WHAT IS THE PROBABILITY OF EXACTLY TWO BONDS DEFAULTING OVER THE NE...

5.

What is the probability of exactly two bonds defaulting over the next year?

a.

1.9%

b.

5.7%

c.

10.8%

d.

32.5%

Correct Answer: b

Rationale:

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 =

Where n = the number of bonds in the portfolio, p = the probability of default of each individual bond, and k = the

number of defaults for which you would like to find the probability. In this case n = 3, p = 0.15, and k = 2.

Entering the variables into the equation, this simplifies to 3 x 0.15

²

x 0.85 = .0574.

Section:

Quantitative Analysis

Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ:

John Wiley & Sons, 2013). Chapter 4, “Distributions.”

Learning Objective:

Distinguish the key properties among the following distributions: uniform distribution, Bernoulli

distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared dis-

tribution, Student’s t, and F-distributions, and identify common occurrences of each distribution.

2015 Financial Risk Manager (FRM®) Practice Exam