[2008] Topic 10: Quantifying Volatility in VAR Models 相关习题 discuss, comparing, different, otherwise, standard

qingshu

 

AIM 1: List and discuss how asset return distributions deviate from the normal distribution, explain reasons for the existence of fat tails in a return distribution, and analyze the implications fat tails have on return distributions.

1、When comparing a fat-tailed distribution to an otherwise similar normal distribution, the fat-tailed distribution often has:

A) a different mean and standard deviation.

B) an equal probability mass close to the mean.

C) a lower probability mass at more than three standard deviations.

D) a lower probability mass at around one standard deviation.

qingshu

 

The correct answer is B

Fat-tailed distributions typically have less probability mass in the intermediate range, around +/– one standard deviation, compared to the normal distribution. The first two moments (mean and variance) of the distributions are similar for the fat-tailed and normal distributions. Fat-tailed distributions have greater mass in the tails and a greater probability mass around the mean than the normal distribution.

qingshu

 

2、A distribution of asset returns that has a significantly higher probability of obtaining large losses is described as:

A) right skewed.

B) fat tailed.

C) left skewed.

D) symmetrical.

qingshu

 

The correct answer is C

A distribution is left skewed when the distribution is asymmetrical and there is a higher probability of large negative returns than there is for large positive returns.

qingshu

 

3、All of the following are examples of why returns distributions can deviate from the normal distribution EXCEPT the distributions:

A) are symmetrical.

B) are fat tailed.

C) are skewed.

D) have unstable parameters.

qingshu

 

The correct answer is A

Examples of common deviations from the normal distribution are fat tails and skewed and/or unstable parameters. The normal distribution is symmetrical.

qingshu

 

4、Which of the following statements regarding fat-tail distributions is/are TRUE? A fat-tailed distribution: I. most likely results from time-varying volatility for the unconditional distribution. II. has a lower probability mass around one standard deviation from the mean than a normal distribution. III. has a lower probability mass around the mean than a normal distribution. IV. most likely results from time-varying means for the conditional distribution.

A) I only. 

B) I and II.

C) I and III.

D) II and IV.

qingshu

 

The correct answer is B

The most likely explanation for “fat tails” is that the second moment or volatility is time-varying. For example, volatility changes in interest rates are observed prior to much anticipated Federal Reserve announcements. Examining a data sample at different points of time from the full sample could generate fat tails in the unconditional distribution even if the conditional distributions are normally distributed. The conditional mean is not expected to deviate over time. The first two moments (mean and variance) of the distributions are similar for the fat-tailed and normal distribution. However, fat-tailed distributions typically have less probability mass in the intermediate range, around +/–1 standard deviation, compared to the normal distribution. Fat-tailed distributions have greater mass in the tails and a greater probability mass around the mean than the normal distribution.

qingshu

 

4、Which of the following deviations from normality leads to underestimating the distribution variance?

?            Higher probability of high returns.

?            Higher probability of mean returns.

?            The mean of the distribution is conditional on the economic environment.

?            The variance of the distribution is conditional on the economic environment.

A) II only.

B) III only.

C) I, II, and IV only.

D) III and IV only.

qingshu

 

The correct answer is A

Statements I & III lead to overestimates of variance. Statement IV leads to over or under estimates of the variance.