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:
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 ≈ 0.82Answer (a)