- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Probability Trees and Conditional Expectations
- Subject 3. Bayes' Formula and Updating Probability Estimates

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**CFA Practice Question**

A mortgage holding company has found that 1% of its mortgage holders default on their mortgages and lose the property. Furthermore, 90% of those who default are late on at least two monthly payments over the life of their mortgage, as compared to 45% of those who do not default.

B. 0.018

C. 0.020

What is the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property?

A. 0.009

B. 0.018

C. 0.020

Correct Answer: C

We have P(def) = 0.01. P(not def) = 0.99. P(two late payments/def) = 0.90. P(two late payments/not def) = 0.45. Using Bayes' formula: p(def/two late payments) = (0.01*0.9)/(0.01*0.9 + 0.99*0.45) = 0.0198 = 0.020

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**User Contributed Comments**
8

User |
Comment |
---|---|

Khadria |
The answer is coming "0.0198" but if you round it to 3 decimal places then "D" is I N C O R R E C T |

bobert |
Significant figures. If they are giving you those answers you generally round the furthest one by rule of thumb unless otherwise specified. |

epizi |
Why will you prefer notation P(def) when it is said loss property when defaultie P(L/D). And that is the denominator: P(lose) Therefore P(Lose/Default)=1% P(lose/no Default)=99% P(Default)=90% |

epizi |
P(No Default)=10% P(Lose)=P(Lose/Default)P(def)+P(Lose/noDef)P(no Def) =90%.1%+99%. 45%=0.4545 Bayee P(Def/Loss)=P(Loss/Def).P(Def)/P(lose) =(0.01x0.90)/0.4545=0.020 |

Beret |
Forget about all the formulas like Bayes etc. Just draw a tree diagram to solve all these kind of problems. It works! |

raymondg |
could somebody please work out probability tree thanks |

farhan92 |
@Raymond Probability of Default 1%. Prob of not default = 99% Prob Default and Late =0.9, Prob Def and not late =0.1 Prob non def and late =0,45 so Prob def and late =0.55. |

ecapocas |
Tried it both ways. Tree is definitely easier and better. For me anyway, YMMV. |