QUIZ: Statistical Measures of Asset Returns

Consider the following annual returns for three different investment portfolios:

If a new portfolio, D, was introduced with a return of 18%, what would be the median return among the four portfolios?

A researcher found that the returns of a certain security followed a bimodal distribution. Which of the following is the most likely reason for this observation?

Zoe is working on a dataset containing the annual incomes of 100 individuals. After calculating the mean, she discovers some extreme values at both ends. She decides to calculate a 2% trimmed mean. How many observations will she exclude from each end to calculate this trimmed mean?

Which of the following best describes a winsorized mean?

In a box and whisker plot, if the largest observation is significantly farther from the box than the smallest observation, it suggests:

A box and whisker plot for a set of data shows the median significantly closer to the third quartile than the first quartile. This indicates:

Which measure can be used to describe the spread of the middle 50% of data?

Given a dataset, if one is interested in understanding the variability and spread of the middle portion of data without being affected by extreme values, they should consider:

In the context of a box and whisker plot, if the ‘box’ represents a smaller portion of the vertical line, this indicates:

A hedge fund manager believes that assets with a higher MAD are riskier. She has computed the MAD for two assets and obtained values of 4.5% for Asset X and 5.5% for Asset Y. Based on MAD alone, which asset is riskier?

An investment advisor wants to present the risk-return profile of two assets to his client. He observes that while both assets have similar MAD values, Asset A has a higher mean return. How should the advisor interpret this?

Which of the following statements is TRUE concerning the properties and interpretation of sample variance?

What is the primary reason for using n-1 as the denominator in the sample variance formula instead of n?

An investment’s mean monthly return is 1.2% with a standard deviation of 0.5%. If another investment has a mean return of 1.5% and a standard deviation of 0.6%, which investment has less risk per unit of monthly return?

Which of the following statements best describes the concept of target downside deviation?

Given the increasing importance of downside risk in investment management, an investment advisor suggests using target semideviation as the preferred metric. Which scenario would justify this recommendation?

Robert is analyzing a data set of housing prices in London over the past year. He noticed that a few homes sold for significantly higher prices than the majority. Which of the following descriptions would best describe this distribution of housing prices?

A professor provided her students with a set of data and found that the sample skewness of the data was -2.5. What can be inferred about the distribution of the data?

Sarah is analysing the distribution of yearly incomes in a specific town. She notices that the mean income is $75,000, while the mode is at $55,000. What can Sarah infer about the skewness of the income distribution?

A hedge fund manager is analysing the return distribution of his portfolio. He finds that the return distribution is platykurtic. Which of the following best describes the implication for risk management?

Based on a large sample size, an analyst calculates the sample kurtosis of a distribution as 4.2. What is the excess kurtosis for this distribution?

A financial analyst is trying to compare the risk of two assets using their return distributions. Asset A has an excess kurtosis of 3 while Asset B has an excess kurtosis of -2. Which statement regarding the risk associated with the assets is most accurate?

When studying relationships between two variables, why might it be misleading to rely solely on correlation coefficients?

Considering two stocks, M and N, with respective variances of 0.004 and 0.006. If their covariance is negative, which of the following statements is most likely true?

Assuming you are given the following data for two stocks, Stock W and Stock Z:

• Variance of returns for Stock W: 0.0064
• Variance of returns for Stock Z: 0.0091
• Covariance of returns between Stock W and Stock Z: 0.0046

Which of the following is the correlation coefficient between the returns of Stock W and Stock Z?

Given that two random variables, J and K, have a correlation of 0. If the variance of J increases, what happens to the covariance of J and K?

Using the concept of spurious correlation, which of the following statements is most accurate?