问题如下：
Brenda Williams is a risk analyst who wants to model the dependence between asset returns using copulas and must convince her manager that this is the best approach. Which of the following statements are correct?
I. The dependence between the return distributions of portfolio assets is critical for risk measurement.
II. Correlation estimates often appear stable in periods of low market volatility and then become volatile in stressed market conditions. Risk measures calculated using correlations estimated over long horizons will therefore underestimate risk in stressed periods.
III. Pearson correlation (ρ) is a linear measure of dependence between the return of two assets equal to the ratio of the covariance of the asset returns to the product of their volatilities.
IV. Using copulas, one can construct joint return distribution functions from marginal distribution functions in a way that allows for more general types of dependence structure of the asset returns.
选项：
A.I, II, and III
B.II and IV
C.I, II, III, and IV
D.I, III, and IV
解释：
D is correct. The dependence is critical, so statement I. is correct. The usual Pearson correlation is a linear measure of dependence, so statement III. is correct. Statement IV. is also correct. For statement II., correlations indeed change over stressed periods, but it is not clear whether this biases long-term correlations upward or downward. Also, the effect on the portfolio risk depends on the positioning. Hence, there is not enough information to support statement II.
老师好，这道题的II，看了之前的提问和解答，还是不太明白。
II的前半句，我理解是在说相关系数的波动率，按照讲义，相关系数的波动性在经济扩展时最低，在经济正常的情况下最高，那么前半句就应该是错误的。
II的后半句，我理解是在说相关系数本身，按照讲义，相关系数在经济好的时候低，在经济不好(stressed market) 的时候会增加，那么如果从一个long horizon来看的话，经济不好时候的相关系数会被平滑，那么long horizon的相关系数就会比经济不好时候的相关系数要低，因此如果用long horizon的相关系数去估计stressed market的风险的话，就会低估，那么后半句就应该是正确的。
