Probability problem

[dymny]

Hello I need help to solve the task
At the start of the year a bond portfolio consists of 2 bonds each worth 100$.At the end of the year if a bond defaults it will be worth 20$.If it does not default the bond will be worth 100$. The probability that both bond default is 20%.The probability that neither bond defaults is 45%. What is the mean of the year end portfolio value??
I know the answer is 140 $ but i don`t know how to calculate. Please help and explain.
Regards
dymny

 

[David Harper CFA FRM]

Hi @dymny if there are 2 bonds, the only other outcome aside from neither/both default is that only one defaults with probability of 100% - 20% - 45% = 35% with value of $20 (one default) + $100 (the other survives) = $120; so mean = [20% * (20 + 20)] + [35% * (100 + 20)] + [45% * (100 + 100)] = $140.00.

Here is a harder follow-up question: given these assumptions, what are (i) the default correlation between the bonds and (ii) the individual default probability of each bond?