问题如下:
A large, international bank has a trading book whose size depends on the opportunities perceived by its traders. The market risk manager estimates the one-day VAR, at the 95% confidence level, to be USD 50 million. You are asked to evaluate how good a job the manager is doing in estimating the one-day VAR. Which of the following would be the most convincing evidence that the manager is doing a poor job, assuming that losses are identical and independently distributed (i.i.d.)?
选项:
A. Over the past 250 days, there are eight exceptions.
B. Over the past 250 days, the largest loss is USD 500 million.
C. Over the past 250 days, the mean loss is USD 60 million.
D. Over the past 250 days, there is no exception.
解释:
D is correct. We should expect exceptions on average. Having eight exceptions is too few, but the difference could be due to luck. Having zero exceptions, however, would be very unusual, with a probability of , which is very low. This means that the risk manager is providing VAR estimates that are much too high. Otherwise, the largest or mean losses are not directly useful without more information on the distribution of profits.
C选项,过去250天的平均损失为60M,是指仅仅平均了损失的部分,而不是平均了全部250天的收益和损失部分,对吗?如果250天的均值为60M,是不是也会说明模型不好?