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fdzh · 2023年10月24日

能否烦请老师解释一下这题

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2023091701000122

问题如下：

A credit analyst covers a portfolio of 10 bonds that are all currently rated investment grade. Under the company's portfolio investment guidelines, no more than two bonds in the portfolio may be rated non-investment grade. The analyst has estimated that each bond has a 20% probability of being downgraded to non-investment grade over the following year and each downgrade is independent of other downgrades. What is the estimated probability that more than two bonds in the portfolio will be rated non-investment grade at the end of next year?

选项：

A.32.2%
B.37.6% C.62.3% D.67.8%

解释：

没有什么思路

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1 个答案

李坏_品职助教 · 2023年10月24日

嗨，从没放弃的小努力你好：


题目说这个投资组合里有10个债券，每个债券有20%的概率被评为高风险，每个债券互相之间是独立的（不相关的）。问你超过2个债券被评为高风险概率是多少？


设：高风险债券的数量为X。

P(X>2) = 1-P(X=0) -P(X=1) - P(X=2)

= 1- (1-20%)^10 - 10 * 20% *（1-20%）^9 - 10*9/2 * 20%^2 * (1-20%)^8

= 32.22%.


注意仅有2个债券属于高风险的概率，应当考虑组合数，10个债券里面任意选2个高风险的，组合的个数是C(2,10) = 10*9/2

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