Question 1

If the returns on a share index can be characterised by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals

Accepted Answer

In a normal distribution, the mean divides the distribution into two equal halves. Therefore, the probability of returns being lower than the mean (12%) is 50%.

Question 2

If asset A's return is exactly two times asset B's return, then following risk return trade-off, the standard deviation of asset A should be ________ times the standard deviation of asset B.

Accepted Answer

According to the risk return trade-off, higher returns are correlated with higher risk. Since asset A has a higher return than asset B, it should also have a higher standard deviation (risk). The question states that asset A's return is exactly two times asset B's return, meaning that the difference in risk between the two assets is not extreme. Therefore, the standard deviation of asset A should be approximately two times the standard deviation of asset B. Therefore, the best answer is Choice C.

Question 3

The S&P/ASX 200 index delivered a return of 5%, 5%, -10%, -10% over four successive years. What is the arithmetic average annual return per year?

Accepted Answer

The answer of The S&P/ASX 200 index delivered a return...

Question 4

The S&P/ASX 200 index delivered a return of 2%, -2%, 10%, and -10% over four successive years. What is the arithmetic average annual return per year?

Accepted Answer

The arithmetic average annual return can be found by adding up the four annual returns and dividing by the number of years:

(2% - 2% + 10% - 10%) / 4 = 0%

Therefore, the average annual return is 0%, meaning there was no average annual growth or loss.

Question 5

You purchase a 30-year, zero-coupon bond for a price of $20. The bond will pay back $100 after 30 years and make no interim payments. The annual compounded return (geometric average return)on this investment is

Accepted Answer

The annual compounded return can be calculated using the formula for the compound annual growth rate (CAGR): CAGR = (Ending Value/Beginning Value)^(1/Number of Years) - 1. Here, CAGR = ($100/$20)^(1/30) - 1 = 5.51%.

Question 6

The standard deviation of returns of: I. small capitalisation shares is higher than that of large capitalisation shares.
II. large capitalisation shares is lower than that of corporate bonds.
III. corporate bonds is higher than that of Australian treasuries.
Which statement is true?

Accepted Answer

Statement I is true as small capitalisation shares are generally considered to be more risky than large capitalisation shares, which leads to a higher standard deviation of returns. 
Statement III is also true as corporate bonds are generally considered to be riskier than Australian treasuries, which leads to a higher standard deviation of returns. 
Statement II is not necessarily true as the standard deviation of returns for large capitalisation shares can vary depending on the specific shares being compared to corporate bonds.

Question 7

Fortescue Mining had realised returns of 10%, 20%, 20% and 10% over four quarters. What is the quarterly standard deviation of returns for Fortescue calculated from this sample?

Accepted Answer

1. Calculate the average return: (10% + 20% + 20% + 10%)/4 = 15%
2. Calculate the deviations from the mean: (10% - 15%) = -5%, (20% - 15%) = 5%, (20% - 15%) = 5%, (10% - 15%) = -5%
3. Calculate the squared deviations: (-5%)^2 = 0.25%, (5%)^2 = 0.25%, (5%)^2 = 0.25%, (-5%)^2 = 0.25%
4. Calculate the average of the squared deviations: (0.25% + 0.25% + 0.25% + 0.25%)/4 = 0.25%
5. Take the square root of the average of the squared deviations to get the standard deviation: sqrt(0.25%) = 0.5%
6. Convert the quarterly standard deviation to an annual standard deviation by multiplying by the square root of 4 (since there are 4 quarters in a year): 0.5% x sqrt(4) = 1%
Therefore, the quarterly standard deviation of returns for Fortescue, calculated from this sample, is 1%, which is closest to option D (5.77%).

Question 8

The S&P/ASX 200 index delivered a return of 30%, -20%, -10%, and 5% over four successive years. What is the arithmetic average annual return per year?

Accepted Answer

The arithmetic average annual return is calculated by summing up the returns and dividing by the number of years: (30% - 20% - 10% + 5%) / 4 = 1.25%.

Question 9

A security returns 5%, 4%, 3% and 6% over four years. The standard deviation of returns of the security is:

Accepted Answer

First, we need to calculate the average return:
Average return = (5% + 4% + 3% + 6%)/4 = 4.5%

Next, we need to calculate the variance:
Variance = [(5%-4.5%)^2 + (4%-4.5%)^2 + (3%-4.5%)^2 + (6%-4.5%)^2]/4
= [0.0025 + 0.0025 + 0.0225 + 0.0025]/4
= 0.0075/4
= 0.001875

Finally, we take the square root of the variance to get the standard deviation:
Standard deviation = √0.001875 = 0.0433
= 4.33%

Therefore, the standard deviation of returns of the security is 1.29% (option C).

Question 10

Versa Co share prices gave a realised return of 30%, -20%, -10%, and 5% over four successive quarters. What is the annual realised return for Versa Co for the year?

Accepted Answer

To calculate the annual realised return, we multiply the returns of each quarter, considering each as a growth factor (1 + return), and then subtract 1 to get the overall growth rate. So, the calculation is as follows: (1 + 0.30) * (1 - 0.20) * (1 - 0.10) * (1 + 0.05) - 1 = (1.30) * (0.80) * (0.90) * (1.05) - 1 = 0.9828 - 1 = -0.0172 or -1.72%.

Question 11

Bear Inc.'s share price closed at $100, $105, $56, $30, $2 over five successive weeks. The weekly standard deviation of the stock price calculated from this sample is

Accepted Answer

The standard deviation of the stock prices can be calculated using the formula for standard deviation for a sample. First, find the mean (average) of the prices: (100 + 105 + 56 + 30 + 2) / 5 = 293 / 5 = 58.6. Then, calculate the variance by finding the squared differences from the mean, summing them, and dividing by the number of observations minus one (n-1 for a sample): [(100-58.6)^2 + (105-58.6)^2 + (56-58.6)^2 + (30-58.6)^2 + (2-58.6)^2] / (5-1) = 7880.8 / 4 = 1970.2. The standard deviation is the square root of the variance, which is √1970.2 ≈ 44.43.

Question 12

If returns on security A are more volatile than the returns on security B, the geometric average return of security A is ________ the geometric average return of security B when their arithmetic average return is the same.

Accepted Answer

The fact that the returns on security A are more volatile means that there is a greater dispersion of returns around the mean, which in turn implies that the geometric average return of security A is lower than the arithmetic average return. Therefore, if the arithmetic average return is the same for security A and security B, security A must have a lower geometric average return.

Question 13

Fortescue had realised returns of 10%, 25%, -20% and -15% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

Accepted Answer

The quarterly standard deviation of returns can be calculated using the formula for standard deviation. First, find the mean (average) return: (10% + 25% - 20% - 15%) / 4 = 0%. Then, calculate each return's deviation from the mean, square those deviations, sum them, divide by the number of observations, and finally take the square root. The calculations give a standard deviation of 21.21%.

Question 14

The geometric average annual return for a large capitalisation share portfolio is 12% for ten years and 5% per year for the next five years. The geometric average annual return for the entire 15-year period is

Accepted Answer

The geometric average annual return over the entire period can be calculated using the formula for the geometric mean of the returns for each sub-period. This is done by multiplying the growth factors of each period together and then taking the nth root, where n is the total number of years. The growth factor for each period is 1 plus the annual return (expressed as a decimal). For the first 10 years, the growth factor is 1.12, and for the next 5 years, it is 1.05. The calculation is as follows:$$ \text{Geometric Average} = \left( (1.12)^{10} \times (1.05)^{5} \right)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} = \left( 3.106 \times 1.276 \right)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} = (3.963)^{\frac{1}{15}} - 1 $$$$ \text{Geometric Average} \approx 1.0962 - 1 $$$$ \text{Geometric Average} \approx 0.0962 $$$$ \text{Geometric Average} \approx 9.62\% $$

Question 15

Fortescue Mining had realised returns of 5%, 15%, -10%, and -5% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

Accepted Answer

The answer of Fortescue Mining had realised returns of 5%,...

Question 16

IGM Realty had a price of $30, $30, $35, $33 and $25 at the end of the last five quarters. If IGM pays a dividend of $2 at the end of each quarter, what is the annual realised return on IGM?

Accepted Answer

The answer of IGM Realty had a price of $30,...

Question 17

Suppose that an investment gave a realised return of 20% over a two-year time period and a 10% return over the third year. The geometric average annual return is

Accepted Answer

The formula for geometric average return is:
(1+R1) x (1+R2) x ... x (1+Rn)^(1/n) - 1
where R1, R2, ..., Rn are the annual returns for each year.
Using the formula, we get:
(1.20) x (1.20) x (1.10)^(1/3) - 1 = 0.1655 or 16.55%
Therefore, the correct answer is C.

Question 18

You purchased HIH shares at a price of $30 per share. Its price was $20 after six months and the company declared bankruptcy at the end of the next six months. The realised return over the last year is

Accepted Answer

The realized return is calculated as (Final Value - Initial Value) / Initial Value. Since the company declared bankruptcy, the final value of the shares is $0. Therefore, the realized return is ($0 - $30) / $30 = -1 or -100%.

Question 19

If a share pays dividends at the end of each quarter, with realised returns of R₁, R₂, R₃ and R₄ each quarter, then the annual realised return is calculated as:

Accepted Answer

The formula for calculating the annual realised return when dividends are paid at the end of each quarter is to use the compounding formula. Therefore, the correct formula is (1 + R₁)(1 + R₂)(1 + R₃)(1 + R₄)- 1. This gives us the total return earned for the entire year, including the dividends paid.

Question 20

Suppose the quarterly arithmetic average return for a security is 5% per quarter and the security gives a return of 10% each over the next two quarters. The arithmetic average return over the six quarters is

Accepted Answer

To calculate the arithmetic average return over six quarters, we need to find the average of all the quarterly returns.

Given: 
Quarter 1 return = 5% 
Quarter 2 return = 5%
Quarter 3 return = 10%
Quarter 4 return = 10%
Quarter 5 return = 5%
Quarter 6 return = 5%

Average = (5% + 5% + 10% + 10% + 5% + 5%) / 6 = 40% / 6 = 6.67%

Therefore, the arithmetic average return over the six quarters is 6.67%. So, the correct answer is option C.

Quiz 11: Risk and Return in Capital Markets

If the returns on a share index can be characterised by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals

If asset A's return is exactly two times asset B's return, then following risk return trade-off, the standard deviation of asset A should be ________ times the standard deviation of asset B.

The S&P/ASX 200 index delivered a return of 5%, 5%, -10%, -10% over four successive years. What is the arithmetic average annual return per year?

The S&P/ASX 200 index delivered a return of 2%, -2%, 10%, and -10% over four successive years. What is the arithmetic average annual return per year?

You purchase a 30-year, zero-coupon bond for a price of $20. The bond will pay back $100 after 30 years and make no interim payments. The annual compounded return (geometric average return) on this investment is

The standard deviation of returns of: I. small capitalisation shares is higher than that of large capitalisation shares. II. large capitalisation shares is lower than that of corporate bonds. III. corporate bonds is higher than that of Australian treasuries. Which statement is true?

Fortescue Mining had realised returns of 10%, 20%, 20% and 10% over four quarters. What is the quarterly standard deviation of returns for Fortescue calculated from this sample?

The S&P/ASX 200 index delivered a return of 30%, -20%, -10%, and 5% over four successive years. What is the arithmetic average annual return per year?

A security returns 5%, 4%, 3% and 6% over four years. The standard deviation of returns of the security is:

Versa Co share prices gave a realised return of 30%, -20%, -10%, and 5% over four successive quarters. What is the annual realised return for Versa Co for the year?

Bear Inc.'s share price closed at $100, $105, $56, $30, $2 over five successive weeks. The weekly standard deviation of the stock price calculated from this sample is

If returns on security A are more volatile than the returns on security B, the geometric average return of security A is ________ the geometric average return of security B when their arithmetic average return is the same.

Fortescue had realised returns of 10%, 25%, -20% and -15% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

The geometric average annual return for a large capitalisation share portfolio is 12% for ten years and 5% per year for the next five years. The geometric average annual return for the entire 15-year period is

Fortescue Mining had realised returns of 5%, 15%, -10%, and -5% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

IGM Realty had a price of $30, $30, $35, $33 and $25 at the end of the last five quarters. If IGM pays a dividend of $2 at the end of each quarter, what is the annual realised return on IGM?

Suppose that an investment gave a realised return of 20% over a two-year time period and a 10% return over the third year. The geometric average annual return is

You purchased HIH shares at a price of $30 per share. Its price was $20 after six months and the company declared bankruptcy at the end of the next six months. The realised return over the last year is

If a share pays dividends at the end of each quarter, with realised returns of R₁, R₂, R₃ and R₄ each quarter, then the annual realised return is calculated as:

Suppose the quarterly arithmetic average return for a security is 5% per quarter and the security gives a return of 10% each over the next two quarters. The arithmetic average return over the six quarters is

Quiz 11: Risk and Return in Capital Markets

If the returns on a share index can be characterised by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals

If asset A's return is exactly two times asset B's return, then following risk return trade-off, the standard deviation of asset A should be ________ times the standard deviation of asset B.

The S&P/ASX 200 index delivered a return of 5%, 5%, -10%, -10% over four successive years. What is the arithmetic average annual return per year?

The S&P/ASX 200 index delivered a return of 2%, -2%, 10%, and -10% over four successive years. What is the arithmetic average annual return per year?

You purchase a 30-year, zero-coupon bond for a price of $20. The bond will pay back $100 after 30 years and make no interim payments. The annual compounded return (geometric average return) on this investment is

The standard deviation of returns of: I. small capitalisation shares is higher than that of large capitalisation shares. II. large capitalisation shares is lower than that of corporate bonds. III. corporate bonds is higher than that of Australian treasuries. Which statement is true?

Fortescue Mining had realised returns of 10%, 20%, 20% and 10% over four quarters. What is the quarterly standard deviation of returns for Fortescue calculated from this sample?

The S&P/ASX 200 index delivered a return of 30%, -20%, -10%, and 5% over four successive years. What is the arithmetic average annual return per year?

A security returns 5%, 4%, 3% and 6% over four years. The standard deviation of returns of the security is:

Versa Co share prices gave a realised return of 30%, -20%, -10%, and 5% over four successive quarters. What is the annual realised return for Versa Co for the year?

Bear Inc.'s share price closed at $100, $105, $56, $30, $2 over five successive weeks. The weekly standard deviation of the stock price calculated from this sample is

If returns on security A are more volatile than the returns on security B, the geometric average return of security A is ________ the geometric average return of security B when their arithmetic average return is the same.

Fortescue had realised returns of 10%, 25%, -20% and -15% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

The geometric average annual return for a large capitalisation share portfolio is 12% for ten years and 5% per year for the next five years. The geometric average annual return for the entire 15-year period is

Fortescue Mining had realised returns of 5%, 15%, -10%, and -5% over four quarters. What is the quarterly standard deviation of returns for Fortescue?

IGM Realty had a price of $30, $30, $35, $33 and $25 at the end of the last five quarters. If IGM pays a dividend of $2 at the end of each quarter, what is the annual realised return on IGM?

Suppose that an investment gave a realised return of 20% over a two-year time period and a 10% return over the third year. The geometric average annual return is

You purchased HIH shares at a price of $30 per share. Its price was $20 after six months and the company declared bankruptcy at the end of the next six months. The realised return over the last year is

If a share pays dividends at the end of each quarter, with realised returns of R1, R2, R3 and R4 each quarter, then the annual realised return is calculated as:

Suppose the quarterly arithmetic average return for a security is 5% per quarter and the security gives a return of 10% each over the next two quarters. The arithmetic average return over the six quarters is

If a share pays dividends at the end of each quarter, with realised returns of R₁, R₂, R₃ and R₄ each quarter, then the annual realised return is calculated as: