A portfolio consists of two (long) assets £100 million each. The probability of default over the next year is 10% for the first asset, 20% for the second asset, and the joint probability of default is 3%. Estimate the expected loss on this portfolio due to credit defaults over the next year assuming zero recovery rate.
Answer to this question is £32million. I don't understand how it is computed? What is the logic behind this answer?
Would any quant finance analyst of Brilliant.org explain it?
Answer:- There are two events. Event 1) First asset defaults over the next year. Event 2) Second asset defaults over the next year. Total worth of portfolio is £200 million.
The probability that the first asset defaults over the next year is 10% of £100 million= £10million. ...(1)
The probability that the second asset defaults over the next year is 20% of £100 million= £20 million....(2)
The joint probability of both these events occurring simultaneously over the next year is 3% of £200 million= £6million....(3).
But it include the probability of both the events occuring jointly and independently =2%of £200 million= £4 million....(4). which should be deducted from (1)+(2)+(3)= £36million. So (1)+(2)+(3)-(4)= £32 million