Exam 8008 Topic 1 Question 31 Discussion
Actual exam question for PRMIA's 8008 exam
Question #: 31
Topic #: 1
Question #: 31
Topic #: 1
A bank extends a loan of $1m to a home buyer to buy a house currently worth $1.5m, with the house serving as the collateral. The volatility of returns (assumed normally distributed) on house prices in that neighborhood is assessed at 10% annually. The expected probability of default of the home buyer is 5%.
What is the probability that the bank will recover less than the principal advanced on this loan; assuming the probability of the home buyer's default is independent of the value of the house?
What is the probability that the bank will recover less than the principal advanced on this loan; assuming the probability of the home buyer's default is independent of the value of the house?
Suggested Answer: B Vote an answer
Explanation
The bank will not be able to recover the principal advanced on this loan if both the home buyer defaults, and the house value falls to less than $1m, ie the price moves adversely by more than $500k, which is
$-500k/$150k = -3.33. (Note that 150k is the 1 year volatility in dollars, ie $1.5m * 10%).
The probability of both these things happening together is just the product of the two probabilities, one of which we know to be 5%. The other is also certainly a small number, and intuitively it is clear that the probability of both the things happening together will be less than 1%.
For a more precise answer, we can calculate the probability of the house price falling by 3.33 standard deviations by calculating the area under the standard normal curve to the left of -3.33. This indeed is a very small number (actually equal to NORMSINV(-3.33)=0.00043), which when multiplied by the probability of default of the home buyer at 5% is certainly going to be less than 1%. Therefore Choice 'b' is the correct answer.
The bank will not be able to recover the principal advanced on this loan if both the home buyer defaults, and the house value falls to less than $1m, ie the price moves adversely by more than $500k, which is
$-500k/$150k = -3.33. (Note that 150k is the 1 year volatility in dollars, ie $1.5m * 10%).
The probability of both these things happening together is just the product of the two probabilities, one of which we know to be 5%. The other is also certainly a small number, and intuitively it is clear that the probability of both the things happening together will be less than 1%.
For a more precise answer, we can calculate the probability of the house price falling by 3.33 standard deviations by calculating the area under the standard normal curve to the left of -3.33. This indeed is a very small number (actually equal to NORMSINV(-3.33)=0.00043), which when multiplied by the probability of default of the home buyer at 5% is certainly going to be less than 1%. Therefore Choice 'b' is the correct answer.
by Ingram at Nov 28, 2025, 02:46 AM
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