Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

False

Question 3

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

Accepted Answer

False

Question 4

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

Accepted Answer

This statement is true. The normal distribution is symmetrical around the mean and 50 percent of the area (or probability) lies to the left of the mean and 50 percent to the right of the mean. The standard deviation describes the spread or variability of the distribution.

Question 5

If you are calculating the variance and standard deviation of returns for a stock, 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 6

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 is the average value of the possible outcomes, taking into account their probabilities. It does not necessarily mean that the person making the bet will receive a cash inflow of that amount. In this case, it is possible that the person making the bet could lose money, receive only a partial return, or receive a different amount than $15 depending on the specifics of the bet.

Question 7

The income component of return for a common stock comes from the dividend cash flow stream.

Accepted Answer

The income component of return for a common stock comes from the dividend cash flow stream, while the other component of return comes from capital appreciation or gain in stock price.

Question 8

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 have been no dividends paid during the holding period of an asset and the price has remained the same, then the only component of return is capital appreciation. Therefore, the total return would be equal to the capital appreciation component return.

Question 9

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

Accepted Answer

The capital appreciation component of a stock's return is calculated as the increase in stock price divided by the beginning stock price of the period. This measures the gain in the stock's value over time, and is a key factor in assessing the performance of a stock investment.

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 percent probability that you will win the wager.

Accepted Answer

If the expected cash receipt of the wager is $9, it means that if you were to repeatedly make this bet, on average you would receive $9 every time you placed a bet. However, since the maximum amount you can receive from winning the bet is $10, it is not possible that there is a 100 percent probability that you will win the bet. The expected value calculation takes into account all possible outcomes and the probability of each outcome occurring, but it does not guarantee a specific outcome with 100 percent certainty.

Question 11

The variance of a distribution can be a negative value.

Accepted Answer

The variance is a measure of the spread or variability of a distribution around its mean, and it is always a non-negative value (i.e., it cannot be negative). If the variance is zero, then all the data points are identical, and if it is very large, then the data points are widely dispersed.

Question 12

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

Accepted Answer

The standard deviation is always a non-negative value because it is calculated as the square root of the variance, which is the average of the squared deviations from the mean, and the squared deviations are always non-negative.

Question 13

The best measure of risk within an investment is its variance.

Accepted Answer

Variance measures the dispersion of returns, but standard deviation is often considered a better measure of risk as it is in the same units as the returns.

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

If the total return of a stock is -100%, it means that the stock has lost all of its value. In this case, the income return component, which is the dividend yield, must be zero because there is no income being generated from the stock.

Question 16

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 17

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 18

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 of an asset by the expected return of that asset.

Question 19

Whenever the outcome of an event has a number of different possibilities that have equal probability of occurrence, then the expected value of the outcome is equal to the simple average of the individual events.

Accepted Answer

This is the definition of the expected value in probability theory.

Question 20

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.

Quiz 7: Risk and Return