Discuss PRMIA 8010 Exam Topic 4 Question 80

Under the actuarial (or CreditRisk+) based modeling of defaults, what is the probability of 4 defaults in a retail portfolio where the number of expected defaults is 2?

A4%

B18%

C9%

D2%

Suggested Answer: C

The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of and standard deviation equal to .

The probability of n defaults is given by (^n e^-) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

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26 comments · newest first

Leontine 5 months ago

I’m going with B too. The expected defaults suggest a higher probability.

Dick 5 months ago

I’m torn between A and C. 4% feels too low for 4 defaults.

Roxanne 6 months ago

I feel like it’s leaning towards option B, 18%. It seems reasonable.

Lawrence 6 months ago

This question is tricky! I think it's about understanding the distribution.

Christa 6 months ago

I calculated it, and I got 9% for option C.

Della 6 months ago

Wait, how can it be 4%? That seems way too low!

Rolande 6 months ago

I’m leaning towards option B, 18%.

Ulysses 6 months ago

I think it's definitely more than 4%!

Brice 7 months ago

The expected defaults are 2, so this is a Poisson distribution problem.

Cory 7 months ago

Wait, is this a trick question? If the expected defaults are 2, then 4 defaults should be way less likely. I'm going to have to go with D) 2% on this one.

Tenesha 7 months ago

Haha, I bet the exam writers are trying to trick us with these actuarial questions. I'm going with C) 9% - it's the middle ground, so it's probably the right answer.

Annice 8 months ago

Hmm, this is a tricky one. I'm going to have to go with B) 18% - the CreditRisk+ model tends to give higher probabilities for larger deviations.

Vannessa 8 months ago

D) 2% seems too low for 4 defaults when the expected is 2. I'd go with C) 9% as the most likely answer.

Fletcher 8 months ago

I think the answer is B) 18%. The actuarial model would give a higher probability for a larger deviation from the expected defaults.

Jenelle 8 months ago

I feel like the answer might be around 9% based on my calculations, but I need to double-check my work on the Poisson probabilities.

Carlota 8 months ago

If I remember correctly, the expected number of defaults is the mean in a Poisson model, so maybe we can use that to find the probability of 4 defaults?

Gary 9 months ago

I practiced a similar question where we had to calculate the probability of a certain number of defaults, but I can't recall the exact formula we used.

Charlena 9 months ago

I think I remember something about using the Poisson distribution for these types of problems, but I'm not entirely sure how to apply it here.

Osvaldo 9 months ago

Ah, I remember learning about these default modeling techniques. I think I can apply the right formulas to find the probability here.

Erasmo 9 months ago

This seems straightforward. If the expected defaults are 2, then the probability of 4 defaults should be one of the answer choices. I'll work it out.

Lemuel 9 months ago

I'm a bit unsure about the actuarial and CreditRisk+ details. I'll need to review those concepts before attempting to solve this.

Skye 9 months ago

Okay, the key here is understanding the expected defaults and then calculating the probability of 4 defaults. I think I can work through this step-by-step.

Tyisha 10 months ago

Hmm, this looks like a probability question related to default modeling. I'll need to think through the actuarial approach and the CreditRisk+ assumptions.

Nana 3 months ago

↳ replying to Tyisha

I’m not so sure. What about option C? It feels safer.

Beatriz 4 months ago

↳ replying to Tyisha

I’m leaning towards option B. Seems reasonable for 4 defaults.

Walker 5 months ago

↳ replying to Tyisha

This is tricky! I think I need to brush up on my probability skills.

PRMIA 8010 Exam - Topic 4 Question 80 Discussion