Financial Risk Manager Part 1

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Explanation:

Binomial Distribution for Bond Defaults

Since the bond defaults are independent and identically distributed Bernoulli random variables, the Binomial distribution can be used to calculate the probability of exactly two bonds defaulting. The correct formula to use is:

P(K = k) = \frac{n!}{k!(n - k)!} p^k (1 - p)^{n - k}

$n$ : number of bonds in the portfolio
$p$ : probability of default of each individual bond
$K$ : number of bond defaults over the next year

Example Calculation

We want $P(K = 2)$ with $n = 5$ and $p = 0.17$ .

P(K = 2) = \frac{5!}{2!(5 - 2)!} (0.17)^2 (0.83)^3

= 10 \times 0.17^2 \times 0.83^3

= 0.1652

Result

The probability of exactly two bonds defaulting is 16.52%.

Explanation:

Binomial Distribution for Bond Defaults

P(K = k) = \frac{n!}{k!(n - k)!} p^k (1 - p)^{n - k}

$n$ : number of bonds in the portfolio
$p$ : probability of default of each individual bond
$K$ : number of bond defaults over the next year

Example Calculation

We want $P(K = 2)$ with $n = 5$ and $p = 0.17$ .

P(K = 2) = \frac{5!}{2!(5 - 2)!} (0.17)^2 (0.83)^3

= 10 \times 0.17^2 \times 0.83^3

= 0.1652

Result

The probability of exactly two bonds defaulting is 16.52%.

Comments (1)

Nicholas MuuzoleehJun 17, 2026 9:07 AM

This question is incomplete

LeetQuiz .Jun 19, 2026 12:08 PM

Hi Nicholas, thank you for your comment. We’ve updated the question to include the full probability statement. The correct answer is C (16.5%); using the binomial formula P = C(5,2)·0.17²·0.83³ ≈ 0.165. Thanks for your feedback.

Comments (1)

Nicholas MuuzoleehJun 17, 2026 9:07 AM

This question is incomplete

LeetQuiz .Jun 19, 2026 12:08 PM

A portfolio manager holds five bonds in a portfolio and each bond has a 1-year default probability of 17%. The event of default for each of the bonds is independent.What is the probability of exactly two bonds defaulting over the next year?

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Last updated: June 19, 2026 at 12:09

-2

1.9%

17.9%

5.7%

53.6%

16.5%

21.4%

32.5%

7.1%