Probability-6 (FRM)

With a portfolio that consists of 20 well-diversified A-rated bonds and assuming a default probability of 1% per annum, what is the approximate probability of sustaining no losses on the portfolio over the next 12 months?

(a)0.82          (b) 0.8        (c) 0.85              (d) 0.99

Solution follows here:

Solution:

Default Probability (per annum) of each portfolio= 1% = 0.01

=> Probability of sustaining no losses (per annum) of each portfolio = (1-0.01) = 0.99

Assuming the portfolios to be independent,

Probability of sustaining no losses = P(E) = P(E₁)* P(E₂)* P(E₃)*..... P(E₂₀)

=   (0.99)²⁰ = 0.8179 ≈ 0.82

Answer (a)