Question 1

The variance is equal to the square root of the standard deviation.

Accepted Answer

The statement is incorrect. The standard deviation is equal to the square root of the variance.

Question 2

The coefficient of variation is a good measure of the amount of risk that an asset will contribute to a diversified portfolio of assets.

Accepted Answer

The coefficient of variation (CV) measures the standard deviation of an asset's returns relative to its mean return. A higher CV indicates higher variability and risk. Therefore, the CV is a good measure of the amount of risk an asset will contribute to a diversified portfolio.

Question 3

The variance is denominated in squared units, whereas the standard deviation is denominated in the same units as the expected value.

Accepted Answer

Variance is calculated as the average of the squared differences from the mean, resulting in squared units, while standard deviation is the square root of variance, bringing it back to the original units of the data.

Question 4

If the price of an asset has not increased or decreased since the original purchase of the asset, then the total return of the asset (if no dividends were paid during the period) is equal to the capital appreciation component return.

Accepted Answer

If there has been no change in the price of the asset, then there can be no return from dividends. Therefore, the total return of the asset would only be from the capital appreciation component.

Question 5

The capital appreciation component of a share's return considers the increase in price of a share divided by the end of period price of the share.

Accepted Answer

The capital appreciation component of a share's return considers the increase in price of a share divided by the initial price of the share, not the end of period price.

Question 6

The normal distribution is completely described by its mean and standard deviation where 50 per cent of the distribution's probability is less than the mean and 50 per cent greater than the mean.

Accepted Answer

This statement is true. The normal distribution is symmetric, with the mean as the center point. Therefore, half of the distribution's area (or probability) is on the left side of the mean, and the other half is on the right side of the mean. The standard deviation corresponds to the spread or width of the distribution.

Question 7

If you are calculating the variance and standard deviation of returns for a share, the variance will always be larger than the standard deviation.

Accepted Answer

The standard deviation is the square root of the variance. Therefore, the variance will always be larger than the standard deviation.

Question 8

The variance of a distribution can be a negative value.

Accepted Answer

The variance of a distribution is always a non-negative value. It represents the average of the squared deviations from the mean, which cannot be negative.

Question 9

The standard deviation of a distribution can be a negative value.

Accepted Answer

The standard deviation is a measure of the spread or dispersion of a distribution and is always a non-negative value. It represents the amount of variation or deviation from the mean or average value of the distribution.

Question 10

You have placed a wager such that you will either receive nothing if you lose the bet or you will receive $10 if you win the bet. If the expected cash receipt of the wager is $9, then there is a 100 per cent probability that you will win the wager.

Accepted Answer

The expected cash receipt is equal to the probability of winning multiplied by the amount won, plus the probability of losing multiplied by the amount lost. Let's call the probability of winning "p". Then we can set up the equation:
$9 = p(10) + (1-p)(0)$
Simplifying the equation, we get:
$9 = 10p$
$p = 0.9$
This means that there is a 90% probability of winning, not a 100% probability as stated in the statement. Therefore, the correct answer is B, false.

Question 11

The capital appreciation component of a share's return considers the increase in price of a share divided by the beginning of period price of the share.

Accepted Answer

The capital appreciation component of a share's return is indeed calculated by dividing the increase in price of a share by the beginning of period price of the share. This is also known as the capital gain or price return component of a share's return.

Question 12

If you are building a portfolio, then you desire assets that have a correlation coefficient of one.

Accepted Answer

If all assets in a portfolio have a correlation coefficient of one, it means they move in perfect sync with each other, which increases the risk of the portfolio as a whole. It is recommended to have a mix of assets with different correlation coefficients to diversify the risk.

Question 13

The income component of return for an ordinary share comes from the dividend cash flow stream.

Accepted Answer

The income component of return for an ordinary share does come from the dividend cash flow stream. However, there may be other components of return such as capital gains or losses from fluctuations in share price.

Question 14

Robert paid $100 for a share one year ago. The total return on the share was 10 per cent. Therefore, the share must be selling for $110 today.

Accepted Answer

The statement is not necessarily true. While the total return on the share was 10%, the current selling price could be more or less than $110. The total return on a share includes not only the change in the share price but also any dividends or distributions received, so without additional information on these factors, it is not possible to determine the current selling price.

Question 15

The coefficient of variation divides the variance of the returns of an asset by the expected return of that asset.

Accepted Answer

The coefficient of variation divides the standard deviation of the returns by the expected return, not the variance.

Question 16

In order for the total return of a share to be equal to -100 per cent, the income return component for that share must be zero.

Accepted Answer

If the total return is -100%, it means that the investor has lost all of their initial investment. In this case, the income return component must be zero, as there is no income to be earned on a lost investment.

Question 17

If the returns for two assets have a correlation coefficient of one, then there are no benefits of diversification by combining these assets in a two-asset portfolio.

Accepted Answer

A correlation coefficient of one indicates a perfect positive correlation between two assets, meaning they move in perfect tandem. Therefore, combining these assets in a portfolio would not provide any diversification benefits as their returns would behave identically.

Question 18

The appropriate measure of risk for a diversified portfolio is beta.

Accepted Answer

Beta is a measure of the systematic risk (market risk) of a security or portfolio in relation to the overall market. As a diversified portfolio is generally designed to reduce unsystematic risk, beta is an appropriate measure of risk for such a portfolio.

Question 19

If the expected return of a bet, which is based on a coin toss, is $15, then that means that the outcome of the bet will be a $15 cash inflow to the person making the bet.

Accepted Answer

The expected return of a bet based on a coin toss being $15 means that over the long run, if the bet is repeated many times, the average return will be $15. It does not guarantee a $15 cash inflow for any individual bet. The outcome of any one specific bet remains uncertain.

Question 20

If the capital appreciation return from owning a share is positive, then the total return from owning the same share can be negative.

Accepted Answer

The answer of If the capital appreciation return from owning...

Quiz 7: Risk and Return