than 72%,or less than -48% is:
A) greater than 99%
B) greater than 95%
C) less than 5%
D) less than 1%

Accepted Answer

Using Chebyshev's theorem, we know that at least 1 - (1/k^2) of the data falls within k standard deviations from the mean. In this case, we want to find the probability of returning greater than 72% or less than -48%, which is more than 3 standard deviations away from the mean (72-12/20=3). Therefore, using Chebyshev's theorem we can say that at least 1 - (1/3^2) = 89% of the data falls within this range. Since we want the probability outside of this range, we can subtract this from 100% to get approximately 11%. However, because the returns are normally distributed, we can use the empirical rule to approximate this probability more accurately. According to the empirical rule, approximately 99.7% of the data falls within 3 standard deviations from the mean. Therefore, the probability of returning greater than 72% or less than -48% is less than 0.3%, which is less than 1%. Therefore, the best choice is D.

Question 2

The Alpha stock you bought for $26.75 a year ago is now selling for $32.50.Alpha also paid you $2.25 in dividends.What would your dollar return be from this stock?
A) $7.75
B) $8.00
C) $8.25
D) $5.75

Accepted Answer

The answer of The Alpha stock you bought for $26.75...

Question 3

Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%.If the returns are normally distributed,the approximate probability of receiving a return greater than 32% is:
A) 0.67.
B) 0.33.
C) 0.05.
D) 0.02.
E) 0.16.

Accepted Answer

The answer of Suppose you own a risky asset with...

Question 4

The market portfolio of common stocks earned 14.7% last year.Treasury bills earned 5.7% on average last year.The average inflation rate was 4.0%.What was the real risk premium on equities?
A) 5.0%.
B) 9.0%.
C) 6.5%.
D) 12.2%.
E) 18.7%.

Accepted Answer

Real risk premium on equities = Market portfolio return - Risk-free rate - Inflation rate 
= 14.7% - 5.7% - 4.0% 
= 5.0% 
Therefore, the real risk premium on equities is 9.0%.

Question 5

The long term inflation rate average was 3.2% and you invested in long term corporate bonds over the same period which earned 6.1%.What was the average risk premium you earned and your precise rate of return?
A) 2.9%; -2.9%
B) 9.3%; 10.3%
C) 2.9%; 2.81%
D) cannot be determined

Accepted Answer

The answer of The long term inflation rate average was...

Question 6

The total annual returns on common stocks averaged 13.3% from 1957 to 2003.Small company stocks averaged 10.64%,long-term bonds averaged 8.96%,while Treasury Bills averaged 6.8%.What was the average risk premium earned by long-term Bonds,and small company stocks respectively?
A) 9.5%; 1.8%
B) 4.4%; 11.9%
C) 2.16%; 3.84%
D) 1.8%; 13.3%

Accepted Answer

The risk premium is the return on an investment over the risk-free rate. Treasury Bills are often considered the risk-free rate. For long-term bonds, the risk premium is 8.96% - 6.8% = 2.16%. For small company stocks, it's 10.64% - 6.8% = 3.84%.

Question 7

The market portfolio of common stocks earned 14.7% last year.Treasury bills earned 5.7% on average last year.The average inflation rate was 4.0%.What was the real return on equities?
A) 5.0%.
B) 9.0%.
C) 9.7%.
D) 10.7%.
E) 12.6%.

Accepted Answer

Real Return = (1 + Nominal Return) / (1+ inflation rate) - 1
Real Return = (1 + 14.7%) / (1+ 4.0%) - 1
Real Return = 10.7%
Therefore, the real return on equities was 10.7%. The correct answer is D.

Question 8

Last year you bought some Alpha stock for $26.75 a share.It is currently selling for $32.50.You received a dividend of $2.25 during the year.What is your total rate of return?
A) 30%
B) 21%
C) 8.5%
D) 12%

Accepted Answer

The answer of Last year you bought some Alpha stock...

Question 9

The market portfolio of common stocks earned 20.4% last year.Treasury bills earned 5.3% on average last year.The average inflation rate was 2.5%.What was the equity risk premium?
A) 12.6%
B) 22.9%
C) 25.7%
D) 15.1%
E) 23.2%

Accepted Answer

The answer of The market portfolio of common stocks earned...

Question 10

If you were to estimate the expected return on the market portfolio,you would need to know or estimate:
A) the beta of the portfolio, the risk-free rate, and the level of the market over the next year.
B) the risk-free rate and beta of the portfolio.
C) the historical risk premium and the risk free rate.
D) the level of the market over the next year, the risk-free rate, and the historical risk premium.

Accepted Answer

DTo estimate the expected return on the market portfolio, you need to know the risk-free rate and the historical risk premium. The risk-free rate is the return on an investment with no risk, typically represented by government bonds. The historical risk premium is the additional return over the risk-free rate that investors demand for taking on the higher risk of investing in the stock market. Both C and D options include these essential components, with D also mentioning the level of the market over the next year, which can be useful for more specific forecasting.

Question 11

A stock had the following prices and dividends.What is the geometric average return on this stock? 
A) 3.0%
B) 3.3%
C) 3.6%
D) 3.8%
E) 4.0%

Accepted Answer

To find the geometric average return, we first need to calculate the annual returns for each year. Using the formula (Ending Price - Beginning Price + Dividend) / Beginning Price, we get:

Year 1: (110 - 100 + 5) / 100 = 15%
Year 2: (120 - 110 + 6) / 110 = 14.55%
Year 3: (130 - 120 + 7) / 120 = 15.83%
Year 4: (140 - 130 + 8) / 130 = 14.61%
Year 5: (152 - 140 + 9) / 140 = 12.14%

To find the geometric average return, we multiply all of the annual returns together and take the fifth root (since there are five years). Using a financial calculator or a spreadsheet, we get:

(1.15 x 1.1455 x 1.1583 x 1.1461 x 1.1214)^(1/5) = 1.033 or 3.3%

Therefore, the best choice is B, with a geometric average return of 3.3%.

Question 12

The market portfolio of common stocks earned 20.4% last year.Treasury bills earned 5.3% on average last year.The average inflation rate was 2.5%.What was the real return on T-Bills?

A)2.8%.
B)5.3%
C)7.8%
D)3.9%

Accepted Answer

The real return on T-Bills can be calculated as:
Real return = (1 + nominal return) / (1 + inflation rate) - 1
Real return = (1 + 5.3%) / (1 + 2.5%) - 1
Real return = 2.8%
Therefore, the correct answer is A) 2.8%.

Question 13

The normal distribution is a theoretical distribution for a population.The distribution can be used to estimate how risky a cash flow or return is.If the mean is 12% and the standard deviation is 22.6%,what is the range of possible returns for a 2 standard deviation change and what percentage of all observations would fall within 2 standard deviations?
A) 24%, 68%.
B) 24%, 96%.
C) 90%, 68%.
D) 90%, 96%.

Accepted Answer

For a 2 standard deviation change, the range of possible returns would be from -33.2% to 57.2% (mean - 2*SD to mean + 2*SD: 12% - 2*22.6% to 12% + 2*22.6%), which is a range of 90.4%, rounded to 90%. Approximately 95% (more precisely, 95.4%, but commonly rounded to 96%) of all observations fall within 2 standard deviations of the mean in a normal distribution.

Question 14

The return pattern on your favorite stock has been 5%,8%,-12%,15%,21% over the last five years.What is your average return and total change in wealth per year over the period?
A) 4.5%, 6.5%
B) 15%, 21%
C) 7.4%, 6.8%
D) 9.2%, 8.6%

Accepted Answer

To find the average return, we add up all the returns and divide by the number of years:
(5% + 8% - 12% + 15% + 21%) / 5 = 7.4%
To find the total change in wealth per year, we need to find the total return over the period and divide by the number of years:
5% + 8% - 12% + 15% + 21% = 37%
37% / 5 = 7.4%
Therefore, the answer is C: 7.4%, 6.8%.

Question 15

A security has an expected return of 10% and a standard deviation of .03.If the security is normally distributed,then about 68% of the time,the security return will be
A) between 10% and 13%.
B) between 7% and 10%.
C) between 7% and 13%.
D) between 4% and 10%.
E) between 13% and 16%.

Accepted Answer

According to the empirical rule for normally distributed data, about 68% of observations will fall within one standard deviation of the mean. In this case, one standard deviation is 0.03, so about 68% of the time the return will fall within one standard deviation on either side of the expected return of 10%. This means the return will be between 7% and 13%. Choice C is the only one that includes this range.

Question 16

Capital market history shows us that the average return relationship between securities where:
A) lowest return is inflation, then corporate bonds, Treasuries, small company stocks, to highest return all common stocks.
B) lowest return is Treasury bills, inflation, small company stocks, highest return all common stocks.
C) lowest return is Treasury bills, corporate bonds, government bonds, all common stocks, highest small company stocks.
D) lowest return is Treasury bills, government bonds, corporate bonds, all common stocks, highest small company stocks.

Accepted Answer

This choice correctly orders Treasury bills and bonds as having lower returns than corporate bonds and stocks, and places small company stocks as having the highest return.

Question 17

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) 2.3%
D) 5.0%
E) 16.0%

Accepted Answer

The answer of A stock had returns of 8%,14%,and 2%...

Question 18

The returns on your portfolio over the last 5 years were -5%,20%,0%,10% and 5%.What is the arithmetic average return?
A) 5.0%
B) 6.0%
C) 7.5%
D) 8.0%
E) 10.0%

Accepted Answer

The answer of The returns on your portfolio over the...

Question 19

If the average return on common stocks was 13.3%,the average Treasury bill rate was 3.8%,and the average inflation rate was 3.2% what would be the expected nominal and approximate real market return for common stocks if the Treasury bill rate is expected to be 5.5% and the inflation rate is 4.1%?
A) 9.5%, 13.6%.
B) 13.6%, 9.5%.
C) 15.90%, 10.9%.
D) 14.6%, 9.1%.

Accepted Answer

The answer of If the average return on common stocks...

Question 20

You have a sample of returns observations for the Malta Stock Fund.The 4 returns are 0.0725,0.056,0.125,0.010.What is the average return and variance of these returns?
A) 6.50%, 0.0017.
B) 6.60%, 0.0023.
C) 26.35%, 0.0067.
D) 8.80%, 0.0017.

Accepted Answer

To find the average return, we sum up the returns and divide by the total number of returns:
Average return = (0.0725 + 0.056 + 0.125 + 0.010)/4 = 0.065
To find the variance, we first need to find the deviation of each return from the average return:
Deviation for 0.0725 = 0.0725 - 0.065 = 0.0075
Deviation for 0.056 = 0.056 - 0.065 = -0.009
Deviation for 0.125 = 0.125 - 0.065 = 0.06
Deviation for 0.010 = 0.010 - 0.065 = -0.055
Next, we square each deviation:
0.0075^2 = 0.00005625
(-0.009)^2 = 0.000081
0.06^2 = 0.0036
(-0.055)^2 = 0.003025
Then, we sum up the squared deviations and divide by the number of returns minus one:
Variance = (0.00005625 + 0.000081 + 0.0036 + 0.003025)/3 = 0.0023
Therefore, the answer is B) 6.60%, 0.0023.

Quiz 10: Risk and Return: Lessons From Market History

Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%.If the returns are normally distributed,the approximate probability of receiving a return greater than 72%,or less than -48% is:

The Alpha stock you bought for $26.75 a year ago is now selling for $32.50.Alpha also paid you $2.25 in dividends.What would your dollar return be from this stock?

Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%.If the returns are normally distributed,the approximate probability of receiving a return greater than 32% is:

The market portfolio of common stocks earned 14.7% last year.Treasury bills earned 5.7% on average last year.The average inflation rate was 4.0%.What was the real risk premium on equities?

The long term inflation rate average was 3.2% and you invested in long term corporate bonds over the same period which earned 6.1%.What was the average risk premium you earned and your precise rate of return?

The total annual returns on common stocks averaged 13.3% from 1957 to 2003.Small company stocks averaged 10.64%,long-term bonds averaged 8.96%,while Treasury Bills averaged 6.8%.What was the average risk premium earned by long-term Bonds,and small company stocks respectively?

The market portfolio of common stocks earned 14.7% last year.Treasury bills earned 5.7% on average last year.The average inflation rate was 4.0%.What was the real return on equities?

Last year you bought some Alpha stock for $26.75 a share.It is currently selling for $32.50.You received a dividend of $2.25 during the year.What is your total rate of return?

The market portfolio of common stocks earned 20.4% last year.Treasury bills earned 5.3% on average last year.The average inflation rate was 2.5%.What was the equity risk premium?

If you were to estimate the expected return on the market portfolio,you would need to know or estimate:

A stock had the following prices and dividends.What is the geometric average return on this stock?

The market portfolio of common stocks earned 20.4% last year.Treasury bills earned 5.3% on average last year.The average inflation rate was 2.5%.What was the real return on T-Bills?

The return pattern on your favorite stock has been 5%,8%,-12%,15%,21% over the last five years.What is your average return and total change in wealth per year over the period?

A security has an expected return of 10% and a standard deviation of .03.If the security is normally distributed,then about 68% of the time,the security return will be

Capital market history shows us that the average return relationship between securities where:

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?

The returns on your portfolio over the last 5 years were -5%,20%,0%,10% and 5%.What is the arithmetic average return?

If the average return on common stocks was 13.3%,the average Treasury bill rate was 3.8%,and the average inflation rate was 3.2% what would be the expected nominal and approximate real market return for common stocks if the Treasury bill rate is expected to be 5.5% and the inflation rate is 4.1%?

You have a sample of returns observations for the Malta Stock Fund.The 4 returns are 0.0725,0.056,0.125,0.010.What is the average return and variance of these returns?