Question 1

If a financial asset has a historical variance of 16, then its standard deviation must be 4.

Accepted Answer

Standard deviation is the square root of variance, so if the variance is 16, the standard deviation is the square root of 16, which is 4.

Question 2

Standard deviation is stated in the same units of measurement (e.g., dollars, percent) as those of the data from which they were generated.

Accepted Answer

Standard deviation is a measure of dispersion or spread of a set of data from its mean. It is expressed in the same units as the original data. For example, if we are calculating the standard deviation of a set of data measured in dollars, then the standard deviation would also be in dollars. Therefore, the statement is true.

Question 3

Standard deviation is the square root of the variance.

Accepted Answer

This is a true statement in statistics.

Question 4

If Stock A has a higher standard deviation than Stock B, it will also have a greater coefficient of variation.

Accepted Answer

The coefficient of variation is calculated as the standard deviation divided by the mean. Therefore, a stock can have a higher standard deviation but a lower coefficient of variation if its mean is also significantly higher.

Question 5

The sum of the deviations always equals the sample size n.

Accepted Answer

The sum of the deviations always equals zero, not the sample size n.

Question 6

The variance or standard deviation measures the risk per unit of return.

Accepted Answer

Variance or standard deviation measures the dispersion or spread of a set of data points around their mean value, not the risk per unit of return. Risk per unit of return is often assessed using metrics like the Sharpe ratio.

Question 7

If standard deviation is used to measure the risk of stocks, one problem that arises is the inability to tell which stock is riskier by looking at the standard deviation alone.

Accepted Answer

Standard deviation only measures the dispersion of data from the average, but it doesn't give information about the direction of the deviation. Therefore, two stocks can have the same standard deviation but exhibit different levels and types of risks.

Question 8

If the expected return is 10%, the standard deviation is 3%, about 68% of the time returns will be expected to fall between 10% and 13%.

Accepted Answer

According to the empirical rule (or 68-95-99.7 rule) for a normal distribution, about 68% of the time returns will be expected to fall within one standard deviation of the mean. Therefore, with a mean (expected return) of 10% and a standard deviation of 3%, returns would be expected to fall between 7% (10% - 3%) and 13% (10% + 3%) about 68% of the time.

Question 9

If the expected return is 10%, the standard deviation is 3%, about 95% of the time returns will be expected to fall between 1% and 19%.

Accepted Answer

The 95% confidence interval for a normal distribution with a mean of 10% and a standard deviation of 3% is approximately between 4% and 16%. Therefore, about 95% of the time returns will be expected to fall between 4% and 16%, not 1% to 19%.

Question 10

If the expected return is 10%, the standard deviation is 3%, about 68% of the time returns will be expected to fall between 7% and 13%.

Accepted Answer

This statement is true according to the empirical rule of statistics, which states that approximately 68% of data falls within one standard deviation of the mean in a normal distribution. If the expected return is 10% and the standard deviation is 3%, 68% of the time returns will fall between 7% and 13%.

Question 11

The coefficient of variation is calculated as the variance divided by average returns R.

Accepted Answer

The coefficient of variation is calculated as the standard deviation divided by the mean, not the variance divided by the average returns.

Question 12

If stock A has a standard deviation of 5 and stock B has a standard deviation of 10, the higher standard deviation for B tells us it has higher risk.

Accepted Answer

The answer of If stock A has a standard deviation...

Question 13

A higher coefficient of variation indicates more risk per unit of return.

Accepted Answer

The coefficient of variation (CV) is a measure of relative variability calculated as the ratio of the standard deviation to the mean of the data. A higher CV indicates that the data has a wider spread and is more variable. Since risk is synonymous with uncertainty or variability, a higher CV implies more risk per unit of return.

Question 14

The coefficient of variation is a measure of total return on a stock.

Accepted Answer

The coefficient of variation is a measure of the risk or volatility of a stock, not its total return. It is calculated as the standard deviation of returns divided by the mean return.

Question 15

In computing the variance, you divide by the sample size n.

Accepted Answer

To compute the variance, you divide by the sample size minus one, denoted as n-1, not by the sample size n. This is because using n-1 gives an unbiased estimate of the population variance, while dividing by n would give a biased estimate.

Question 16

Standard deviation is the square root of the coefficient of variation.

Accepted Answer

Standard deviation is not the square root of the coefficient of variation. The coefficient of variation is calculated as the ratio of the standard deviation to the mean, and therefore involves both measures.

Question 17

If a financial asset has a historical variance of 25, then its standard deviation must be 12.5%.

Accepted Answer

The formula for calculating standard deviation is the square root of variance. Therefore, if the historical variance is 25, the standard deviation would be the square root of 25, which is 5. In percentage terms, it would be 20%, not 12.5%.

Question 18

The standard deviation is computed first and then squared to find the variance.

Accepted Answer

The variance is computed first by taking the sum of the squared differences from the mean, dividing by the number of data points minus one, and then the square root of the variance is taken to find the standard deviation.

Question 19

The variance is the square root of the standard deviation.

Accepted Answer

The standard deviation is the square root of the variance, not the other way around.

Question 20

A stock that went from $40 per share at the beginning of the year to $45 at the end of the year and paid a $2 dividend provided an investor with a 14% return.

Accepted Answer

The answer of A stock that went from $40 per...

Quiz 12: Financial Return and Risk Concepts