Letting n equal the number of bonds in the portfolio and p equal the individual default probability, the formulas to use are as follows:

Mean = E(K) = n × p = 5 × 0.17 = 0.85.

Variance = Variance(K) = n × p × (1-p) = 5 × 0.17 × (0.83) = 0.7055

Standard deviation = sqrt(0.7055) = 0.8399.

Section: Quantitative Analysis

Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2019. Chapter 3. Common Univariate Random Variables.

Learning Objective: Distinguish the key properties and identify the common occurrences of the following distributions: uniform distribution, Bernoulli distribution, binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student's t, and F-distributions.