这题是什么意思呢？

问题如下：

选项：

A portfolio manager is assessing whether the 1-year probability of default of a longevity bond issued by a life insurance company is uncorrelated with returns of the equity market. The portfolio manager creates the following probability matrix based on 1-year probabilities from the preliminary research:

3%

4%

7.89%

10.53%

解释：

Using Bayes’ theorem, let A = bond default and let B = 20% decrease in market returns. Then we must solve: [𝐴|𝐵]=𝑃[𝐴∩𝐵]/𝑃[𝐵]

Using the values from the table, we have [𝐴∩𝐵]=3% and 𝑃[𝐵]=35%+3%=38%.Thus, 𝑃[𝐴|𝐵]=0.03/0.38=.0789→7.89%.

A is incorrect. It is the probability that the bond defaults and market returns decrease by 20% in 1 year.

B is incorrect. It is the unconditional probability that the bond defaults.

D is incorrect. It uses the unconditional probability that the bond defaults in the numerator of the Bayes’ theorem equation. 0.04/0.38=0.1053.