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粗眉毛辣椒油 · 2024年01月01日

不理解这个计算公式，是什么知识点？

  1. FRM I
  2. Quantitative

NO.PZ2020010301000006

问题如下：

Suppose that 10% of fund managers are superstars. Superstars have a 20% chance of beating their benchmark by more than 5% each year(high return), whereas normal fund managers have only a 5% chance of beating their benchmark by more than 5%.

Continue the application of Bayes’ rule to compute the probability that a manager is a superstar after observing two years of “high” returns.

选项：

解释：

Consider the three scenarios: (High, High), (High, Low) and (Low, Low). We are interested in Pr (Star|High, High) using Bayes’ rule, this is equal to

Pr(High, High|Star)Pr(Star) /Pr(High, High).

Stars produce high returns in 20% of years, and so Pr(High, High|Star) = 20% * 20% Pr (Star) is still 10%.

Finally, we need to compute Pr (High, High), which is Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal).

This value is 20% * 20% * 10% + 5% * 5% * 90% = 0.625%. Combing these values,

20% * 20% * 10%/0.625%=64%

This is a large increase from the 30% chance after one year.

‘Finally, we need to compute Pr (High, High), which is Pr(High, High|Star) Pr(Star) + Pr(High, High|Normal)Pr(Normal).’

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3 个答案

DD仔_品职助教 · 2024年01月10日

嗨，爱思考的PZer你好：


20%已经是在10%的基础上得出的概率了，再乘10%就是double count了。

运用场景要根据题目给出的条件来决定，给出什么概率就用相关的公式来计算

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

DD仔_品职助教 · 2024年01月09日

嗨，爱思考的PZer你好：


这就是条件概率啊

start每年high收益的可能是20%，start连续两年的high收益概率就是20%*20%

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努力的时光都是限量版，加油！

粗眉毛辣椒油 · 2024年01月09日

Pr(High, High|Star) 不是要先让P（star）=10%发生吗，再P（star）发生的基础上，再连续两年的High，那就是10%* 20% * 20%？这是我的理解。另外， Pr (Star|High, High)=Pr(High, High|Star)Pr(Star) /Pr(High, High)是考查P(A|B)=P(B|A)P(A)/P(B)，请问这个公式和P(A|B)=P(AB)/P(B)运用场景有什么不同？

DD仔_品职助教 · 2024年01月02日

嗨，爱思考的PZer你好：


同学你好，

翻译成中文应该会更好理解一些：

题目给的前提是发现了一个人连续两年高收益，star连续两年高收益的概率是20%*20%=4%，普通人连续两年高收益的概率是5%*5%=0.25%，然后10%的人是star，90%的是普通，所以随意一个人连续高收益的概率就是4%*10%+0.25%*90%=0.625%。

其中这人是star的概率就是4%*10%=0.4%，

现在已知连续高收益的话，star的概率就是0.4/0.625

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加油吧，让我们一起遇见更好的自己！

粗眉毛辣椒油 · 2024年01月08日

“Pr(High, High|Star) = 20% * 20%”。请问条件概率，为什么不考虑条件的概率，直接用该条件下事件发生概率的乘积呢？这是什么知识点？

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