Question

a) A country’s sovereign debt is classified according to that country’s capacity to pay its debt as C or high risk (low capacity to pay its debt), B or moderate risk (decent capacity to pay its debt) and A or low risk (high capacity to pay its debt). If for some reason a country is unable to pay its debt then is said to have defaulted. Over the last year out of all the countries that issue debt

• 10% were classified as C

• 30% were classified as B

• The rest were classified as A

• 40% of high risk countries defualted

• 10% of moderate risk countries defualted

• 1% of low risk countries defualted

Given that a country did not defaulted calculate the probability that it was classified as a moderate risk country.

Answer 1

We know the following probabilities

10% were classified as C

The probability that a country is classified as high risk is

• 30% were classified as B

The probability that a country is classified as moderate risk is

• The rest were classified as A

The probability that a country is classified as low risk is

• 40% of high risk countries defualted

The probability of default given that the country is high risk is

• 10% of moderate risk countries defualted

The probability of default given that the country is moderate risk is

• 1% of low risk countries defualted

The probability of default given that the country is low risk is

The probability that any given country defaults is

Given that a country did not default, the probability that it was classified as a moderate risk country is

ans: Given that a country did not default, the probability that it was classified as a moderate risk country is 0.2922